text
stringlengths
594
23.8k
conversation_id
int64
97
109k
embedding
list
cluster
int64
0
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Submitted Solution: ``` for _ in range(int(input())): mylist = [] mylist1 = [] n,m = map(int,input().split()) for _ in range(n): mylist.append(int(input(),2)) ans = min(2**m-1,100) for num in range(ans+1): if num not in mylist: mylist1.append(num) mylist1.sort() answer = bin(mylist1[int((len(mylist1)-1)/2)])[2:] while len(answer)<m: answer='0'+answer if n == 1 and mylist == ['1']: print('0') else: print(answer) ``` No
105,433
[ 0.0460205078125, -0.195556640625, 0.125244140625, 0.2181396484375, -0.62646484375, -0.292236328125, 0.059417724609375, -0.0218963623046875, 0.04266357421875, 1.08203125, 0.68896484375, -0.483154296875, -0.0321044921875, -1.0927734375, -0.84423828125, -0.11602783203125, -0.71630859375, -0.60595703125, -0.296875, -0.1336669921875, 0.1947021484375, 0.0229644775390625, -1.2138671875, 0.2010498046875, -0.51904296875, 0.9833984375, 0.481201171875, -0.04534912109375, 1.134765625, 1.1162109375, -0.2496337890625, -0.273681640625, 0.58544921875, -0.923828125, -0.330810546875, -0.356201171875, 0.89501953125, -0.5517578125, -0.247314453125, -0.3486328125, 0.452880859375, -0.53271484375, 0.64697265625, -0.6064453125, -1.1787109375, -0.0921630859375, -0.319091796875, -0.2890625, -0.297607421875, -0.7109375, -0.0311737060546875, -0.39990234375, 0.62548828125, -0.51318359375, 0.04327392578125, 0.2242431640625, 0.01166534423828125, -0.1248779296875, -0.6015625, 0.5771484375, -0.08074951171875, 0.395751953125, 0.1217041015625, -0.68798828125, 0.006744384765625, 0.323486328125, -0.004390716552734375, -0.45703125, 0.015899658203125, -1.0087890625, -0.0960693359375, 0.40234375, -0.548828125, -0.33837890625, -0.2037353515625, 0.1522216796875, 0.208740234375, -0.031158447265625, -0.67236328125, 0.98095703125, 0.1822509765625, 1.341796875, 0.381591796875, 0.5205078125, -0.45361328125, -0.458251953125, 0.042327880859375, 0.288330078125, 0.09393310546875, -0.142333984375, 0.020599365234375, 0.54052734375, -0.47412109375, -0.039794921875, 0.81591796875, 0.390625, -0.26025390625, 0.440185546875, 0.42578125, 0.08740234375, 0.98095703125, 1.0009765625, 0.07867431640625, 1.1982421875, -0.6904296875, 0.07861328125, 0.05718994140625, -0.1982421875, -0.25537109375, -0.29443359375, -0.2266845703125, -0.04010009765625, 0.1019287109375, 0.1524658203125, -0.51318359375, 0.98193359375, -0.0693359375, 0.3251953125, -0.7294921875, 0.393310546875, 0.484130859375, 0.157958984375, 0.64013671875, -0.474609375, -0.03350830078125, -0.329345703125, -0.402587890625, 0.96484375, -0.4521484375, -0.155029296875, 0.1326904296875, 0.309814453125, -0.2149658203125, 0.010955810546875, 0.1839599609375, 0.625, -0.1744384765625, 0.409912109375, 0.478271484375, -0.552734375, 0.76123046875, -0.285888671875, -0.22705078125, 1.4599609375, 0.048614501953125, -0.267578125, 0.64306640625, 0.315185546875, -0.46923828125, 0.50146484375, -1.154296875, 0.70361328125, -0.18896484375, -0.163330078125, -0.260498046875, 0.28125, -0.309814453125, 0.6005859375, 0.462646484375, -0.27783203125, -0.55419921875, -0.175048828125, -0.034698486328125, 0.84423828125, -0.36767578125, 0.92822265625, -0.58349609375, -0.381591796875, -0.197509765625, -0.256591796875, 0.1612548828125, -0.35888671875, -0.094482421875, 0.84716796875, 0.6123046875, 1.1796875, 0.83447265625, -0.242919921875, 0.2012939453125, 0.1934814453125, -0.3857421875, 0.1123046875, 0.332275390625, 0.64208984375, -0.00467681884765625, 0.265625, 0.055755615234375, -0.7001953125, -0.626953125, -0.63525390625, -0.08380126953125, 0.75537109375, -0.625, -0.03802490234375, -0.27197265625, 0.014007568359375, -0.63671875, 0.08056640625, -0.2132568359375, -1.193359375, -0.3681640625, 0.45703125, -0.0176239013671875, 0.354248046875, -0.53369140625, -0.433837890625, 0.447265625, 1.1591796875, -0.46044921875, 0.1485595703125, 0.486328125, 0.351806640625, -0.144775390625, 0.224609375, -0.09075927734375, 0.11444091796875, -0.397705078125, 0.61376953125, -0.111572265625, -0.0294189453125, 0.09381103515625, 0.88427734375, 0.41748046875, 0.53759765625, -0.41162109375, -0.01012420654296875, 0.52001953125, 1.322265625, 0.1463623046875, 0.53515625, 0.401123046875, 0.90087890625, 0.72021484375, 0.66357421875, 0.7138671875, 0.4541015625, 0.9833984375, 0.84619140625, -0.292236328125, 0.2073974609375, -0.01116943359375, 0.728515625, 0.54736328125, 0.53662109375, 0.1846923828125, 0.39501953125, 0.11517333984375, 0.033660888671875, -0.42431640625, 0.4296875, -0.27392578125, 0.59521484375, -0.058868408203125, 0.356201171875, -0.450439453125, -0.70947265625, 0.09619140625, 0.5322265625, -0.9853515625, -0.5341796875, 0.217041015625, 0.1312255859375, 0.269287109375, -0.1505126953125, 0.1021728515625, 0.6884765625, 0.681640625, 0.5, -0.09161376953125, -0.412353515625, -0.99267578125, -0.87109375, -1.1787109375, -0.2257080078125, -0.63134765625, 0.1082763671875, 0.17822265625, -0.74365234375, 0.244140625, -0.46728515625, -0.408935546875, -0.059967041015625, -0.488037109375, 0.434326171875, -0.455810546875, 0.10552978515625, -0.7451171875, 0.62890625, 0.184814453125, 1.02734375, -0.80419921875, -0.00726318359375, -0.216552734375, -0.697265625, 0.27880859375, 0.357666015625, 0.7216796875, 0.1453857421875, -0.3212890625, -0.92529296875, -0.505859375, -0.045745849609375, -0.374755859375, -0.031768798828125, -0.7255859375, 1.220703125, 0.8017578125, -0.56787109375, 0.52783203125, 0.94140625, -0.8427734375, 0.269287109375, 0.333251953125, 0.0892333984375, -0.65576171875, 1.28515625, 0.350341796875, 0.325439453125, -0.45556640625, -0.47705078125, -0.2288818359375, 0.079833984375, 0.09442138671875, -0.673828125, -0.1170654296875, 0.449462890625, -0.08642578125, -0.96484375, 0.480224609375, -1.005859375, -0.544921875, -0.151123046875, -0.484619140625, 0.6884765625, 0.79150390625, 0.09619140625, -0.1578369140625, -0.317138671875, 0.1739501953125, 0.69287109375, 0.50439453125, -0.4853515625, -0.2071533203125, 0.90625, 0.08612060546875, 0.0716552734375, 0.1837158203125, -0.2041015625, -0.014862060546875, -0.0224151611328125, 0.270751953125, 0.6796875, 0.199951171875, 0.42333984375, 0.30859375, 0.5693359375, -1.0234375, -0.044342041015625, -0.339111328125, 0.5791015625, 0.385009765625, 0.237548828125, 0.348388671875, -0.18408203125, -0.76611328125, -1.212890625, 0.231201171875, -0.1011962890625, 0.474365234375, -0.50927734375, 0.98828125, 0.2451171875, -0.341552734375, 0.564453125, -0.52392578125, 0.384521484375, 0.88525390625, -0.37060546875, 0.9775390625, -0.91162109375, 0.1531982421875, -0.07196044921875, 0.056854248046875, 0.4873046875, 0.228759765625, 0.72119140625, -0.27490234375, -0.23046875, -0.312255859375, -0.1456298828125, 0.1907958984375, -0.265625, 0.190185546875, -0.112060546875, -0.60205078125, -0.98583984375, 0.2548828125, 1.1083984375, 0.60107421875, 0.042205810546875, 0.60888671875, 0.047210693359375, -0.072021484375, 0.66455078125, -0.09075927734375, -0.099609375, -0.63916015625, 0.8359375, 0.1397705078125, -0.35986328125, -0.5556640625, -0.377197265625, -0.1849365234375, 0.33203125, 0.042144775390625, -0.1295166015625, -0.9033203125, 0.440185546875, -0.028167724609375, 0.6591796875, -0.62158203125, -0.071533203125, -0.377197265625, 0.278076171875, 0.177490234375, -0.744140625, 0.330810546875, -0.837890625, 0.56494140625, 0.371337890625, -0.17138671875, -0.472412109375, -0.765625, -1.056640625, -0.66162109375, 0.411865234375, 0.9521484375, -0.2054443359375, 0.36083984375, -1.4560546875, 0.3974609375, 0.40869140625, -0.65869140625, 0.1378173828125, -0.0061187744140625, 0.515625, 0.155029296875, 0.83935546875, -0.4619140625, -0.463134765625, -0.11602783203125, -1.259765625, 0.64990234375, -0.67822265625, 0.56884765625, 0.09423828125, -0.06854248046875, 0.07208251953125, 0.494384765625, -0.394287109375, 0.26611328125, -0.2430419921875, 0.1605224609375, -1.02734375, -0.955078125, 0.54443359375, -0.29345703125, -0.200439453125, 0.97900390625, -0.3193359375, -0.26171875, 0.1336669921875, 0.368408203125, -0.491455078125, 0.8173828125, -0.1929931640625, 0.70703125, -0.5185546875, -0.274169921875, -0.177001953125, -0.5283203125, 1.0458984375, -0.01537322998046875, -0.5595703125, -0.4248046875, -1.123046875, -0.201904296875, 0.12030029296875, -0.2198486328125, 0.338623046875, -0.061370849609375, -0.13525390625, -0.37060546875, -0.1165771484375, -0.482666015625, -0.2734375, -0.53076171875, -0.459716796875, 0.1424560546875, 0.39306640625, 0.5517578125, -0.0186767578125, -0.391845703125, -0.102294921875, 0.10284423828125, -0.320068359375, -0.55322265625, 0.0751953125, -0.219482421875, -0.398681640625, -0.239501953125, 0.38037109375, 0.21533203125, 0.41357421875, 0.77392578125, -0.0845947265625, 0.47412109375, 0.289306640625, -0.87353515625, 0.60888671875, 0.177978515625, -0.86376953125, -0.31396484375, 0.72265625, 0.086181640625, 0.458251953125, 0.071533203125, -0.99951171875, -0.66259765625, -0.7412109375, 0.391845703125, -0.5517578125, -0.1312255859375, -0.9931640625, -0.209716796875, -0.343994140625, 0.37646484375, -0.239990234375, -0.3505859375, 0.07012939453125, -1.3046875, 0.051513671875, -0.8408203125, -0.299560546875, -0.6259765625, -0.454833984375, -0.485595703125, 0.86474609375, 0.037109375, 0.1131591796875, 0.043609619140625, 0.0268707275390625, 0.00153350830078125, -0.08734130859375, -0.71630859375, -0.425048828125, -0.24609375, 0.06597900390625, -0.039306640625, -0.392578125, -0.77099609375, 0.96484375, -0.77587890625, 0.168701171875, 0.1396484375, -0.22705078125, -0.30078125, -0.5556640625, 1.375, -0.1741943359375, -0.064208984375, -0.263427734375, 0.321533203125, 0.8798828125, -0.56689453125, -0.31396484375, -0.9140625, -0.255126953125, -1.23828125, 0.70703125, -0.44921875, 0.388671875, -0.748046875, -0.470947265625, 1.2861328125, -0.8369140625, 0.37109375, 0.94775390625, -0.1436767578125, 0.5986328125, -0.78271484375, 0.51513671875, 0.49267578125, -0.68017578125, 0.471923828125, 0.0755615234375, -0.7451171875, -0.053375244140625, -0.333740234375, -1.009765625, -0.70849609375, 0.446533203125, 1.1943359375, -0.03814697265625, 0.256591796875, -0.0029582977294921875, -1.12890625, -0.57763671875, 0.978515625, 0.26611328125, 0.335205078125, 0.8369140625, -0.26025390625, -0.12384033203125, -0.1922607421875, -0.451904296875, -0.07806396484375, -0.269287109375, 1.4296875, -0.39306640625, -0.51220703125, 1.2626953125, 0.8544921875, -1.1484375, -0.98779296875, -0.1763916015625, -0.06866455078125, 0.07928466796875, -1.123046875, 0.040618896484375, 0.58251953125, -0.9462890625, -0.057037353515625, 0.07525634765625, -0.2264404296875, 0.51513671875, 0.21826171875, 0.63134765625, -0.59033203125, 0.06793212890625, 0.69189453125, -0.60693359375, -0.136962890625, -0.97119140625, -0.0887451171875, -0.1810302734375, 0.0948486328125, 0.755859375, -0.57373046875, 0.32080078125, 0.50146484375, -0.0921630859375, 0.6767578125, -0.453369140625, -0.2001953125, 0.141845703125, -0.693359375, -0.5703125, -0.2164306640625, 0.2445068359375, -0.19287109375, 0.477783203125, -0.74462890625, 0.042510986328125, 0.038360595703125, 0.10791015625, -0.51171875, -0.73681640625, -0.172607421875, -0.84912109375, -0.3720703125, -0.70947265625, -0.88330078125, -0.08538818359375, 0.290283203125, 0.08013916015625, -0.72607421875, 0.07550048828125, 0.49072265625, -0.54150390625, 0.94091796875, -0.6982421875, 0.31201171875, -0.6044921875, -0.077392578125, -0.68408203125, 0.0009546279907226562, -0.392822265625, -0.07574462890625, -0.43994140625, 0.1162109375, -0.01287078857421875, 0.462890625, -0.36767578125, 0.65869140625, -0.486572265625, -0.50830078125, 0.374755859375, 0.01253509521484375, -0.315185546875, 0.56298828125, 0.556640625, 0.271484375, 0.2388916015625, -0.272705078125, -0.438720703125, -0.2362060546875, 0.5322265625, 0.7724609375, -0.0701904296875, -0.1007080078125, 0.166015625, 0.0290069580078125, -0.97607421875, 0.44189453125, -0.72412109375, -0.08441162109375, 0.41455078125, -0.495849609375, 0.5478515625, 1.25, -0.358154296875, 0.249755859375, -0.027191162109375, 0.08837890625, 0.1689453125, 0.10321044921875, -0.13232421875, 0.51953125, 0.09661865234375, -0.2425537109375, 0.1048583984375, 0.38818359375, 0.19873046875, 0.41552734375, -0.1864013671875, -0.794921875, -0.8798828125, -0.053466796875, -0.150390625, 0.379150390625, 0.66064453125, -0.158935546875, -0.11553955078125, -0.1368408203125, -0.56640625, 0.671875, -0.8369140625, -1.0322265625, 0.53173828125, -0.0789794921875, -0.482666015625, -0.218505859375, -0.5673828125, 0.07611083984375, -0.08160400390625, 0.381103515625, -0.449462890625, 0.2315673828125, -0.08807373046875, 0.470947265625, -0.306640625, -0.07861328125, 0.121826171875, 0.5927734375, -0.61767578125, -0.1387939453125, 0.00604248046875, 0.79931640625, -0.1258544921875, -0.12335205078125, -0.46337890625, 0.06427001953125, 0.279052734375, 0.320556640625, -0.296875, -0.2232666015625, -0.13232421875, 0.493896484375, -1.162109375, -0.0335693359375, -0.1253662109375, 0.1937255859375, 0.1441650390625, -0.52099609375, -0.54833984375, 0.77978515625, 0.69970703125, 0.137451171875, 0.4912109375, 0.1585693359375, 0.4931640625, -0.1837158203125, -0.041168212890625, -0.23046875, 0.96484375, 0.765625, 0.62646484375, -0.1209716796875, 0.44189453125, 0.74658203125, 0.1976318359375, -0.25830078125, 0.464111328125, -0.12493896484375, 0.1282958984375, 0.27294921875, -0.470947265625, -0.2408447265625, 0.3271484375, -0.425048828125, 0.59521484375, -0.459716796875, -0.00876617431640625, -0.23486328125, -0.783203125, 0.88427734375, -0.29638671875, -0.376953125, -0.10986328125, -0.1842041015625, 0.114990234375, 0.41943359375, -0.220703125, -0.2666015625, 0.98095703125, 0.80859375, 0.343505859375, 1.0224609375, 0.705078125, 0.379150390625, -0.615234375, 0.2313232421875, -0.04962158203125, -0.358154296875, -0.13037109375, -0.60009765625, -0.88720703125, 0.472412109375, -0.052001953125, -0.1998291015625, 0.437744140625, -1.16015625, 0.176513671875, -0.51220703125, 0.89892578125, -0.5869140625, 0.0635986328125, 0.27294921875, -0.60107421875, -0.818359375, 1.0810546875, -0.2459716796875, 0.38916015625, 0.07427978515625, 0.677734375, 0.4345703125, 1.525390625, 0.491943359375, -0.282958984375, 0.1114501953125, 0.59033203125, -0.47265625, -0.42041015625, -0.63037109375, -0.2423095703125, 0.07305908203125, -0.50244140625, -0.332275390625, -0.3359375, 0.69091796875, 0.37646484375, -1.236328125, -0.54248046875, 0.16748046875, -0.88232421875, 0.4423828125, 0.33203125, 0.403076171875, 0.228759765625, -0.146240234375, -0.370361328125, -0.71826171875, 0.237060546875, -0.3505859375, 0.45654296875, -0.76611328125, -0.385498046875, -0.69287109375, -0.6396484375, -0.324951171875, -0.12152099609375, -0.427001953125, -0.87109375, 0.66552734375, 0.402099609375, 0.62744140625, 0.0019388198852539062, -0.437255859375, 0.1688232421875, 0.85888671875, 0.755859375, -0.05816650390625, 0.76123046875, 0.321533203125, -0.0240936279296875, 0.23779296875, -0.07373046875, 0.2548828125, -0.09307861328125, 0.369384765625, -0.55322265625, -0.104248046875, -0.73486328125, -1.076171875, -0.09222412109375, 0.3876953125, 0.12249755859375, -0.488037109375, -1.0986328125, -0.7490234375, -0.8525390625, 0.129150390625, -0.6748046875, 0.9560546875, -0.489501953125, -0.0216064453125, 0.12274169921875, -1.16015625, 4.34765625, 0.98046875, 0.56884765625, 0.5927734375, 0.272216796875, 0.85986328125, 0.556640625, -0.61083984375, -0.07958984375, -0.438720703125, 0.630859375, -0.595703125, 0.078369140625, 0.95166015625, 0.46923828125, 0.41796875, -0.5908203125, -0.1749267578125, 0.47509765625, -0.8408203125, -0.8505859375, 0.47119140625, -0.006061553955078125, 0.3935546875, 0.330078125, 0.1304931640625, 0.65771484375, -0.8017578125, -0.09613037109375, -0.615234375, 0.09326171875, -0.482177734375, 0.748046875, 0.1820068359375, -0.1737060546875, 0.56494140625, 0.24951171875, -0.270263671875, -0.061370849609375, 0.372314453125, -0.23681640625, 0.04632568359375, 0.90771484375, -0.69287109375, -0.2110595703125, 0.5830078125, -0.763671875, 0.34716796875, 0.34619140625, -1.072265625, 0.97119140625, -0.40966796875, 0.19189453125, -0.476318359375, -1.1220703125, 0.2005615234375, 0.24560546875, -0.1246337890625, -0.405029296875, 0.1488037109375, 0.81005859375, 0.53466796875, 0.051727294921875, 0.81884765625, -1.234375, 0.4775390625, -0.1512451171875, 0.6201171875, -0.385009765625, 0.056365966796875, -0.36181640625, -0.31396484375, -0.3916015625, -0.3828125, 0.673828125, 0.058013916015625, -0.152099609375, 0.72705078125, 0.447021484375, -0.57861328125, 0.11456298828125, -0.08575439453125, -0.0264434814453125, -0.59033203125, 0.87939453125, 1.3076171875, -0.71435546875, -0.367919921875, -0.11669921875, 0.304443359375, 0.363037109375, 0.71435546875, 0.06427001953125, -0.452392578125, -0.257080078125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Submitted Solution: ``` import math def calculate(med,count,l,dir): if dir=='left' : med=int(med)+1 while ( count>0 ) : med=med-1 if (not(med in l)): count=count-1 return med elif dir=='right' : med=int(med) while ( count>0 ) : med=med+1 if (not(med in l)): count=count-1 return med t=int(input()) while ( t > 0 ): n,m=map(int,input().split()) l=[] med=float('{:.1f}'.format(float((math.pow(2,m)-1)/2))) #print('med start = ',med) right=0 left=0 for i in range(0,n): val=int(input(),2) l.append(val) if val > med: right+=1 elif val <= med: left+=1 if right>left : count=int(((right-left)/2)+1) #print('count',count) med=calculate(med,count,l,'left') elif right<left : count=int(((left-right)+1)/2) #print('count',count) med=calculate(med,count,l,'right') elif right==left : count=1 med=calculate(med,count,l,'left') print('{:0>{}}'.format('{:b}'.format(med),m)) #print(l) #print('left',left,'right',right) l.clear() t=t-1 ``` No
105,434
[ 0.0460205078125, -0.195556640625, 0.125244140625, 0.2181396484375, -0.62646484375, -0.292236328125, 0.059417724609375, -0.0218963623046875, 0.04266357421875, 1.08203125, 0.68896484375, -0.483154296875, -0.0321044921875, -1.0927734375, -0.84423828125, -0.11602783203125, -0.71630859375, -0.60595703125, -0.296875, -0.1336669921875, 0.1947021484375, 0.0229644775390625, -1.2138671875, 0.2010498046875, -0.51904296875, 0.9833984375, 0.481201171875, -0.04534912109375, 1.134765625, 1.1162109375, -0.2496337890625, -0.273681640625, 0.58544921875, -0.923828125, -0.330810546875, -0.356201171875, 0.89501953125, -0.5517578125, -0.247314453125, -0.3486328125, 0.452880859375, -0.53271484375, 0.64697265625, -0.6064453125, -1.1787109375, -0.0921630859375, -0.319091796875, -0.2890625, -0.297607421875, -0.7109375, -0.0311737060546875, -0.39990234375, 0.62548828125, -0.51318359375, 0.04327392578125, 0.2242431640625, 0.01166534423828125, -0.1248779296875, -0.6015625, 0.5771484375, -0.08074951171875, 0.395751953125, 0.1217041015625, -0.68798828125, 0.006744384765625, 0.323486328125, -0.004390716552734375, -0.45703125, 0.015899658203125, -1.0087890625, -0.0960693359375, 0.40234375, -0.548828125, -0.33837890625, -0.2037353515625, 0.1522216796875, 0.208740234375, -0.031158447265625, -0.67236328125, 0.98095703125, 0.1822509765625, 1.341796875, 0.381591796875, 0.5205078125, -0.45361328125, -0.458251953125, 0.042327880859375, 0.288330078125, 0.09393310546875, -0.142333984375, 0.020599365234375, 0.54052734375, -0.47412109375, -0.039794921875, 0.81591796875, 0.390625, -0.26025390625, 0.440185546875, 0.42578125, 0.08740234375, 0.98095703125, 1.0009765625, 0.07867431640625, 1.1982421875, -0.6904296875, 0.07861328125, 0.05718994140625, -0.1982421875, -0.25537109375, -0.29443359375, -0.2266845703125, -0.04010009765625, 0.1019287109375, 0.1524658203125, -0.51318359375, 0.98193359375, -0.0693359375, 0.3251953125, -0.7294921875, 0.393310546875, 0.484130859375, 0.157958984375, 0.64013671875, -0.474609375, -0.03350830078125, -0.329345703125, -0.402587890625, 0.96484375, -0.4521484375, -0.155029296875, 0.1326904296875, 0.309814453125, -0.2149658203125, 0.010955810546875, 0.1839599609375, 0.625, -0.1744384765625, 0.409912109375, 0.478271484375, -0.552734375, 0.76123046875, -0.285888671875, -0.22705078125, 1.4599609375, 0.048614501953125, -0.267578125, 0.64306640625, 0.315185546875, -0.46923828125, 0.50146484375, -1.154296875, 0.70361328125, -0.18896484375, -0.163330078125, -0.260498046875, 0.28125, -0.309814453125, 0.6005859375, 0.462646484375, -0.27783203125, -0.55419921875, -0.175048828125, -0.034698486328125, 0.84423828125, -0.36767578125, 0.92822265625, -0.58349609375, -0.381591796875, -0.197509765625, -0.256591796875, 0.1612548828125, -0.35888671875, -0.094482421875, 0.84716796875, 0.6123046875, 1.1796875, 0.83447265625, -0.242919921875, 0.2012939453125, 0.1934814453125, -0.3857421875, 0.1123046875, 0.332275390625, 0.64208984375, -0.00467681884765625, 0.265625, 0.055755615234375, -0.7001953125, -0.626953125, -0.63525390625, -0.08380126953125, 0.75537109375, -0.625, -0.03802490234375, -0.27197265625, 0.014007568359375, -0.63671875, 0.08056640625, -0.2132568359375, -1.193359375, -0.3681640625, 0.45703125, -0.0176239013671875, 0.354248046875, -0.53369140625, -0.433837890625, 0.447265625, 1.1591796875, -0.46044921875, 0.1485595703125, 0.486328125, 0.351806640625, -0.144775390625, 0.224609375, -0.09075927734375, 0.11444091796875, -0.397705078125, 0.61376953125, -0.111572265625, -0.0294189453125, 0.09381103515625, 0.88427734375, 0.41748046875, 0.53759765625, -0.41162109375, -0.01012420654296875, 0.52001953125, 1.322265625, 0.1463623046875, 0.53515625, 0.401123046875, 0.90087890625, 0.72021484375, 0.66357421875, 0.7138671875, 0.4541015625, 0.9833984375, 0.84619140625, -0.292236328125, 0.2073974609375, -0.01116943359375, 0.728515625, 0.54736328125, 0.53662109375, 0.1846923828125, 0.39501953125, 0.11517333984375, 0.033660888671875, -0.42431640625, 0.4296875, -0.27392578125, 0.59521484375, -0.058868408203125, 0.356201171875, -0.450439453125, -0.70947265625, 0.09619140625, 0.5322265625, -0.9853515625, -0.5341796875, 0.217041015625, 0.1312255859375, 0.269287109375, -0.1505126953125, 0.1021728515625, 0.6884765625, 0.681640625, 0.5, -0.09161376953125, -0.412353515625, -0.99267578125, -0.87109375, -1.1787109375, -0.2257080078125, -0.63134765625, 0.1082763671875, 0.17822265625, -0.74365234375, 0.244140625, -0.46728515625, -0.408935546875, -0.059967041015625, -0.488037109375, 0.434326171875, -0.455810546875, 0.10552978515625, -0.7451171875, 0.62890625, 0.184814453125, 1.02734375, -0.80419921875, -0.00726318359375, -0.216552734375, -0.697265625, 0.27880859375, 0.357666015625, 0.7216796875, 0.1453857421875, -0.3212890625, -0.92529296875, -0.505859375, -0.045745849609375, -0.374755859375, -0.031768798828125, -0.7255859375, 1.220703125, 0.8017578125, -0.56787109375, 0.52783203125, 0.94140625, -0.8427734375, 0.269287109375, 0.333251953125, 0.0892333984375, -0.65576171875, 1.28515625, 0.350341796875, 0.325439453125, -0.45556640625, -0.47705078125, -0.2288818359375, 0.079833984375, 0.09442138671875, -0.673828125, -0.1170654296875, 0.449462890625, -0.08642578125, -0.96484375, 0.480224609375, -1.005859375, -0.544921875, -0.151123046875, -0.484619140625, 0.6884765625, 0.79150390625, 0.09619140625, -0.1578369140625, -0.317138671875, 0.1739501953125, 0.69287109375, 0.50439453125, -0.4853515625, -0.2071533203125, 0.90625, 0.08612060546875, 0.0716552734375, 0.1837158203125, -0.2041015625, -0.014862060546875, -0.0224151611328125, 0.270751953125, 0.6796875, 0.199951171875, 0.42333984375, 0.30859375, 0.5693359375, -1.0234375, -0.044342041015625, -0.339111328125, 0.5791015625, 0.385009765625, 0.237548828125, 0.348388671875, -0.18408203125, -0.76611328125, -1.212890625, 0.231201171875, -0.1011962890625, 0.474365234375, -0.50927734375, 0.98828125, 0.2451171875, -0.341552734375, 0.564453125, -0.52392578125, 0.384521484375, 0.88525390625, -0.37060546875, 0.9775390625, -0.91162109375, 0.1531982421875, -0.07196044921875, 0.056854248046875, 0.4873046875, 0.228759765625, 0.72119140625, -0.27490234375, -0.23046875, -0.312255859375, -0.1456298828125, 0.1907958984375, -0.265625, 0.190185546875, -0.112060546875, -0.60205078125, -0.98583984375, 0.2548828125, 1.1083984375, 0.60107421875, 0.042205810546875, 0.60888671875, 0.047210693359375, -0.072021484375, 0.66455078125, -0.09075927734375, -0.099609375, -0.63916015625, 0.8359375, 0.1397705078125, -0.35986328125, -0.5556640625, -0.377197265625, -0.1849365234375, 0.33203125, 0.042144775390625, -0.1295166015625, -0.9033203125, 0.440185546875, -0.028167724609375, 0.6591796875, -0.62158203125, -0.071533203125, -0.377197265625, 0.278076171875, 0.177490234375, -0.744140625, 0.330810546875, -0.837890625, 0.56494140625, 0.371337890625, -0.17138671875, -0.472412109375, -0.765625, -1.056640625, -0.66162109375, 0.411865234375, 0.9521484375, -0.2054443359375, 0.36083984375, -1.4560546875, 0.3974609375, 0.40869140625, -0.65869140625, 0.1378173828125, -0.0061187744140625, 0.515625, 0.155029296875, 0.83935546875, -0.4619140625, -0.463134765625, -0.11602783203125, -1.259765625, 0.64990234375, -0.67822265625, 0.56884765625, 0.09423828125, -0.06854248046875, 0.07208251953125, 0.494384765625, -0.394287109375, 0.26611328125, -0.2430419921875, 0.1605224609375, -1.02734375, -0.955078125, 0.54443359375, -0.29345703125, -0.200439453125, 0.97900390625, -0.3193359375, -0.26171875, 0.1336669921875, 0.368408203125, -0.491455078125, 0.8173828125, -0.1929931640625, 0.70703125, -0.5185546875, -0.274169921875, -0.177001953125, -0.5283203125, 1.0458984375, -0.01537322998046875, -0.5595703125, -0.4248046875, -1.123046875, -0.201904296875, 0.12030029296875, -0.2198486328125, 0.338623046875, -0.061370849609375, -0.13525390625, -0.37060546875, -0.1165771484375, -0.482666015625, -0.2734375, -0.53076171875, -0.459716796875, 0.1424560546875, 0.39306640625, 0.5517578125, -0.0186767578125, -0.391845703125, -0.102294921875, 0.10284423828125, -0.320068359375, -0.55322265625, 0.0751953125, -0.219482421875, -0.398681640625, -0.239501953125, 0.38037109375, 0.21533203125, 0.41357421875, 0.77392578125, -0.0845947265625, 0.47412109375, 0.289306640625, -0.87353515625, 0.60888671875, 0.177978515625, -0.86376953125, -0.31396484375, 0.72265625, 0.086181640625, 0.458251953125, 0.071533203125, -0.99951171875, -0.66259765625, -0.7412109375, 0.391845703125, -0.5517578125, -0.1312255859375, -0.9931640625, -0.209716796875, -0.343994140625, 0.37646484375, -0.239990234375, -0.3505859375, 0.07012939453125, -1.3046875, 0.051513671875, -0.8408203125, -0.299560546875, -0.6259765625, -0.454833984375, -0.485595703125, 0.86474609375, 0.037109375, 0.1131591796875, 0.043609619140625, 0.0268707275390625, 0.00153350830078125, -0.08734130859375, -0.71630859375, -0.425048828125, -0.24609375, 0.06597900390625, -0.039306640625, -0.392578125, -0.77099609375, 0.96484375, -0.77587890625, 0.168701171875, 0.1396484375, -0.22705078125, -0.30078125, -0.5556640625, 1.375, -0.1741943359375, -0.064208984375, -0.263427734375, 0.321533203125, 0.8798828125, -0.56689453125, -0.31396484375, -0.9140625, -0.255126953125, -1.23828125, 0.70703125, -0.44921875, 0.388671875, -0.748046875, -0.470947265625, 1.2861328125, -0.8369140625, 0.37109375, 0.94775390625, -0.1436767578125, 0.5986328125, -0.78271484375, 0.51513671875, 0.49267578125, -0.68017578125, 0.471923828125, 0.0755615234375, -0.7451171875, -0.053375244140625, -0.333740234375, -1.009765625, -0.70849609375, 0.446533203125, 1.1943359375, -0.03814697265625, 0.256591796875, -0.0029582977294921875, -1.12890625, -0.57763671875, 0.978515625, 0.26611328125, 0.335205078125, 0.8369140625, -0.26025390625, -0.12384033203125, -0.1922607421875, -0.451904296875, -0.07806396484375, -0.269287109375, 1.4296875, -0.39306640625, -0.51220703125, 1.2626953125, 0.8544921875, -1.1484375, -0.98779296875, -0.1763916015625, -0.06866455078125, 0.07928466796875, -1.123046875, 0.040618896484375, 0.58251953125, -0.9462890625, -0.057037353515625, 0.07525634765625, -0.2264404296875, 0.51513671875, 0.21826171875, 0.63134765625, -0.59033203125, 0.06793212890625, 0.69189453125, -0.60693359375, -0.136962890625, -0.97119140625, -0.0887451171875, -0.1810302734375, 0.0948486328125, 0.755859375, -0.57373046875, 0.32080078125, 0.50146484375, -0.0921630859375, 0.6767578125, -0.453369140625, -0.2001953125, 0.141845703125, -0.693359375, -0.5703125, -0.2164306640625, 0.2445068359375, -0.19287109375, 0.477783203125, -0.74462890625, 0.042510986328125, 0.038360595703125, 0.10791015625, -0.51171875, -0.73681640625, -0.172607421875, -0.84912109375, -0.3720703125, -0.70947265625, -0.88330078125, -0.08538818359375, 0.290283203125, 0.08013916015625, -0.72607421875, 0.07550048828125, 0.49072265625, -0.54150390625, 0.94091796875, -0.6982421875, 0.31201171875, -0.6044921875, -0.077392578125, -0.68408203125, 0.0009546279907226562, -0.392822265625, -0.07574462890625, -0.43994140625, 0.1162109375, -0.01287078857421875, 0.462890625, -0.36767578125, 0.65869140625, -0.486572265625, -0.50830078125, 0.374755859375, 0.01253509521484375, -0.315185546875, 0.56298828125, 0.556640625, 0.271484375, 0.2388916015625, -0.272705078125, -0.438720703125, -0.2362060546875, 0.5322265625, 0.7724609375, -0.0701904296875, -0.1007080078125, 0.166015625, 0.0290069580078125, -0.97607421875, 0.44189453125, -0.72412109375, -0.08441162109375, 0.41455078125, -0.495849609375, 0.5478515625, 1.25, -0.358154296875, 0.249755859375, -0.027191162109375, 0.08837890625, 0.1689453125, 0.10321044921875, -0.13232421875, 0.51953125, 0.09661865234375, -0.2425537109375, 0.1048583984375, 0.38818359375, 0.19873046875, 0.41552734375, -0.1864013671875, -0.794921875, -0.8798828125, -0.053466796875, -0.150390625, 0.379150390625, 0.66064453125, -0.158935546875, -0.11553955078125, -0.1368408203125, -0.56640625, 0.671875, -0.8369140625, -1.0322265625, 0.53173828125, -0.0789794921875, -0.482666015625, -0.218505859375, -0.5673828125, 0.07611083984375, -0.08160400390625, 0.381103515625, -0.449462890625, 0.2315673828125, -0.08807373046875, 0.470947265625, -0.306640625, -0.07861328125, 0.121826171875, 0.5927734375, -0.61767578125, -0.1387939453125, 0.00604248046875, 0.79931640625, -0.1258544921875, -0.12335205078125, -0.46337890625, 0.06427001953125, 0.279052734375, 0.320556640625, -0.296875, -0.2232666015625, -0.13232421875, 0.493896484375, -1.162109375, -0.0335693359375, -0.1253662109375, 0.1937255859375, 0.1441650390625, -0.52099609375, -0.54833984375, 0.77978515625, 0.69970703125, 0.137451171875, 0.4912109375, 0.1585693359375, 0.4931640625, -0.1837158203125, -0.041168212890625, -0.23046875, 0.96484375, 0.765625, 0.62646484375, -0.1209716796875, 0.44189453125, 0.74658203125, 0.1976318359375, -0.25830078125, 0.464111328125, -0.12493896484375, 0.1282958984375, 0.27294921875, -0.470947265625, -0.2408447265625, 0.3271484375, -0.425048828125, 0.59521484375, -0.459716796875, -0.00876617431640625, -0.23486328125, -0.783203125, 0.88427734375, -0.29638671875, -0.376953125, -0.10986328125, -0.1842041015625, 0.114990234375, 0.41943359375, -0.220703125, -0.2666015625, 0.98095703125, 0.80859375, 0.343505859375, 1.0224609375, 0.705078125, 0.379150390625, -0.615234375, 0.2313232421875, -0.04962158203125, -0.358154296875, -0.13037109375, -0.60009765625, -0.88720703125, 0.472412109375, -0.052001953125, -0.1998291015625, 0.437744140625, -1.16015625, 0.176513671875, -0.51220703125, 0.89892578125, -0.5869140625, 0.0635986328125, 0.27294921875, -0.60107421875, -0.818359375, 1.0810546875, -0.2459716796875, 0.38916015625, 0.07427978515625, 0.677734375, 0.4345703125, 1.525390625, 0.491943359375, -0.282958984375, 0.1114501953125, 0.59033203125, -0.47265625, -0.42041015625, -0.63037109375, -0.2423095703125, 0.07305908203125, -0.50244140625, -0.332275390625, -0.3359375, 0.69091796875, 0.37646484375, -1.236328125, -0.54248046875, 0.16748046875, -0.88232421875, 0.4423828125, 0.33203125, 0.403076171875, 0.228759765625, -0.146240234375, -0.370361328125, -0.71826171875, 0.237060546875, -0.3505859375, 0.45654296875, -0.76611328125, -0.385498046875, -0.69287109375, -0.6396484375, -0.324951171875, -0.12152099609375, -0.427001953125, -0.87109375, 0.66552734375, 0.402099609375, 0.62744140625, 0.0019388198852539062, -0.437255859375, 0.1688232421875, 0.85888671875, 0.755859375, -0.05816650390625, 0.76123046875, 0.321533203125, -0.0240936279296875, 0.23779296875, -0.07373046875, 0.2548828125, -0.09307861328125, 0.369384765625, -0.55322265625, -0.104248046875, -0.73486328125, -1.076171875, -0.09222412109375, 0.3876953125, 0.12249755859375, -0.488037109375, -1.0986328125, -0.7490234375, -0.8525390625, 0.129150390625, -0.6748046875, 0.9560546875, -0.489501953125, -0.0216064453125, 0.12274169921875, -1.16015625, 4.34765625, 0.98046875, 0.56884765625, 0.5927734375, 0.272216796875, 0.85986328125, 0.556640625, -0.61083984375, -0.07958984375, -0.438720703125, 0.630859375, -0.595703125, 0.078369140625, 0.95166015625, 0.46923828125, 0.41796875, -0.5908203125, -0.1749267578125, 0.47509765625, -0.8408203125, -0.8505859375, 0.47119140625, -0.006061553955078125, 0.3935546875, 0.330078125, 0.1304931640625, 0.65771484375, -0.8017578125, -0.09613037109375, -0.615234375, 0.09326171875, -0.482177734375, 0.748046875, 0.1820068359375, -0.1737060546875, 0.56494140625, 0.24951171875, -0.270263671875, -0.061370849609375, 0.372314453125, -0.23681640625, 0.04632568359375, 0.90771484375, -0.69287109375, -0.2110595703125, 0.5830078125, -0.763671875, 0.34716796875, 0.34619140625, -1.072265625, 0.97119140625, -0.40966796875, 0.19189453125, -0.476318359375, -1.1220703125, 0.2005615234375, 0.24560546875, -0.1246337890625, -0.405029296875, 0.1488037109375, 0.81005859375, 0.53466796875, 0.051727294921875, 0.81884765625, -1.234375, 0.4775390625, -0.1512451171875, 0.6201171875, -0.385009765625, 0.056365966796875, -0.36181640625, -0.31396484375, -0.3916015625, -0.3828125, 0.673828125, 0.058013916015625, -0.152099609375, 0.72705078125, 0.447021484375, -0.57861328125, 0.11456298828125, -0.08575439453125, -0.0264434814453125, -0.59033203125, 0.87939453125, 1.3076171875, -0.71435546875, -0.367919921875, -0.11669921875, 0.304443359375, 0.363037109375, 0.71435546875, 0.06427001953125, -0.452392578125, -0.257080078125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Submitted Solution: ``` from collections import Counter T = int(input()) for _ in range(T): n,m = map(int,input().split()) l = [] for i in range(n): l.append(int(input(),2)) d = Counter(l) mid = ((2**m - n)-1)//2 i = 0 j = mid while i<=j: if d.get(i,0) == 1: j += 1 i += 1 r = bin(j)[2:] r.zfill(m) print(r) ``` No
105,435
[ 0.0460205078125, -0.195556640625, 0.125244140625, 0.2181396484375, -0.62646484375, -0.292236328125, 0.059417724609375, -0.0218963623046875, 0.04266357421875, 1.08203125, 0.68896484375, -0.483154296875, -0.0321044921875, -1.0927734375, -0.84423828125, -0.11602783203125, -0.71630859375, -0.60595703125, -0.296875, -0.1336669921875, 0.1947021484375, 0.0229644775390625, -1.2138671875, 0.2010498046875, -0.51904296875, 0.9833984375, 0.481201171875, -0.04534912109375, 1.134765625, 1.1162109375, -0.2496337890625, -0.273681640625, 0.58544921875, -0.923828125, -0.330810546875, -0.356201171875, 0.89501953125, -0.5517578125, -0.247314453125, -0.3486328125, 0.452880859375, -0.53271484375, 0.64697265625, -0.6064453125, -1.1787109375, -0.0921630859375, -0.319091796875, -0.2890625, -0.297607421875, -0.7109375, -0.0311737060546875, -0.39990234375, 0.62548828125, -0.51318359375, 0.04327392578125, 0.2242431640625, 0.01166534423828125, -0.1248779296875, -0.6015625, 0.5771484375, -0.08074951171875, 0.395751953125, 0.1217041015625, -0.68798828125, 0.006744384765625, 0.323486328125, -0.004390716552734375, -0.45703125, 0.015899658203125, -1.0087890625, -0.0960693359375, 0.40234375, -0.548828125, -0.33837890625, -0.2037353515625, 0.1522216796875, 0.208740234375, -0.031158447265625, -0.67236328125, 0.98095703125, 0.1822509765625, 1.341796875, 0.381591796875, 0.5205078125, -0.45361328125, -0.458251953125, 0.042327880859375, 0.288330078125, 0.09393310546875, -0.142333984375, 0.020599365234375, 0.54052734375, -0.47412109375, -0.039794921875, 0.81591796875, 0.390625, -0.26025390625, 0.440185546875, 0.42578125, 0.08740234375, 0.98095703125, 1.0009765625, 0.07867431640625, 1.1982421875, -0.6904296875, 0.07861328125, 0.05718994140625, -0.1982421875, -0.25537109375, -0.29443359375, -0.2266845703125, -0.04010009765625, 0.1019287109375, 0.1524658203125, -0.51318359375, 0.98193359375, -0.0693359375, 0.3251953125, -0.7294921875, 0.393310546875, 0.484130859375, 0.157958984375, 0.64013671875, -0.474609375, -0.03350830078125, -0.329345703125, -0.402587890625, 0.96484375, -0.4521484375, -0.155029296875, 0.1326904296875, 0.309814453125, -0.2149658203125, 0.010955810546875, 0.1839599609375, 0.625, -0.1744384765625, 0.409912109375, 0.478271484375, -0.552734375, 0.76123046875, -0.285888671875, -0.22705078125, 1.4599609375, 0.048614501953125, -0.267578125, 0.64306640625, 0.315185546875, -0.46923828125, 0.50146484375, -1.154296875, 0.70361328125, -0.18896484375, -0.163330078125, -0.260498046875, 0.28125, -0.309814453125, 0.6005859375, 0.462646484375, -0.27783203125, -0.55419921875, -0.175048828125, -0.034698486328125, 0.84423828125, -0.36767578125, 0.92822265625, -0.58349609375, -0.381591796875, -0.197509765625, -0.256591796875, 0.1612548828125, -0.35888671875, -0.094482421875, 0.84716796875, 0.6123046875, 1.1796875, 0.83447265625, -0.242919921875, 0.2012939453125, 0.1934814453125, -0.3857421875, 0.1123046875, 0.332275390625, 0.64208984375, -0.00467681884765625, 0.265625, 0.055755615234375, -0.7001953125, -0.626953125, -0.63525390625, -0.08380126953125, 0.75537109375, -0.625, -0.03802490234375, -0.27197265625, 0.014007568359375, -0.63671875, 0.08056640625, -0.2132568359375, -1.193359375, -0.3681640625, 0.45703125, -0.0176239013671875, 0.354248046875, -0.53369140625, -0.433837890625, 0.447265625, 1.1591796875, -0.46044921875, 0.1485595703125, 0.486328125, 0.351806640625, -0.144775390625, 0.224609375, -0.09075927734375, 0.11444091796875, -0.397705078125, 0.61376953125, -0.111572265625, -0.0294189453125, 0.09381103515625, 0.88427734375, 0.41748046875, 0.53759765625, -0.41162109375, -0.01012420654296875, 0.52001953125, 1.322265625, 0.1463623046875, 0.53515625, 0.401123046875, 0.90087890625, 0.72021484375, 0.66357421875, 0.7138671875, 0.4541015625, 0.9833984375, 0.84619140625, -0.292236328125, 0.2073974609375, -0.01116943359375, 0.728515625, 0.54736328125, 0.53662109375, 0.1846923828125, 0.39501953125, 0.11517333984375, 0.033660888671875, -0.42431640625, 0.4296875, -0.27392578125, 0.59521484375, -0.058868408203125, 0.356201171875, -0.450439453125, -0.70947265625, 0.09619140625, 0.5322265625, -0.9853515625, -0.5341796875, 0.217041015625, 0.1312255859375, 0.269287109375, -0.1505126953125, 0.1021728515625, 0.6884765625, 0.681640625, 0.5, -0.09161376953125, -0.412353515625, -0.99267578125, -0.87109375, -1.1787109375, -0.2257080078125, -0.63134765625, 0.1082763671875, 0.17822265625, -0.74365234375, 0.244140625, -0.46728515625, -0.408935546875, -0.059967041015625, -0.488037109375, 0.434326171875, -0.455810546875, 0.10552978515625, -0.7451171875, 0.62890625, 0.184814453125, 1.02734375, -0.80419921875, -0.00726318359375, -0.216552734375, -0.697265625, 0.27880859375, 0.357666015625, 0.7216796875, 0.1453857421875, -0.3212890625, -0.92529296875, -0.505859375, -0.045745849609375, -0.374755859375, -0.031768798828125, -0.7255859375, 1.220703125, 0.8017578125, -0.56787109375, 0.52783203125, 0.94140625, -0.8427734375, 0.269287109375, 0.333251953125, 0.0892333984375, -0.65576171875, 1.28515625, 0.350341796875, 0.325439453125, -0.45556640625, -0.47705078125, -0.2288818359375, 0.079833984375, 0.09442138671875, -0.673828125, -0.1170654296875, 0.449462890625, -0.08642578125, -0.96484375, 0.480224609375, -1.005859375, -0.544921875, -0.151123046875, -0.484619140625, 0.6884765625, 0.79150390625, 0.09619140625, -0.1578369140625, -0.317138671875, 0.1739501953125, 0.69287109375, 0.50439453125, -0.4853515625, -0.2071533203125, 0.90625, 0.08612060546875, 0.0716552734375, 0.1837158203125, -0.2041015625, -0.014862060546875, -0.0224151611328125, 0.270751953125, 0.6796875, 0.199951171875, 0.42333984375, 0.30859375, 0.5693359375, -1.0234375, -0.044342041015625, -0.339111328125, 0.5791015625, 0.385009765625, 0.237548828125, 0.348388671875, -0.18408203125, -0.76611328125, -1.212890625, 0.231201171875, -0.1011962890625, 0.474365234375, -0.50927734375, 0.98828125, 0.2451171875, -0.341552734375, 0.564453125, -0.52392578125, 0.384521484375, 0.88525390625, -0.37060546875, 0.9775390625, -0.91162109375, 0.1531982421875, -0.07196044921875, 0.056854248046875, 0.4873046875, 0.228759765625, 0.72119140625, -0.27490234375, -0.23046875, -0.312255859375, -0.1456298828125, 0.1907958984375, -0.265625, 0.190185546875, -0.112060546875, -0.60205078125, -0.98583984375, 0.2548828125, 1.1083984375, 0.60107421875, 0.042205810546875, 0.60888671875, 0.047210693359375, -0.072021484375, 0.66455078125, -0.09075927734375, -0.099609375, -0.63916015625, 0.8359375, 0.1397705078125, -0.35986328125, -0.5556640625, -0.377197265625, -0.1849365234375, 0.33203125, 0.042144775390625, -0.1295166015625, -0.9033203125, 0.440185546875, -0.028167724609375, 0.6591796875, -0.62158203125, -0.071533203125, -0.377197265625, 0.278076171875, 0.177490234375, -0.744140625, 0.330810546875, -0.837890625, 0.56494140625, 0.371337890625, -0.17138671875, -0.472412109375, -0.765625, -1.056640625, -0.66162109375, 0.411865234375, 0.9521484375, -0.2054443359375, 0.36083984375, -1.4560546875, 0.3974609375, 0.40869140625, -0.65869140625, 0.1378173828125, -0.0061187744140625, 0.515625, 0.155029296875, 0.83935546875, -0.4619140625, -0.463134765625, -0.11602783203125, -1.259765625, 0.64990234375, -0.67822265625, 0.56884765625, 0.09423828125, -0.06854248046875, 0.07208251953125, 0.494384765625, -0.394287109375, 0.26611328125, -0.2430419921875, 0.1605224609375, -1.02734375, -0.955078125, 0.54443359375, -0.29345703125, -0.200439453125, 0.97900390625, -0.3193359375, -0.26171875, 0.1336669921875, 0.368408203125, -0.491455078125, 0.8173828125, -0.1929931640625, 0.70703125, -0.5185546875, -0.274169921875, -0.177001953125, -0.5283203125, 1.0458984375, -0.01537322998046875, -0.5595703125, -0.4248046875, -1.123046875, -0.201904296875, 0.12030029296875, -0.2198486328125, 0.338623046875, -0.061370849609375, -0.13525390625, -0.37060546875, -0.1165771484375, -0.482666015625, -0.2734375, -0.53076171875, -0.459716796875, 0.1424560546875, 0.39306640625, 0.5517578125, -0.0186767578125, -0.391845703125, -0.102294921875, 0.10284423828125, -0.320068359375, -0.55322265625, 0.0751953125, -0.219482421875, -0.398681640625, -0.239501953125, 0.38037109375, 0.21533203125, 0.41357421875, 0.77392578125, -0.0845947265625, 0.47412109375, 0.289306640625, -0.87353515625, 0.60888671875, 0.177978515625, -0.86376953125, -0.31396484375, 0.72265625, 0.086181640625, 0.458251953125, 0.071533203125, -0.99951171875, -0.66259765625, -0.7412109375, 0.391845703125, -0.5517578125, -0.1312255859375, -0.9931640625, -0.209716796875, -0.343994140625, 0.37646484375, -0.239990234375, -0.3505859375, 0.07012939453125, -1.3046875, 0.051513671875, -0.8408203125, -0.299560546875, -0.6259765625, -0.454833984375, -0.485595703125, 0.86474609375, 0.037109375, 0.1131591796875, 0.043609619140625, 0.0268707275390625, 0.00153350830078125, -0.08734130859375, -0.71630859375, -0.425048828125, -0.24609375, 0.06597900390625, -0.039306640625, -0.392578125, -0.77099609375, 0.96484375, -0.77587890625, 0.168701171875, 0.1396484375, -0.22705078125, -0.30078125, -0.5556640625, 1.375, -0.1741943359375, -0.064208984375, -0.263427734375, 0.321533203125, 0.8798828125, -0.56689453125, -0.31396484375, -0.9140625, -0.255126953125, -1.23828125, 0.70703125, -0.44921875, 0.388671875, -0.748046875, -0.470947265625, 1.2861328125, -0.8369140625, 0.37109375, 0.94775390625, -0.1436767578125, 0.5986328125, -0.78271484375, 0.51513671875, 0.49267578125, -0.68017578125, 0.471923828125, 0.0755615234375, -0.7451171875, -0.053375244140625, -0.333740234375, -1.009765625, -0.70849609375, 0.446533203125, 1.1943359375, -0.03814697265625, 0.256591796875, -0.0029582977294921875, -1.12890625, -0.57763671875, 0.978515625, 0.26611328125, 0.335205078125, 0.8369140625, -0.26025390625, -0.12384033203125, -0.1922607421875, -0.451904296875, -0.07806396484375, -0.269287109375, 1.4296875, -0.39306640625, -0.51220703125, 1.2626953125, 0.8544921875, -1.1484375, -0.98779296875, -0.1763916015625, -0.06866455078125, 0.07928466796875, -1.123046875, 0.040618896484375, 0.58251953125, -0.9462890625, -0.057037353515625, 0.07525634765625, -0.2264404296875, 0.51513671875, 0.21826171875, 0.63134765625, -0.59033203125, 0.06793212890625, 0.69189453125, -0.60693359375, -0.136962890625, -0.97119140625, -0.0887451171875, -0.1810302734375, 0.0948486328125, 0.755859375, -0.57373046875, 0.32080078125, 0.50146484375, -0.0921630859375, 0.6767578125, -0.453369140625, -0.2001953125, 0.141845703125, -0.693359375, -0.5703125, -0.2164306640625, 0.2445068359375, -0.19287109375, 0.477783203125, -0.74462890625, 0.042510986328125, 0.038360595703125, 0.10791015625, -0.51171875, -0.73681640625, -0.172607421875, -0.84912109375, -0.3720703125, -0.70947265625, -0.88330078125, -0.08538818359375, 0.290283203125, 0.08013916015625, -0.72607421875, 0.07550048828125, 0.49072265625, -0.54150390625, 0.94091796875, -0.6982421875, 0.31201171875, -0.6044921875, -0.077392578125, -0.68408203125, 0.0009546279907226562, -0.392822265625, -0.07574462890625, -0.43994140625, 0.1162109375, -0.01287078857421875, 0.462890625, -0.36767578125, 0.65869140625, -0.486572265625, -0.50830078125, 0.374755859375, 0.01253509521484375, -0.315185546875, 0.56298828125, 0.556640625, 0.271484375, 0.2388916015625, -0.272705078125, -0.438720703125, -0.2362060546875, 0.5322265625, 0.7724609375, -0.0701904296875, -0.1007080078125, 0.166015625, 0.0290069580078125, -0.97607421875, 0.44189453125, -0.72412109375, -0.08441162109375, 0.41455078125, -0.495849609375, 0.5478515625, 1.25, -0.358154296875, 0.249755859375, -0.027191162109375, 0.08837890625, 0.1689453125, 0.10321044921875, -0.13232421875, 0.51953125, 0.09661865234375, -0.2425537109375, 0.1048583984375, 0.38818359375, 0.19873046875, 0.41552734375, -0.1864013671875, -0.794921875, -0.8798828125, -0.053466796875, -0.150390625, 0.379150390625, 0.66064453125, -0.158935546875, -0.11553955078125, -0.1368408203125, -0.56640625, 0.671875, -0.8369140625, -1.0322265625, 0.53173828125, -0.0789794921875, -0.482666015625, -0.218505859375, -0.5673828125, 0.07611083984375, -0.08160400390625, 0.381103515625, -0.449462890625, 0.2315673828125, -0.08807373046875, 0.470947265625, -0.306640625, -0.07861328125, 0.121826171875, 0.5927734375, -0.61767578125, -0.1387939453125, 0.00604248046875, 0.79931640625, -0.1258544921875, -0.12335205078125, -0.46337890625, 0.06427001953125, 0.279052734375, 0.320556640625, -0.296875, -0.2232666015625, -0.13232421875, 0.493896484375, -1.162109375, -0.0335693359375, -0.1253662109375, 0.1937255859375, 0.1441650390625, -0.52099609375, -0.54833984375, 0.77978515625, 0.69970703125, 0.137451171875, 0.4912109375, 0.1585693359375, 0.4931640625, -0.1837158203125, -0.041168212890625, -0.23046875, 0.96484375, 0.765625, 0.62646484375, -0.1209716796875, 0.44189453125, 0.74658203125, 0.1976318359375, -0.25830078125, 0.464111328125, -0.12493896484375, 0.1282958984375, 0.27294921875, -0.470947265625, -0.2408447265625, 0.3271484375, -0.425048828125, 0.59521484375, -0.459716796875, -0.00876617431640625, -0.23486328125, -0.783203125, 0.88427734375, -0.29638671875, -0.376953125, -0.10986328125, -0.1842041015625, 0.114990234375, 0.41943359375, -0.220703125, -0.2666015625, 0.98095703125, 0.80859375, 0.343505859375, 1.0224609375, 0.705078125, 0.379150390625, -0.615234375, 0.2313232421875, -0.04962158203125, -0.358154296875, -0.13037109375, -0.60009765625, -0.88720703125, 0.472412109375, -0.052001953125, -0.1998291015625, 0.437744140625, -1.16015625, 0.176513671875, -0.51220703125, 0.89892578125, -0.5869140625, 0.0635986328125, 0.27294921875, -0.60107421875, -0.818359375, 1.0810546875, -0.2459716796875, 0.38916015625, 0.07427978515625, 0.677734375, 0.4345703125, 1.525390625, 0.491943359375, -0.282958984375, 0.1114501953125, 0.59033203125, -0.47265625, -0.42041015625, -0.63037109375, -0.2423095703125, 0.07305908203125, -0.50244140625, -0.332275390625, -0.3359375, 0.69091796875, 0.37646484375, -1.236328125, -0.54248046875, 0.16748046875, -0.88232421875, 0.4423828125, 0.33203125, 0.403076171875, 0.228759765625, -0.146240234375, -0.370361328125, -0.71826171875, 0.237060546875, -0.3505859375, 0.45654296875, -0.76611328125, -0.385498046875, -0.69287109375, -0.6396484375, -0.324951171875, -0.12152099609375, -0.427001953125, -0.87109375, 0.66552734375, 0.402099609375, 0.62744140625, 0.0019388198852539062, -0.437255859375, 0.1688232421875, 0.85888671875, 0.755859375, -0.05816650390625, 0.76123046875, 0.321533203125, -0.0240936279296875, 0.23779296875, -0.07373046875, 0.2548828125, -0.09307861328125, 0.369384765625, -0.55322265625, -0.104248046875, -0.73486328125, -1.076171875, -0.09222412109375, 0.3876953125, 0.12249755859375, -0.488037109375, -1.0986328125, -0.7490234375, -0.8525390625, 0.129150390625, -0.6748046875, 0.9560546875, -0.489501953125, -0.0216064453125, 0.12274169921875, -1.16015625, 4.34765625, 0.98046875, 0.56884765625, 0.5927734375, 0.272216796875, 0.85986328125, 0.556640625, -0.61083984375, -0.07958984375, -0.438720703125, 0.630859375, -0.595703125, 0.078369140625, 0.95166015625, 0.46923828125, 0.41796875, -0.5908203125, -0.1749267578125, 0.47509765625, -0.8408203125, -0.8505859375, 0.47119140625, -0.006061553955078125, 0.3935546875, 0.330078125, 0.1304931640625, 0.65771484375, -0.8017578125, -0.09613037109375, -0.615234375, 0.09326171875, -0.482177734375, 0.748046875, 0.1820068359375, -0.1737060546875, 0.56494140625, 0.24951171875, -0.270263671875, -0.061370849609375, 0.372314453125, -0.23681640625, 0.04632568359375, 0.90771484375, -0.69287109375, -0.2110595703125, 0.5830078125, -0.763671875, 0.34716796875, 0.34619140625, -1.072265625, 0.97119140625, -0.40966796875, 0.19189453125, -0.476318359375, -1.1220703125, 0.2005615234375, 0.24560546875, -0.1246337890625, -0.405029296875, 0.1488037109375, 0.81005859375, 0.53466796875, 0.051727294921875, 0.81884765625, -1.234375, 0.4775390625, -0.1512451171875, 0.6201171875, -0.385009765625, 0.056365966796875, -0.36181640625, -0.31396484375, -0.3916015625, -0.3828125, 0.673828125, 0.058013916015625, -0.152099609375, 0.72705078125, 0.447021484375, -0.57861328125, 0.11456298828125, -0.08575439453125, -0.0264434814453125, -0.59033203125, 0.87939453125, 1.3076171875, -0.71435546875, -0.367919921875, -0.11669921875, 0.304443359375, 0.363037109375, 0.71435546875, 0.06427001953125, -0.452392578125, -0.257080078125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Submitted Solution: ``` # data=[] # with open('input.txt') as f: # data = [i for i in f] # data.reverse() # input = data.pop def get_ints(): return list(map(int, input().split())) for _ in range(int(input())): N,M = get_ints() a = [] for i in range(N): a.append(int(input(),2)) g = [i for i in range(1,1<<M) if not i in a] # print(g) if len(g)==0: print("0"*M) else: d = bin(g[(len(g)-1)//2])[2:] print("0"*(M-len(d)) + d) ``` No
105,436
[ 0.0460205078125, -0.195556640625, 0.125244140625, 0.2181396484375, -0.62646484375, -0.292236328125, 0.059417724609375, -0.0218963623046875, 0.04266357421875, 1.08203125, 0.68896484375, -0.483154296875, -0.0321044921875, -1.0927734375, -0.84423828125, -0.11602783203125, -0.71630859375, -0.60595703125, -0.296875, -0.1336669921875, 0.1947021484375, 0.0229644775390625, -1.2138671875, 0.2010498046875, -0.51904296875, 0.9833984375, 0.481201171875, -0.04534912109375, 1.134765625, 1.1162109375, -0.2496337890625, -0.273681640625, 0.58544921875, -0.923828125, -0.330810546875, -0.356201171875, 0.89501953125, -0.5517578125, -0.247314453125, -0.3486328125, 0.452880859375, -0.53271484375, 0.64697265625, -0.6064453125, -1.1787109375, -0.0921630859375, -0.319091796875, -0.2890625, -0.297607421875, -0.7109375, -0.0311737060546875, -0.39990234375, 0.62548828125, -0.51318359375, 0.04327392578125, 0.2242431640625, 0.01166534423828125, -0.1248779296875, -0.6015625, 0.5771484375, -0.08074951171875, 0.395751953125, 0.1217041015625, -0.68798828125, 0.006744384765625, 0.323486328125, -0.004390716552734375, -0.45703125, 0.015899658203125, -1.0087890625, -0.0960693359375, 0.40234375, -0.548828125, -0.33837890625, -0.2037353515625, 0.1522216796875, 0.208740234375, -0.031158447265625, -0.67236328125, 0.98095703125, 0.1822509765625, 1.341796875, 0.381591796875, 0.5205078125, -0.45361328125, -0.458251953125, 0.042327880859375, 0.288330078125, 0.09393310546875, -0.142333984375, 0.020599365234375, 0.54052734375, -0.47412109375, -0.039794921875, 0.81591796875, 0.390625, -0.26025390625, 0.440185546875, 0.42578125, 0.08740234375, 0.98095703125, 1.0009765625, 0.07867431640625, 1.1982421875, -0.6904296875, 0.07861328125, 0.05718994140625, -0.1982421875, -0.25537109375, -0.29443359375, -0.2266845703125, -0.04010009765625, 0.1019287109375, 0.1524658203125, -0.51318359375, 0.98193359375, -0.0693359375, 0.3251953125, -0.7294921875, 0.393310546875, 0.484130859375, 0.157958984375, 0.64013671875, -0.474609375, -0.03350830078125, -0.329345703125, -0.402587890625, 0.96484375, -0.4521484375, -0.155029296875, 0.1326904296875, 0.309814453125, -0.2149658203125, 0.010955810546875, 0.1839599609375, 0.625, -0.1744384765625, 0.409912109375, 0.478271484375, -0.552734375, 0.76123046875, -0.285888671875, -0.22705078125, 1.4599609375, 0.048614501953125, -0.267578125, 0.64306640625, 0.315185546875, -0.46923828125, 0.50146484375, -1.154296875, 0.70361328125, -0.18896484375, -0.163330078125, -0.260498046875, 0.28125, -0.309814453125, 0.6005859375, 0.462646484375, -0.27783203125, -0.55419921875, -0.175048828125, -0.034698486328125, 0.84423828125, -0.36767578125, 0.92822265625, -0.58349609375, -0.381591796875, -0.197509765625, -0.256591796875, 0.1612548828125, -0.35888671875, -0.094482421875, 0.84716796875, 0.6123046875, 1.1796875, 0.83447265625, -0.242919921875, 0.2012939453125, 0.1934814453125, -0.3857421875, 0.1123046875, 0.332275390625, 0.64208984375, -0.00467681884765625, 0.265625, 0.055755615234375, -0.7001953125, -0.626953125, -0.63525390625, -0.08380126953125, 0.75537109375, -0.625, -0.03802490234375, -0.27197265625, 0.014007568359375, -0.63671875, 0.08056640625, -0.2132568359375, -1.193359375, -0.3681640625, 0.45703125, -0.0176239013671875, 0.354248046875, -0.53369140625, -0.433837890625, 0.447265625, 1.1591796875, -0.46044921875, 0.1485595703125, 0.486328125, 0.351806640625, -0.144775390625, 0.224609375, -0.09075927734375, 0.11444091796875, -0.397705078125, 0.61376953125, -0.111572265625, -0.0294189453125, 0.09381103515625, 0.88427734375, 0.41748046875, 0.53759765625, -0.41162109375, -0.01012420654296875, 0.52001953125, 1.322265625, 0.1463623046875, 0.53515625, 0.401123046875, 0.90087890625, 0.72021484375, 0.66357421875, 0.7138671875, 0.4541015625, 0.9833984375, 0.84619140625, -0.292236328125, 0.2073974609375, -0.01116943359375, 0.728515625, 0.54736328125, 0.53662109375, 0.1846923828125, 0.39501953125, 0.11517333984375, 0.033660888671875, -0.42431640625, 0.4296875, -0.27392578125, 0.59521484375, -0.058868408203125, 0.356201171875, -0.450439453125, -0.70947265625, 0.09619140625, 0.5322265625, -0.9853515625, -0.5341796875, 0.217041015625, 0.1312255859375, 0.269287109375, -0.1505126953125, 0.1021728515625, 0.6884765625, 0.681640625, 0.5, -0.09161376953125, -0.412353515625, -0.99267578125, -0.87109375, -1.1787109375, -0.2257080078125, -0.63134765625, 0.1082763671875, 0.17822265625, -0.74365234375, 0.244140625, -0.46728515625, -0.408935546875, -0.059967041015625, -0.488037109375, 0.434326171875, -0.455810546875, 0.10552978515625, -0.7451171875, 0.62890625, 0.184814453125, 1.02734375, -0.80419921875, -0.00726318359375, -0.216552734375, -0.697265625, 0.27880859375, 0.357666015625, 0.7216796875, 0.1453857421875, -0.3212890625, -0.92529296875, -0.505859375, -0.045745849609375, -0.374755859375, -0.031768798828125, -0.7255859375, 1.220703125, 0.8017578125, -0.56787109375, 0.52783203125, 0.94140625, -0.8427734375, 0.269287109375, 0.333251953125, 0.0892333984375, -0.65576171875, 1.28515625, 0.350341796875, 0.325439453125, -0.45556640625, -0.47705078125, -0.2288818359375, 0.079833984375, 0.09442138671875, -0.673828125, -0.1170654296875, 0.449462890625, -0.08642578125, -0.96484375, 0.480224609375, -1.005859375, -0.544921875, -0.151123046875, -0.484619140625, 0.6884765625, 0.79150390625, 0.09619140625, -0.1578369140625, -0.317138671875, 0.1739501953125, 0.69287109375, 0.50439453125, -0.4853515625, -0.2071533203125, 0.90625, 0.08612060546875, 0.0716552734375, 0.1837158203125, -0.2041015625, -0.014862060546875, -0.0224151611328125, 0.270751953125, 0.6796875, 0.199951171875, 0.42333984375, 0.30859375, 0.5693359375, -1.0234375, -0.044342041015625, -0.339111328125, 0.5791015625, 0.385009765625, 0.237548828125, 0.348388671875, -0.18408203125, -0.76611328125, -1.212890625, 0.231201171875, -0.1011962890625, 0.474365234375, -0.50927734375, 0.98828125, 0.2451171875, -0.341552734375, 0.564453125, -0.52392578125, 0.384521484375, 0.88525390625, -0.37060546875, 0.9775390625, -0.91162109375, 0.1531982421875, -0.07196044921875, 0.056854248046875, 0.4873046875, 0.228759765625, 0.72119140625, -0.27490234375, -0.23046875, -0.312255859375, -0.1456298828125, 0.1907958984375, -0.265625, 0.190185546875, -0.112060546875, -0.60205078125, -0.98583984375, 0.2548828125, 1.1083984375, 0.60107421875, 0.042205810546875, 0.60888671875, 0.047210693359375, -0.072021484375, 0.66455078125, -0.09075927734375, -0.099609375, -0.63916015625, 0.8359375, 0.1397705078125, -0.35986328125, -0.5556640625, -0.377197265625, -0.1849365234375, 0.33203125, 0.042144775390625, -0.1295166015625, -0.9033203125, 0.440185546875, -0.028167724609375, 0.6591796875, -0.62158203125, -0.071533203125, -0.377197265625, 0.278076171875, 0.177490234375, -0.744140625, 0.330810546875, -0.837890625, 0.56494140625, 0.371337890625, -0.17138671875, -0.472412109375, -0.765625, -1.056640625, -0.66162109375, 0.411865234375, 0.9521484375, -0.2054443359375, 0.36083984375, -1.4560546875, 0.3974609375, 0.40869140625, -0.65869140625, 0.1378173828125, -0.0061187744140625, 0.515625, 0.155029296875, 0.83935546875, -0.4619140625, -0.463134765625, -0.11602783203125, -1.259765625, 0.64990234375, -0.67822265625, 0.56884765625, 0.09423828125, -0.06854248046875, 0.07208251953125, 0.494384765625, -0.394287109375, 0.26611328125, -0.2430419921875, 0.1605224609375, -1.02734375, -0.955078125, 0.54443359375, -0.29345703125, -0.200439453125, 0.97900390625, -0.3193359375, -0.26171875, 0.1336669921875, 0.368408203125, -0.491455078125, 0.8173828125, -0.1929931640625, 0.70703125, -0.5185546875, -0.274169921875, -0.177001953125, -0.5283203125, 1.0458984375, -0.01537322998046875, -0.5595703125, -0.4248046875, -1.123046875, -0.201904296875, 0.12030029296875, -0.2198486328125, 0.338623046875, -0.061370849609375, -0.13525390625, -0.37060546875, -0.1165771484375, -0.482666015625, -0.2734375, -0.53076171875, -0.459716796875, 0.1424560546875, 0.39306640625, 0.5517578125, -0.0186767578125, -0.391845703125, -0.102294921875, 0.10284423828125, -0.320068359375, -0.55322265625, 0.0751953125, -0.219482421875, -0.398681640625, -0.239501953125, 0.38037109375, 0.21533203125, 0.41357421875, 0.77392578125, -0.0845947265625, 0.47412109375, 0.289306640625, -0.87353515625, 0.60888671875, 0.177978515625, -0.86376953125, -0.31396484375, 0.72265625, 0.086181640625, 0.458251953125, 0.071533203125, -0.99951171875, -0.66259765625, -0.7412109375, 0.391845703125, -0.5517578125, -0.1312255859375, -0.9931640625, -0.209716796875, -0.343994140625, 0.37646484375, -0.239990234375, -0.3505859375, 0.07012939453125, -1.3046875, 0.051513671875, -0.8408203125, -0.299560546875, -0.6259765625, -0.454833984375, -0.485595703125, 0.86474609375, 0.037109375, 0.1131591796875, 0.043609619140625, 0.0268707275390625, 0.00153350830078125, -0.08734130859375, -0.71630859375, -0.425048828125, -0.24609375, 0.06597900390625, -0.039306640625, -0.392578125, -0.77099609375, 0.96484375, -0.77587890625, 0.168701171875, 0.1396484375, -0.22705078125, -0.30078125, -0.5556640625, 1.375, -0.1741943359375, -0.064208984375, -0.263427734375, 0.321533203125, 0.8798828125, -0.56689453125, -0.31396484375, -0.9140625, -0.255126953125, -1.23828125, 0.70703125, -0.44921875, 0.388671875, -0.748046875, -0.470947265625, 1.2861328125, -0.8369140625, 0.37109375, 0.94775390625, -0.1436767578125, 0.5986328125, -0.78271484375, 0.51513671875, 0.49267578125, -0.68017578125, 0.471923828125, 0.0755615234375, -0.7451171875, -0.053375244140625, -0.333740234375, -1.009765625, -0.70849609375, 0.446533203125, 1.1943359375, -0.03814697265625, 0.256591796875, -0.0029582977294921875, -1.12890625, -0.57763671875, 0.978515625, 0.26611328125, 0.335205078125, 0.8369140625, -0.26025390625, -0.12384033203125, -0.1922607421875, -0.451904296875, -0.07806396484375, -0.269287109375, 1.4296875, -0.39306640625, -0.51220703125, 1.2626953125, 0.8544921875, -1.1484375, -0.98779296875, -0.1763916015625, -0.06866455078125, 0.07928466796875, -1.123046875, 0.040618896484375, 0.58251953125, -0.9462890625, -0.057037353515625, 0.07525634765625, -0.2264404296875, 0.51513671875, 0.21826171875, 0.63134765625, -0.59033203125, 0.06793212890625, 0.69189453125, -0.60693359375, -0.136962890625, -0.97119140625, -0.0887451171875, -0.1810302734375, 0.0948486328125, 0.755859375, -0.57373046875, 0.32080078125, 0.50146484375, -0.0921630859375, 0.6767578125, -0.453369140625, -0.2001953125, 0.141845703125, -0.693359375, -0.5703125, -0.2164306640625, 0.2445068359375, -0.19287109375, 0.477783203125, -0.74462890625, 0.042510986328125, 0.038360595703125, 0.10791015625, -0.51171875, -0.73681640625, -0.172607421875, -0.84912109375, -0.3720703125, -0.70947265625, -0.88330078125, -0.08538818359375, 0.290283203125, 0.08013916015625, -0.72607421875, 0.07550048828125, 0.49072265625, -0.54150390625, 0.94091796875, -0.6982421875, 0.31201171875, -0.6044921875, -0.077392578125, -0.68408203125, 0.0009546279907226562, -0.392822265625, -0.07574462890625, -0.43994140625, 0.1162109375, -0.01287078857421875, 0.462890625, -0.36767578125, 0.65869140625, -0.486572265625, -0.50830078125, 0.374755859375, 0.01253509521484375, -0.315185546875, 0.56298828125, 0.556640625, 0.271484375, 0.2388916015625, -0.272705078125, -0.438720703125, -0.2362060546875, 0.5322265625, 0.7724609375, -0.0701904296875, -0.1007080078125, 0.166015625, 0.0290069580078125, -0.97607421875, 0.44189453125, -0.72412109375, -0.08441162109375, 0.41455078125, -0.495849609375, 0.5478515625, 1.25, -0.358154296875, 0.249755859375, -0.027191162109375, 0.08837890625, 0.1689453125, 0.10321044921875, -0.13232421875, 0.51953125, 0.09661865234375, -0.2425537109375, 0.1048583984375, 0.38818359375, 0.19873046875, 0.41552734375, -0.1864013671875, -0.794921875, -0.8798828125, -0.053466796875, -0.150390625, 0.379150390625, 0.66064453125, -0.158935546875, -0.11553955078125, -0.1368408203125, -0.56640625, 0.671875, -0.8369140625, -1.0322265625, 0.53173828125, -0.0789794921875, -0.482666015625, -0.218505859375, -0.5673828125, 0.07611083984375, -0.08160400390625, 0.381103515625, -0.449462890625, 0.2315673828125, -0.08807373046875, 0.470947265625, -0.306640625, -0.07861328125, 0.121826171875, 0.5927734375, -0.61767578125, -0.1387939453125, 0.00604248046875, 0.79931640625, -0.1258544921875, -0.12335205078125, -0.46337890625, 0.06427001953125, 0.279052734375, 0.320556640625, -0.296875, -0.2232666015625, -0.13232421875, 0.493896484375, -1.162109375, -0.0335693359375, -0.1253662109375, 0.1937255859375, 0.1441650390625, -0.52099609375, -0.54833984375, 0.77978515625, 0.69970703125, 0.137451171875, 0.4912109375, 0.1585693359375, 0.4931640625, -0.1837158203125, -0.041168212890625, -0.23046875, 0.96484375, 0.765625, 0.62646484375, -0.1209716796875, 0.44189453125, 0.74658203125, 0.1976318359375, -0.25830078125, 0.464111328125, -0.12493896484375, 0.1282958984375, 0.27294921875, -0.470947265625, -0.2408447265625, 0.3271484375, -0.425048828125, 0.59521484375, -0.459716796875, -0.00876617431640625, -0.23486328125, -0.783203125, 0.88427734375, -0.29638671875, -0.376953125, -0.10986328125, -0.1842041015625, 0.114990234375, 0.41943359375, -0.220703125, -0.2666015625, 0.98095703125, 0.80859375, 0.343505859375, 1.0224609375, 0.705078125, 0.379150390625, -0.615234375, 0.2313232421875, -0.04962158203125, -0.358154296875, -0.13037109375, -0.60009765625, -0.88720703125, 0.472412109375, -0.052001953125, -0.1998291015625, 0.437744140625, -1.16015625, 0.176513671875, -0.51220703125, 0.89892578125, -0.5869140625, 0.0635986328125, 0.27294921875, -0.60107421875, -0.818359375, 1.0810546875, -0.2459716796875, 0.38916015625, 0.07427978515625, 0.677734375, 0.4345703125, 1.525390625, 0.491943359375, -0.282958984375, 0.1114501953125, 0.59033203125, -0.47265625, -0.42041015625, -0.63037109375, -0.2423095703125, 0.07305908203125, -0.50244140625, -0.332275390625, -0.3359375, 0.69091796875, 0.37646484375, -1.236328125, -0.54248046875, 0.16748046875, -0.88232421875, 0.4423828125, 0.33203125, 0.403076171875, 0.228759765625, -0.146240234375, -0.370361328125, -0.71826171875, 0.237060546875, -0.3505859375, 0.45654296875, -0.76611328125, -0.385498046875, -0.69287109375, -0.6396484375, -0.324951171875, -0.12152099609375, -0.427001953125, -0.87109375, 0.66552734375, 0.402099609375, 0.62744140625, 0.0019388198852539062, -0.437255859375, 0.1688232421875, 0.85888671875, 0.755859375, -0.05816650390625, 0.76123046875, 0.321533203125, -0.0240936279296875, 0.23779296875, -0.07373046875, 0.2548828125, -0.09307861328125, 0.369384765625, -0.55322265625, -0.104248046875, -0.73486328125, -1.076171875, -0.09222412109375, 0.3876953125, 0.12249755859375, -0.488037109375, -1.0986328125, -0.7490234375, -0.8525390625, 0.129150390625, -0.6748046875, 0.9560546875, -0.489501953125, -0.0216064453125, 0.12274169921875, -1.16015625, 4.34765625, 0.98046875, 0.56884765625, 0.5927734375, 0.272216796875, 0.85986328125, 0.556640625, -0.61083984375, -0.07958984375, -0.438720703125, 0.630859375, -0.595703125, 0.078369140625, 0.95166015625, 0.46923828125, 0.41796875, -0.5908203125, -0.1749267578125, 0.47509765625, -0.8408203125, -0.8505859375, 0.47119140625, -0.006061553955078125, 0.3935546875, 0.330078125, 0.1304931640625, 0.65771484375, -0.8017578125, -0.09613037109375, -0.615234375, 0.09326171875, -0.482177734375, 0.748046875, 0.1820068359375, -0.1737060546875, 0.56494140625, 0.24951171875, -0.270263671875, -0.061370849609375, 0.372314453125, -0.23681640625, 0.04632568359375, 0.90771484375, -0.69287109375, -0.2110595703125, 0.5830078125, -0.763671875, 0.34716796875, 0.34619140625, -1.072265625, 0.97119140625, -0.40966796875, 0.19189453125, -0.476318359375, -1.1220703125, 0.2005615234375, 0.24560546875, -0.1246337890625, -0.405029296875, 0.1488037109375, 0.81005859375, 0.53466796875, 0.051727294921875, 0.81884765625, -1.234375, 0.4775390625, -0.1512451171875, 0.6201171875, -0.385009765625, 0.056365966796875, -0.36181640625, -0.31396484375, -0.3916015625, -0.3828125, 0.673828125, 0.058013916015625, -0.152099609375, 0.72705078125, 0.447021484375, -0.57861328125, 0.11456298828125, -0.08575439453125, -0.0264434814453125, -0.59033203125, 0.87939453125, 1.3076171875, -0.71435546875, -0.367919921875, -0.11669921875, 0.304443359375, 0.363037109375, 0.71435546875, 0.06427001953125, -0.452392578125, -0.257080078125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Tags: constructive algorithms, data structures, implementation, strings, two pointers Correct Solution: ``` class Solution: def __init__(self, debug=False, n=None, a=None, b=None): if n is None: n, a, b = Solution.input() self.n = n self.a = a self.b = b self.real = [x for x in self.a] self.inverse = [not x for x in self.a] self.curr_zero = 0 self.curr_last = self.n - 1 self.real_idx = self.n - 1 self.inv = False self.debug = debug if debug: self.current_state = [x for x in self.a] self.operations = [self.n + 1000] @staticmethod def input(): n = int(input()) a = [x == '1' for x in input()] b = [x == '1' for x in input()] return n, a, b def iteration(self): if self.inv: if self.inverse[self.curr_last] != self.b[self.real_idx]: if self.inverse[self.curr_zero] != self.inverse[self.curr_last]: self.operation(0) self.real[self.curr_zero], self.inverse[self.curr_zero] = self.inverse[self.curr_zero], self.real[ self.curr_zero] self.operation(self.real_idx) self.inv = False self.curr_zero, self.curr_last = self.curr_last, self.curr_zero else: if self.real[self.curr_last] != self.b[self.real_idx]: if self.real[self.curr_zero] != self.real[self.curr_last]: self.operation(0) self.real[self.curr_zero], self.inverse[self.curr_zero] = self.inverse[self.curr_zero], self.real[ self.curr_zero] self.operation(self.real_idx) self.inv = True self.curr_zero, self.curr_last = self.curr_last, self.curr_zero if self.inv: self.curr_last += 1 else: self.curr_last -= 1 self.real_idx -= 1 def solve(self): while self.real_idx >= 0: self.iteration() return self.return_answer() def special_cases(self): if self.n == 1: if self.a[0] != self.b[0]: self.operation(0) return self.return_answer # if self.n == 2: # if self.a[1] != self.b[1]: # if self.a[0] != self.a[1]: # self.operation(0) # self.a[0] = not self.a[0] # self.operation(1) # self.a = [not x for x in self.a][::-1] # if self.debug: # assert self.current_state[1] == self.b[1] # if self.a[0] != self.b[0]: # self.operation(1) # return self.return_answer def operation(self, i): self.operations.append(i + 1) if self.debug: self.current_state[:i + 1] = [not x for x in self.current_state[:i + 1]][::-1] if self.n < 2: return def return_answer(self): if self.debug: assert all(x == y for x, y in zip(self.b, self.current_state)) ans = f'{len(self.operations) - 1} {" ".join(str(x) for x in self.operations[1:])}' print(ans) return ans def solve(): n = int(input()) a = [int(x) for x in input()] b = [int(x) for x in input()] # state real = [x for x in a] inverse = [(x + 1) % 2 for x in a] inv_idx = 0 real_idx = n - 1 inv = False operations = [] # fix all seq = [] while real_idx > 0: if not inv: if real[real_idx] == b[real_idx]: real_idx -= 1 inv_idx += 1 seq.append(real[real_idx]) continue if real[0] != real[real_idx]: operations.append(1) real[0], inverse[-1] = inverse[-1], real[0] operations.append(real_idx + 1) real[real_idx] = b[real_idx] seq.append(real[real_idx]) inverse[inv_idx] = (real[real_idx] + 1) % 2 inv = True else: if inverse[inv_idx] == b[real_idx]: real_idx -= 1 inv_idx += 1 seq.append(inverse[inv_idx]) continue if inverse[-1] != inverse[inv_idx]: operations.append(1) real[0], inverse[-1] = inverse[-1], real[0] operations.append(real_idx + 1) inverse[inv_idx] = b[real_idx] real[real_idx] = (b[real_idx] + 1) % 2 seq.append(inverse[inv_idx]) inv = False real_idx -= 1 inv_idx += 1 # fix 0 if (inv and inverse[-1] != b[0]) or (real[0] != b[0] and not inv): operations.append(1) seq.append(b[0]) print(seq, b) print(len(operations), *operations) if __name__ == '__main__': for _ in range(int(input())): n, a, b = Solution.input() Solution(False, n, a, b).solve() ```
105,437
[ 0.1553955078125, -0.41650390625, -0.03643798828125, 0.058349609375, -0.371337890625, -0.79052734375, -0.007495880126953125, -0.2264404296875, 0.1739501953125, 1.0234375, 0.7783203125, -0.27099609375, 0.3466796875, -0.87109375, -0.53271484375, 0.32861328125, -0.384521484375, -0.60107421875, -0.30859375, -0.5546875, -0.0574951171875, -0.11712646484375, -1.3525390625, -0.10833740234375, -0.5927734375, 0.8076171875, 0.321044921875, -0.135498046875, 1.0126953125, 1.0712890625, -0.4072265625, -0.447509765625, 0.73974609375, -1.0078125, -0.426513671875, -0.483154296875, 0.591796875, -0.8134765625, -0.1533203125, -0.2919921875, 0.57958984375, -0.25927734375, 0.232666015625, -0.939453125, -1.2978515625, 0.240478515625, -0.365966796875, -0.294189453125, -0.1500244140625, -0.478515625, 0.0256195068359375, -0.244873046875, 0.64404296875, -0.0826416015625, 0.061431884765625, 0.1446533203125, 0.208740234375, -0.55419921875, -0.466552734375, 0.1988525390625, 0.10650634765625, 0.13671875, 0.1995849609375, -0.76025390625, 0.080322265625, 0.176513671875, -0.2418212890625, -0.43408203125, -0.416748046875, -0.99658203125, -0.314697265625, -0.0443115234375, -0.7119140625, -0.32421875, -0.1405029296875, 0.286376953125, 0.2470703125, -0.17724609375, -0.84375, 0.76171875, -0.291748046875, 0.92529296875, 0.07476806640625, 0.2149658203125, -0.4716796875, -0.55078125, -0.05755615234375, 0.214599609375, 0.1767578125, -0.1353759765625, -0.385986328125, 0.59765625, -0.50341796875, 0.09869384765625, 0.402587890625, 0.6748046875, -0.29150390625, 0.268310546875, 0.433349609375, -0.044708251953125, 0.8037109375, 1.2490234375, -0.2275390625, 1.1611328125, -0.6181640625, -0.227294921875, -0.07525634765625, 0.1473388671875, -0.0239105224609375, -0.03912353515625, -0.0157318115234375, -0.184814453125, 0.68701171875, 0.30078125, -0.40380859375, 0.7763671875, -0.00940704345703125, 0.411865234375, -0.97802734375, 0.46484375, 0.65283203125, -0.0545654296875, 0.73974609375, -0.26123046875, -0.131591796875, -0.2276611328125, -0.32421875, 1.1396484375, -0.436767578125, -0.3779296875, 0.298828125, -0.0248565673828125, -0.26171875, 0.336669921875, -0.023590087890625, 0.7333984375, -0.2188720703125, 0.43896484375, 0.74267578125, -0.482421875, 0.7802734375, -0.1820068359375, -0.1890869140625, 1.6904296875, 0.4892578125, 0.10845947265625, 1.0244140625, 0.403076171875, -0.32275390625, 0.444580078125, -0.91552734375, 0.60595703125, 0.259033203125, 0.340576171875, -0.14111328125, -0.10699462890625, -0.27001953125, 0.52001953125, 0.09368896484375, 0.15087890625, -0.04742431640625, 0.254150390625, 0.037384033203125, 0.9462890625, -0.139892578125, 1.0751953125, -0.3935546875, -0.358642578125, -0.2705078125, -0.67529296875, 0.50048828125, -0.2159423828125, -0.404541015625, 0.60595703125, 0.521484375, 1.142578125, 1.3740234375, -0.460693359375, 0.232666015625, 0.30810546875, -0.72412109375, -0.00029730796813964844, 0.70068359375, 0.958984375, -0.151123046875, 0.2215576171875, -0.0885009765625, -0.39501953125, -0.509765625, -0.71142578125, -0.126220703125, 0.71240234375, -0.75732421875, 0.1485595703125, 0.349609375, 0.283935546875, -0.896484375, -0.1300048828125, -0.292724609375, -0.68359375, -0.256103515625, 0.51513671875, -0.450439453125, 0.5390625, -0.7705078125, -0.46875, 0.6162109375, 1.046875, -0.27001953125, 0.3408203125, 0.377197265625, 0.1884765625, -0.216552734375, 0.371337890625, 0.300537109375, -0.200927734375, -0.457275390625, 1.138671875, 0.292724609375, -0.09765625, 0.057403564453125, 0.6806640625, 0.63623046875, 0.4091796875, -0.2049560546875, 0.020477294921875, 0.30615234375, 1.1767578125, 0.14013671875, 0.83447265625, 0.01120758056640625, 0.76025390625, 0.68408203125, 0.66845703125, 0.53955078125, 0.099609375, 0.59130859375, 0.84912109375, 0.2008056640625, 0.399169921875, 0.4169921875, 0.430908203125, 0.361328125, 0.46875, 0.25830078125, 0.1962890625, 0.253662109375, 0.042327880859375, -0.4423828125, 0.17578125, -0.412353515625, 0.8642578125, -0.085693359375, 0.1536865234375, -0.33203125, -0.439208984375, 0.1683349609375, 0.908203125, -0.75634765625, -0.1641845703125, 0.1553955078125, 0.040985107421875, 0.1304931640625, -0.263427734375, 0.345458984375, 0.3759765625, 0.4521484375, 0.52880859375, -0.423583984375, -0.2462158203125, -1.19921875, -0.86767578125, -0.8466796875, -0.49072265625, -0.8271484375, 0.055816650390625, 0.13232421875, -0.70556640625, 0.34033203125, -0.517578125, -0.277587890625, 0.2705078125, -0.693359375, 0.6484375, -0.131103515625, 0.304443359375, -1.3955078125, 0.8037109375, 0.340576171875, 1.1357421875, -0.76171875, 0.06640625, 0.1153564453125, -0.8291015625, 0.02618408203125, 0.09222412109375, 0.22705078125, -0.052581787109375, -0.74755859375, -0.658203125, -0.74072265625, -0.21142578125, -0.29248046875, 0.380859375, -0.5234375, 0.92822265625, 0.73828125, -0.57470703125, 0.7685546875, 0.88037109375, -0.5947265625, 0.38623046875, 0.42236328125, 0.12445068359375, -0.8115234375, 1.583984375, 0.5068359375, 0.384033203125, -0.45263671875, -0.419189453125, -0.2249755859375, -0.1427001953125, 0.186767578125, -0.68896484375, -0.499755859375, 0.56298828125, -0.1094970703125, -0.9951171875, 0.129150390625, -0.89697265625, -0.60986328125, -0.2420654296875, -0.71337890625, 1.3212890625, 0.978515625, -0.08258056640625, -0.0309600830078125, -0.1046142578125, -0.08489990234375, 0.59326171875, 0.479248046875, -0.0850830078125, -0.0080413818359375, 0.828125, 0.310302734375, 0.02001953125, 0.1771240234375, -0.541015625, 0.0079498291015625, -0.045013427734375, 0.3671875, 0.465576171875, 0.177978515625, 0.40576171875, 0.27392578125, 0.5078125, -1.1982421875, -0.208251953125, -0.2271728515625, 0.5341796875, 0.5302734375, 0.368896484375, -0.0278472900390625, -0.56005859375, -0.83251953125, -1.052734375, 0.1602783203125, 0.11297607421875, 0.76416015625, -0.85107421875, 0.76416015625, 0.1700439453125, -0.334228515625, 0.5380859375, -0.65478515625, -0.06658935546875, 0.93408203125, -0.5654296875, 0.91455078125, -0.98486328125, 0.32080078125, 0.01483917236328125, 0.042327880859375, 0.338623046875, 0.470458984375, 0.430419921875, -0.47705078125, -0.426025390625, -0.638671875, 0.051849365234375, 0.016265869140625, -0.36572265625, 0.1112060546875, -0.30224609375, -0.33154296875, -0.84912109375, 0.38037109375, 0.86474609375, 0.85693359375, -0.075439453125, 0.488037109375, 0.3984375, 0.47021484375, 0.63427734375, -0.128173828125, 0.250732421875, -0.95703125, 0.6083984375, 0.2113037109375, -0.32763671875, -0.71630859375, -0.1600341796875, -0.2032470703125, -0.0208282470703125, -0.1671142578125, -0.31298828125, -0.86279296875, 0.38232421875, -0.2010498046875, 0.78857421875, -0.38671875, -0.26220703125, -0.72314453125, 0.47412109375, 0.51025390625, -0.78515625, 0.50732421875, -0.958984375, 0.64453125, 0.50341796875, -0.308837890625, -0.2900390625, -0.7431640625, -0.72314453125, -0.4814453125, 0.2548828125, 1.0537109375, -0.15771484375, 0.50048828125, -1.32421875, 0.3359375, 0.156494140625, -0.7392578125, -0.0772705078125, -0.07379150390625, 0.472900390625, 0.1629638671875, 0.78759765625, -0.1368408203125, -0.31396484375, 0.0270233154296875, -1.2958984375, 0.55517578125, -0.57177734375, 0.48876953125, 0.10760498046875, -0.2384033203125, 0.06488037109375, 0.357666015625, -0.141845703125, 0.08172607421875, -0.322265625, 0.261474609375, -0.93603515625, -0.59423828125, 0.5791015625, -0.2156982421875, -0.306640625, 0.99267578125, 0.0672607421875, -0.09930419921875, 0.227783203125, 0.5537109375, -0.467529296875, 0.432861328125, -0.26171875, 0.88720703125, -0.52294921875, -0.67724609375, -0.416015625, -0.331787109375, 0.736328125, -0.09228515625, -0.4853515625, -0.220947265625, -1.11328125, -0.0791015625, 0.192626953125, -0.42138671875, 0.2578125, 0.1151123046875, 0.184814453125, -0.27490234375, -0.024658203125, -0.4150390625, -0.1728515625, -0.52587890625, -0.58251953125, 0.58349609375, 0.361572265625, 0.564453125, 0.09991455078125, -0.59716796875, -0.1790771484375, 0.434814453125, -0.1002197265625, -0.60986328125, -0.214599609375, -0.407470703125, -0.1690673828125, -0.46484375, 0.0640869140625, -0.1007080078125, 0.3486328125, 1.00390625, -0.006072998046875, 0.346435546875, 0.354248046875, -0.77734375, 0.890625, 0.35009765625, -0.70166015625, -0.3837890625, 0.255126953125, -0.06256103515625, 0.65087890625, 0.5927734375, -0.77294921875, -0.56884765625, -0.78564453125, 0.232666015625, -0.79296875, -0.1651611328125, -0.93701171875, -0.5693359375, -0.379150390625, 0.57421875, -0.11383056640625, -0.6796875, 0.045806884765625, -0.8759765625, -0.0572509765625, -0.82763671875, -0.2149658203125, -0.7978515625, -0.66357421875, -0.2401123046875, 0.884765625, 0.1031494140625, -0.0039520263671875, 0.25244140625, -0.11187744140625, 0.151611328125, 0.30029296875, -0.759765625, -0.1514892578125, -0.01959228515625, 0.0623779296875, -0.1981201171875, 0.032989501953125, -0.818359375, 0.5966796875, -0.8564453125, 0.205078125, -0.2127685546875, -0.00836944580078125, -0.3388671875, -0.200927734375, 0.97705078125, -0.32861328125, 0.3681640625, -0.33154296875, 0.34326171875, 0.77197265625, -0.71826171875, -0.449951171875, -1.0048828125, -0.8134765625, -1.4111328125, 0.7119140625, -0.445556640625, 0.139404296875, -0.72265625, -0.56884765625, 0.96337890625, -0.69482421875, 0.32958984375, 1.162109375, 0.003154754638671875, 0.4130859375, -0.274169921875, 0.654296875, 0.2086181640625, -0.63037109375, 0.23046875, 0.386474609375, -0.62646484375, -0.10870361328125, -0.388916015625, -0.99462890625, -0.458984375, 0.427001953125, 1.13671875, -0.0166168212890625, 0.28369140625, -0.449951171875, -1.0673828125, -0.5361328125, 0.6845703125, 0.267822265625, 0.405517578125, 1.03125, 0.17431640625, -0.054656982421875, 0.08123779296875, -0.495361328125, -0.287841796875, -0.374755859375, 1.17578125, -0.165771484375, -0.60009765625, 0.810546875, 0.876953125, -0.96826171875, -0.99755859375, -0.06561279296875, -0.15966796875, -0.0860595703125, -0.7421875, -0.037567138671875, 0.56884765625, -0.432861328125, 0.01020050048828125, 0.26806640625, -0.134521484375, 0.22607421875, 0.169921875, 0.277099609375, -0.087158203125, 0.369140625, 0.9501953125, -0.277099609375, -0.5732421875, -0.94287109375, -0.55859375, -0.447509765625, 0.1273193359375, 0.6591796875, -0.35986328125, 0.1365966796875, 0.38623046875, 0.020477294921875, 1.0244140625, -0.298828125, -0.4404296875, 0.362060546875, -0.853515625, -0.630859375, 0.1607666015625, 0.07135009765625, -0.468505859375, 0.65673828125, -0.64208984375, 0.0325927734375, 0.186767578125, 0.07196044921875, -0.388671875, -1.0498046875, -0.2127685546875, -1.3046875, -0.405517578125, -0.5322265625, -0.92431640625, -0.177734375, 0.0478515625, 0.209228515625, -0.72998046875, 0.072265625, 0.432861328125, -0.25146484375, 0.9169921875, -0.61962890625, 0.1138916015625, -0.4765625, -0.5, -0.58251953125, 0.03863525390625, -0.402587890625, -0.004085540771484375, -0.9189453125, 0.162841796875, -0.037200927734375, 0.4970703125, -0.255859375, 0.6005859375, -0.5654296875, -1.173828125, 0.2066650390625, -0.0458984375, 0.037139892578125, 0.74365234375, 0.38134765625, -0.116455078125, 0.486328125, -0.032806396484375, -0.289306640625, -0.398681640625, 0.5751953125, 0.5126953125, -0.2313232421875, -0.1904296875, -0.1778564453125, 0.263427734375, -1.2080078125, 0.54443359375, -0.603515625, 0.22412109375, 0.29150390625, -0.52783203125, 0.437255859375, 1.142578125, -0.49609375, 0.255615234375, -0.1116943359375, 0.13916015625, 0.1563720703125, 0.29345703125, -0.1580810546875, 0.75244140625, -0.212158203125, -0.53564453125, -0.0116729736328125, 0.30126953125, -0.222412109375, 0.4296875, -0.1387939453125, -1.01953125, -0.8720703125, -0.1358642578125, 0.006412506103515625, 0.214599609375, 0.041168212890625, -0.2398681640625, -0.02960205078125, 0.1485595703125, -0.84423828125, 0.22900390625, -0.9296875, -0.853515625, 0.5439453125, -0.2022705078125, -0.22998046875, 0.04583740234375, -0.336669921875, -0.37890625, 0.1856689453125, 0.56640625, -0.6728515625, 0.5234375, -0.1973876953125, 0.634765625, -0.436279296875, -0.2445068359375, 0.101806640625, 0.65087890625, -0.76123046875, -0.548828125, -0.30517578125, 0.916015625, 0.2325439453125, -0.360595703125, -0.638671875, 0.07965087890625, 0.219970703125, 0.313720703125, -0.5869140625, 0.1839599609375, -0.251953125, 0.6806640625, -1.2119140625, 0.053955078125, 0.03326416015625, 0.192626953125, 0.1431884765625, -0.354248046875, -0.69384765625, 1.1123046875, 0.348388671875, -0.06866455078125, 0.6025390625, 0.01087188720703125, 0.357666015625, -0.0241851806640625, -0.0204010009765625, -0.06494140625, 0.7646484375, 0.64306640625, 0.59033203125, -0.181396484375, 0.1435546875, 0.7607421875, 0.1998291015625, -0.335693359375, 0.29296875, 0.01056671142578125, -0.0806884765625, 0.356689453125, -0.2093505859375, -0.278564453125, -0.153076171875, -0.3720703125, 0.6396484375, -0.5244140625, -0.04888916015625, -0.2333984375, -0.86572265625, 0.703125, -0.296142578125, -0.365966796875, 0.40869140625, -0.1573486328125, 0.179443359375, 0.572265625, -0.414794921875, -0.320556640625, 1.1220703125, 0.76220703125, 0.412841796875, 0.7431640625, 0.3486328125, 0.5751953125, -0.52978515625, 0.34521484375, 0.049713134765625, -0.07110595703125, -0.09820556640625, -0.7646484375, -0.98828125, 0.54541015625, -0.316650390625, -0.2626953125, 0.5830078125, -0.5576171875, 0.315673828125, -0.5146484375, 0.955078125, -0.368408203125, 0.32421875, 0.357177734375, -0.49853515625, -0.640625, 0.66845703125, -0.30078125, 0.34619140625, 0.1036376953125, 0.908203125, -0.01515960693359375, 1.685546875, 0.5498046875, -0.1201171875, 0.0240478515625, 0.45654296875, -0.291259765625, -0.30419921875, -0.70361328125, -0.327392578125, 0.1251220703125, -0.25439453125, -0.8701171875, -0.0638427734375, 0.78662109375, 0.12249755859375, -0.88427734375, -0.2529296875, 0.372802734375, -1.138671875, 0.386474609375, 0.368408203125, 0.24755859375, 0.16162109375, -0.216064453125, -0.12353515625, -0.5712890625, 0.462646484375, -0.7919921875, 0.31884765625, -0.49658203125, -0.376708984375, -0.61669921875, -0.6806640625, -0.383544921875, -0.08056640625, -0.533203125, -0.73291015625, 0.578125, 0.32470703125, 0.7119140625, 0.52783203125, -0.2861328125, 0.2384033203125, 0.7158203125, 0.98046875, -0.1904296875, 1.1103515625, 0.324462890625, -0.08856201171875, 0.2373046875, -0.3486328125, 0.316162109375, -0.05804443359375, 0.3466796875, -0.488037109375, -0.250732421875, -0.80078125, -1.12890625, 0.449462890625, 0.453369140625, 0.36279296875, -0.71630859375, -1.109375, -0.043487548828125, -1.236328125, -0.44091796875, -0.67138671875, 0.77197265625, -0.71923828125, -0.04248046875, 0.059783935546875, -1.1337890625, 4.31640625, 0.94091796875, 0.640625, 0.49560546875, 0.11468505859375, 0.79248046875, 0.479248046875, -0.296875, -0.379638671875, -0.270751953125, 0.60693359375, -0.5380859375, -0.0350341796875, 0.95654296875, 0.497802734375, 0.302001953125, -0.26025390625, 0.07647705078125, 0.19970703125, -0.8349609375, -0.712890625, 0.3369140625, 0.08612060546875, 0.5546875, 0.28955078125, 0.254638671875, 0.77197265625, -0.68896484375, -0.1744384765625, -0.79736328125, 0.0751953125, -0.38232421875, 0.982421875, 0.278564453125, -0.08428955078125, 0.70263671875, -0.058563232421875, -0.478271484375, 0.0302886962890625, 0.115478515625, -0.069091796875, 0.187744140625, 0.5517578125, -0.689453125, -0.2822265625, 0.51025390625, -0.5966796875, 0.60791015625, 0.380126953125, -1.021484375, 1.029296875, -0.13916015625, 0.483154296875, -0.85986328125, -0.59375, 0.2022705078125, 0.08502197265625, 0.0782470703125, -0.359130859375, 0.6025390625, 0.61376953125, 0.62255859375, 0.04290771484375, 0.469970703125, -0.92578125, 0.54736328125, -0.2003173828125, 0.59326171875, -0.412109375, -0.0047454833984375, -0.2064208984375, -0.294677734375, -0.296142578125, -0.5556640625, 0.51806640625, 0.0772705078125, -0.292724609375, 0.9033203125, 0.3203125, -0.76513671875, 0.08563232421875, -0.286376953125, -0.06671142578125, -0.294189453125, 0.76904296875, 1.205078125, -0.423583984375, 0.1673583984375, -0.2462158203125, 0.54345703125, 0.56396484375, 0.76025390625, -0.154052734375, -0.513671875, -0.27294921875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Tags: constructive algorithms, data structures, implementation, strings, two pointers Correct Solution: ``` from sys import stdin t = int(stdin.readline().strip()) for _ in range(t): n = int(stdin.readline().strip()) a = stdin.readline().strip() b = stdin.readline().strip() #n,m = list(map(int, stdin.readline().strip().split(' '))) out = [] for i in range(n-1): if a[i] != a[i+1]: out.append(i+1) current = a[-1] for i in range(n-1, -1, -1): if b[i] != current: out.append(i+1) current = '0' if current == '1' else '1' print(len(out), end=" ") print(*out) ```
105,438
[ 0.153564453125, -0.4228515625, -0.0277252197265625, 0.0732421875, -0.385986328125, -0.77392578125, -0.007328033447265625, -0.20361328125, 0.1865234375, 1.0166015625, 0.775390625, -0.290771484375, 0.332275390625, -0.8994140625, -0.55126953125, 0.326171875, -0.359375, -0.5791015625, -0.3115234375, -0.548828125, -0.02301025390625, -0.1217041015625, -1.357421875, -0.0821533203125, -0.60302734375, 0.8154296875, 0.31884765625, -0.1417236328125, 1.0341796875, 1.056640625, -0.40771484375, -0.452392578125, 0.744140625, -0.98388671875, -0.4345703125, -0.496826171875, 0.59814453125, -0.82470703125, -0.1358642578125, -0.279541015625, 0.5732421875, -0.25390625, 0.234130859375, -0.91357421875, -1.3173828125, 0.189208984375, -0.3544921875, -0.303955078125, -0.1495361328125, -0.459716796875, 0.02960205078125, -0.230712890625, 0.60595703125, -0.11480712890625, 0.06622314453125, 0.1519775390625, 0.2271728515625, -0.55517578125, -0.4560546875, 0.1612548828125, 0.08197021484375, 0.131591796875, 0.1962890625, -0.74169921875, 0.11822509765625, 0.1927490234375, -0.258056640625, -0.431640625, -0.406005859375, -0.9931640625, -0.310791015625, -0.0506591796875, -0.72021484375, -0.331787109375, -0.1009521484375, 0.254638671875, 0.2509765625, -0.1640625, -0.86376953125, 0.7666015625, -0.2890625, 0.923828125, 0.089599609375, 0.2066650390625, -0.478271484375, -0.5361328125, -0.04327392578125, 0.191162109375, 0.1610107421875, -0.1287841796875, -0.383056640625, 0.572265625, -0.470703125, 0.0885009765625, 0.394775390625, 0.69580078125, -0.3154296875, 0.259033203125, 0.4404296875, -0.03192138671875, 0.7900390625, 1.232421875, -0.192138671875, 1.1826171875, -0.61376953125, -0.214111328125, -0.021820068359375, 0.135986328125, -0.04559326171875, -0.03448486328125, 0.01007843017578125, -0.164794921875, 0.67529296875, 0.3759765625, -0.415771484375, 0.78515625, -0.0286712646484375, 0.41650390625, -0.99755859375, 0.472412109375, 0.65478515625, -0.06817626953125, 0.732421875, -0.26708984375, -0.164794921875, -0.236572265625, -0.32470703125, 1.138671875, -0.41650390625, -0.428955078125, 0.27099609375, 0.004726409912109375, -0.281005859375, 0.342041015625, -0.042236328125, 0.7216796875, -0.2364501953125, 0.41064453125, 0.72705078125, -0.47900390625, 0.78564453125, -0.1802978515625, -0.162353515625, 1.703125, 0.5, 0.1302490234375, 1.0205078125, 0.42724609375, -0.31103515625, 0.4912109375, -0.9091796875, 0.5810546875, 0.257568359375, 0.33154296875, -0.12432861328125, -0.10906982421875, -0.269775390625, 0.5380859375, 0.1080322265625, 0.1788330078125, -0.051910400390625, 0.27880859375, 0.049285888671875, 0.9287109375, -0.120849609375, 1.076171875, -0.387939453125, -0.358642578125, -0.260986328125, -0.6513671875, 0.52490234375, -0.2244873046875, -0.4287109375, 0.59814453125, 0.55224609375, 1.1435546875, 1.3544921875, -0.46875, 0.2366943359375, 0.332275390625, -0.75244140625, 0.017913818359375, 0.69970703125, 0.95361328125, -0.140869140625, 0.2431640625, -0.07366943359375, -0.404052734375, -0.499267578125, -0.73828125, -0.11859130859375, 0.68798828125, -0.7470703125, 0.188720703125, 0.32666015625, 0.2890625, -0.89697265625, -0.10906982421875, -0.2626953125, -0.685546875, -0.295166015625, 0.494140625, -0.43994140625, 0.51904296875, -0.76806640625, -0.48486328125, 0.6005859375, 1.06640625, -0.2327880859375, 0.372314453125, 0.412109375, 0.1552734375, -0.242431640625, 0.347900390625, 0.306884765625, -0.218017578125, -0.4453125, 1.1083984375, 0.308349609375, -0.072998046875, 0.08050537109375, 0.69873046875, 0.619140625, 0.393798828125, -0.2171630859375, 0.040557861328125, 0.3359375, 1.1708984375, 0.138427734375, 0.81884765625, 0.026214599609375, 0.7587890625, 0.66943359375, 0.65478515625, 0.5322265625, 0.08660888671875, 0.63330078125, 0.86474609375, 0.1585693359375, 0.408447265625, 0.41064453125, 0.46435546875, 0.305419921875, 0.49267578125, 0.260986328125, 0.1895751953125, 0.260498046875, 0.044036865234375, -0.44384765625, 0.17529296875, -0.417724609375, 0.85888671875, -0.11126708984375, 0.14794921875, -0.352783203125, -0.464599609375, 0.1483154296875, 0.8896484375, -0.7587890625, -0.1837158203125, 0.142578125, 0.049560546875, 0.1229248046875, -0.2666015625, 0.333251953125, 0.369873046875, 0.41845703125, 0.501953125, -0.3955078125, -0.2188720703125, -1.169921875, -0.84375, -0.84130859375, -0.5087890625, -0.85205078125, 0.06341552734375, 0.1259765625, -0.7001953125, 0.3251953125, -0.5498046875, -0.2587890625, 0.233154296875, -0.67236328125, 0.6357421875, -0.171875, 0.279541015625, -1.390625, 0.8125, 0.297607421875, 1.1630859375, -0.75146484375, 0.09808349609375, 0.1253662109375, -0.8076171875, 0.041015625, 0.090576171875, 0.225341796875, -0.0308685302734375, -0.7197265625, -0.66357421875, -0.7421875, -0.260986328125, -0.301513671875, 0.359130859375, -0.52490234375, 0.8994140625, 0.751953125, -0.5791015625, 0.75927734375, 0.87841796875, -0.619140625, 0.362548828125, 0.4228515625, 0.1287841796875, -0.80224609375, 1.607421875, 0.49072265625, 0.368896484375, -0.431640625, -0.436279296875, -0.2095947265625, -0.1341552734375, 0.1812744140625, -0.66162109375, -0.52880859375, 0.5498046875, -0.11688232421875, -0.96923828125, 0.1566162109375, -0.9111328125, -0.5888671875, -0.220458984375, -0.72509765625, 1.349609375, 0.97119140625, -0.07037353515625, -0.053375244140625, -0.1163330078125, -0.10382080078125, 0.57568359375, 0.47021484375, -0.07666015625, -0.031646728515625, 0.82763671875, 0.310302734375, 0.0384521484375, 0.190673828125, -0.56494140625, 0.0178680419921875, -0.07940673828125, 0.36474609375, 0.447021484375, 0.1539306640625, 0.412109375, 0.2734375, 0.48583984375, -1.2216796875, -0.21337890625, -0.2479248046875, 0.51416015625, 0.537109375, 0.359130859375, -0.0033664703369140625, -0.513671875, -0.8193359375, -1.072265625, 0.1605224609375, 0.09124755859375, 0.76611328125, -0.818359375, 0.76220703125, 0.138916015625, -0.358154296875, 0.53662109375, -0.6455078125, -0.015625, 0.92236328125, -0.57861328125, 0.904296875, -0.9794921875, 0.311279296875, 0.039764404296875, 0.01508331298828125, 0.35595703125, 0.450927734375, 0.45361328125, -0.463623046875, -0.4287109375, -0.6640625, 0.0606689453125, -0.004039764404296875, -0.353271484375, 0.1009521484375, -0.299560546875, -0.3447265625, -0.8564453125, 0.338623046875, 0.8837890625, 0.86474609375, -0.03741455078125, 0.4951171875, 0.410400390625, 0.454345703125, 0.662109375, -0.1036376953125, 0.24755859375, -0.92919921875, 0.6689453125, 0.2093505859375, -0.316650390625, -0.7099609375, -0.1651611328125, -0.1632080078125, 0.0051116943359375, -0.218017578125, -0.30224609375, -0.875, 0.34228515625, -0.2071533203125, 0.775390625, -0.430419921875, -0.2425537109375, -0.74658203125, 0.43701171875, 0.529296875, -0.77294921875, 0.49755859375, -0.95166015625, 0.63525390625, 0.47802734375, -0.313720703125, -0.3115234375, -0.7490234375, -0.7392578125, -0.5126953125, 0.311279296875, 1.04296875, -0.1683349609375, 0.513671875, -1.326171875, 0.331787109375, 0.1507568359375, -0.7333984375, -0.072021484375, -0.062286376953125, 0.51171875, 0.178955078125, 0.74462890625, -0.1180419921875, -0.29345703125, 0.050994873046875, -1.298828125, 0.57080078125, -0.5869140625, 0.51708984375, 0.1212158203125, -0.25341796875, 0.048431396484375, 0.362548828125, -0.135498046875, 0.0850830078125, -0.2919921875, 0.268310546875, -0.97314453125, -0.59521484375, 0.58544921875, -0.2119140625, -0.294921875, 1.017578125, 0.08837890625, -0.0760498046875, 0.240966796875, 0.544921875, -0.465576171875, 0.43359375, -0.271240234375, 0.8828125, -0.509765625, -0.64111328125, -0.472900390625, -0.322265625, 0.74462890625, -0.09832763671875, -0.44921875, -0.2215576171875, -1.1396484375, -0.1114501953125, 0.181640625, -0.40673828125, 0.2423095703125, 0.11669921875, 0.1790771484375, -0.255859375, -0.018646240234375, -0.45361328125, -0.174560546875, -0.5126953125, -0.59521484375, 0.56298828125, 0.3779296875, 0.54736328125, 0.0970458984375, -0.57666015625, -0.15283203125, 0.4140625, -0.1458740234375, -0.58984375, -0.212646484375, -0.392578125, -0.16015625, -0.485107421875, 0.06134033203125, -0.1087646484375, 0.35888671875, 0.96240234375, -0.010528564453125, 0.356689453125, 0.3642578125, -0.783203125, 0.90771484375, 0.34521484375, -0.70751953125, -0.359619140625, 0.253173828125, -0.08489990234375, 0.66455078125, 0.5576171875, -0.8046875, -0.57470703125, -0.79150390625, 0.26513671875, -0.81298828125, -0.1859130859375, -0.9306640625, -0.59912109375, -0.391357421875, 0.59912109375, -0.0938720703125, -0.67822265625, 0.034637451171875, -0.85498046875, -0.06524658203125, -0.84619140625, -0.2174072265625, -0.77294921875, -0.69189453125, -0.2388916015625, 0.89892578125, 0.081298828125, -0.016021728515625, 0.260009765625, -0.09814453125, 0.126708984375, 0.3046875, -0.734375, -0.169677734375, -0.00811767578125, 0.0838623046875, -0.184326171875, 0.0212860107421875, -0.83154296875, 0.58251953125, -0.869140625, 0.2335205078125, -0.2244873046875, 0.00637054443359375, -0.32763671875, -0.1766357421875, 0.96142578125, -0.353759765625, 0.357421875, -0.297119140625, 0.356689453125, 0.76611328125, -0.66943359375, -0.415771484375, -0.9892578125, -0.82958984375, -1.4033203125, 0.68603515625, -0.4541015625, 0.1513671875, -0.7275390625, -0.5478515625, 0.939453125, -0.70263671875, 0.35205078125, 1.16015625, 0.01342010498046875, 0.403564453125, -0.2822265625, 0.64404296875, 0.2178955078125, -0.6259765625, 0.228271484375, 0.419189453125, -0.6337890625, -0.12396240234375, -0.406982421875, -1.0146484375, -0.4580078125, 0.4091796875, 1.1259765625, -0.00203704833984375, 0.287109375, -0.4267578125, -1.052734375, -0.5078125, 0.7041015625, 0.2666015625, 0.417236328125, 0.998046875, 0.15966796875, -0.09326171875, 0.09979248046875, -0.525390625, -0.286376953125, -0.376953125, 1.1611328125, -0.198974609375, -0.5966796875, 0.8232421875, 0.86181640625, -0.9638671875, -1.0361328125, -0.0867919921875, -0.1292724609375, -0.06390380859375, -0.7646484375, -0.0457763671875, 0.54736328125, -0.421142578125, -0.00473785400390625, 0.2359619140625, -0.1265869140625, 0.2388916015625, 0.18798828125, 0.2802734375, -0.08709716796875, 0.377197265625, 0.974609375, -0.294921875, -0.5751953125, -0.935546875, -0.55859375, -0.442626953125, 0.1466064453125, 0.66162109375, -0.358642578125, 0.1763916015625, 0.402587890625, 0.0164642333984375, 1.03515625, -0.288818359375, -0.430908203125, 0.3642578125, -0.82763671875, -0.630859375, 0.1646728515625, 0.06671142578125, -0.48291015625, 0.685546875, -0.63623046875, 0.01343536376953125, 0.20751953125, 0.052215576171875, -0.382568359375, -1.0400390625, -0.193115234375, -1.2958984375, -0.372802734375, -0.51123046875, -0.93603515625, -0.18212890625, 0.037017822265625, 0.1937255859375, -0.7509765625, 0.046844482421875, 0.43359375, -0.2275390625, 0.8935546875, -0.65625, 0.10986328125, -0.4677734375, -0.4814453125, -0.591796875, 0.0282745361328125, -0.43310546875, -0.052520751953125, -0.87109375, 0.1126708984375, -0.02264404296875, 0.471923828125, -0.2177734375, 0.60009765625, -0.5537109375, -1.1455078125, 0.195556640625, -0.045623779296875, 0.01007080078125, 0.76611328125, 0.400390625, -0.0755615234375, 0.5107421875, -0.0306396484375, -0.2685546875, -0.397216796875, 0.54443359375, 0.54443359375, -0.25341796875, -0.21337890625, -0.1796875, 0.2509765625, -1.2109375, 0.537109375, -0.58837890625, 0.2130126953125, 0.301513671875, -0.53271484375, 0.451904296875, 1.115234375, -0.49267578125, 0.2366943359375, -0.07012939453125, 0.1336669921875, 0.1427001953125, 0.30615234375, -0.1434326171875, 0.78466796875, -0.2154541015625, -0.52978515625, 0.0127716064453125, 0.29443359375, -0.2113037109375, 0.440185546875, -0.1485595703125, -1.0419921875, -0.8994140625, -0.1329345703125, 0.0193634033203125, 0.2376708984375, 0.06378173828125, -0.2227783203125, -0.040069580078125, 0.1317138671875, -0.85693359375, 0.24365234375, -0.9248046875, -0.87109375, 0.52783203125, -0.2271728515625, -0.257080078125, 0.09906005859375, -0.3046875, -0.34716796875, 0.1546630859375, 0.52880859375, -0.65625, 0.4921875, -0.2032470703125, 0.619140625, -0.44189453125, -0.220947265625, 0.1182861328125, 0.6357421875, -0.76318359375, -0.541015625, -0.322021484375, 0.9150390625, 0.205322265625, -0.397705078125, -0.64794921875, 0.0908203125, 0.2105712890625, 0.296875, -0.607421875, 0.2083740234375, -0.23779296875, 0.6787109375, -1.2451171875, 0.050048828125, 0.031524658203125, 0.200927734375, 0.130859375, -0.3251953125, -0.6953125, 1.130859375, 0.372802734375, -0.029266357421875, 0.59814453125, 0.021484375, 0.37744140625, 0.01117706298828125, 0.0013151168823242188, -0.06304931640625, 0.71923828125, 0.640625, 0.59033203125, -0.1829833984375, 0.2020263671875, 0.77001953125, 0.1893310546875, -0.3642578125, 0.29248046875, 0.019378662109375, -0.1009521484375, 0.380615234375, -0.2242431640625, -0.28369140625, -0.1602783203125, -0.348876953125, 0.64306640625, -0.5126953125, -0.0202178955078125, -0.2371826171875, -0.869140625, 0.69140625, -0.295654296875, -0.369140625, 0.4169921875, -0.1456298828125, 0.1993408203125, 0.54150390625, -0.402587890625, -0.310791015625, 1.1142578125, 0.74951171875, 0.404541015625, 0.724609375, 0.366943359375, 0.5517578125, -0.5673828125, 0.341796875, 0.046722412109375, -0.073486328125, -0.08123779296875, -0.71875, -0.9990234375, 0.57080078125, -0.296142578125, -0.23095703125, 0.5478515625, -0.56005859375, 0.341796875, -0.5146484375, 0.99560546875, -0.373046875, 0.294677734375, 0.351806640625, -0.50927734375, -0.6474609375, 0.6689453125, -0.2998046875, 0.319091796875, 0.10882568359375, 0.9072265625, 0.008056640625, 1.7177734375, 0.5634765625, -0.11566162109375, 0.02099609375, 0.458984375, -0.2890625, -0.307861328125, -0.6923828125, -0.312255859375, 0.156982421875, -0.221435546875, -0.85986328125, -0.03179931640625, 0.77197265625, 0.1302490234375, -0.8447265625, -0.259765625, 0.334716796875, -1.138671875, 0.400390625, 0.36474609375, 0.28857421875, 0.1513671875, -0.211181640625, -0.1636962890625, -0.61083984375, 0.447265625, -0.76953125, 0.33642578125, -0.48291015625, -0.373291015625, -0.63720703125, -0.66650390625, -0.400634765625, -0.08428955078125, -0.515625, -0.73828125, 0.58544921875, 0.294921875, 0.71240234375, 0.5400390625, -0.279052734375, 0.26220703125, 0.70361328125, 0.96630859375, -0.1907958984375, 1.1064453125, 0.305908203125, -0.083251953125, 0.2230224609375, -0.336669921875, 0.311279296875, -0.06787109375, 0.341552734375, -0.51171875, -0.251220703125, -0.796875, -1.1220703125, 0.427490234375, 0.432861328125, 0.339599609375, -0.740234375, -1.109375, -0.089599609375, -1.2255859375, -0.4326171875, -0.70654296875, 0.755859375, -0.7255859375, -0.0259552001953125, 0.0755615234375, -1.1142578125, 4.32421875, 0.93359375, 0.63671875, 0.433837890625, 0.1318359375, 0.79833984375, 0.46630859375, -0.31640625, -0.382568359375, -0.315185546875, 0.60498046875, -0.51611328125, -0.051666259765625, 0.97802734375, 0.515625, 0.308349609375, -0.2783203125, 0.0418701171875, 0.2271728515625, -0.84814453125, -0.69580078125, 0.3193359375, 0.08123779296875, 0.56298828125, 0.29931640625, 0.305908203125, 0.80859375, -0.67822265625, -0.178466796875, -0.79833984375, 0.0863037109375, -0.375244140625, 0.93994140625, 0.26708984375, -0.08837890625, 0.7294921875, -0.08184814453125, -0.454345703125, 0.034423828125, 0.112060546875, -0.0443115234375, 0.17333984375, 0.5400390625, -0.70458984375, -0.288330078125, 0.53955078125, -0.56103515625, 0.61474609375, 0.385009765625, -1.03515625, 1.04296875, -0.1470947265625, 0.46875, -0.876953125, -0.6025390625, 0.2176513671875, 0.0880126953125, 0.0828857421875, -0.3662109375, 0.607421875, 0.61474609375, 0.61962890625, 0.023956298828125, 0.50830078125, -0.88623046875, 0.53857421875, -0.2322998046875, 0.59423828125, -0.4375, 0.00145721435546875, -0.20654296875, -0.287353515625, -0.309814453125, -0.55126953125, 0.513671875, 0.0648193359375, -0.2471923828125, 0.85009765625, 0.33203125, -0.7470703125, 0.0806884765625, -0.27099609375, -0.08355712890625, -0.311767578125, 0.77099609375, 1.1904296875, -0.427978515625, 0.178955078125, -0.242919921875, 0.50439453125, 0.54345703125, 0.75, -0.18115234375, -0.53173828125, -0.326171875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Tags: constructive algorithms, data structures, implementation, strings, two pointers Correct Solution: ``` import sys, os, io def rs(): return sys.stdin.readline().rstrip() def ri(): return int(sys.stdin.readline()) def ria(): return list(map(int, sys.stdin.readline().split())) def ws(s): sys.stdout.write(s + '\n') def wi(n): sys.stdout.write(str(n) + '\n') def wia(a): sys.stdout.write(' '.join([str(x) for x in a]) + '\n') import math,datetime,functools,itertools from collections import deque,defaultdict,OrderedDict import collections def main(): starttime=datetime.datetime.now() if(os.path.exists('input.txt')): sys.stdin = open("input.txt","r") sys.stdout = open("output.txt","w") #Solving Area Starts--> #Solving Area Starts--> for _ in range(ri()): n=ri() a=rs() b=rs() s="" if a==b: print(0) continue if n==1: print(1,1) continue ans1=[] ans2=[] z=0 c=0 for j in range(n): if a[j]=='0': break else: c+=1 if c>0: ans1.append(c) i=c while i<n: if a[i]=='1': if i-1>=0: ans1.append(i) s='1'*(i) if a[i:]=='1'*(n-len(s)): z=1 break for k in range(i,n): if a[k]=='0': break ans1.append(k) i=k+1 else: i+=1 if z==1: ans1.append(n) z=0 c=0 for j in range(n): if b[j]=='0': break else: c+=1 if c>0: ans2.append(c) i=c while i<n: if b[i]=='1': if i-1>=0: ans2.append(i) s='1'*(i) if b[i:]=='1'*(n-len(s)): z=1 break for k in range(i,n): if b[k]=='0': break ans2.append(k) i=k+1 else: i+=1 if z==1: ans2.append(n) # print(ans1) # print(ans2) print(len(ans1)+len(ans2),*(ans1+ans2[::-1])) #<--Solving Area Ends endtime=datetime.datetime.now() time=(endtime-starttime).total_seconds()*1000 if(os.path.exists('input.txt')): print("Time:",time,"ms") class FastReader(io.IOBase): newlines = 0 def __init__(self, fd, chunk_size=1024 * 8): self._fd = fd self._chunk_size = chunk_size self.buffer = io.BytesIO() def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, self._chunk_size)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self, size=-1): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, self._chunk_size if size == -1 else size)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() class FastWriter(io.IOBase): def __init__(self, fd): self._fd = fd self.buffer = io.BytesIO() self.write = self.buffer.write def flush(self): os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class FastStdin(io.IOBase): def __init__(self, fd=0): self.buffer = FastReader(fd) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") class FastStdout(io.IOBase): def __init__(self, fd=1): self.buffer = FastWriter(fd) self.write = lambda s: self.buffer.write(s.encode("ascii")) self.flush = self.buffer.flush if __name__ == '__main__': sys.stdin = FastStdin() sys.stdout = FastStdout() main() ```
105,439
[ 0.1650390625, -0.40576171875, -0.00907135009765625, 0.10333251953125, -0.414306640625, -0.76171875, -0.032867431640625, -0.2060546875, 0.182373046875, 1.0146484375, 0.76318359375, -0.2958984375, 0.331298828125, -0.876953125, -0.58447265625, 0.325439453125, -0.339111328125, -0.5927734375, -0.334228515625, -0.5634765625, 0.0123443603515625, -0.12274169921875, -1.3798828125, -0.07073974609375, -0.626953125, 0.8251953125, 0.2890625, -0.12335205078125, 1.005859375, 1.0615234375, -0.421142578125, -0.458740234375, 0.73779296875, -1.0078125, -0.43505859375, -0.495849609375, 0.5986328125, -0.83740234375, -0.13720703125, -0.27783203125, 0.56201171875, -0.2349853515625, 0.2457275390625, -0.9326171875, -1.291015625, 0.1566162109375, -0.345703125, -0.31689453125, -0.1507568359375, -0.440185546875, 0.064208984375, -0.208984375, 0.60302734375, -0.134521484375, 0.04736328125, 0.16943359375, 0.2293701171875, -0.541015625, -0.4609375, 0.147216796875, 0.076171875, 0.16259765625, 0.2020263671875, -0.716796875, 0.12298583984375, 0.1956787109375, -0.253662109375, -0.4423828125, -0.4111328125, -0.97998046875, -0.318115234375, -0.0443115234375, -0.68408203125, -0.331787109375, -0.0859375, 0.26171875, 0.248779296875, -0.1610107421875, -0.85546875, 0.7392578125, -0.286865234375, 0.94482421875, 0.10675048828125, 0.210693359375, -0.473388671875, -0.52197265625, -0.02349853515625, 0.1890869140625, 0.1556396484375, -0.117919921875, -0.351806640625, 0.580078125, -0.46728515625, 0.081787109375, 0.404296875, 0.70849609375, -0.314453125, 0.2509765625, 0.434326171875, -0.0185089111328125, 0.77490234375, 1.2197265625, -0.1986083984375, 1.2041015625, -0.619140625, -0.1988525390625, -0.005939483642578125, 0.126708984375, -0.04364013671875, -0.00514984130859375, 0.006931304931640625, -0.1614990234375, 0.69091796875, 0.397216796875, -0.418701171875, 0.81005859375, -0.03375244140625, 0.442138671875, -1.005859375, 0.486083984375, 0.63427734375, -0.042694091796875, 0.7197265625, -0.2490234375, -0.1949462890625, -0.25732421875, -0.314453125, 1.1474609375, -0.415283203125, -0.439697265625, 0.27294921875, -0.0028057098388671875, -0.29052734375, 0.349853515625, -0.040283203125, 0.72216796875, -0.2279052734375, 0.404052734375, 0.73486328125, -0.482177734375, 0.77587890625, -0.1947021484375, -0.135986328125, 1.7255859375, 0.50830078125, 0.1109619140625, 1.0498046875, 0.45361328125, -0.3095703125, 0.478759765625, -0.92041015625, 0.59423828125, 0.258056640625, 0.3427734375, -0.11566162109375, -0.1202392578125, -0.25341796875, 0.5302734375, 0.07080078125, 0.211669921875, -0.07049560546875, 0.265869140625, 0.0615234375, 0.94482421875, -0.119873046875, 1.078125, -0.3740234375, -0.361083984375, -0.24267578125, -0.6240234375, 0.54150390625, -0.2261962890625, -0.445556640625, 0.57958984375, 0.51318359375, 1.1455078125, 1.365234375, -0.46728515625, 0.2376708984375, 0.35400390625, -0.80224609375, 0.0139312744140625, 0.72705078125, 0.947265625, -0.08734130859375, 0.2408447265625, -0.06646728515625, -0.40869140625, -0.5185546875, -0.7568359375, -0.0860595703125, 0.71484375, -0.720703125, 0.193359375, 0.314453125, 0.29736328125, -0.90673828125, -0.1307373046875, -0.2357177734375, -0.69091796875, -0.301025390625, 0.488037109375, -0.436279296875, 0.50732421875, -0.77294921875, -0.455078125, 0.5908203125, 1.083984375, -0.215576171875, 0.38427734375, 0.418212890625, 0.13037109375, -0.286865234375, 0.34423828125, 0.28466796875, -0.206298828125, -0.465087890625, 1.099609375, 0.3115234375, -0.0811767578125, 0.08453369140625, 0.68994140625, 0.595703125, 0.374267578125, -0.2154541015625, 0.0487060546875, 0.3193359375, 1.177734375, 0.1622314453125, 0.8046875, 0.041900634765625, 0.767578125, 0.6513671875, 0.67236328125, 0.515625, 0.091552734375, 0.6484375, 0.86572265625, 0.11334228515625, 0.434326171875, 0.389892578125, 0.4521484375, 0.309814453125, 0.50732421875, 0.248046875, 0.2054443359375, 0.2724609375, 0.052093505859375, -0.468505859375, 0.12939453125, -0.41748046875, 0.83837890625, -0.128662109375, 0.1632080078125, -0.37353515625, -0.475341796875, 0.1483154296875, 0.89990234375, -0.76513671875, -0.1885986328125, 0.1129150390625, 0.0799560546875, 0.139404296875, -0.26171875, 0.31298828125, 0.339599609375, 0.39794921875, 0.47509765625, -0.395751953125, -0.175048828125, -1.1689453125, -0.841796875, -0.85302734375, -0.5068359375, -0.8349609375, 0.05615234375, 0.1416015625, -0.705078125, 0.3427734375, -0.57861328125, -0.24560546875, 0.213134765625, -0.65087890625, 0.64453125, -0.1734619140625, 0.264404296875, -1.3828125, 0.8154296875, 0.3134765625, 1.19140625, -0.7578125, 0.07513427734375, 0.1500244140625, -0.82177734375, 0.03887939453125, 0.07452392578125, 0.224365234375, -0.03424072265625, -0.71923828125, -0.67724609375, -0.73876953125, -0.2420654296875, -0.31201171875, 0.362548828125, -0.54296875, 0.88037109375, 0.7587890625, -0.59716796875, 0.75634765625, 0.8974609375, -0.62890625, 0.37451171875, 0.423828125, 0.1053466796875, -0.80322265625, 1.6201171875, 0.46533203125, 0.363525390625, -0.442138671875, -0.448974609375, -0.2288818359375, -0.123046875, 0.2025146484375, -0.66455078125, -0.52392578125, 0.55126953125, -0.09613037109375, -0.96728515625, 0.1634521484375, -0.9228515625, -0.54931640625, -0.2142333984375, -0.72412109375, 1.3515625, 0.96484375, -0.045135498046875, -0.041961669921875, -0.1436767578125, -0.1256103515625, 0.59375, 0.492431640625, -0.067138671875, -0.035247802734375, 0.845703125, 0.3232421875, 0.0657958984375, 0.2099609375, -0.5703125, 0.004459381103515625, -0.08349609375, 0.3505859375, 0.437255859375, 0.1666259765625, 0.41455078125, 0.305908203125, 0.49755859375, -1.224609375, -0.2279052734375, -0.261962890625, 0.5, 0.54052734375, 0.338134765625, 0.01398468017578125, -0.492431640625, -0.79345703125, -1.060546875, 0.1385498046875, 0.08489990234375, 0.79736328125, -0.8125, 0.748046875, 0.12371826171875, -0.369873046875, 0.54296875, -0.6494140625, -0.0187530517578125, 0.92578125, -0.60302734375, 0.8955078125, -0.982421875, 0.292724609375, 0.0462646484375, 0.027984619140625, 0.34912109375, 0.438232421875, 0.491943359375, -0.4560546875, -0.421875, -0.693359375, 0.0267486572265625, 0.00791168212890625, -0.378662109375, 0.10968017578125, -0.270751953125, -0.36962890625, -0.87060546875, 0.31494140625, 0.884765625, 0.8896484375, -0.045196533203125, 0.5009765625, 0.372314453125, 0.4765625, 0.70263671875, -0.07684326171875, 0.250244140625, -0.93994140625, 0.66357421875, 0.209716796875, -0.29052734375, -0.71875, -0.1793212890625, -0.1295166015625, 0.03802490234375, -0.2081298828125, -0.321533203125, -0.87109375, 0.323486328125, -0.216064453125, 0.76220703125, -0.430908203125, -0.26220703125, -0.7724609375, 0.416259765625, 0.53857421875, -0.771484375, 0.474365234375, -0.9384765625, 0.62890625, 0.494384765625, -0.322998046875, -0.315185546875, -0.7802734375, -0.71630859375, -0.5244140625, 0.306884765625, 1.0400390625, -0.154052734375, 0.52392578125, -1.3388671875, 0.339111328125, 0.1651611328125, -0.7109375, -0.08758544921875, -0.0562744140625, 0.50927734375, 0.1912841796875, 0.72216796875, -0.11480712890625, -0.31591796875, 0.055938720703125, -1.3037109375, 0.59423828125, -0.61572265625, 0.51904296875, 0.118408203125, -0.248291015625, 0.041046142578125, 0.37548828125, -0.1279296875, 0.07769775390625, -0.29150390625, 0.272705078125, -1.015625, -0.60791015625, 0.634765625, -0.20947265625, -0.29052734375, 1.044921875, 0.0965576171875, -0.09539794921875, 0.260009765625, 0.52734375, -0.470703125, 0.430908203125, -0.318115234375, 0.87353515625, -0.5068359375, -0.6591796875, -0.49609375, -0.315185546875, 0.76904296875, -0.0982666015625, -0.46484375, -0.2249755859375, -1.146484375, -0.12261962890625, 0.178466796875, -0.376220703125, 0.2335205078125, 0.11181640625, 0.16943359375, -0.25927734375, -0.014068603515625, -0.427490234375, -0.166015625, -0.53271484375, -0.56591796875, 0.55615234375, 0.37353515625, 0.544921875, 0.095458984375, -0.60400390625, -0.1624755859375, 0.42138671875, -0.15380859375, -0.5859375, -0.23095703125, -0.375732421875, -0.143310546875, -0.50830078125, 0.07073974609375, -0.1004638671875, 0.37353515625, 0.970703125, 0.0096282958984375, 0.353759765625, 0.369384765625, -0.77734375, 0.912109375, 0.36669921875, -0.70654296875, -0.33984375, 0.2354736328125, -0.09417724609375, 0.65673828125, 0.552734375, -0.80078125, -0.5712890625, -0.7958984375, 0.250732421875, -0.80810546875, -0.168212890625, -0.92919921875, -0.58642578125, -0.42431640625, 0.60546875, -0.05902099609375, -0.66650390625, 0.00238037109375, -0.88623046875, -0.08331298828125, -0.86572265625, -0.2117919921875, -0.7880859375, -0.7119140625, -0.2279052734375, 0.89892578125, 0.07965087890625, -0.002307891845703125, 0.271484375, -0.09967041015625, 0.1275634765625, 0.309814453125, -0.71728515625, -0.1988525390625, 0.01209259033203125, 0.0828857421875, -0.162353515625, 0.024444580078125, -0.830078125, 0.55419921875, -0.8603515625, 0.2135009765625, -0.237060546875, 0.0098114013671875, -0.30029296875, -0.1778564453125, 0.96923828125, -0.3564453125, 0.3427734375, -0.2919921875, 0.3681640625, 0.78369140625, -0.63818359375, -0.42919921875, -0.958984375, -0.81396484375, -1.3994140625, 0.6474609375, -0.459716796875, 0.1531982421875, -0.69091796875, -0.53466796875, 0.9609375, -0.71484375, 0.34423828125, 1.1728515625, 0.011474609375, 0.37939453125, -0.3095703125, 0.63720703125, 0.2216796875, -0.6552734375, 0.2279052734375, 0.446044921875, -0.66015625, -0.150390625, -0.421875, -1.0263671875, -0.44580078125, 0.376953125, 1.1376953125, 0.01192474365234375, 0.294921875, -0.445068359375, -1.0458984375, -0.488037109375, 0.732421875, 0.28076171875, 0.433837890625, 0.99267578125, 0.151611328125, -0.1043701171875, 0.07135009765625, -0.50244140625, -0.28955078125, -0.378662109375, 1.1904296875, -0.193603515625, -0.6005859375, 0.822265625, 0.8857421875, -0.94873046875, -1.0498046875, -0.0938720703125, -0.12213134765625, -0.03143310546875, -0.78564453125, -0.01082611083984375, 0.51806640625, -0.4228515625, -0.0190582275390625, 0.2216796875, -0.12939453125, 0.239501953125, 0.1949462890625, 0.251953125, -0.1326904296875, 0.38916015625, 0.97119140625, -0.29638671875, -0.5703125, -0.9443359375, -0.54931640625, -0.483642578125, 0.12353515625, 0.66455078125, -0.341796875, 0.190185546875, 0.4052734375, 0.049285888671875, 1.0703125, -0.274658203125, -0.42236328125, 0.374755859375, -0.8369140625, -0.638671875, 0.143310546875, 0.058380126953125, -0.5087890625, 0.68017578125, -0.6513671875, 0.0138092041015625, 0.218994140625, 0.0474853515625, -0.411376953125, -1.0380859375, -0.1890869140625, -1.2958984375, -0.361083984375, -0.52294921875, -0.93115234375, -0.1988525390625, 0.047210693359375, 0.199462890625, -0.72802734375, 0.046478271484375, 0.45849609375, -0.214111328125, 0.8857421875, -0.66259765625, 0.08062744140625, -0.457275390625, -0.455322265625, -0.61376953125, 0.046142578125, -0.455078125, -0.05584716796875, -0.865234375, 0.08758544921875, -0.041259765625, 0.480712890625, -0.18408203125, 0.58251953125, -0.5712890625, -1.1474609375, 0.2022705078125, -0.0258941650390625, -0.026641845703125, 0.7861328125, 0.4033203125, -0.08477783203125, 0.50244140625, -0.062408447265625, -0.25732421875, -0.408447265625, 0.51953125, 0.568359375, -0.2392578125, -0.222900390625, -0.1884765625, 0.226806640625, -1.1982421875, 0.5166015625, -0.5849609375, 0.20458984375, 0.322265625, -0.546875, 0.477783203125, 1.0908203125, -0.48046875, 0.2415771484375, -0.06292724609375, 0.1295166015625, 0.124267578125, 0.2939453125, -0.1573486328125, 0.796875, -0.2357177734375, -0.5244140625, 0.033782958984375, 0.3232421875, -0.2115478515625, 0.4384765625, -0.1527099609375, -1.04296875, -0.890625, -0.1190185546875, 0.04534912109375, 0.23291015625, 0.05645751953125, -0.24072265625, -0.043212890625, 0.12103271484375, -0.8671875, 0.264404296875, -0.9140625, -0.8935546875, 0.49462890625, -0.2064208984375, -0.278076171875, 0.11761474609375, -0.3017578125, -0.3212890625, 0.1343994140625, 0.5185546875, -0.64794921875, 0.47314453125, -0.19189453125, 0.59814453125, -0.4404296875, -0.2340087890625, 0.11981201171875, 0.62353515625, -0.75537109375, -0.5439453125, -0.31787109375, 0.90869140625, 0.1680908203125, -0.430908203125, -0.6572265625, 0.11187744140625, 0.2169189453125, 0.296142578125, -0.63134765625, 0.215576171875, -0.2442626953125, 0.66162109375, -1.25390625, 0.04632568359375, 0.043731689453125, 0.2081298828125, 0.12225341796875, -0.35107421875, -0.7216796875, 1.1201171875, 0.405517578125, -0.041107177734375, 0.61572265625, 0.016754150390625, 0.384765625, 0.028717041015625, -0.0234375, -0.08624267578125, 0.72021484375, 0.6318359375, 0.59423828125, -0.21240234375, 0.198486328125, 0.7666015625, 0.1868896484375, -0.375732421875, 0.296875, 0.034027099609375, -0.10357666015625, 0.37744140625, -0.2335205078125, -0.28564453125, -0.1663818359375, -0.337158203125, 0.6533203125, -0.529296875, -0.043853759765625, -0.2298583984375, -0.8603515625, 0.673828125, -0.30078125, -0.374755859375, 0.446533203125, -0.1287841796875, 0.2115478515625, 0.55712890625, -0.400146484375, -0.299072265625, 1.115234375, 0.7470703125, 0.415283203125, 0.6982421875, 0.3779296875, 0.57763671875, -0.5810546875, 0.33349609375, 0.0523681640625, -0.06451416015625, -0.09564208984375, -0.69580078125, -1.013671875, 0.59228515625, -0.31494140625, -0.2388916015625, 0.53369140625, -0.5849609375, 0.358154296875, -0.486083984375, 1.0185546875, -0.363037109375, 0.291015625, 0.35791015625, -0.49169921875, -0.65234375, 0.65771484375, -0.27734375, 0.320556640625, 0.108642578125, 0.916015625, 0.0167236328125, 1.724609375, 0.5810546875, -0.1060791015625, 0.006458282470703125, 0.453857421875, -0.288818359375, -0.313232421875, -0.70068359375, -0.29052734375, 0.156982421875, -0.2222900390625, -0.83642578125, 0.006320953369140625, 0.7802734375, 0.1304931640625, -0.8203125, -0.2490234375, 0.334228515625, -1.1337890625, 0.40771484375, 0.35791015625, 0.3212890625, 0.1455078125, -0.197998046875, -0.1805419921875, -0.611328125, 0.475341796875, -0.767578125, 0.340087890625, -0.47265625, -0.3759765625, -0.638671875, -0.64697265625, -0.42822265625, -0.08453369140625, -0.498291015625, -0.73876953125, 0.576171875, 0.274169921875, 0.7080078125, 0.578125, -0.26953125, 0.2705078125, 0.728515625, 0.958984375, -0.2025146484375, 1.109375, 0.271484375, -0.12646484375, 0.223876953125, -0.306396484375, 0.300537109375, -0.0784912109375, 0.32861328125, -0.50341796875, -0.26220703125, -0.791015625, -1.1201171875, 0.427490234375, 0.415283203125, 0.332275390625, -0.73193359375, -1.1025390625, -0.10626220703125, -1.248046875, -0.431640625, -0.72802734375, 0.76806640625, -0.72509765625, -0.02008056640625, 0.0721435546875, -1.10546875, 4.30859375, 0.93994140625, 0.6650390625, 0.40283203125, 0.1175537109375, 0.80712890625, 0.45849609375, -0.293701171875, -0.366455078125, -0.328857421875, 0.6005859375, -0.498046875, -0.07183837890625, 0.986328125, 0.5185546875, 0.290283203125, -0.283447265625, 0.0386962890625, 0.23828125, -0.85693359375, -0.71044921875, 0.32080078125, 0.04815673828125, 0.56005859375, 0.312255859375, 0.32177734375, 0.830078125, -0.68310546875, -0.179931640625, -0.7861328125, 0.0986328125, -0.369873046875, 0.9345703125, 0.258544921875, -0.07958984375, 0.73095703125, -0.0802001953125, -0.458740234375, 0.0172271728515625, 0.0887451171875, -0.048187255859375, 0.1810302734375, 0.56005859375, -0.7177734375, -0.2939453125, 0.55419921875, -0.53173828125, 0.6171875, 0.386474609375, -1.0361328125, 1.091796875, -0.14501953125, 0.447265625, -0.890625, -0.59423828125, 0.2266845703125, 0.10107421875, 0.0767822265625, -0.362060546875, 0.619140625, 0.611328125, 0.63671875, 0.012298583984375, 0.5146484375, -0.87744140625, 0.51318359375, -0.2373046875, 0.5830078125, -0.473388671875, -0.016815185546875, -0.1845703125, -0.29345703125, -0.32373046875, -0.55322265625, 0.54296875, 0.0350341796875, -0.251953125, 0.8466796875, 0.360595703125, -0.74755859375, 0.07269287109375, -0.2587890625, -0.102294921875, -0.3134765625, 0.7958984375, 1.1982421875, -0.426025390625, 0.139892578125, -0.23828125, 0.475341796875, 0.53173828125, 0.73681640625, -0.16015625, -0.5078125, -0.33056640625 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Tags: constructive algorithms, data structures, implementation, strings, two pointers Correct Solution: ``` for _ in range(int(input())): n=int(input()) #e=[int(x) for x in input().split()] #a=list(input()) #b=list(input()) a=[int(x) for x in input()] b=[int(x) for x in input()] a.append(0) b.append(0) ans=[] for i in range(n): if a[i]!=a[i+1]: ans.append(i+1) #a= [i-a[j] for j in range(i,-1,-1)]+ a[i+1:] for i in range(n-1,-1,-1): if b[i]!=b[i+1]: ans.append(i+1) print(len(ans),end=" ") for x in ans: print(x,end=" ") print() ```
105,440
[ 0.1285400390625, -0.465087890625, -0.020294189453125, 0.08697509765625, -0.38037109375, -0.798828125, 0.0194244384765625, -0.2099609375, 0.1695556640625, 1.0546875, 0.796875, -0.2783203125, 0.323486328125, -0.9052734375, -0.53271484375, 0.332275390625, -0.40625, -0.580078125, -0.33154296875, -0.54443359375, -0.032684326171875, -0.1307373046875, -1.3701171875, -0.09783935546875, -0.54931640625, 0.80859375, 0.303466796875, -0.1651611328125, 1.0234375, 1.08203125, -0.38525390625, -0.43115234375, 0.76904296875, -0.97265625, -0.45751953125, -0.5029296875, 0.55029296875, -0.81201171875, -0.1285400390625, -0.256591796875, 0.59814453125, -0.2332763671875, 0.2491455078125, -0.9013671875, -1.3232421875, 0.204833984375, -0.364501953125, -0.317626953125, -0.1728515625, -0.453125, 0.0135498046875, -0.2371826171875, 0.6171875, -0.130615234375, 0.058624267578125, 0.11663818359375, 0.2314453125, -0.58056640625, -0.487548828125, 0.1748046875, 0.060791015625, 0.12359619140625, 0.177978515625, -0.74072265625, 0.121337890625, 0.1737060546875, -0.226806640625, -0.426025390625, -0.375244140625, -1.01171875, -0.324462890625, -0.0390625, -0.7392578125, -0.3564453125, -0.10577392578125, 0.261962890625, 0.256103515625, -0.157958984375, -0.85791015625, 0.7802734375, -0.286865234375, 0.8876953125, 0.06573486328125, 0.18603515625, -0.51611328125, -0.52734375, -0.06951904296875, 0.218994140625, 0.183349609375, -0.129638671875, -0.39599609375, 0.578125, -0.47998046875, 0.09100341796875, 0.380126953125, 0.6923828125, -0.3408203125, 0.2406005859375, 0.456787109375, -0.064697265625, 0.806640625, 1.2626953125, -0.2076416015625, 1.146484375, -0.61962890625, -0.2261962890625, -0.064697265625, 0.1356201171875, -0.031341552734375, -0.06494140625, -0.0150604248046875, -0.1768798828125, 0.70068359375, 0.339599609375, -0.4228515625, 0.76953125, -0.0189666748046875, 0.4091796875, -0.951171875, 0.5166015625, 0.64599609375, -0.051239013671875, 0.787109375, -0.2374267578125, -0.110107421875, -0.2042236328125, -0.3154296875, 1.08984375, -0.458984375, -0.37841796875, 0.289794921875, -0.0272369384765625, -0.273193359375, 0.355224609375, -0.02154541015625, 0.7216796875, -0.2315673828125, 0.43798828125, 0.724609375, -0.448486328125, 0.81103515625, -0.17822265625, -0.184326171875, 1.68359375, 0.488525390625, 0.12744140625, 1.0205078125, 0.42431640625, -0.2939453125, 0.447998046875, -0.931640625, 0.6015625, 0.255859375, 0.32373046875, -0.073974609375, -0.09423828125, -0.281494140625, 0.494384765625, 0.0709228515625, 0.19189453125, -0.04693603515625, 0.255859375, 0.04705810546875, 0.93896484375, -0.1258544921875, 1.0791015625, -0.407958984375, -0.3369140625, -0.27294921875, -0.69091796875, 0.5283203125, -0.1998291015625, -0.41650390625, 0.61865234375, 0.5390625, 1.146484375, 1.3671875, -0.472900390625, 0.2332763671875, 0.30322265625, -0.7109375, 0.040771484375, 0.70068359375, 0.9443359375, -0.1722412109375, 0.2225341796875, -0.08697509765625, -0.363037109375, -0.50146484375, -0.73681640625, -0.1474609375, 0.6796875, -0.69970703125, 0.1737060546875, 0.330322265625, 0.301513671875, -0.86669921875, -0.0828857421875, -0.26953125, -0.72509765625, -0.298583984375, 0.489013671875, -0.418212890625, 0.54052734375, -0.76611328125, -0.49560546875, 0.6025390625, 1.064453125, -0.247802734375, 0.3154296875, 0.366943359375, 0.17041015625, -0.2349853515625, 0.375244140625, 0.2998046875, -0.234375, -0.42919921875, 1.1474609375, 0.31591796875, -0.049041748046875, 0.062255859375, 0.66748046875, 0.625, 0.41162109375, -0.1815185546875, 0.034698486328125, 0.285888671875, 1.162109375, 0.11712646484375, 0.833984375, -0.004726409912109375, 0.751953125, 0.677734375, 0.65478515625, 0.533203125, 0.06512451171875, 0.60302734375, 0.8798828125, 0.17236328125, 0.392333984375, 0.396240234375, 0.474609375, 0.352783203125, 0.45556640625, 0.23583984375, 0.2322998046875, 0.2685546875, 0.041290283203125, -0.4296875, 0.208251953125, -0.453125, 0.90869140625, -0.094482421875, 0.15673828125, -0.349365234375, -0.461669921875, 0.1341552734375, 0.90625, -0.76416015625, -0.1639404296875, 0.1634521484375, 0.046661376953125, 0.1680908203125, -0.265869140625, 0.375244140625, 0.412109375, 0.44482421875, 0.53369140625, -0.398193359375, -0.2388916015625, -1.1591796875, -0.84228515625, -0.86328125, -0.488525390625, -0.8125, 0.04986572265625, 0.1441650390625, -0.71630859375, 0.338623046875, -0.541015625, -0.272216796875, 0.2451171875, -0.71728515625, 0.64599609375, -0.14404296875, 0.2734375, -1.3837890625, 0.80126953125, 0.3134765625, 1.1357421875, -0.75341796875, 0.0869140625, 0.126708984375, -0.84716796875, 0.004489898681640625, 0.0958251953125, 0.25048828125, -0.03851318359375, -0.72119140625, -0.662109375, -0.724609375, -0.24609375, -0.335205078125, 0.38720703125, -0.5517578125, 0.89794921875, 0.77001953125, -0.57470703125, 0.74951171875, 0.8408203125, -0.59130859375, 0.39208984375, 0.42822265625, 0.15185546875, -0.77783203125, 1.5869140625, 0.521484375, 0.396728515625, -0.46728515625, -0.4638671875, -0.23193359375, -0.162841796875, 0.164794921875, -0.65478515625, -0.52392578125, 0.56201171875, -0.11895751953125, -1.005859375, 0.1336669921875, -0.90478515625, -0.60595703125, -0.236328125, -0.70654296875, 1.330078125, 0.97119140625, -0.07781982421875, -0.060394287109375, -0.1072998046875, -0.10064697265625, 0.59765625, 0.477294921875, -0.033935546875, -0.014434814453125, 0.81591796875, 0.3173828125, 0.05145263671875, 0.1795654296875, -0.5478515625, -0.003879547119140625, -0.055877685546875, 0.389404296875, 0.46337890625, 0.1683349609375, 0.412109375, 0.267822265625, 0.5087890625, -1.2001953125, -0.2041015625, -0.254150390625, 0.55419921875, 0.51904296875, 0.378662109375, -0.006038665771484375, -0.53076171875, -0.83544921875, -1.099609375, 0.143310546875, 0.06500244140625, 0.7724609375, -0.83251953125, 0.75439453125, 0.159423828125, -0.350830078125, 0.5205078125, -0.6416015625, -0.0252838134765625, 0.94677734375, -0.5537109375, 0.92822265625, -0.98583984375, 0.3173828125, 0.040283203125, 0.0081787109375, 0.379638671875, 0.486328125, 0.43505859375, -0.483154296875, -0.43701171875, -0.59228515625, 0.071044921875, -0.02801513671875, -0.339599609375, 0.10247802734375, -0.32080078125, -0.349609375, -0.86279296875, 0.37890625, 0.8876953125, 0.8671875, -0.0009489059448242188, 0.47265625, 0.385986328125, 0.435791015625, 0.63623046875, -0.106689453125, 0.2257080078125, -0.95751953125, 0.6904296875, 0.1888427734375, -0.301025390625, -0.69189453125, -0.148681640625, -0.1715087890625, 0.0002288818359375, -0.201416015625, -0.300048828125, -0.91162109375, 0.356201171875, -0.21484375, 0.80029296875, -0.385986328125, -0.250732421875, -0.71728515625, 0.4853515625, 0.52392578125, -0.80615234375, 0.52099609375, -0.9599609375, 0.6533203125, 0.45166015625, -0.296142578125, -0.303466796875, -0.75439453125, -0.73095703125, -0.52197265625, 0.3046875, 1.025390625, -0.1785888671875, 0.5107421875, -1.3291015625, 0.26513671875, 0.1087646484375, -0.70458984375, -0.060394287109375, -0.09381103515625, 0.493408203125, 0.159423828125, 0.75634765625, -0.1612548828125, -0.319580078125, 0.0523681640625, -1.3359375, 0.5771484375, -0.5625, 0.499267578125, 0.06768798828125, -0.243896484375, 0.073974609375, 0.335693359375, -0.1280517578125, 0.10467529296875, -0.289306640625, 0.25732421875, -0.94384765625, -0.59619140625, 0.5576171875, -0.19970703125, -0.327880859375, 0.95751953125, 0.0718994140625, -0.08367919921875, 0.22607421875, 0.5322265625, -0.4560546875, 0.410888671875, -0.2269287109375, 0.88720703125, -0.5361328125, -0.62451171875, -0.4423828125, -0.344482421875, 0.73828125, -0.1385498046875, -0.45068359375, -0.2479248046875, -1.109375, -0.12176513671875, 0.21142578125, -0.389404296875, 0.285888671875, 0.14208984375, 0.1741943359375, -0.264892578125, -0.03533935546875, -0.407470703125, -0.2020263671875, -0.544921875, -0.6103515625, 0.6328125, 0.383056640625, 0.53759765625, 0.104736328125, -0.5419921875, -0.1412353515625, 0.406494140625, -0.091064453125, -0.591796875, -0.1922607421875, -0.370361328125, -0.1619873046875, -0.4658203125, 0.0677490234375, -0.1265869140625, 0.351318359375, 0.9658203125, 0.008575439453125, 0.36669921875, 0.38720703125, -0.79296875, 0.8984375, 0.329345703125, -0.6728515625, -0.386474609375, 0.273681640625, -0.09906005859375, 0.65478515625, 0.5771484375, -0.787109375, -0.55712890625, -0.77978515625, 0.226318359375, -0.7890625, -0.165283203125, -0.9248046875, -0.6025390625, -0.375244140625, 0.56591796875, -0.09722900390625, -0.67529296875, 0.047088623046875, -0.88427734375, -0.00493621826171875, -0.82666015625, -0.2310791015625, -0.7607421875, -0.66357421875, -0.225341796875, 0.87646484375, 0.052459716796875, -0.01526641845703125, 0.27001953125, -0.11834716796875, 0.1654052734375, 0.26513671875, -0.71923828125, -0.16796875, -0.03741455078125, 0.056640625, -0.158935546875, 0.00681304931640625, -0.83642578125, 0.6005859375, -0.84326171875, 0.2216796875, -0.19775390625, -0.0016832351684570312, -0.3525390625, -0.2012939453125, 0.96044921875, -0.30517578125, 0.378173828125, -0.31884765625, 0.356201171875, 0.75634765625, -0.70068359375, -0.407958984375, -1.00390625, -0.80615234375, -1.4150390625, 0.6943359375, -0.453125, 0.1282958984375, -0.7060546875, -0.56396484375, 0.978515625, -0.6904296875, 0.3330078125, 1.16015625, 0.01074981689453125, 0.4287109375, -0.29345703125, 0.646484375, 0.223876953125, -0.60498046875, 0.2353515625, 0.38623046875, -0.62255859375, -0.10394287109375, -0.369873046875, -1.0263671875, -0.443359375, 0.431396484375, 1.1708984375, -0.0177764892578125, 0.275390625, -0.42431640625, -1.076171875, -0.521484375, 0.67724609375, 0.285888671875, 0.388427734375, 1.021484375, 0.1488037109375, -0.08477783203125, 0.12939453125, -0.4892578125, -0.27294921875, -0.369873046875, 1.1640625, -0.1807861328125, -0.5859375, 0.82275390625, 0.86279296875, -0.9765625, -1.01171875, -0.072509765625, -0.16943359375, -0.0545654296875, -0.74462890625, -0.083740234375, 0.54443359375, -0.411865234375, 0.0224609375, 0.2568359375, -0.10693359375, 0.254150390625, 0.1953125, 0.28564453125, -0.0712890625, 0.366943359375, 0.9638671875, -0.29296875, -0.5830078125, -0.958984375, -0.57080078125, -0.450927734375, 0.154052734375, 0.69287109375, -0.361083984375, 0.154052734375, 0.391845703125, 0.048675537109375, 0.9580078125, -0.255859375, -0.415283203125, 0.402099609375, -0.828125, -0.6416015625, 0.18115234375, 0.07647705078125, -0.48388671875, 0.6748046875, -0.63037109375, 0.020263671875, 0.2000732421875, 0.048919677734375, -0.40673828125, -1.0810546875, -0.164306640625, -1.302734375, -0.40087890625, -0.4853515625, -0.9208984375, -0.150390625, 0.06671142578125, 0.1961669921875, -0.75634765625, 0.044830322265625, 0.431396484375, -0.2403564453125, 0.87646484375, -0.59912109375, 0.1356201171875, -0.438720703125, -0.482666015625, -0.57373046875, 0.02978515625, -0.43115234375, -0.031890869140625, -0.9248046875, 0.15771484375, -0.0302581787109375, 0.46630859375, -0.25732421875, 0.6318359375, -0.5322265625, -1.146484375, 0.2086181640625, -0.0562744140625, 0.0101165771484375, 0.74658203125, 0.390869140625, -0.10272216796875, 0.50927734375, 0.01500701904296875, -0.277587890625, -0.38720703125, 0.55078125, 0.54638671875, -0.267822265625, -0.1865234375, -0.1865234375, 0.259765625, -1.2021484375, 0.5390625, -0.6123046875, 0.2017822265625, 0.293212890625, -0.494140625, 0.43603515625, 1.1298828125, -0.474853515625, 0.2305908203125, -0.112548828125, 0.1378173828125, 0.1702880859375, 0.287109375, -0.13037109375, 0.8037109375, -0.1871337890625, -0.56201171875, 0.00756072998046875, 0.30615234375, -0.237548828125, 0.40673828125, -0.15380859375, -1.044921875, -0.86376953125, -0.1485595703125, -0.027801513671875, 0.2271728515625, 0.08135986328125, -0.2330322265625, -0.027923583984375, 0.141845703125, -0.85400390625, 0.224365234375, -0.94970703125, -0.85498046875, 0.515625, -0.200927734375, -0.217041015625, 0.0557861328125, -0.357421875, -0.356201171875, 0.1318359375, 0.54296875, -0.72998046875, 0.5234375, -0.2012939453125, 0.61181640625, -0.420654296875, -0.255615234375, 0.134033203125, 0.66455078125, -0.7802734375, -0.53564453125, -0.330322265625, 0.91748046875, 0.2127685546875, -0.3291015625, -0.6279296875, 0.054473876953125, 0.2230224609375, 0.314208984375, -0.60546875, 0.1600341796875, -0.244873046875, 0.67919921875, -1.26953125, 0.058807373046875, 0.01271820068359375, 0.224853515625, 0.11041259765625, -0.3486328125, -0.72021484375, 1.1318359375, 0.3525390625, -0.048126220703125, 0.60107421875, 0.01140594482421875, 0.33740234375, -0.034423828125, -0.002445220947265625, -0.0556640625, 0.7265625, 0.634765625, 0.59716796875, -0.1243896484375, 0.1705322265625, 0.76220703125, 0.162841796875, -0.369384765625, 0.2939453125, 0.038299560546875, -0.10504150390625, 0.3603515625, -0.248779296875, -0.273681640625, -0.1773681640625, -0.343505859375, 0.67431640625, -0.517578125, -0.036712646484375, -0.2125244140625, -0.88232421875, 0.6904296875, -0.29150390625, -0.388671875, 0.404052734375, -0.172607421875, 0.1693115234375, 0.546875, -0.422119140625, -0.33544921875, 1.1220703125, 0.7470703125, 0.38671875, 0.72412109375, 0.368408203125, 0.55224609375, -0.53125, 0.354736328125, 0.04925537109375, -0.08660888671875, -0.10870361328125, -0.75, -0.98095703125, 0.54931640625, -0.32080078125, -0.247314453125, 0.58203125, -0.52783203125, 0.2998046875, -0.53125, 0.97265625, -0.386962890625, 0.324462890625, 0.375244140625, -0.49853515625, -0.65087890625, 0.6826171875, -0.29150390625, 0.3271484375, 0.10369873046875, 0.91064453125, -0.037017822265625, 1.69140625, 0.5419921875, -0.0916748046875, 0.0043487548828125, 0.466796875, -0.296875, -0.33203125, -0.71728515625, -0.3271484375, 0.1072998046875, -0.2330322265625, -0.83154296875, -0.067626953125, 0.76220703125, 0.1309814453125, -0.873046875, -0.290771484375, 0.348876953125, -1.1552734375, 0.4052734375, 0.35205078125, 0.229736328125, 0.162353515625, -0.24560546875, -0.19091796875, -0.5888671875, 0.438720703125, -0.765625, 0.3330078125, -0.5068359375, -0.388427734375, -0.63525390625, -0.66357421875, -0.399658203125, -0.0887451171875, -0.53857421875, -0.73193359375, 0.5849609375, 0.313720703125, 0.73095703125, 0.5380859375, -0.31005859375, 0.2396240234375, 0.69921875, 0.9755859375, -0.174560546875, 1.0947265625, 0.322265625, -0.065185546875, 0.23486328125, -0.36279296875, 0.30224609375, -0.00667572021484375, 0.33056640625, -0.48193359375, -0.236083984375, -0.796875, -1.0927734375, 0.440673828125, 0.4208984375, 0.341796875, -0.71728515625, -1.1142578125, -0.07830810546875, -1.2060546875, -0.413818359375, -0.69091796875, 0.78125, -0.74951171875, -0.0109405517578125, 0.07403564453125, -1.09375, 4.32421875, 0.935546875, 0.6083984375, 0.491455078125, 0.093994140625, 0.77685546875, 0.48388671875, -0.34619140625, -0.3681640625, -0.292236328125, 0.59423828125, -0.552734375, -0.034912109375, 0.95458984375, 0.52197265625, 0.31103515625, -0.279052734375, 0.05194091796875, 0.1973876953125, -0.84716796875, -0.69580078125, 0.341552734375, 0.12042236328125, 0.5556640625, 0.29833984375, 0.263427734375, 0.7578125, -0.69970703125, -0.12200927734375, -0.8203125, 0.07684326171875, -0.39306640625, 0.96923828125, 0.293212890625, -0.0811767578125, 0.71923828125, -0.08673095703125, -0.44189453125, 0.0845947265625, 0.113525390625, -0.060791015625, 0.162353515625, 0.51904296875, -0.67626953125, -0.267333984375, 0.509765625, -0.55810546875, 0.572265625, 0.369140625, -1.0048828125, 1.025390625, -0.17431640625, 0.431396484375, -0.85986328125, -0.6484375, 0.21533203125, 0.105712890625, 0.06707763671875, -0.346923828125, 0.64306640625, 0.60888671875, 0.6064453125, 0.05322265625, 0.50830078125, -0.87841796875, 0.56591796875, -0.23095703125, 0.6044921875, -0.38232421875, -0.0175018310546875, -0.2010498046875, -0.274169921875, -0.3154296875, -0.57958984375, 0.490478515625, 0.051605224609375, -0.274658203125, 0.8740234375, 0.326904296875, -0.77099609375, 0.076904296875, -0.2666015625, -0.046630859375, -0.273193359375, 0.78564453125, 1.2177734375, -0.437255859375, 0.200927734375, -0.2626953125, 0.537109375, 0.50927734375, 0.74951171875, -0.183349609375, -0.52197265625, -0.310546875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Tags: constructive algorithms, data structures, implementation, strings, two pointers Correct Solution: ``` import sys input = lambda: sys.stdin.readline().rstrip() # import sys # import math # input = sys.stdin.readline from collections import deque from queue import LifoQueue for _ in range(int(input())): n = int(input()) a = input() b = input() a1 = [] a2 = [] # if n==1: # if a[0]==b[0]: # print(0) # else: # print(1,1) for i in range(0,n,2): if a[i:i+2]=='01': a1.append(i+1) a1.append(i+2) elif a[i:i+2]=='10': if i!=0: a1.append(i) a1.append(i+1) elif a[i:i+2]=='11': if i!=0: a1.append(i) a1.append(i+2) elif a[i:i+2]=='1': if n-1>0: a1.append(n-1) a1.append(n) for i in range(0,n,2): if b[i:i+2]=='01': a2.append(i+1) a2.append(i+2) elif b[i:i+2]=='10': if i!=0: a2.append(i) a2.append(i+1) elif b[i:i+2]=='11': if i!=0: a2.append(i) a2.append(i+2) elif b[i:i+2]=='1': if n-1>0: a2.append(n-1) a2.append(n) a2.reverse() c = a1+a2 # print(*c) for i in range(len(c)-1): if c[i]==c[i+1]: c.pop(i) c.pop(i) break print(len(c),*c) ```
105,441
[ 0.1650390625, -0.401123046875, -0.002330780029296875, 0.096923828125, -0.426513671875, -0.7490234375, -0.0404052734375, -0.2044677734375, 0.1849365234375, 1.01953125, 0.75439453125, -0.2978515625, 0.33203125, -0.88818359375, -0.59912109375, 0.320068359375, -0.342041015625, -0.591796875, -0.3359375, -0.5673828125, 0.02587890625, -0.1185302734375, -1.37890625, -0.076171875, -0.63623046875, 0.826171875, 0.29248046875, -0.1328125, 1.0068359375, 1.0556640625, -0.425048828125, -0.45703125, 0.73828125, -1.0126953125, -0.443359375, -0.492431640625, 0.6005859375, -0.8447265625, -0.1434326171875, -0.280029296875, 0.55908203125, -0.233154296875, 0.2374267578125, -0.93212890625, -1.283203125, 0.150634765625, -0.345458984375, -0.3271484375, -0.156982421875, -0.439697265625, 0.07135009765625, -0.210693359375, 0.62109375, -0.13134765625, 0.03814697265625, 0.16845703125, 0.2376708984375, -0.5390625, -0.464599609375, 0.137451171875, 0.0697021484375, 0.1654052734375, 0.19580078125, -0.70849609375, 0.109375, 0.19921875, -0.2568359375, -0.446044921875, -0.39892578125, -0.97802734375, -0.32177734375, -0.0489501953125, -0.677734375, -0.330078125, -0.07684326171875, 0.27294921875, 0.2474365234375, -0.15625, -0.8544921875, 0.7353515625, -0.296875, 0.9453125, 0.10595703125, 0.2132568359375, -0.4697265625, -0.51220703125, -0.0229339599609375, 0.18603515625, 0.15625, -0.1094970703125, -0.3505859375, 0.58642578125, -0.476318359375, 0.08599853515625, 0.419677734375, 0.71728515625, -0.31787109375, 0.2529296875, 0.423583984375, -0.012847900390625, 0.7734375, 1.228515625, -0.1983642578125, 1.212890625, -0.62353515625, -0.1917724609375, 0.0009450912475585938, 0.1373291015625, -0.04949951171875, -0.0012407302856445312, 0.00504302978515625, -0.1629638671875, 0.69482421875, 0.41162109375, -0.419921875, 0.82275390625, -0.039031982421875, 0.439697265625, -1.0146484375, 0.480712890625, 0.626953125, -0.042236328125, 0.72607421875, -0.2484130859375, -0.19775390625, -0.265869140625, -0.3232421875, 1.1474609375, -0.418212890625, -0.441162109375, 0.278076171875, 0.006298065185546875, -0.2939453125, 0.3515625, -0.04010009765625, 0.71728515625, -0.2269287109375, 0.3916015625, 0.7431640625, -0.46875, 0.7744140625, -0.199462890625, -0.1431884765625, 1.7333984375, 0.50146484375, 0.10552978515625, 1.056640625, 0.4619140625, -0.30810546875, 0.474853515625, -0.92724609375, 0.59326171875, 0.255615234375, 0.341796875, -0.116943359375, -0.11260986328125, -0.2412109375, 0.53271484375, 0.0736083984375, 0.218017578125, -0.08087158203125, 0.26318359375, 0.061492919921875, 0.94482421875, -0.11859130859375, 1.07421875, -0.375732421875, -0.368896484375, -0.24609375, -0.62939453125, 0.5537109375, -0.2296142578125, -0.44189453125, 0.5654296875, 0.51171875, 1.14453125, 1.3681640625, -0.46923828125, 0.2332763671875, 0.35986328125, -0.81494140625, 0.00859832763671875, 0.74365234375, 0.9501953125, -0.072509765625, 0.2432861328125, -0.06817626953125, -0.404296875, -0.51708984375, -0.76123046875, -0.0714111328125, 0.72216796875, -0.708984375, 0.1893310546875, 0.302978515625, 0.291748046875, -0.90478515625, -0.130859375, -0.2349853515625, -0.6806640625, -0.297119140625, 0.487548828125, -0.4384765625, 0.50244140625, -0.76806640625, -0.4560546875, 0.58544921875, 1.1005859375, -0.2144775390625, 0.381103515625, 0.4228515625, 0.1273193359375, -0.28955078125, 0.346923828125, 0.27685546875, -0.2047119140625, -0.468994140625, 1.099609375, 0.30224609375, -0.0738525390625, 0.09075927734375, 0.693359375, 0.59814453125, 0.36181640625, -0.221435546875, 0.052520751953125, 0.3291015625, 1.1806640625, 0.175537109375, 0.80810546875, 0.04010009765625, 0.76220703125, 0.6455078125, 0.67333984375, 0.5224609375, 0.08343505859375, 0.65673828125, 0.8642578125, 0.10089111328125, 0.4296875, 0.39306640625, 0.45751953125, 0.311279296875, 0.51904296875, 0.2359619140625, 0.2109375, 0.270263671875, 0.0638427734375, -0.481201171875, 0.12841796875, -0.423583984375, 0.83154296875, -0.1260986328125, 0.171875, -0.3759765625, -0.486328125, 0.1595458984375, 0.90234375, -0.7734375, -0.1951904296875, 0.10882568359375, 0.09466552734375, 0.142822265625, -0.258056640625, 0.314697265625, 0.33935546875, 0.390380859375, 0.4677734375, -0.392822265625, -0.165771484375, -1.1650390625, -0.84619140625, -0.85009765625, -0.51220703125, -0.828125, 0.046600341796875, 0.1300048828125, -0.7001953125, 0.345947265625, -0.5771484375, -0.2490234375, 0.203857421875, -0.6435546875, 0.64404296875, -0.1683349609375, 0.264404296875, -1.390625, 0.80908203125, 0.31982421875, 1.1943359375, -0.7626953125, 0.07110595703125, 0.1597900390625, -0.8173828125, 0.042999267578125, 0.06671142578125, 0.22509765625, -0.0276031494140625, -0.7158203125, -0.673828125, -0.734375, -0.239501953125, -0.307373046875, 0.365234375, -0.5390625, 0.8818359375, 0.759765625, -0.60009765625, 0.75, 0.89990234375, -0.63330078125, 0.378662109375, 0.423095703125, 0.09869384765625, -0.80517578125, 1.623046875, 0.46923828125, 0.349609375, -0.432373046875, -0.4501953125, -0.2376708984375, -0.11865234375, 0.2020263671875, -0.66162109375, -0.52294921875, 0.56494140625, -0.09765625, -0.96533203125, 0.15869140625, -0.931640625, -0.55126953125, -0.215087890625, -0.716796875, 1.3623046875, 0.9658203125, -0.0367431640625, -0.033294677734375, -0.1512451171875, -0.126708984375, 0.5947265625, 0.4873046875, -0.072265625, -0.039337158203125, 0.84619140625, 0.326171875, 0.061553955078125, 0.224853515625, -0.57421875, 0.00333404541015625, -0.07757568359375, 0.353271484375, 0.43359375, 0.167724609375, 0.41064453125, 0.30517578125, 0.494140625, -1.2177734375, -0.2353515625, -0.260498046875, 0.49951171875, 0.546875, 0.34228515625, 0.01265716552734375, -0.49072265625, -0.7822265625, -1.064453125, 0.1268310546875, 0.09161376953125, 0.806640625, -0.8154296875, 0.755859375, 0.1302490234375, -0.37548828125, 0.548828125, -0.65380859375, -0.010009765625, 0.927734375, -0.6064453125, 0.88916015625, -0.98974609375, 0.291748046875, 0.0382080078125, 0.02008056640625, 0.34130859375, 0.434814453125, 0.50439453125, -0.444091796875, -0.427978515625, -0.701171875, 0.0305938720703125, 0.0198822021484375, -0.387451171875, 0.1116943359375, -0.2734375, -0.376708984375, -0.873046875, 0.31494140625, 0.88037109375, 0.89013671875, -0.049896240234375, 0.51123046875, 0.371337890625, 0.4814453125, 0.7119140625, -0.0736083984375, 0.2462158203125, -0.9462890625, 0.67822265625, 0.2200927734375, -0.296142578125, -0.71142578125, -0.1859130859375, -0.12054443359375, 0.046539306640625, -0.2073974609375, -0.315185546875, -0.86376953125, 0.309814453125, -0.2208251953125, 0.75830078125, -0.428466796875, -0.2783203125, -0.78662109375, 0.42431640625, 0.53955078125, -0.78173828125, 0.4697265625, -0.93408203125, 0.625, 0.49658203125, -0.31298828125, -0.316650390625, -0.78369140625, -0.71630859375, -0.5244140625, 0.3046875, 1.0498046875, -0.1529541015625, 0.53076171875, -1.34375, 0.34521484375, 0.1649169921875, -0.69873046875, -0.08807373046875, -0.046844482421875, 0.51318359375, 0.1859130859375, 0.73046875, -0.10882568359375, -0.32080078125, 0.058929443359375, -1.3134765625, 0.61376953125, -0.61572265625, 0.5390625, 0.12310791015625, -0.256103515625, 0.03253173828125, 0.383056640625, -0.1243896484375, 0.07940673828125, -0.2890625, 0.2666015625, -1.009765625, -0.609375, 0.6435546875, -0.217041015625, -0.29052734375, 1.0537109375, 0.09320068359375, -0.08673095703125, 0.262939453125, 0.52880859375, -0.477294921875, 0.431884765625, -0.330078125, 0.86669921875, -0.5029296875, -0.671875, -0.489501953125, -0.3056640625, 0.76904296875, -0.08941650390625, -0.474853515625, -0.2186279296875, -1.15625, -0.13330078125, 0.1768798828125, -0.367919921875, 0.2276611328125, 0.10540771484375, 0.160888671875, -0.259765625, -0.01971435546875, -0.41796875, -0.1607666015625, -0.53076171875, -0.5654296875, 0.55908203125, 0.367431640625, 0.5546875, 0.0941162109375, -0.61474609375, -0.1610107421875, 0.412353515625, -0.1622314453125, -0.5859375, -0.23291015625, -0.37060546875, -0.1485595703125, -0.5087890625, 0.0711669921875, -0.09442138671875, 0.376220703125, 0.96630859375, 0.00970458984375, 0.360595703125, 0.378662109375, -0.77978515625, 0.9169921875, 0.371826171875, -0.708984375, -0.3369140625, 0.232421875, -0.09368896484375, 0.6533203125, 0.55517578125, -0.8017578125, -0.5634765625, -0.80517578125, 0.256103515625, -0.80859375, -0.1668701171875, -0.93798828125, -0.59228515625, -0.43994140625, 0.61181640625, -0.0667724609375, -0.666015625, -0.0015649795532226562, -0.892578125, -0.08428955078125, -0.87353515625, -0.2147216796875, -0.7890625, -0.72314453125, -0.2327880859375, 0.888671875, 0.0712890625, -0.001491546630859375, 0.277587890625, -0.10272216796875, 0.125, 0.311279296875, -0.72216796875, -0.2003173828125, 0.01229095458984375, 0.07794189453125, -0.1602783203125, 0.02166748046875, -0.83203125, 0.5537109375, -0.86181640625, 0.2098388671875, -0.239501953125, 0.0008692741394042969, -0.289306640625, -0.1746826171875, 0.970703125, -0.353515625, 0.33349609375, -0.2861328125, 0.36962890625, 0.779296875, -0.62646484375, -0.4365234375, -0.95654296875, -0.81396484375, -1.396484375, 0.64111328125, -0.459716796875, 0.15380859375, -0.6875, -0.5322265625, 0.9599609375, -0.70703125, 0.3349609375, 1.177734375, 0.01180267333984375, 0.387451171875, -0.31103515625, 0.63623046875, 0.220703125, -0.66455078125, 0.22705078125, 0.456298828125, -0.666015625, -0.1553955078125, -0.425048828125, -1.0322265625, -0.4453125, 0.373779296875, 1.1513671875, 0.0174713134765625, 0.287353515625, -0.449462890625, -1.0546875, -0.47265625, 0.7421875, 0.282958984375, 0.43408203125, 0.99560546875, 0.14697265625, -0.104248046875, 0.06549072265625, -0.498291015625, -0.286865234375, -0.373291015625, 1.201171875, -0.1964111328125, -0.6044921875, 0.830078125, 0.8955078125, -0.95361328125, -1.0625, -0.1021728515625, -0.117431640625, -0.01513671875, -0.7919921875, -0.0055694580078125, 0.51220703125, -0.4267578125, -0.0316162109375, 0.216796875, -0.131591796875, 0.2386474609375, 0.199462890625, 0.258056640625, -0.141845703125, 0.39990234375, 0.9736328125, -0.28857421875, -0.57958984375, -0.9453125, -0.54541015625, -0.4931640625, 0.11737060546875, 0.6611328125, -0.34521484375, 0.1915283203125, 0.412353515625, 0.047576904296875, 1.0712890625, -0.28515625, -0.42578125, 0.37744140625, -0.8427734375, -0.64111328125, 0.144775390625, 0.0638427734375, -0.5068359375, 0.69091796875, -0.65625, 0.00281524658203125, 0.2125244140625, 0.05157470703125, -0.413330078125, -1.0361328125, -0.1815185546875, -1.3017578125, -0.368408203125, -0.5341796875, -0.93505859375, -0.20263671875, 0.041900634765625, 0.1966552734375, -0.7197265625, 0.051788330078125, 0.46044921875, -0.221435546875, 0.88525390625, -0.669921875, 0.0789794921875, -0.45263671875, -0.44970703125, -0.625, 0.05621337890625, -0.45458984375, -0.0648193359375, -0.865234375, 0.0792236328125, -0.04595947265625, 0.4697265625, -0.1751708984375, 0.58544921875, -0.56396484375, -1.1416015625, 0.2066650390625, -0.0194549560546875, -0.033203125, 0.796875, 0.411376953125, -0.08673095703125, 0.50341796875, -0.06072998046875, -0.2548828125, -0.40771484375, 0.51611328125, 0.57470703125, -0.241455078125, -0.22802734375, -0.1878662109375, 0.235595703125, -1.197265625, 0.5068359375, -0.5859375, 0.204833984375, 0.33056640625, -0.55908203125, 0.48486328125, 1.0927734375, -0.47265625, 0.2393798828125, -0.05426025390625, 0.132080078125, 0.11785888671875, 0.281005859375, -0.165283203125, 0.8046875, -0.2427978515625, -0.529296875, 0.036590576171875, 0.329833984375, -0.2030029296875, 0.44189453125, -0.1494140625, -1.0498046875, -0.89501953125, -0.111328125, 0.046295166015625, 0.2318115234375, 0.055572509765625, -0.255615234375, -0.04058837890625, 0.12017822265625, -0.87353515625, 0.274658203125, -0.89892578125, -0.89306640625, 0.48779296875, -0.204345703125, -0.297607421875, 0.11724853515625, -0.300537109375, -0.30029296875, 0.127685546875, 0.515625, -0.650390625, 0.45947265625, -0.1942138671875, 0.58984375, -0.439453125, -0.236083984375, 0.11895751953125, 0.61962890625, -0.751953125, -0.54052734375, -0.31787109375, 0.91552734375, 0.16357421875, -0.4404296875, -0.65185546875, 0.11077880859375, 0.2275390625, 0.302734375, -0.62939453125, 0.2156982421875, -0.24560546875, 0.65087890625, -1.255859375, 0.04522705078125, 0.032745361328125, 0.21337890625, 0.11614990234375, -0.357666015625, -0.72216796875, 1.12109375, 0.414794921875, -0.037353515625, 0.60888671875, 0.01195526123046875, 0.388916015625, 0.0276031494140625, -0.029388427734375, -0.08349609375, 0.708984375, 0.638671875, 0.59912109375, -0.2073974609375, 0.20703125, 0.767578125, 0.1695556640625, -0.36669921875, 0.292724609375, 0.036956787109375, -0.11053466796875, 0.3662109375, -0.2435302734375, -0.28466796875, -0.1715087890625, -0.343017578125, 0.654296875, -0.525390625, -0.0489501953125, -0.2269287109375, -0.86181640625, 0.68212890625, -0.295654296875, -0.36767578125, 0.452880859375, -0.11962890625, 0.2236328125, 0.55810546875, -0.3955078125, -0.296142578125, 1.12109375, 0.7451171875, 0.41796875, 0.6953125, 0.378173828125, 0.578125, -0.58203125, 0.3359375, 0.048858642578125, -0.0634765625, -0.09906005859375, -0.6845703125, -1.015625, 0.595703125, -0.3232421875, -0.234130859375, 0.53369140625, -0.58544921875, 0.367919921875, -0.486328125, 1.0439453125, -0.35498046875, 0.28662109375, 0.362060546875, -0.49072265625, -0.65625, 0.65380859375, -0.27734375, 0.323974609375, 0.099365234375, 0.923828125, 0.0256195068359375, 1.7333984375, 0.58740234375, -0.11328125, 0.01546478271484375, 0.451904296875, -0.280517578125, -0.309814453125, -0.6953125, -0.2900390625, 0.16162109375, -0.2216796875, -0.83935546875, 0.013824462890625, 0.7822265625, 0.130615234375, -0.81298828125, -0.2391357421875, 0.331298828125, -1.1259765625, 0.405029296875, 0.34814453125, 0.321533203125, 0.1417236328125, -0.203857421875, -0.1845703125, -0.619140625, 0.4775390625, -0.76904296875, 0.343017578125, -0.466552734375, -0.378662109375, -0.6435546875, -0.64208984375, -0.430419921875, -0.0853271484375, -0.497314453125, -0.73828125, 0.5732421875, 0.26611328125, 0.70947265625, 0.58154296875, -0.26416015625, 0.2724609375, 0.728515625, 0.95947265625, -0.2130126953125, 1.10546875, 0.267822265625, -0.1395263671875, 0.2261962890625, -0.298095703125, 0.300537109375, -0.07891845703125, 0.330810546875, -0.50341796875, -0.26171875, -0.7890625, -1.126953125, 0.427001953125, 0.403076171875, 0.325927734375, -0.73193359375, -1.0966796875, -0.1123046875, -1.2490234375, -0.429931640625, -0.7373046875, 0.7646484375, -0.724609375, -0.0182647705078125, 0.0670166015625, -1.11328125, 4.30078125, 0.94677734375, 0.6796875, 0.383056640625, 0.11419677734375, 0.81494140625, 0.449951171875, -0.287353515625, -0.359375, -0.33984375, 0.59326171875, -0.501953125, -0.0765380859375, 0.99267578125, 0.5263671875, 0.2919921875, -0.277587890625, 0.04400634765625, 0.2318115234375, -0.86181640625, -0.7119140625, 0.312744140625, 0.048919677734375, 0.5498046875, 0.315673828125, 0.324462890625, 0.82958984375, -0.689453125, -0.174072265625, -0.78857421875, 0.10858154296875, -0.363037109375, 0.92919921875, 0.256591796875, -0.0853271484375, 0.7294921875, -0.08056640625, -0.458251953125, 0.0104217529296875, 0.0831298828125, -0.04522705078125, 0.1812744140625, 0.5693359375, -0.72021484375, -0.289794921875, 0.55712890625, -0.52978515625, 0.615234375, 0.391845703125, -1.04296875, 1.0947265625, -0.156982421875, 0.441650390625, -0.88525390625, -0.6015625, 0.237548828125, 0.10076904296875, 0.07373046875, -0.36181640625, 0.6181640625, 0.611328125, 0.6376953125, 0.0053558349609375, 0.5078125, -0.86962890625, 0.50244140625, -0.2393798828125, 0.580078125, -0.479248046875, -0.02239990234375, -0.17919921875, -0.29443359375, -0.3193359375, -0.55517578125, 0.54443359375, 0.0361328125, -0.252685546875, 0.8388671875, 0.37353515625, -0.74658203125, 0.0736083984375, -0.2447509765625, -0.1021728515625, -0.31787109375, 0.80615234375, 1.20703125, -0.412841796875, 0.134765625, -0.23193359375, 0.46630859375, 0.53125, 0.73876953125, -0.1629638671875, -0.5087890625, -0.333984375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Tags: constructive algorithms, data structures, implementation, strings, two pointers Correct Solution: ``` t=int(input()) for _ in range(t): n=int(input()) a=input() b=input() aToAllOnesOrZeros=[] for i in range(n-1): if a[i]!=a[i+1]: #flip up to a[i]. Then a[0,1,...i+1] will be uniform. a will become all = to a[-1] aToAllOnesOrZeros.append(i+1) bToAllOnesOrZeros=[] for i in range(n-1): if b[i]!=b[i+1]: #b will become all = to b[-1] bToAllOnesOrZeros.append(i+1) res=aToAllOnesOrZeros if a[-1]!=b[-1]: #flip all aTransformed so that aTransformed==bTransformed res.append(n) for i in range(len(bToAllOnesOrZeros)-1,-1,-1): res.append(bToAllOnesOrZeros[i]) #reverse the process l=len(res) res.insert(0,l) print(' '.join([str(x) for x in res])) #def flip(s,l): # S=list(s[:l]) # for i in range(l): # S[i]='0' if S[i]=='1' else '1' # return ''.join(S)+s[l:] # #y=a #for i in range(n-1): # if y[i]!=y[i+1]: # y=flip(y,i+1) #print(y) #y will be all a[-1] # #z=b #for i in range(n-1): # if z[i]!=z[i+1]: # z=flip(z,i+1) #print(z) #z will be all b[-1] ```
105,442
[ 0.150634765625, -0.4287109375, -0.0660400390625, 0.05181884765625, -0.384765625, -0.78466796875, 0.0010194778442382812, -0.2130126953125, 0.1436767578125, 1.0009765625, 0.7568359375, -0.262451171875, 0.3095703125, -0.88427734375, -0.5361328125, 0.310791015625, -0.3740234375, -0.59326171875, -0.329833984375, -0.5341796875, -0.0914306640625, -0.12213134765625, -1.3466796875, -0.0858154296875, -0.595703125, 0.81591796875, 0.3193359375, -0.155029296875, 1.0087890625, 1.091796875, -0.41455078125, -0.421142578125, 0.74560546875, -0.97265625, -0.455078125, -0.469970703125, 0.56396484375, -0.80615234375, -0.109375, -0.266357421875, 0.54736328125, -0.2401123046875, 0.227294921875, -0.90673828125, -1.318359375, 0.2042236328125, -0.33740234375, -0.32421875, -0.1458740234375, -0.50927734375, 0.0031871795654296875, -0.247314453125, 0.60888671875, -0.0733642578125, 0.051483154296875, 0.1712646484375, 0.1953125, -0.564453125, -0.459228515625, 0.189208984375, 0.0811767578125, 0.11944580078125, 0.1571044921875, -0.77197265625, 0.1185302734375, 0.1678466796875, -0.22998046875, -0.4248046875, -0.368408203125, -1.0263671875, -0.37158203125, -0.0703125, -0.73779296875, -0.326904296875, -0.1082763671875, 0.296875, 0.2335205078125, -0.1544189453125, -0.876953125, 0.72998046875, -0.3134765625, 0.9404296875, 0.0675048828125, 0.227294921875, -0.460205078125, -0.55322265625, -0.043670654296875, 0.22119140625, 0.1893310546875, -0.1611328125, -0.405517578125, 0.5693359375, -0.46826171875, 0.07568359375, 0.391357421875, 0.70556640625, -0.337646484375, 0.263427734375, 0.439208984375, -0.06854248046875, 0.7744140625, 1.22265625, -0.2061767578125, 1.1904296875, -0.607421875, -0.1937255859375, -0.035491943359375, 0.145751953125, -0.046844482421875, -0.060791015625, 0.0014400482177734375, -0.1689453125, 0.705078125, 0.331787109375, -0.405029296875, 0.76513671875, -0.02734375, 0.382568359375, -0.9951171875, 0.468017578125, 0.693359375, -0.0972900390625, 0.76416015625, -0.249267578125, -0.1385498046875, -0.241455078125, -0.296142578125, 1.125, -0.4306640625, -0.3818359375, 0.240966796875, -0.0141143798828125, -0.251708984375, 0.358154296875, -0.028472900390625, 0.76318359375, -0.256103515625, 0.423828125, 0.68994140625, -0.4658203125, 0.75634765625, -0.1590576171875, -0.175048828125, 1.7060546875, 0.51416015625, 0.1259765625, 0.98388671875, 0.427001953125, -0.3173828125, 0.442626953125, -0.91064453125, 0.58837890625, 0.2391357421875, 0.325927734375, -0.1370849609375, -0.09576416015625, -0.288818359375, 0.496826171875, 0.0792236328125, 0.1719970703125, -0.053680419921875, 0.267333984375, 0.0804443359375, 0.96337890625, -0.08599853515625, 1.111328125, -0.409912109375, -0.3603515625, -0.29638671875, -0.6640625, 0.52197265625, -0.2349853515625, -0.43896484375, 0.63818359375, 0.55517578125, 1.2041015625, 1.3525390625, -0.47900390625, 0.26416015625, 0.3232421875, -0.71875, 0.006450653076171875, 0.65625, 0.92724609375, -0.18896484375, 0.217529296875, -0.072509765625, -0.406494140625, -0.48291015625, -0.705078125, -0.1817626953125, 0.716796875, -0.771484375, 0.16162109375, 0.32666015625, 0.25732421875, -0.88525390625, -0.1298828125, -0.3115234375, -0.69140625, -0.31591796875, 0.5146484375, -0.44775390625, 0.51611328125, -0.77001953125, -0.48974609375, 0.5859375, 1.0810546875, -0.2381591796875, 0.3564453125, 0.365478515625, 0.1844482421875, -0.2232666015625, 0.40869140625, 0.300537109375, -0.206787109375, -0.412353515625, 1.1357421875, 0.319580078125, -0.06494140625, 0.058197021484375, 0.69482421875, 0.62060546875, 0.417236328125, -0.2198486328125, 0.04290771484375, 0.31396484375, 1.1884765625, 0.14501953125, 0.82373046875, 0.03533935546875, 0.77001953125, 0.69384765625, 0.69140625, 0.5673828125, 0.09222412109375, 0.611328125, 0.85107421875, 0.195556640625, 0.3662109375, 0.440185546875, 0.446533203125, 0.3408203125, 0.471923828125, 0.21875, 0.1925048828125, 0.269287109375, 0.033935546875, -0.439453125, 0.2022705078125, -0.4150390625, 0.8359375, -0.09197998046875, 0.146484375, -0.3427734375, -0.46142578125, 0.187744140625, 0.86474609375, -0.71533203125, -0.1925048828125, 0.1729736328125, 0.03765869140625, 0.150146484375, -0.285400390625, 0.347412109375, 0.373291015625, 0.4404296875, 0.53369140625, -0.390625, -0.25537109375, -1.1572265625, -0.841796875, -0.8466796875, -0.5078125, -0.837890625, 0.06280517578125, 0.142822265625, -0.7060546875, 0.34423828125, -0.5390625, -0.30224609375, 0.26123046875, -0.677734375, 0.68505859375, -0.153076171875, 0.286376953125, -1.3681640625, 0.8046875, 0.307373046875, 1.109375, -0.74755859375, 0.07647705078125, 0.12457275390625, -0.787109375, 0.0423583984375, 0.08697509765625, 0.2237548828125, -0.070556640625, -0.73974609375, -0.65966796875, -0.75732421875, -0.2269287109375, -0.30419921875, 0.379638671875, -0.5224609375, 0.92431640625, 0.7470703125, -0.57177734375, 0.7724609375, 0.8388671875, -0.58056640625, 0.345703125, 0.41455078125, 0.14453125, -0.79150390625, 1.595703125, 0.51123046875, 0.3740234375, -0.422119140625, -0.428466796875, -0.19970703125, -0.093994140625, 0.1585693359375, -0.67333984375, -0.50830078125, 0.52587890625, -0.1226806640625, -0.9599609375, 0.1346435546875, -0.90966796875, -0.578125, -0.21240234375, -0.71142578125, 1.3623046875, 0.9765625, -0.0802001953125, -0.060943603515625, -0.12493896484375, -0.08074951171875, 0.5400390625, 0.484130859375, -0.0787353515625, -0.057830810546875, 0.7998046875, 0.31884765625, 0.0509033203125, 0.16552734375, -0.54833984375, -0.0222625732421875, -0.0921630859375, 0.3896484375, 0.46826171875, 0.150390625, 0.416015625, 0.277587890625, 0.51513671875, -1.21484375, -0.2391357421875, -0.267333984375, 0.53466796875, 0.53857421875, 0.285400390625, -0.0252532958984375, -0.55517578125, -0.84228515625, -1.056640625, 0.20703125, 0.11370849609375, 0.79248046875, -0.8603515625, 0.77294921875, 0.1727294921875, -0.35009765625, 0.52197265625, -0.63720703125, -0.05133056640625, 0.93310546875, -0.546875, 0.8916015625, -0.97021484375, 0.30029296875, 0.03741455078125, -0.0003147125244140625, 0.384033203125, 0.46484375, 0.4228515625, -0.49560546875, -0.44091796875, -0.6083984375, 0.08563232421875, -0.0225372314453125, -0.33154296875, 0.125732421875, -0.28173828125, -0.319580078125, -0.857421875, 0.351318359375, 0.892578125, 0.84765625, -0.046905517578125, 0.490478515625, 0.39794921875, 0.474365234375, 0.6416015625, -0.1109619140625, 0.225830078125, -0.900390625, 0.62646484375, 0.239990234375, -0.354248046875, -0.6787109375, -0.1937255859375, -0.1884765625, -0.03143310546875, -0.1920166015625, -0.293212890625, -0.853515625, 0.371826171875, -0.230224609375, 0.8037109375, -0.385009765625, -0.255859375, -0.72900390625, 0.446044921875, 0.50244140625, -0.7392578125, 0.484619140625, -0.9306640625, 0.6650390625, 0.46923828125, -0.29931640625, -0.28466796875, -0.734375, -0.75732421875, -0.51025390625, 0.310546875, 1.060546875, -0.1854248046875, 0.50732421875, -1.3525390625, 0.308837890625, 0.1580810546875, -0.70947265625, -0.1007080078125, -0.09161376953125, 0.464111328125, 0.1768798828125, 0.76953125, -0.1363525390625, -0.291748046875, 0.0276641845703125, -1.3310546875, 0.57421875, -0.5625, 0.50341796875, 0.116455078125, -0.240478515625, 0.071533203125, 0.36083984375, -0.15771484375, 0.0789794921875, -0.324462890625, 0.28955078125, -0.92431640625, -0.61083984375, 0.53857421875, -0.2291259765625, -0.285400390625, 1.025390625, 0.07110595703125, -0.04559326171875, 0.263671875, 0.54541015625, -0.477294921875, 0.44775390625, -0.2666015625, 0.859375, -0.556640625, -0.6513671875, -0.446044921875, -0.323974609375, 0.7509765625, -0.09088134765625, -0.421875, -0.2232666015625, -1.1044921875, -0.084716796875, 0.2027587890625, -0.38818359375, 0.216552734375, 0.105712890625, 0.208984375, -0.246826171875, 0.01513671875, -0.45703125, -0.156982421875, -0.53759765625, -0.61181640625, 0.583984375, 0.34033203125, 0.53955078125, 0.089111328125, -0.57568359375, -0.14453125, 0.388427734375, -0.1314697265625, -0.6123046875, -0.2252197265625, -0.42236328125, -0.192626953125, -0.470458984375, 0.03076171875, -0.1185302734375, 0.32177734375, 0.9970703125, 0.027923583984375, 0.35009765625, 0.3203125, -0.77099609375, 0.8779296875, 0.305419921875, -0.67333984375, -0.33154296875, 0.2489013671875, -0.047149658203125, 0.654296875, 0.58056640625, -0.79052734375, -0.55322265625, -0.80859375, 0.26123046875, -0.81494140625, -0.171630859375, -0.9443359375, -0.583984375, -0.3603515625, 0.5791015625, -0.1322021484375, -0.6796875, 0.05865478515625, -0.84375, -0.05474853515625, -0.85498046875, -0.197998046875, -0.79638671875, -0.6962890625, -0.23291015625, 0.8876953125, 0.06695556640625, 0.0021495819091796875, 0.237548828125, -0.10302734375, 0.1654052734375, 0.3173828125, -0.72802734375, -0.154296875, -0.0100555419921875, 0.10394287109375, -0.163818359375, 0.04669189453125, -0.8056640625, 0.6357421875, -0.85498046875, 0.2266845703125, -0.1810302734375, -0.0078582763671875, -0.346923828125, -0.205810546875, 0.96044921875, -0.339599609375, 0.38330078125, -0.31640625, 0.304443359375, 0.7880859375, -0.7080078125, -0.444580078125, -1.005859375, -0.83837890625, -1.37890625, 0.7197265625, -0.44384765625, 0.1351318359375, -0.7216796875, -0.529296875, 0.96142578125, -0.720703125, 0.351318359375, 1.19921875, -0.0164337158203125, 0.4140625, -0.26318359375, 0.666015625, 0.21630859375, -0.61669921875, 0.215576171875, 0.35205078125, -0.6259765625, -0.144775390625, -0.415771484375, -1.015625, -0.45068359375, 0.443359375, 1.1240234375, -0.038055419921875, 0.292236328125, -0.4248046875, -1.07421875, -0.56005859375, 0.6875, 0.297607421875, 0.3955078125, 0.97802734375, 0.1759033203125, -0.0986328125, 0.0906982421875, -0.51708984375, -0.289794921875, -0.404052734375, 1.1611328125, -0.1923828125, -0.611328125, 0.8251953125, 0.853515625, -0.9619140625, -1.0107421875, -0.11767578125, -0.16162109375, -0.11322021484375, -0.7490234375, -0.08197021484375, 0.583984375, -0.430908203125, 0.020904541015625, 0.28759765625, -0.11199951171875, 0.222412109375, 0.18798828125, 0.333984375, -0.06646728515625, 0.34423828125, 0.947265625, -0.2744140625, -0.5419921875, -0.95458984375, -0.52587890625, -0.420166015625, 0.13623046875, 0.65380859375, -0.38330078125, 0.153076171875, 0.3955078125, -0.027679443359375, 0.9990234375, -0.34033203125, -0.456298828125, 0.378173828125, -0.82666015625, -0.63037109375, 0.158447265625, 0.08990478515625, -0.44580078125, 0.69677734375, -0.64111328125, 0.037628173828125, 0.2315673828125, 0.045196533203125, -0.412353515625, -1.0361328125, -0.1837158203125, -1.29296875, -0.40087890625, -0.537109375, -0.89404296875, -0.173828125, 0.006694793701171875, 0.188232421875, -0.75390625, 0.04876708984375, 0.400146484375, -0.2171630859375, 0.9482421875, -0.63720703125, 0.1588134765625, -0.471923828125, -0.50048828125, -0.61962890625, 0.00621795654296875, -0.44140625, 0.01428985595703125, -0.89892578125, 0.149169921875, -0.04522705078125, 0.47607421875, -0.2293701171875, 0.62109375, -0.53076171875, -1.1083984375, 0.2093505859375, -0.0102996826171875, 0.0413818359375, 0.74560546875, 0.384033203125, -0.09423828125, 0.5166015625, -0.0175628662109375, -0.286376953125, -0.415283203125, 0.62060546875, 0.5234375, -0.2265625, -0.1859130859375, -0.1815185546875, 0.263671875, -1.201171875, 0.54931640625, -0.580078125, 0.203857421875, 0.313720703125, -0.492919921875, 0.4658203125, 1.12109375, -0.484375, 0.2457275390625, -0.11712646484375, 0.10882568359375, 0.189208984375, 0.31884765625, -0.1988525390625, 0.763671875, -0.1949462890625, -0.513671875, -0.0127716064453125, 0.25, -0.228759765625, 0.451904296875, -0.1268310546875, -1.02734375, -0.87548828125, -0.158447265625, 0.038360595703125, 0.1900634765625, 0.08282470703125, -0.222412109375, -0.0450439453125, 0.1163330078125, -0.83447265625, 0.236328125, -0.91162109375, -0.876953125, 0.55419921875, -0.1942138671875, -0.21875, 0.11181640625, -0.318359375, -0.3759765625, 0.1553955078125, 0.53564453125, -0.64892578125, 0.5068359375, -0.16162109375, 0.63623046875, -0.43603515625, -0.220703125, 0.10369873046875, 0.6669921875, -0.763671875, -0.53466796875, -0.2978515625, 0.88232421875, 0.20947265625, -0.366455078125, -0.63525390625, 0.06072998046875, 0.236328125, 0.307373046875, -0.58740234375, 0.1683349609375, -0.195068359375, 0.66455078125, -1.240234375, 0.050537109375, 0.053314208984375, 0.1939697265625, 0.145751953125, -0.3359375, -0.69921875, 1.13671875, 0.34033203125, -0.031219482421875, 0.61181640625, -0.00873565673828125, 0.372314453125, -0.01204681396484375, -0.00634765625, -0.0257415771484375, 0.7568359375, 0.6376953125, 0.63134765625, -0.156005859375, 0.174072265625, 0.74365234375, 0.20263671875, -0.322265625, 0.29736328125, -0.016357421875, -0.0806884765625, 0.38330078125, -0.217529296875, -0.271728515625, -0.1793212890625, -0.357421875, 0.646484375, -0.52294921875, -0.01180267333984375, -0.229248046875, -0.8740234375, 0.69873046875, -0.25244140625, -0.37939453125, 0.4443359375, -0.1861572265625, 0.16552734375, 0.54638671875, -0.424560546875, -0.32763671875, 1.140625, 0.74462890625, 0.431640625, 0.736328125, 0.348876953125, 0.583984375, -0.53759765625, 0.384033203125, 0.07794189453125, -0.0789794921875, -0.078369140625, -0.74560546875, -1.0009765625, 0.55078125, -0.30419921875, -0.24755859375, 0.58740234375, -0.56787109375, 0.283935546875, -0.5400390625, 0.9775390625, -0.3486328125, 0.314453125, 0.32958984375, -0.529296875, -0.64599609375, 0.68701171875, -0.285400390625, 0.349853515625, 0.0887451171875, 0.8896484375, -0.00965118408203125, 1.72265625, 0.5830078125, -0.1265869140625, 0.00975799560546875, 0.45849609375, -0.313720703125, -0.300537109375, -0.6953125, -0.3466796875, 0.166259765625, -0.1934814453125, -0.85205078125, -0.07012939453125, 0.78515625, 0.1614990234375, -0.88037109375, -0.3037109375, 0.365478515625, -1.115234375, 0.410400390625, 0.3955078125, 0.2425537109375, 0.1441650390625, -0.214111328125, -0.1485595703125, -0.6005859375, 0.46826171875, -0.76123046875, 0.3037109375, -0.490234375, -0.390869140625, -0.60302734375, -0.67578125, -0.407958984375, -0.068603515625, -0.50244140625, -0.705078125, 0.6220703125, 0.27734375, 0.7021484375, 0.51025390625, -0.288818359375, 0.251953125, 0.71923828125, 0.9833984375, -0.1790771484375, 1.126953125, 0.274658203125, -0.10626220703125, 0.2320556640625, -0.394775390625, 0.313232421875, -0.048980712890625, 0.3623046875, -0.50146484375, -0.250732421875, -0.8203125, -1.1142578125, 0.38720703125, 0.4541015625, 0.35546875, -0.736328125, -1.1142578125, -0.06280517578125, -1.232421875, -0.423583984375, -0.68115234375, 0.7216796875, -0.7607421875, -0.0215606689453125, 0.10833740234375, -1.109375, 4.3203125, 0.97021484375, 0.65478515625, 0.47119140625, 0.1051025390625, 0.79248046875, 0.474853515625, -0.298095703125, -0.427978515625, -0.282958984375, 0.62109375, -0.52587890625, -0.0472412109375, 0.94189453125, 0.5126953125, 0.283447265625, -0.267578125, 0.0100250244140625, 0.228515625, -0.84423828125, -0.6806640625, 0.336181640625, 0.08966064453125, 0.560546875, 0.277099609375, 0.265869140625, 0.77392578125, -0.69921875, -0.180419921875, -0.8369140625, 0.06597900390625, -0.39697265625, 0.94287109375, 0.29345703125, -0.1290283203125, 0.72412109375, -0.03936767578125, -0.4326171875, 0.041046142578125, 0.0849609375, -0.076416015625, 0.18994140625, 0.54736328125, -0.703125, -0.287109375, 0.498291015625, -0.56884765625, 0.62646484375, 0.38134765625, -1.0283203125, 1.03515625, -0.1707763671875, 0.462890625, -0.86669921875, -0.6201171875, 0.201171875, 0.0743408203125, 0.09967041015625, -0.346923828125, 0.60986328125, 0.63232421875, 0.58544921875, 0.04034423828125, 0.50048828125, -0.9189453125, 0.56396484375, -0.258544921875, 0.63037109375, -0.4111328125, -0.0330810546875, -0.203369140625, -0.30322265625, -0.292236328125, -0.58251953125, 0.5361328125, 0.07244873046875, -0.2376708984375, 0.88134765625, 0.303955078125, -0.7666015625, 0.049407958984375, -0.2568359375, -0.060394287109375, -0.324951171875, 0.7646484375, 1.1865234375, -0.43212890625, 0.177978515625, -0.282958984375, 0.52197265625, 0.57568359375, 0.77197265625, -0.163330078125, -0.5439453125, -0.3447265625 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Tags: constructive algorithms, data structures, implementation, strings, two pointers Correct Solution: ``` import collections t1=int(input()) for _ in range(t1): flipflag=0 bitflag=0 n=int(input()) a2=input() a=collections.deque([]) for i in range(n): a.append(a2[i]) b=input() ans=[] for i in range(n-1,-1,-1): if flipflag==0: p=a[-1] else: p=a[0] if bitflag==1: if p=='0': p='1' else: p='0' if flipflag==0: q=a[0] else: q=a[-1] if bitflag==1: if q=='0': q='1' else: q='0' if p!=b[i]: if q!=b[i]: ans.append(str(i+1)) if flipflag==0: a.popleft() else: a.pop() flipflag=1-flipflag bitflag=1-bitflag else: ans.append('1') ans.append(str(i+1)) if flipflag==0: a.popleft() else: a.pop() flipflag=1-flipflag bitflag=1-bitflag else: if flipflag==0: a.pop() else: a.popleft() print(len(ans)) if len(ans)>0: print(' '.join(ans)) ```
105,443
[ 0.1298828125, -0.3974609375, -0.03948974609375, 0.044586181640625, -0.390380859375, -0.78515625, -0.01459503173828125, -0.2470703125, 0.251708984375, 1.0087890625, 0.7783203125, -0.27099609375, 0.342041015625, -0.89697265625, -0.58349609375, 0.330078125, -0.379638671875, -0.580078125, -0.331787109375, -0.52490234375, -0.033050537109375, -0.1170654296875, -1.3662109375, -0.08917236328125, -0.58056640625, 0.82470703125, 0.34130859375, -0.1258544921875, 1.05078125, 1.0947265625, -0.37353515625, -0.442626953125, 0.76953125, -0.99658203125, -0.428955078125, -0.470458984375, 0.6005859375, -0.8125, -0.08880615234375, -0.278076171875, 0.59033203125, -0.27685546875, 0.2325439453125, -0.89794921875, -1.294921875, 0.207275390625, -0.28857421875, -0.296630859375, -0.1522216796875, -0.54150390625, 0.0091400146484375, -0.27001953125, 0.6396484375, -0.0849609375, 0.04486083984375, 0.1365966796875, 0.2352294921875, -0.580078125, -0.4375, 0.1651611328125, 0.09490966796875, 0.12054443359375, 0.1903076171875, -0.76220703125, 0.0921630859375, 0.1973876953125, -0.221923828125, -0.4580078125, -0.398681640625, -1.033203125, -0.346435546875, -0.0256500244140625, -0.7001953125, -0.33203125, -0.1341552734375, 0.283447265625, 0.261962890625, -0.1783447265625, -0.85009765625, 0.7705078125, -0.2890625, 0.9384765625, 0.0997314453125, 0.248291015625, -0.492919921875, -0.58740234375, -0.01454925537109375, 0.20361328125, 0.167236328125, -0.1322021484375, -0.416748046875, 0.58203125, -0.455078125, 0.09375, 0.4013671875, 0.73046875, -0.284423828125, 0.2626953125, 0.45947265625, -0.048065185546875, 0.77880859375, 1.2275390625, -0.207275390625, 1.1708984375, -0.5927734375, -0.192626953125, -0.0880126953125, 0.10614013671875, -0.05267333984375, -0.040985107421875, -0.0081787109375, -0.212158203125, 0.68359375, 0.328857421875, -0.391845703125, 0.81005859375, -0.00039076805114746094, 0.381103515625, -0.99609375, 0.484375, 0.689453125, -0.05047607421875, 0.7431640625, -0.281494140625, -0.134521484375, -0.26953125, -0.284912109375, 1.1513671875, -0.415283203125, -0.41015625, 0.29931640625, 0.0151519775390625, -0.266357421875, 0.335205078125, -0.039581298828125, 0.736328125, -0.2210693359375, 0.437255859375, 0.7509765625, -0.493896484375, 0.77734375, -0.1634521484375, -0.1998291015625, 1.6826171875, 0.486328125, 0.12408447265625, 0.9951171875, 0.428955078125, -0.334228515625, 0.4208984375, -0.9326171875, 0.57421875, 0.25146484375, 0.28369140625, -0.1505126953125, -0.10955810546875, -0.291015625, 0.5078125, 0.11517333984375, 0.1339111328125, -0.1190185546875, 0.244384765625, 0.064697265625, 0.9091796875, -0.09881591796875, 1.095703125, -0.421630859375, -0.353759765625, -0.2529296875, -0.642578125, 0.47314453125, -0.20849609375, -0.4189453125, 0.6259765625, 0.54541015625, 1.1484375, 1.3427734375, -0.47900390625, 0.2724609375, 0.288818359375, -0.6728515625, 0.0162353515625, 0.7080078125, 0.93310546875, -0.20947265625, 0.228271484375, -0.05999755859375, -0.40185546875, -0.495849609375, -0.72998046875, -0.09637451171875, 0.68115234375, -0.7529296875, 0.162841796875, 0.311279296875, 0.3203125, -0.9072265625, -0.0823974609375, -0.266357421875, -0.69970703125, -0.3134765625, 0.51123046875, -0.447021484375, 0.53369140625, -0.74560546875, -0.51318359375, 0.62353515625, 1.0078125, -0.2449951171875, 0.332275390625, 0.444580078125, 0.2410888671875, -0.2398681640625, 0.396728515625, 0.293701171875, -0.230224609375, -0.4453125, 1.109375, 0.2529296875, -0.0872802734375, 0.041351318359375, 0.68359375, 0.6455078125, 0.39111328125, -0.2115478515625, 0.10009765625, 0.346435546875, 1.158203125, 0.11456298828125, 0.82080078125, 0.0341796875, 0.72216796875, 0.6767578125, 0.671875, 0.55908203125, 0.1107177734375, 0.5849609375, 0.90771484375, 0.1796875, 0.384765625, 0.425537109375, 0.46240234375, 0.336181640625, 0.475830078125, 0.2222900390625, 0.17578125, 0.273193359375, 0.09320068359375, -0.434326171875, 0.2178955078125, -0.4326171875, 0.84130859375, -0.08575439453125, 0.1728515625, -0.31494140625, -0.492919921875, 0.140625, 0.87109375, -0.7412109375, -0.2095947265625, 0.1617431640625, 0.07354736328125, 0.1195068359375, -0.293701171875, 0.353759765625, 0.3623046875, 0.42431640625, 0.51806640625, -0.38916015625, -0.2158203125, -1.1796875, -0.849609375, -0.8193359375, -0.457763671875, -0.828125, 0.08184814453125, 0.1318359375, -0.7333984375, 0.332763671875, -0.501953125, -0.305419921875, 0.209716796875, -0.6953125, 0.642578125, -0.1429443359375, 0.279541015625, -1.4169921875, 0.78515625, 0.307373046875, 1.1357421875, -0.76513671875, 0.1195068359375, 0.1400146484375, -0.82470703125, 0.0280303955078125, 0.1375732421875, 0.2012939453125, -0.06524658203125, -0.73388671875, -0.6591796875, -0.7529296875, -0.246826171875, -0.29931640625, 0.3916015625, -0.5009765625, 0.921875, 0.75537109375, -0.56201171875, 0.7822265625, 0.84375, -0.57470703125, 0.3369140625, 0.42578125, 0.1015625, -0.80322265625, 1.5732421875, 0.505859375, 0.399658203125, -0.437744140625, -0.37646484375, -0.25634765625, -0.158447265625, 0.156982421875, -0.67333984375, -0.469482421875, 0.57568359375, -0.132568359375, -0.9892578125, 0.145263671875, -0.90087890625, -0.6181640625, -0.1947021484375, -0.67236328125, 1.322265625, 0.966796875, -0.055572509765625, -0.03936767578125, -0.12335205078125, -0.10455322265625, 0.5576171875, 0.487060546875, -0.09893798828125, -0.06048583984375, 0.78369140625, 0.32568359375, 0.020904541015625, 0.149658203125, -0.5556640625, -0.005168914794921875, -0.061798095703125, 0.33984375, 0.50146484375, 0.138671875, 0.4365234375, 0.2734375, 0.50537109375, -1.2119140625, -0.19189453125, -0.2276611328125, 0.6171875, 0.5576171875, 0.406005859375, -0.033355712890625, -0.56201171875, -0.82275390625, -1.0693359375, 0.144287109375, 0.09295654296875, 0.76318359375, -0.90478515625, 0.79296875, 0.1829833984375, -0.344970703125, 0.56787109375, -0.638671875, -0.03179931640625, 0.94580078125, -0.59375, 0.88671875, -0.9892578125, 0.294189453125, 0.0015859603881835938, 0.040130615234375, 0.354248046875, 0.5234375, 0.44921875, -0.48681640625, -0.4091796875, -0.6328125, 0.07330322265625, -0.005840301513671875, -0.348876953125, 0.148193359375, -0.3232421875, -0.3359375, -0.84716796875, 0.357421875, 0.88134765625, 0.84814453125, -0.04180908203125, 0.435791015625, 0.40576171875, 0.4404296875, 0.67236328125, -0.1016845703125, 0.2237548828125, -0.939453125, 0.60302734375, 0.23583984375, -0.360595703125, -0.70263671875, -0.1732177734375, -0.2164306640625, -0.01165771484375, -0.14306640625, -0.285400390625, -0.85107421875, 0.326904296875, -0.177978515625, 0.81591796875, -0.353271484375, -0.2421875, -0.74169921875, 0.489990234375, 0.486572265625, -0.80029296875, 0.51611328125, -0.93994140625, 0.6279296875, 0.458740234375, -0.327880859375, -0.3095703125, -0.70703125, -0.7744140625, -0.51513671875, 0.29345703125, 1.0654296875, -0.1920166015625, 0.5068359375, -1.3349609375, 0.316162109375, 0.13134765625, -0.6845703125, -0.0694580078125, -0.057464599609375, 0.472412109375, 0.143310546875, 0.75830078125, -0.1300048828125, -0.313232421875, 0.0242156982421875, -1.3046875, 0.5634765625, -0.56787109375, 0.5185546875, 0.12298583984375, -0.223388671875, 0.05487060546875, 0.36962890625, -0.1495361328125, 0.082275390625, -0.32568359375, 0.2861328125, -0.96337890625, -0.6220703125, 0.59619140625, -0.178466796875, -0.30908203125, 1.0390625, 0.08355712890625, -0.105224609375, 0.252197265625, 0.55322265625, -0.476318359375, 0.428466796875, -0.231201171875, 0.84716796875, -0.55029296875, -0.67236328125, -0.381103515625, -0.300048828125, 0.75439453125, -0.1148681640625, -0.419189453125, -0.2374267578125, -1.0791015625, -0.09698486328125, 0.1976318359375, -0.435302734375, 0.2198486328125, 0.10595703125, 0.2030029296875, -0.255859375, 0.0116729736328125, -0.44482421875, -0.194091796875, -0.5419921875, -0.591796875, 0.56787109375, 0.31494140625, 0.52001953125, 0.0916748046875, -0.6220703125, -0.1400146484375, 0.45703125, -0.11639404296875, -0.59765625, -0.2308349609375, -0.3828125, -0.21240234375, -0.494384765625, 0.03533935546875, -0.09222412109375, 0.327880859375, 0.95556640625, 0.039642333984375, 0.3369140625, 0.373291015625, -0.76416015625, 0.89404296875, 0.3125, -0.69970703125, -0.390380859375, 0.275390625, -0.06231689453125, 0.71240234375, 0.59033203125, -0.74072265625, -0.54736328125, -0.81298828125, 0.2138671875, -0.8037109375, -0.2222900390625, -0.92529296875, -0.5791015625, -0.385498046875, 0.5751953125, -0.085205078125, -0.6376953125, 0.083984375, -0.88720703125, -0.054840087890625, -0.8173828125, -0.205322265625, -0.77880859375, -0.66455078125, -0.23974609375, 0.90234375, 0.052093505859375, 0.012542724609375, 0.2127685546875, -0.11883544921875, 0.1549072265625, 0.321533203125, -0.7509765625, -0.1273193359375, -0.0184173583984375, 0.073974609375, -0.156982421875, 0.03436279296875, -0.7978515625, 0.58642578125, -0.8896484375, 0.169677734375, -0.2109375, -0.0005159378051757812, -0.331298828125, -0.20068359375, 0.9677734375, -0.337890625, 0.35205078125, -0.33740234375, 0.3310546875, 0.73681640625, -0.6953125, -0.40869140625, -0.97314453125, -0.82861328125, -1.369140625, 0.68994140625, -0.471923828125, 0.150634765625, -0.7529296875, -0.5625, 0.99365234375, -0.68212890625, 0.309326171875, 1.14453125, -0.024688720703125, 0.435546875, -0.26220703125, 0.626953125, 0.2008056640625, -0.64892578125, 0.20068359375, 0.381591796875, -0.6416015625, -0.1317138671875, -0.387939453125, -1.0185546875, -0.468994140625, 0.442138671875, 1.1513671875, -0.04705810546875, 0.2734375, -0.411376953125, -1.0634765625, -0.55810546875, 0.6552734375, 0.296875, 0.41357421875, 1.01171875, 0.1531982421875, -0.073486328125, 0.035125732421875, -0.495849609375, -0.297119140625, -0.39794921875, 1.162109375, -0.17236328125, -0.609375, 0.80517578125, 0.8623046875, -0.96630859375, -0.97509765625, -0.11895751953125, -0.1591796875, -0.058258056640625, -0.75439453125, -0.044769287109375, 0.591796875, -0.446533203125, 0.033416748046875, 0.280517578125, -0.159423828125, 0.18798828125, 0.1956787109375, 0.293212890625, -0.09918212890625, 0.347412109375, 0.93115234375, -0.2880859375, -0.60595703125, -0.8984375, -0.564453125, -0.3984375, 0.1337890625, 0.68310546875, -0.349365234375, 0.166015625, 0.40234375, 0.0408935546875, 1, -0.254150390625, -0.460693359375, 0.39404296875, -0.8623046875, -0.6220703125, 0.187744140625, 0.04296875, -0.479736328125, 0.68359375, -0.64892578125, 0.034912109375, 0.220947265625, 0.093994140625, -0.373046875, -1.048828125, -0.19775390625, -1.310546875, -0.3544921875, -0.52587890625, -0.96044921875, -0.131591796875, 0.01177215576171875, 0.1966552734375, -0.796875, 0.08062744140625, 0.467041015625, -0.261474609375, 0.87353515625, -0.63232421875, 0.1373291015625, -0.474853515625, -0.50341796875, -0.576171875, 0.04766845703125, -0.4140625, 0.0053558349609375, -0.923828125, 0.1322021484375, -0.05572509765625, 0.4990234375, -0.208251953125, 0.62451171875, -0.5615234375, -1.1640625, 0.1959228515625, -0.048614501953125, 0.07421875, 0.70556640625, 0.39453125, -0.08685302734375, 0.5, -0.0120697021484375, -0.31982421875, -0.428466796875, 0.59716796875, 0.5, -0.275146484375, -0.1748046875, -0.1907958984375, 0.2685546875, -1.2275390625, 0.51513671875, -0.5556640625, 0.2105712890625, 0.28857421875, -0.5126953125, 0.429443359375, 1.1767578125, -0.51123046875, 0.25146484375, -0.1153564453125, 0.1058349609375, 0.10650634765625, 0.322021484375, -0.16943359375, 0.78173828125, -0.2342529296875, -0.56982421875, -0.0335693359375, 0.2420654296875, -0.216064453125, 0.4365234375, -0.1485595703125, -1.0244140625, -0.86767578125, -0.1474609375, 0.0108489990234375, 0.23291015625, 0.1279296875, -0.205810546875, -0.02716064453125, 0.08953857421875, -0.85546875, 0.170166015625, -0.9365234375, -0.91455078125, 0.54052734375, -0.23046875, -0.213623046875, 0.057861328125, -0.298583984375, -0.364501953125, 0.1827392578125, 0.51123046875, -0.6630859375, 0.498046875, -0.181396484375, 0.61328125, -0.4189453125, -0.231689453125, 0.1353759765625, 0.66650390625, -0.7451171875, -0.5361328125, -0.324951171875, 0.89306640625, 0.2313232421875, -0.3505859375, -0.64697265625, 0.07086181640625, 0.1968994140625, 0.26171875, -0.60400390625, 0.1734619140625, -0.213134765625, 0.69970703125, -1.2216796875, 0.0216827392578125, 0.057769775390625, 0.2161865234375, 0.1865234375, -0.3212890625, -0.69921875, 1.15625, 0.354736328125, -0.049835205078125, 0.63671875, -0.007106781005859375, 0.372802734375, -0.0025730133056640625, -0.017791748046875, -0.03826904296875, 0.76220703125, 0.57861328125, 0.6201171875, -0.1505126953125, 0.13037109375, 0.75, 0.2296142578125, -0.3369140625, 0.308837890625, -0.004383087158203125, -0.0592041015625, 0.322021484375, -0.1865234375, -0.3154296875, -0.172607421875, -0.3427734375, 0.68408203125, -0.5234375, -0.055267333984375, -0.2371826171875, -0.83984375, 0.72021484375, -0.295166015625, -0.337158203125, 0.39697265625, -0.177978515625, 0.1746826171875, 0.53564453125, -0.368408203125, -0.3349609375, 1.125, 0.74169921875, 0.40283203125, 0.76123046875, 0.37109375, 0.57666015625, -0.55029296875, 0.3330078125, 0.05731201171875, -0.0372314453125, -0.09759521484375, -0.74951171875, -0.96484375, 0.54931640625, -0.336181640625, -0.260009765625, 0.5703125, -0.556640625, 0.301513671875, -0.54443359375, 1.0166015625, -0.36572265625, 0.342041015625, 0.342529296875, -0.5009765625, -0.6484375, 0.6884765625, -0.281494140625, 0.351806640625, 0.1021728515625, 0.91015625, -0.0133514404296875, 1.669921875, 0.578125, -0.1322021484375, 0.0016088485717773438, 0.44921875, -0.2744140625, -0.327880859375, -0.72607421875, -0.34912109375, 0.1627197265625, -0.24951171875, -0.84130859375, -0.03900146484375, 0.7900390625, 0.148681640625, -0.85107421875, -0.311767578125, 0.37158203125, -1.197265625, 0.40673828125, 0.3984375, 0.23974609375, 0.154052734375, -0.233642578125, -0.118408203125, -0.62158203125, 0.464599609375, -0.79345703125, 0.30322265625, -0.489013671875, -0.3896484375, -0.61962890625, -0.70849609375, -0.38671875, -0.0843505859375, -0.5166015625, -0.72314453125, 0.5439453125, 0.2430419921875, 0.69140625, 0.521484375, -0.301025390625, 0.283447265625, 0.70703125, 0.9482421875, -0.1649169921875, 1.1103515625, 0.307861328125, -0.104248046875, 0.2342529296875, -0.3408203125, 0.31884765625, -0.0684814453125, 0.362548828125, -0.51318359375, -0.245849609375, -0.77392578125, -1.1181640625, 0.410888671875, 0.44873046875, 0.34716796875, -0.78759765625, -1.072265625, -0.06976318359375, -1.177734375, -0.43505859375, -0.69580078125, 0.76123046875, -0.734375, -0.016326904296875, 0.0640869140625, -1.1484375, 4.31640625, 0.95849609375, 0.658203125, 0.47998046875, 0.089599609375, 0.87646484375, 0.45166015625, -0.311767578125, -0.382080078125, -0.274658203125, 0.61572265625, -0.548828125, -0.034088134765625, 0.96142578125, 0.48876953125, 0.32763671875, -0.242919921875, 0.056915283203125, 0.23291015625, -0.81640625, -0.73583984375, 0.361328125, 0.0865478515625, 0.5830078125, 0.3134765625, 0.2166748046875, 0.80615234375, -0.693359375, -0.2095947265625, -0.8232421875, 0.0491943359375, -0.3564453125, 0.96630859375, 0.2666015625, -0.058685302734375, 0.70751953125, -0.032562255859375, -0.459716796875, 0.061737060546875, 0.10821533203125, -0.06866455078125, 0.16064453125, 0.5439453125, -0.67041015625, -0.296875, 0.485107421875, -0.595703125, 0.6083984375, 0.35205078125, -1.03125, 1.01171875, -0.09320068359375, 0.469482421875, -0.8583984375, -0.59375, 0.1697998046875, 0.078369140625, 0.068603515625, -0.34765625, 0.6142578125, 0.61181640625, 0.61474609375, 0.035369873046875, 0.5126953125, -0.93994140625, 0.55224609375, -0.2108154296875, 0.57958984375, -0.40283203125, 0.01000213623046875, -0.177001953125, -0.29150390625, -0.32763671875, -0.5703125, 0.501953125, 0.073974609375, -0.307373046875, 0.91748046875, 0.33203125, -0.74853515625, 0.07867431640625, -0.294677734375, -0.07562255859375, -0.28271484375, 0.79833984375, 1.22265625, -0.464599609375, 0.15673828125, -0.2132568359375, 0.496826171875, 0.54541015625, 0.7607421875, -0.153564453125, -0.494384765625, -0.276611328125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Tags: constructive algorithms, data structures, implementation, strings, two pointers Correct Solution: ``` import sys input = sys.stdin.readline from collections import deque t = int(input()) for _ in range(t): n = int(input()) a = input() b = input() q = deque([i for i in range(n)]) rev = False ans = [] for i in range(n)[::-1]: if rev: a_ind = q[0] if a[a_ind] != b[i]: q.popleft() continue else: if a[q[-1]] == b[i]: ans.append(i + 1) else: ans.append(1) ans.append(i + 1) q.pop() rev = False else: a_ind = q[-1] if a[a_ind] == b[i]: q.pop() continue else: if a[q[0]] != b[i]: ans.append(i + 1) else: ans.append(1) ans.append(i + 1) q.popleft() rev = True print(len(ans), *ans) ```
105,444
[ 0.1650390625, -0.401123046875, -0.002330780029296875, 0.096923828125, -0.426513671875, -0.7490234375, -0.0404052734375, -0.2044677734375, 0.1849365234375, 1.01953125, 0.75439453125, -0.2978515625, 0.33203125, -0.88818359375, -0.59912109375, 0.320068359375, -0.342041015625, -0.591796875, -0.3359375, -0.5673828125, 0.02587890625, -0.1185302734375, -1.37890625, -0.076171875, -0.63623046875, 0.826171875, 0.29248046875, -0.1328125, 1.0068359375, 1.0556640625, -0.425048828125, -0.45703125, 0.73828125, -1.0126953125, -0.443359375, -0.492431640625, 0.6005859375, -0.8447265625, -0.1434326171875, -0.280029296875, 0.55908203125, -0.233154296875, 0.2374267578125, -0.93212890625, -1.283203125, 0.150634765625, -0.345458984375, -0.3271484375, -0.156982421875, -0.439697265625, 0.07135009765625, -0.210693359375, 0.62109375, -0.13134765625, 0.03814697265625, 0.16845703125, 0.2376708984375, -0.5390625, -0.464599609375, 0.137451171875, 0.0697021484375, 0.1654052734375, 0.19580078125, -0.70849609375, 0.109375, 0.19921875, -0.2568359375, -0.446044921875, -0.39892578125, -0.97802734375, -0.32177734375, -0.0489501953125, -0.677734375, -0.330078125, -0.07684326171875, 0.27294921875, 0.2474365234375, -0.15625, -0.8544921875, 0.7353515625, -0.296875, 0.9453125, 0.10595703125, 0.2132568359375, -0.4697265625, -0.51220703125, -0.0229339599609375, 0.18603515625, 0.15625, -0.1094970703125, -0.3505859375, 0.58642578125, -0.476318359375, 0.08599853515625, 0.419677734375, 0.71728515625, -0.31787109375, 0.2529296875, 0.423583984375, -0.012847900390625, 0.7734375, 1.228515625, -0.1983642578125, 1.212890625, -0.62353515625, -0.1917724609375, 0.0009450912475585938, 0.1373291015625, -0.04949951171875, -0.0012407302856445312, 0.00504302978515625, -0.1629638671875, 0.69482421875, 0.41162109375, -0.419921875, 0.82275390625, -0.039031982421875, 0.439697265625, -1.0146484375, 0.480712890625, 0.626953125, -0.042236328125, 0.72607421875, -0.2484130859375, -0.19775390625, -0.265869140625, -0.3232421875, 1.1474609375, -0.418212890625, -0.441162109375, 0.278076171875, 0.006298065185546875, -0.2939453125, 0.3515625, -0.04010009765625, 0.71728515625, -0.2269287109375, 0.3916015625, 0.7431640625, -0.46875, 0.7744140625, -0.199462890625, -0.1431884765625, 1.7333984375, 0.50146484375, 0.10552978515625, 1.056640625, 0.4619140625, -0.30810546875, 0.474853515625, -0.92724609375, 0.59326171875, 0.255615234375, 0.341796875, -0.116943359375, -0.11260986328125, -0.2412109375, 0.53271484375, 0.0736083984375, 0.218017578125, -0.08087158203125, 0.26318359375, 0.061492919921875, 0.94482421875, -0.11859130859375, 1.07421875, -0.375732421875, -0.368896484375, -0.24609375, -0.62939453125, 0.5537109375, -0.2296142578125, -0.44189453125, 0.5654296875, 0.51171875, 1.14453125, 1.3681640625, -0.46923828125, 0.2332763671875, 0.35986328125, -0.81494140625, 0.00859832763671875, 0.74365234375, 0.9501953125, -0.072509765625, 0.2432861328125, -0.06817626953125, -0.404296875, -0.51708984375, -0.76123046875, -0.0714111328125, 0.72216796875, -0.708984375, 0.1893310546875, 0.302978515625, 0.291748046875, -0.90478515625, -0.130859375, -0.2349853515625, -0.6806640625, -0.297119140625, 0.487548828125, -0.4384765625, 0.50244140625, -0.76806640625, -0.4560546875, 0.58544921875, 1.1005859375, -0.2144775390625, 0.381103515625, 0.4228515625, 0.1273193359375, -0.28955078125, 0.346923828125, 0.27685546875, -0.2047119140625, -0.468994140625, 1.099609375, 0.30224609375, -0.0738525390625, 0.09075927734375, 0.693359375, 0.59814453125, 0.36181640625, -0.221435546875, 0.052520751953125, 0.3291015625, 1.1806640625, 0.175537109375, 0.80810546875, 0.04010009765625, 0.76220703125, 0.6455078125, 0.67333984375, 0.5224609375, 0.08343505859375, 0.65673828125, 0.8642578125, 0.10089111328125, 0.4296875, 0.39306640625, 0.45751953125, 0.311279296875, 0.51904296875, 0.2359619140625, 0.2109375, 0.270263671875, 0.0638427734375, -0.481201171875, 0.12841796875, -0.423583984375, 0.83154296875, -0.1260986328125, 0.171875, -0.3759765625, -0.486328125, 0.1595458984375, 0.90234375, -0.7734375, -0.1951904296875, 0.10882568359375, 0.09466552734375, 0.142822265625, -0.258056640625, 0.314697265625, 0.33935546875, 0.390380859375, 0.4677734375, -0.392822265625, -0.165771484375, -1.1650390625, -0.84619140625, -0.85009765625, -0.51220703125, -0.828125, 0.046600341796875, 0.1300048828125, -0.7001953125, 0.345947265625, -0.5771484375, -0.2490234375, 0.203857421875, -0.6435546875, 0.64404296875, -0.1683349609375, 0.264404296875, -1.390625, 0.80908203125, 0.31982421875, 1.1943359375, -0.7626953125, 0.07110595703125, 0.1597900390625, -0.8173828125, 0.042999267578125, 0.06671142578125, 0.22509765625, -0.0276031494140625, -0.7158203125, -0.673828125, -0.734375, -0.239501953125, -0.307373046875, 0.365234375, -0.5390625, 0.8818359375, 0.759765625, -0.60009765625, 0.75, 0.89990234375, -0.63330078125, 0.378662109375, 0.423095703125, 0.09869384765625, -0.80517578125, 1.623046875, 0.46923828125, 0.349609375, -0.432373046875, -0.4501953125, -0.2376708984375, -0.11865234375, 0.2020263671875, -0.66162109375, -0.52294921875, 0.56494140625, -0.09765625, -0.96533203125, 0.15869140625, -0.931640625, -0.55126953125, -0.215087890625, -0.716796875, 1.3623046875, 0.9658203125, -0.0367431640625, -0.033294677734375, -0.1512451171875, -0.126708984375, 0.5947265625, 0.4873046875, -0.072265625, -0.039337158203125, 0.84619140625, 0.326171875, 0.061553955078125, 0.224853515625, -0.57421875, 0.00333404541015625, -0.07757568359375, 0.353271484375, 0.43359375, 0.167724609375, 0.41064453125, 0.30517578125, 0.494140625, -1.2177734375, -0.2353515625, -0.260498046875, 0.49951171875, 0.546875, 0.34228515625, 0.01265716552734375, -0.49072265625, -0.7822265625, -1.064453125, 0.1268310546875, 0.09161376953125, 0.806640625, -0.8154296875, 0.755859375, 0.1302490234375, -0.37548828125, 0.548828125, -0.65380859375, -0.010009765625, 0.927734375, -0.6064453125, 0.88916015625, -0.98974609375, 0.291748046875, 0.0382080078125, 0.02008056640625, 0.34130859375, 0.434814453125, 0.50439453125, -0.444091796875, -0.427978515625, -0.701171875, 0.0305938720703125, 0.0198822021484375, -0.387451171875, 0.1116943359375, -0.2734375, -0.376708984375, -0.873046875, 0.31494140625, 0.88037109375, 0.89013671875, -0.049896240234375, 0.51123046875, 0.371337890625, 0.4814453125, 0.7119140625, -0.0736083984375, 0.2462158203125, -0.9462890625, 0.67822265625, 0.2200927734375, -0.296142578125, -0.71142578125, -0.1859130859375, -0.12054443359375, 0.046539306640625, -0.2073974609375, -0.315185546875, -0.86376953125, 0.309814453125, -0.2208251953125, 0.75830078125, -0.428466796875, -0.2783203125, -0.78662109375, 0.42431640625, 0.53955078125, -0.78173828125, 0.4697265625, -0.93408203125, 0.625, 0.49658203125, -0.31298828125, -0.316650390625, -0.78369140625, -0.71630859375, -0.5244140625, 0.3046875, 1.0498046875, -0.1529541015625, 0.53076171875, -1.34375, 0.34521484375, 0.1649169921875, -0.69873046875, -0.08807373046875, -0.046844482421875, 0.51318359375, 0.1859130859375, 0.73046875, -0.10882568359375, -0.32080078125, 0.058929443359375, -1.3134765625, 0.61376953125, -0.61572265625, 0.5390625, 0.12310791015625, -0.256103515625, 0.03253173828125, 0.383056640625, -0.1243896484375, 0.07940673828125, -0.2890625, 0.2666015625, -1.009765625, -0.609375, 0.6435546875, -0.217041015625, -0.29052734375, 1.0537109375, 0.09320068359375, -0.08673095703125, 0.262939453125, 0.52880859375, -0.477294921875, 0.431884765625, -0.330078125, 0.86669921875, -0.5029296875, -0.671875, -0.489501953125, -0.3056640625, 0.76904296875, -0.08941650390625, -0.474853515625, -0.2186279296875, -1.15625, -0.13330078125, 0.1768798828125, -0.367919921875, 0.2276611328125, 0.10540771484375, 0.160888671875, -0.259765625, -0.01971435546875, -0.41796875, -0.1607666015625, -0.53076171875, -0.5654296875, 0.55908203125, 0.367431640625, 0.5546875, 0.0941162109375, -0.61474609375, -0.1610107421875, 0.412353515625, -0.1622314453125, -0.5859375, -0.23291015625, -0.37060546875, -0.1485595703125, -0.5087890625, 0.0711669921875, -0.09442138671875, 0.376220703125, 0.96630859375, 0.00970458984375, 0.360595703125, 0.378662109375, -0.77978515625, 0.9169921875, 0.371826171875, -0.708984375, -0.3369140625, 0.232421875, -0.09368896484375, 0.6533203125, 0.55517578125, -0.8017578125, -0.5634765625, -0.80517578125, 0.256103515625, -0.80859375, -0.1668701171875, -0.93798828125, -0.59228515625, -0.43994140625, 0.61181640625, -0.0667724609375, -0.666015625, -0.0015649795532226562, -0.892578125, -0.08428955078125, -0.87353515625, -0.2147216796875, -0.7890625, -0.72314453125, -0.2327880859375, 0.888671875, 0.0712890625, -0.001491546630859375, 0.277587890625, -0.10272216796875, 0.125, 0.311279296875, -0.72216796875, -0.2003173828125, 0.01229095458984375, 0.07794189453125, -0.1602783203125, 0.02166748046875, -0.83203125, 0.5537109375, -0.86181640625, 0.2098388671875, -0.239501953125, 0.0008692741394042969, -0.289306640625, -0.1746826171875, 0.970703125, -0.353515625, 0.33349609375, -0.2861328125, 0.36962890625, 0.779296875, -0.62646484375, -0.4365234375, -0.95654296875, -0.81396484375, -1.396484375, 0.64111328125, -0.459716796875, 0.15380859375, -0.6875, -0.5322265625, 0.9599609375, -0.70703125, 0.3349609375, 1.177734375, 0.01180267333984375, 0.387451171875, -0.31103515625, 0.63623046875, 0.220703125, -0.66455078125, 0.22705078125, 0.456298828125, -0.666015625, -0.1553955078125, -0.425048828125, -1.0322265625, -0.4453125, 0.373779296875, 1.1513671875, 0.0174713134765625, 0.287353515625, -0.449462890625, -1.0546875, -0.47265625, 0.7421875, 0.282958984375, 0.43408203125, 0.99560546875, 0.14697265625, -0.104248046875, 0.06549072265625, -0.498291015625, -0.286865234375, -0.373291015625, 1.201171875, -0.1964111328125, -0.6044921875, 0.830078125, 0.8955078125, -0.95361328125, -1.0625, -0.1021728515625, -0.117431640625, -0.01513671875, -0.7919921875, -0.0055694580078125, 0.51220703125, -0.4267578125, -0.0316162109375, 0.216796875, -0.131591796875, 0.2386474609375, 0.199462890625, 0.258056640625, -0.141845703125, 0.39990234375, 0.9736328125, -0.28857421875, -0.57958984375, -0.9453125, -0.54541015625, -0.4931640625, 0.11737060546875, 0.6611328125, -0.34521484375, 0.1915283203125, 0.412353515625, 0.047576904296875, 1.0712890625, -0.28515625, -0.42578125, 0.37744140625, -0.8427734375, -0.64111328125, 0.144775390625, 0.0638427734375, -0.5068359375, 0.69091796875, -0.65625, 0.00281524658203125, 0.2125244140625, 0.05157470703125, -0.413330078125, -1.0361328125, -0.1815185546875, -1.3017578125, -0.368408203125, -0.5341796875, -0.93505859375, -0.20263671875, 0.041900634765625, 0.1966552734375, -0.7197265625, 0.051788330078125, 0.46044921875, -0.221435546875, 0.88525390625, -0.669921875, 0.0789794921875, -0.45263671875, -0.44970703125, -0.625, 0.05621337890625, -0.45458984375, -0.0648193359375, -0.865234375, 0.0792236328125, -0.04595947265625, 0.4697265625, -0.1751708984375, 0.58544921875, -0.56396484375, -1.1416015625, 0.2066650390625, -0.0194549560546875, -0.033203125, 0.796875, 0.411376953125, -0.08673095703125, 0.50341796875, -0.06072998046875, -0.2548828125, -0.40771484375, 0.51611328125, 0.57470703125, -0.241455078125, -0.22802734375, -0.1878662109375, 0.235595703125, -1.197265625, 0.5068359375, -0.5859375, 0.204833984375, 0.33056640625, -0.55908203125, 0.48486328125, 1.0927734375, -0.47265625, 0.2393798828125, -0.05426025390625, 0.132080078125, 0.11785888671875, 0.281005859375, -0.165283203125, 0.8046875, -0.2427978515625, -0.529296875, 0.036590576171875, 0.329833984375, -0.2030029296875, 0.44189453125, -0.1494140625, -1.0498046875, -0.89501953125, -0.111328125, 0.046295166015625, 0.2318115234375, 0.055572509765625, -0.255615234375, -0.04058837890625, 0.12017822265625, -0.87353515625, 0.274658203125, -0.89892578125, -0.89306640625, 0.48779296875, -0.204345703125, -0.297607421875, 0.11724853515625, -0.300537109375, -0.30029296875, 0.127685546875, 0.515625, -0.650390625, 0.45947265625, -0.1942138671875, 0.58984375, -0.439453125, -0.236083984375, 0.11895751953125, 0.61962890625, -0.751953125, -0.54052734375, -0.31787109375, 0.91552734375, 0.16357421875, -0.4404296875, -0.65185546875, 0.11077880859375, 0.2275390625, 0.302734375, -0.62939453125, 0.2156982421875, -0.24560546875, 0.65087890625, -1.255859375, 0.04522705078125, 0.032745361328125, 0.21337890625, 0.11614990234375, -0.357666015625, -0.72216796875, 1.12109375, 0.414794921875, -0.037353515625, 0.60888671875, 0.01195526123046875, 0.388916015625, 0.0276031494140625, -0.029388427734375, -0.08349609375, 0.708984375, 0.638671875, 0.59912109375, -0.2073974609375, 0.20703125, 0.767578125, 0.1695556640625, -0.36669921875, 0.292724609375, 0.036956787109375, -0.11053466796875, 0.3662109375, -0.2435302734375, -0.28466796875, -0.1715087890625, -0.343017578125, 0.654296875, -0.525390625, -0.0489501953125, -0.2269287109375, -0.86181640625, 0.68212890625, -0.295654296875, -0.36767578125, 0.452880859375, -0.11962890625, 0.2236328125, 0.55810546875, -0.3955078125, -0.296142578125, 1.12109375, 0.7451171875, 0.41796875, 0.6953125, 0.378173828125, 0.578125, -0.58203125, 0.3359375, 0.048858642578125, -0.0634765625, -0.09906005859375, -0.6845703125, -1.015625, 0.595703125, -0.3232421875, -0.234130859375, 0.53369140625, -0.58544921875, 0.367919921875, -0.486328125, 1.0439453125, -0.35498046875, 0.28662109375, 0.362060546875, -0.49072265625, -0.65625, 0.65380859375, -0.27734375, 0.323974609375, 0.099365234375, 0.923828125, 0.0256195068359375, 1.7333984375, 0.58740234375, -0.11328125, 0.01546478271484375, 0.451904296875, -0.280517578125, -0.309814453125, -0.6953125, -0.2900390625, 0.16162109375, -0.2216796875, -0.83935546875, 0.013824462890625, 0.7822265625, 0.130615234375, -0.81298828125, -0.2391357421875, 0.331298828125, -1.1259765625, 0.405029296875, 0.34814453125, 0.321533203125, 0.1417236328125, -0.203857421875, -0.1845703125, -0.619140625, 0.4775390625, -0.76904296875, 0.343017578125, -0.466552734375, -0.378662109375, -0.6435546875, -0.64208984375, -0.430419921875, -0.0853271484375, -0.497314453125, -0.73828125, 0.5732421875, 0.26611328125, 0.70947265625, 0.58154296875, -0.26416015625, 0.2724609375, 0.728515625, 0.95947265625, -0.2130126953125, 1.10546875, 0.267822265625, -0.1395263671875, 0.2261962890625, -0.298095703125, 0.300537109375, -0.07891845703125, 0.330810546875, -0.50341796875, -0.26171875, -0.7890625, -1.126953125, 0.427001953125, 0.403076171875, 0.325927734375, -0.73193359375, -1.0966796875, -0.1123046875, -1.2490234375, -0.429931640625, -0.7373046875, 0.7646484375, -0.724609375, -0.0182647705078125, 0.0670166015625, -1.11328125, 4.30078125, 0.94677734375, 0.6796875, 0.383056640625, 0.11419677734375, 0.81494140625, 0.449951171875, -0.287353515625, -0.359375, -0.33984375, 0.59326171875, -0.501953125, -0.0765380859375, 0.99267578125, 0.5263671875, 0.2919921875, -0.277587890625, 0.04400634765625, 0.2318115234375, -0.86181640625, -0.7119140625, 0.312744140625, 0.048919677734375, 0.5498046875, 0.315673828125, 0.324462890625, 0.82958984375, -0.689453125, -0.174072265625, -0.78857421875, 0.10858154296875, -0.363037109375, 0.92919921875, 0.256591796875, -0.0853271484375, 0.7294921875, -0.08056640625, -0.458251953125, 0.0104217529296875, 0.0831298828125, -0.04522705078125, 0.1812744140625, 0.5693359375, -0.72021484375, -0.289794921875, 0.55712890625, -0.52978515625, 0.615234375, 0.391845703125, -1.04296875, 1.0947265625, -0.156982421875, 0.441650390625, -0.88525390625, -0.6015625, 0.237548828125, 0.10076904296875, 0.07373046875, -0.36181640625, 0.6181640625, 0.611328125, 0.6376953125, 0.0053558349609375, 0.5078125, -0.86962890625, 0.50244140625, -0.2393798828125, 0.580078125, -0.479248046875, -0.02239990234375, -0.17919921875, -0.29443359375, -0.3193359375, -0.55517578125, 0.54443359375, 0.0361328125, -0.252685546875, 0.8388671875, 0.37353515625, -0.74658203125, 0.0736083984375, -0.2447509765625, -0.1021728515625, -0.31787109375, 0.80615234375, 1.20703125, -0.412841796875, 0.134765625, -0.23193359375, 0.46630859375, 0.53125, 0.73876953125, -0.1629638671875, -0.5087890625, -0.333984375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Submitted Solution: ``` import os t1=int(input()) while t1: t1-=1 n=int(input()) s=input() t=input() s+="0" t+="0" ans=[] for i in range(n): if s[i]!=s[i+1]: ans.append(i+1) for i in range(n,0,-1): if t[i]!=t[i-1]: ans.append(i) print(len(ans),end=' ') for x in ans: print(x,end=' ') print() ``` Yes
105,445
[ 0.294677734375, -0.36669921875, -0.1600341796875, 0.050537109375, -0.5537109375, -0.63623046875, -0.0164947509765625, -0.12200927734375, 0.0933837890625, 1.064453125, 0.78564453125, -0.26171875, 0.2099609375, -0.98876953125, -0.55419921875, 0.2152099609375, -0.28759765625, -0.6943359375, -0.2119140625, -0.517578125, -0.076904296875, -0.2081298828125, -1.375, 0.0202484130859375, -0.54052734375, 0.7626953125, 0.4150390625, -0.14697265625, 0.84130859375, 0.9462890625, -0.51171875, -0.493896484375, 0.78271484375, -0.8828125, -0.330810546875, -0.421630859375, 0.6982421875, -0.763671875, -0.2076416015625, -0.42529296875, 0.398681640625, -0.27099609375, 0.2568359375, -0.7041015625, -1.4072265625, 0.050933837890625, -0.239501953125, -0.3291015625, -0.18505859375, -0.40185546875, 0.04986572265625, -0.297119140625, 0.59765625, -0.0457763671875, 0.154541015625, 0.32861328125, 0.275634765625, -0.452880859375, -0.48388671875, 0.1209716796875, 0.01377105712890625, 0.1259765625, 0.1885986328125, -0.76513671875, 0.11016845703125, 0.364990234375, -0.205810546875, -0.400390625, -0.283447265625, -0.78173828125, -0.292724609375, -0.09466552734375, -0.677734375, -0.149658203125, -0.0897216796875, 0.2083740234375, 0.128173828125, -0.11285400390625, -1.060546875, 0.888671875, -0.42529296875, 1.025390625, 0.312255859375, 0.2318115234375, -0.53515625, -0.441650390625, 0.1419677734375, 0.1689453125, 0.171142578125, -0.11260986328125, -0.29248046875, 0.44091796875, -0.5625, -0.031494140625, 0.44287109375, 0.62353515625, -0.35107421875, 0.342529296875, 0.3818359375, 0.0277862548828125, 0.74072265625, 0.9619140625, -0.167724609375, 1.3408203125, -0.515625, -0.1932373046875, -0.0440673828125, 0.015411376953125, -0.11663818359375, -0.0518798828125, -0.0249786376953125, -0.328369140625, 0.716796875, 0.2998046875, -0.33642578125, 0.71630859375, -0.06402587890625, 0.52783203125, -0.85986328125, 0.286376953125, 0.6474609375, -0.250732421875, 0.81201171875, -0.311767578125, -0.006778717041015625, -0.312255859375, -0.50244140625, 1.0546875, -0.483642578125, -0.5556640625, 0.2445068359375, -0.044586181640625, -0.3759765625, 0.320068359375, -0.1287841796875, 0.6435546875, -0.1512451171875, 0.3779296875, 0.67822265625, -0.453125, 0.7880859375, -0.1224365234375, -0.135498046875, 1.8125, 0.39794921875, -0.04248046875, 0.7900390625, 0.427978515625, -0.3671875, 0.5751953125, -0.958984375, 0.41748046875, 0.0723876953125, 0.2139892578125, -0.313232421875, 0.0120697021484375, -0.384033203125, 0.46435546875, 0.2208251953125, 0.119140625, -0.09600830078125, 0.3046875, -0.028594970703125, 0.84326171875, -0.137451171875, 0.9501953125, -0.4365234375, -0.392822265625, -0.244140625, -0.490966796875, 0.3037109375, -0.20751953125, -0.3046875, 0.71142578125, 0.61572265625, 1.1533203125, 1.275390625, -0.461669921875, 0.239013671875, 0.320068359375, -0.6904296875, 0.046051025390625, 0.5771484375, 0.8984375, -0.2088623046875, 0.25537109375, -0.076416015625, -0.33935546875, -0.356689453125, -0.75390625, -0.0340576171875, 0.82861328125, -0.74169921875, 0.242431640625, 0.0947265625, 0.2197265625, -0.826171875, -0.168701171875, -0.153076171875, -0.822265625, -0.455810546875, 0.4638671875, -0.337890625, 0.59619140625, -0.7060546875, -0.67333984375, 0.53759765625, 1.1943359375, -0.18310546875, 0.5078125, 0.458984375, 0.254638671875, -0.294189453125, 0.2607421875, 0.268310546875, -0.23291015625, -0.4658203125, 0.9765625, 0.2646484375, -0.031585693359375, -0.0833740234375, 0.7275390625, 0.5009765625, 0.4248046875, -0.40185546875, 0.005279541015625, 0.47998046875, 1.376953125, 0.054901123046875, 0.7900390625, 0.2291259765625, 0.82421875, 0.64794921875, 0.830078125, 0.455322265625, 0.1923828125, 0.89013671875, 0.74755859375, -0.08575439453125, 0.405029296875, 0.37646484375, 0.486328125, 0.360595703125, 0.65576171875, 0.276123046875, 0.179443359375, 0.10345458984375, -0.045654296875, -0.44482421875, 0.3134765625, -0.42822265625, 0.748046875, -0.149658203125, 0.384765625, -0.30810546875, -0.40576171875, 0.43017578125, 0.8291015625, -0.82421875, -0.4755859375, 0.21044921875, 0.003299713134765625, 0.11859130859375, -0.1417236328125, 0.323486328125, 0.2230224609375, 0.455078125, 0.474853515625, -0.273193359375, -0.20361328125, -1.0419921875, -0.869140625, -0.9560546875, -0.5185546875, -0.93115234375, 0.07659912109375, 0.0777587890625, -0.82958984375, 0.293212890625, -0.6435546875, -0.1658935546875, 0.275146484375, -0.67529296875, 0.7802734375, -0.271484375, 0.291259765625, -1.2509765625, 0.7919921875, 0.343994140625, 1.2041015625, -0.79248046875, 0.1837158203125, 0.0826416015625, -0.7060546875, 0.0298614501953125, 0.04296875, 0.314453125, 0.09906005859375, -0.69580078125, -0.62109375, -0.69091796875, -0.1622314453125, -0.273681640625, 0.09222412109375, -0.56591796875, 0.95068359375, 0.7255859375, -0.7578125, 0.6953125, 0.845703125, -0.68505859375, 0.5810546875, 0.448486328125, 0.38232421875, -0.6787109375, 1.525390625, 0.435302734375, 0.419677734375, -0.45458984375, -0.44677734375, -0.2008056640625, -0.0693359375, 0.164306640625, -0.493408203125, -0.57080078125, 0.51953125, -0.145751953125, -1.037109375, 0.349853515625, -0.97998046875, -0.51171875, -0.2001953125, -0.8896484375, 1.3212890625, 1.076171875, -0.005939483642578125, -0.0204315185546875, -0.318115234375, -0.0919189453125, 0.53125, 0.54150390625, -0.346923828125, -0.023895263671875, 0.86181640625, 0.293212890625, 0.2447509765625, 0.178955078125, -0.61767578125, -0.05523681640625, -0.1942138671875, 0.3681640625, 0.57958984375, 0.1365966796875, 0.464599609375, 0.2200927734375, 0.5751953125, -1.2666015625, -0.1900634765625, -0.398193359375, 0.57958984375, 0.51513671875, 0.35302734375, 0.1497802734375, -0.33056640625, -0.7587890625, -1.0009765625, 0.149658203125, 0.0662841796875, 0.76123046875, -0.63427734375, 0.71435546875, -0.0177154541015625, -0.498046875, 0.73193359375, -0.67724609375, 0.166748046875, 0.97119140625, -0.5, 0.728515625, -1.08203125, 0.439697265625, -0.01290130615234375, -0.2109375, 0.27490234375, 0.340087890625, 0.5380859375, -0.434326171875, -0.38427734375, -0.556640625, 0.07135009765625, 0.0264434814453125, -0.36865234375, -0.0273284912109375, -0.352783203125, -0.41845703125, -0.90234375, 0.398193359375, 0.72119140625, 0.9189453125, 0.0258026123046875, 0.58251953125, 0.3232421875, 0.375244140625, 0.61474609375, -0.0570068359375, 0.2310791015625, -0.86376953125, 0.81591796875, 0.25341796875, -0.275634765625, -0.53466796875, -0.2489013671875, -0.20263671875, 0.0097808837890625, -0.233642578125, -0.2371826171875, -0.8427734375, 0.509765625, -0.1478271484375, 0.703125, -0.62353515625, -0.023681640625, -0.72216796875, 0.327392578125, 0.54833984375, -0.84716796875, 0.452880859375, -0.90869140625, 0.468017578125, 0.57666015625, -0.25537109375, -0.4208984375, -0.56640625, -0.89111328125, -0.7607421875, 0.2469482421875, 1.0009765625, -0.2303466796875, 0.4951171875, -1.40234375, 0.3994140625, 0.405029296875, -0.93115234375, 0.047119140625, -0.1964111328125, 0.389892578125, 0.233154296875, 0.71484375, -0.1942138671875, -0.283203125, 0.01287841796875, -1.2451171875, 0.422607421875, -0.68017578125, 0.52392578125, 0.1859130859375, -0.186767578125, 0.12054443359375, 0.40234375, -0.12066650390625, 0.08447265625, -0.2493896484375, 0.39599609375, -1.0673828125, -0.73486328125, 0.5283203125, -0.1119384765625, -0.34765625, 1.03125, 0.0977783203125, -0.173828125, 0.208984375, 0.404052734375, -0.432861328125, 0.53759765625, -0.284423828125, 0.76513671875, -0.5087890625, -0.57421875, -0.5048828125, -0.349853515625, 0.71826171875, -0.2200927734375, -0.41748046875, -0.2001953125, -1.1806640625, -0.09649658203125, 0.23828125, -0.5107421875, 0.173583984375, 0.08245849609375, 0.26611328125, -0.2578125, -0.05255126953125, -0.453125, -0.11175537109375, -0.4638671875, -0.62451171875, 0.6044921875, 0.377197265625, 0.55517578125, 0.13134765625, -0.471923828125, -0.05450439453125, 0.2156982421875, -0.15673828125, -0.65478515625, -0.2685546875, -0.27392578125, -0.326904296875, -0.56787109375, 0.280517578125, -0.11627197265625, 0.41064453125, 0.9794921875, -0.016021728515625, 0.52734375, 0.31787109375, -0.81787109375, 1.1123046875, 0.2626953125, -0.86328125, -0.27783203125, 0.380859375, 0.00453948974609375, 0.859375, 0.302978515625, -0.794921875, -0.6318359375, -0.88818359375, 0.411376953125, -0.9189453125, -0.2432861328125, -0.9755859375, -0.607421875, -0.436279296875, 0.69091796875, -0.16845703125, -0.65283203125, 0.192626953125, -0.9658203125, -0.0015287399291992188, -0.96533203125, -0.1923828125, -0.7353515625, -0.61474609375, -0.37451171875, 1.0107421875, -0.017303466796875, -0.0242462158203125, 0.274169921875, 0.05987548828125, 0.04595947265625, 0.22216796875, -0.78076171875, -0.260986328125, 0.052978515625, -0.02899169921875, -0.355712890625, -0.024261474609375, -0.7568359375, 0.6806640625, -0.82568359375, 0.18994140625, -0.1424560546875, -0.039947509765625, -0.343017578125, -0.205810546875, 0.97119140625, -0.587890625, 0.33544921875, -0.443359375, 0.32177734375, 0.9208984375, -0.59228515625, -0.355712890625, -0.8720703125, -0.759765625, -1.388671875, 0.63671875, -0.351318359375, 0.2470703125, -0.68798828125, -0.57177734375, 1.056640625, -0.79541015625, 0.365478515625, 1.08984375, 0.02117919921875, 0.3173828125, -0.34912109375, 0.701171875, 0.47021484375, -0.615234375, 0.25390625, 0.359130859375, -0.642578125, -0.16259765625, -0.576171875, -0.962890625, -0.59521484375, 0.354736328125, 1.0185546875, -0.0220184326171875, 0.5830078125, -0.4501953125, -1.189453125, -0.28759765625, 0.69384765625, 0.1666259765625, 0.3349609375, 1.072265625, 0.2332763671875, -0.13037109375, 0.309814453125, -0.6181640625, -0.2393798828125, -0.329833984375, 1.2197265625, -0.337890625, -0.595703125, 0.97265625, 0.7919921875, -1.0322265625, -1.0146484375, -0.14013671875, -0.00118255615234375, -0.0287017822265625, -0.92236328125, -0.045684814453125, 0.496337890625, -0.449951171875, 0.14453125, 0.2294921875, -0.11688232421875, 0.310546875, 0.139892578125, 0.4326171875, -0.2393798828125, 0.282958984375, 1.0498046875, -0.341064453125, -0.7314453125, -0.984375, -0.39208984375, -0.31396484375, 0.2269287109375, 0.68408203125, -0.27490234375, 0.33154296875, 0.66796875, -0.05023193359375, 1.029296875, -0.3701171875, -0.2388916015625, 0.337646484375, -0.73828125, -0.59814453125, 0.0914306640625, 0.1346435546875, -0.337646484375, 0.7216796875, -0.59423828125, -0.08306884765625, 0.2900390625, 0.1175537109375, -0.467041015625, -0.99462890625, -0.281982421875, -1.1865234375, -0.416259765625, -0.421875, -0.90869140625, -0.052032470703125, 0.1297607421875, 0.2449951171875, -0.76220703125, 0.06243896484375, 0.517578125, -0.3330078125, 0.81494140625, -0.71142578125, 0.058349609375, -0.481201171875, -0.417236328125, -0.634765625, -0.09625244140625, -0.6044921875, -0.1171875, -0.56982421875, 0.15771484375, -0.1903076171875, 0.54296875, -0.256591796875, 0.64697265625, -0.376220703125, -0.7763671875, 0.267578125, 0.07781982421875, -0.23974609375, 0.90673828125, 0.391845703125, 0.1190185546875, 0.5185546875, -0.10113525390625, -0.148193359375, -0.218505859375, 0.75048828125, 0.5078125, -0.2208251953125, -0.289306640625, -0.09716796875, 0.080810546875, -1.19140625, 0.57763671875, -0.65283203125, 0.2205810546875, 0.286865234375, -0.36767578125, 0.356201171875, 1.0556640625, -0.59814453125, 0.375244140625, 0.0167999267578125, 0.11053466796875, 0.2548828125, 0.25048828125, -0.1536865234375, 0.7392578125, -0.2200927734375, -0.5673828125, -0.09771728515625, 0.277587890625, -0.12408447265625, 0.387451171875, -0.2861328125, -1.1494140625, -1.0546875, -0.10894775390625, -0.07232666015625, 0.235595703125, 0.2374267578125, -0.30810546875, -0.00980377197265625, 0.19287109375, -0.93896484375, 0.25634765625, -1.08203125, -0.93408203125, 0.73876953125, -0.1885986328125, -0.35791015625, 0.2188720703125, -0.2509765625, -0.1727294921875, 0.1483154296875, 0.33154296875, -0.51611328125, 0.42138671875, -0.1553955078125, 0.67578125, -0.3447265625, -0.1602783203125, 0.040069580078125, 0.65478515625, -0.90771484375, -0.387939453125, -0.341796875, 0.79443359375, 0.11285400390625, -0.458984375, -0.599609375, 0.1226806640625, 0.233642578125, 0.1934814453125, -0.447509765625, 0.1904296875, -0.0220947265625, 0.75341796875, -1.0029296875, 0.07452392578125, -0.00568389892578125, 0.257080078125, -0.0372314453125, -0.386474609375, -0.7421875, 1.025390625, 0.51025390625, 0.0946044921875, 0.63427734375, -0.0020999908447265625, 0.49609375, -0.0156402587890625, 0.0299224853515625, -0.273193359375, 0.7041015625, 0.775390625, 0.73046875, -0.1732177734375, 0.371826171875, 0.82421875, 0.2384033203125, -0.1932373046875, 0.418212890625, -0.00954437255859375, -0.11956787109375, 0.3115234375, -0.267822265625, -0.314453125, -0.0792236328125, -0.416259765625, 0.54248046875, -0.56298828125, -0.022247314453125, -0.315185546875, -0.7724609375, 0.79541015625, -0.44775390625, -0.2232666015625, 0.390869140625, -0.22802734375, 0.361328125, 0.52978515625, -0.259033203125, -0.326171875, 1.1767578125, 0.79736328125, 0.51904296875, 0.78076171875, 0.445068359375, 0.4150390625, -0.583984375, 0.29736328125, 0.1553955078125, -0.06268310546875, 0.008453369140625, -0.65478515625, -1.2685546875, 0.58154296875, -0.19873046875, -0.1341552734375, 0.372314453125, -0.7412109375, 0.2509765625, -0.57763671875, 1.12109375, -0.55126953125, 0.277099609375, 0.265625, -0.60595703125, -0.654296875, 0.69921875, -0.1978759765625, 0.288818359375, 0.154296875, 0.92529296875, 0.12286376953125, 1.724609375, 0.73486328125, -0.1888427734375, 0.04974365234375, 0.5615234375, -0.25830078125, -0.27978515625, -0.587890625, -0.349365234375, -0.03546142578125, -0.31494140625, -0.74462890625, -0.187255859375, 0.7607421875, 0.2359619140625, -0.87158203125, -0.440185546875, 0.31103515625, -0.9736328125, 0.52490234375, 0.1690673828125, 0.412109375, 0.289794921875, -0.1781005859375, -0.278076171875, -0.6689453125, 0.399169921875, -0.666015625, 0.30859375, -0.5341796875, -0.2425537109375, -0.64794921875, -0.5830078125, -0.33447265625, -0.06451416015625, -0.5205078125, -0.71142578125, 0.63134765625, 0.23486328125, 0.476806640625, 0.424072265625, -0.361328125, 0.291259765625, 0.81591796875, 1, -0.2880859375, 1.1103515625, 0.295166015625, -0.0386962890625, 0.10064697265625, -0.382568359375, 0.4072265625, -0.016937255859375, 0.33154296875, -0.58642578125, -0.13232421875, -0.9814453125, -1.0380859375, 0.27099609375, 0.427001953125, 0.219970703125, -0.841796875, -1.3125, -0.255615234375, -1.13671875, -0.32470703125, -0.72607421875, 0.75732421875, -0.68212890625, -0.03765869140625, 0.095703125, -1.0107421875, 4.24609375, 0.86083984375, 0.51416015625, 0.28662109375, 0.2392578125, 0.83544921875, 0.388671875, -0.4296875, -0.32275390625, -0.529296875, 0.59521484375, -0.55517578125, 0.0355224609375, 1.02734375, 0.53662109375, 0.38037109375, -0.33154296875, -0.1802978515625, 0.279541015625, -0.927734375, -0.85302734375, 0.3701171875, 0.185302734375, 0.4140625, 0.194580078125, 0.401611328125, 1.0078125, -0.67626953125, -0.3349609375, -0.78564453125, 0.2105712890625, -0.343017578125, 0.96826171875, 0.256103515625, -0.057647705078125, 0.78662109375, -0.0224456787109375, -0.49951171875, 0.0228271484375, 0.249755859375, -0.154296875, 0.2120361328125, 0.60302734375, -0.6484375, -0.447509765625, 0.67236328125, -0.60302734375, 0.62890625, 0.428955078125, -1.048828125, 1.0361328125, -0.10882568359375, 0.56005859375, -0.7353515625, -0.61279296875, 0.31787109375, 0.1513671875, 0.07232666015625, -0.382568359375, 0.544921875, 0.560546875, 0.60693359375, -0.140869140625, 0.72900390625, -1.0439453125, 0.4501953125, -0.10198974609375, 0.60595703125, -0.445556640625, 0.032958984375, -0.430419921875, -0.374755859375, -0.31787109375, -0.68359375, 0.59033203125, 0.0748291015625, -0.326416015625, 0.83984375, 0.287841796875, -0.7275390625, 0.20068359375, -0.398681640625, -0.06060791015625, -0.425048828125, 0.69775390625, 1.1328125, -0.456298828125, 0.0731201171875, -0.235107421875, 0.59765625, 0.6171875, 0.82470703125, -0.10125732421875, -0.67041015625, -0.496826171875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Submitted Solution: ``` def convert_to_1(s): L=[] for i in range(len(s)-1): if s[i]!=s[i+1]:L.append(i+1) if s[-1]=='0':L.append(len(s)) return L for i in ' '*(int(input())): n=int(input()) s1=input() s2=input() L1=convert_to_1(s1) L2=convert_to_1(s2) L=L1+L2[::-1] print(len(L),end=' ') for i in L:print(i,end=' ') print() ``` Yes
105,446
[ 0.290283203125, -0.3623046875, -0.1722412109375, 0.056976318359375, -0.55078125, -0.6259765625, 0.0127716064453125, -0.118896484375, 0.1051025390625, 1.0576171875, 0.78759765625, -0.287353515625, 0.2327880859375, -1.0107421875, -0.591796875, 0.2333984375, -0.25830078125, -0.69482421875, -0.1922607421875, -0.5361328125, -0.0987548828125, -0.204345703125, -1.369140625, 0.0031604766845703125, -0.5146484375, 0.76953125, 0.47216796875, -0.10430908203125, 0.8837890625, 0.970703125, -0.484619140625, -0.5390625, 0.78125, -0.8935546875, -0.323486328125, -0.38037109375, 0.6748046875, -0.77294921875, -0.230712890625, -0.419921875, 0.40087890625, -0.260986328125, 0.273193359375, -0.70166015625, -1.4560546875, 0.09954833984375, -0.26904296875, -0.32568359375, -0.1785888671875, -0.364990234375, 0.060791015625, -0.2958984375, 0.62890625, -0.008758544921875, 0.1824951171875, 0.32763671875, 0.275634765625, -0.449462890625, -0.5048828125, 0.1103515625, 0.031829833984375, 0.162353515625, 0.24462890625, -0.7734375, 0.08795166015625, 0.39306640625, -0.246337890625, -0.42529296875, -0.27490234375, -0.8037109375, -0.248779296875, -0.127685546875, -0.6669921875, -0.1591796875, -0.08563232421875, 0.2138671875, 0.1158447265625, -0.12109375, -1.072265625, 0.896484375, -0.441650390625, 1.0498046875, 0.3271484375, 0.1817626953125, -0.611328125, -0.417236328125, 0.1468505859375, 0.2037353515625, 0.2412109375, -0.09222412109375, -0.2900390625, 0.489013671875, -0.56689453125, -0.03179931640625, 0.446044921875, 0.63037109375, -0.318359375, 0.358642578125, 0.40625, 0.0240478515625, 0.7470703125, 0.93603515625, -0.20361328125, 1.3349609375, -0.487548828125, -0.2205810546875, -0.045654296875, 0.0013952255249023438, -0.11993408203125, -0.0246734619140625, -0.05181884765625, -0.406982421875, 0.70361328125, 0.2061767578125, -0.323974609375, 0.7548828125, -0.10845947265625, 0.5390625, -0.828125, 0.25244140625, 0.6123046875, -0.241943359375, 0.7998046875, -0.26318359375, 0.0057220458984375, -0.3203125, -0.4404296875, 1.0234375, -0.47802734375, -0.53564453125, 0.251953125, -0.06683349609375, -0.393310546875, 0.32275390625, -0.15673828125, 0.56689453125, -0.11865234375, 0.393310546875, 0.6806640625, -0.414794921875, 0.77099609375, -0.0977783203125, -0.11383056640625, 1.8271484375, 0.4111328125, -0.0318603515625, 0.8330078125, 0.432861328125, -0.404541015625, 0.5732421875, -0.9833984375, 0.424072265625, 0.11016845703125, 0.224853515625, -0.313232421875, 0.01494598388671875, -0.4150390625, 0.484619140625, 0.19921875, 0.0635986328125, -0.07891845703125, 0.312255859375, -0.11602783203125, 0.85986328125, -0.1920166015625, 0.93017578125, -0.42138671875, -0.374755859375, -0.27099609375, -0.50927734375, 0.290283203125, -0.2052001953125, -0.2734375, 0.767578125, 0.62451171875, 1.13671875, 1.255859375, -0.4501953125, 0.2410888671875, 0.36962890625, -0.67919921875, 0.045745849609375, 0.65966796875, 0.921875, -0.198974609375, 0.2392578125, -0.08087158203125, -0.3466796875, -0.294677734375, -0.75341796875, -0.0072479248046875, 0.85546875, -0.75439453125, 0.29150390625, 0.0670166015625, 0.16748046875, -0.83642578125, -0.19677734375, -0.140380859375, -0.833984375, -0.440185546875, 0.48046875, -0.320068359375, 0.61767578125, -0.73583984375, -0.6787109375, 0.541015625, 1.1748046875, -0.2254638671875, 0.50244140625, 0.398681640625, 0.260498046875, -0.2734375, 0.2352294921875, 0.2384033203125, -0.1700439453125, -0.48779296875, 1.01171875, 0.260986328125, -0.025543212890625, -0.07989501953125, 0.67919921875, 0.5283203125, 0.434814453125, -0.368408203125, -0.0289154052734375, 0.50146484375, 1.3759765625, 0.0165252685546875, 0.74169921875, 0.256591796875, 0.78369140625, 0.64501953125, 0.802734375, 0.43212890625, 0.23681640625, 0.8955078125, 0.78759765625, -0.0889892578125, 0.394775390625, 0.342529296875, 0.4873046875, 0.433837890625, 0.64208984375, 0.262451171875, 0.15234375, 0.08941650390625, -0.0882568359375, -0.460205078125, 0.308349609375, -0.4423828125, 0.734375, -0.139892578125, 0.395263671875, -0.329833984375, -0.408203125, 0.404541015625, 0.86962890625, -0.822265625, -0.46630859375, 0.2347412109375, 0.01105499267578125, 0.1309814453125, -0.17431640625, 0.365478515625, 0.220458984375, 0.43896484375, 0.50830078125, -0.2451171875, -0.1868896484375, -1.087890625, -0.9013671875, -0.98193359375, -0.53466796875, -0.9384765625, 0.034881591796875, 0.041107177734375, -0.8056640625, 0.297607421875, -0.60400390625, -0.2125244140625, 0.261474609375, -0.705078125, 0.7578125, -0.255615234375, 0.3427734375, -1.2490234375, 0.81201171875, 0.3955078125, 1.146484375, -0.74560546875, 0.2100830078125, 0.1412353515625, -0.7314453125, 0.05535888671875, 0.0723876953125, 0.3154296875, 0.0716552734375, -0.7294921875, -0.64990234375, -0.689453125, -0.180908203125, -0.299072265625, 0.09259033203125, -0.5556640625, 0.96142578125, 0.71240234375, -0.77783203125, 0.685546875, 0.861328125, -0.65625, 0.58837890625, 0.459228515625, 0.3818359375, -0.7109375, 1.5029296875, 0.46533203125, 0.394775390625, -0.46826171875, -0.4521484375, -0.1845703125, -0.08111572265625, 0.1612548828125, -0.481201171875, -0.56689453125, 0.56640625, -0.1539306640625, -1.0380859375, 0.357421875, -0.92919921875, -0.5263671875, -0.2493896484375, -0.94677734375, 1.29296875, 1.072265625, -0.027740478515625, -0.019256591796875, -0.30029296875, -0.092041015625, 0.54248046875, 0.513671875, -0.378662109375, -0.025970458984375, 0.8603515625, 0.2744140625, 0.2294921875, 0.1673583984375, -0.6025390625, -0.06402587890625, -0.16015625, 0.323974609375, 0.60986328125, 0.1549072265625, 0.484130859375, 0.2122802734375, 0.6005859375, -1.2041015625, -0.162353515625, -0.36865234375, 0.59716796875, 0.52978515625, 0.39208984375, 0.145263671875, -0.3603515625, -0.80908203125, -1.01953125, 0.1357421875, 0.055419921875, 0.77197265625, -0.61474609375, 0.69287109375, -0.0034027099609375, -0.509765625, 0.74365234375, -0.64794921875, 0.1759033203125, 0.94677734375, -0.47021484375, 0.75390625, -1.115234375, 0.4345703125, -0.014129638671875, -0.2392578125, 0.2012939453125, 0.35546875, 0.51806640625, -0.43701171875, -0.348388671875, -0.5947265625, 0.0465087890625, 0.0491943359375, -0.4033203125, -0.059295654296875, -0.3935546875, -0.40478515625, -0.88232421875, 0.44921875, 0.67431640625, 0.9248046875, 0.01507568359375, 0.5908203125, 0.347412109375, 0.409423828125, 0.65478515625, -0.0771484375, 0.209228515625, -0.8916015625, 0.84130859375, 0.2266845703125, -0.1988525390625, -0.5126953125, -0.26611328125, -0.2161865234375, -0.00738525390625, -0.177001953125, -0.261474609375, -0.82763671875, 0.50146484375, -0.144287109375, 0.73681640625, -0.63330078125, -0.08599853515625, -0.73583984375, 0.326171875, 0.55517578125, -0.85546875, 0.44775390625, -0.93701171875, 0.470947265625, 0.625, -0.25537109375, -0.44189453125, -0.6240234375, -0.86376953125, -0.77001953125, 0.2406005859375, 1.05859375, -0.2420654296875, 0.52490234375, -1.4140625, 0.421142578125, 0.392333984375, -0.97021484375, 0.015960693359375, -0.1890869140625, 0.415283203125, 0.178955078125, 0.71484375, -0.218505859375, -0.29296875, -0.004344940185546875, -1.2353515625, 0.44384765625, -0.69482421875, 0.54248046875, 0.197998046875, -0.2406005859375, 0.12396240234375, 0.373291015625, -0.1102294921875, 0.07037353515625, -0.23388671875, 0.40380859375, -1.0595703125, -0.7275390625, 0.515625, -0.04412841796875, -0.368896484375, 1.0576171875, 0.05255126953125, -0.1712646484375, 0.1907958984375, 0.34228515625, -0.4404296875, 0.5380859375, -0.280517578125, 0.767578125, -0.489013671875, -0.59375, -0.52734375, -0.31884765625, 0.7236328125, -0.214599609375, -0.426513671875, -0.1904296875, -1.2060546875, -0.109130859375, 0.262451171875, -0.580078125, 0.2432861328125, 0.09796142578125, 0.280029296875, -0.2138671875, -0.045135498046875, -0.415771484375, -0.07403564453125, -0.4423828125, -0.603515625, 0.60693359375, 0.375, 0.58056640625, 0.129638671875, -0.456787109375, -0.0433349609375, 0.1895751953125, -0.150390625, -0.68017578125, -0.242431640625, -0.2110595703125, -0.32470703125, -0.53564453125, 0.3359375, -0.153564453125, 0.3994140625, 0.99609375, -0.08563232421875, 0.5595703125, 0.275390625, -0.853515625, 1.1162109375, 0.265869140625, -0.83251953125, -0.280517578125, 0.3798828125, 0.019561767578125, 0.85498046875, 0.33056640625, -0.7724609375, -0.64599609375, -0.90234375, 0.446044921875, -0.99169921875, -0.2353515625, -0.98583984375, -0.6083984375, -0.4677734375, 0.70263671875, -0.1990966796875, -0.64501953125, 0.1844482421875, -0.96630859375, 0.038848876953125, -0.99658203125, -0.20751953125, -0.75244140625, -0.5322265625, -0.364013671875, 0.97119140625, -0.030181884765625, -0.039031982421875, 0.319580078125, 0.04608154296875, 0.10626220703125, 0.2198486328125, -0.7763671875, -0.296142578125, 0.048858642578125, -0.07403564453125, -0.3974609375, -0.04669189453125, -0.7568359375, 0.68603515625, -0.82666015625, 0.2052001953125, -0.139404296875, -0.0841064453125, -0.322509765625, -0.24951171875, 0.9892578125, -0.5576171875, 0.354248046875, -0.4853515625, 0.2802734375, 0.90576171875, -0.56640625, -0.344482421875, -0.869140625, -0.79296875, -1.41796875, 0.64306640625, -0.315673828125, 0.261474609375, -0.615234375, -0.697265625, 1.0693359375, -0.7548828125, 0.31494140625, 1.115234375, 0.02520751953125, 0.32763671875, -0.382080078125, 0.6826171875, 0.48974609375, -0.61767578125, 0.25732421875, 0.386962890625, -0.630859375, -0.1600341796875, -0.62060546875, -0.97509765625, -0.61962890625, 0.355712890625, 1.01953125, -0.06439208984375, 0.57666015625, -0.454833984375, -1.23046875, -0.312255859375, 0.66162109375, 0.2081298828125, 0.301513671875, 1.0458984375, 0.180419921875, -0.122802734375, 0.284912109375, -0.6083984375, -0.2178955078125, -0.322509765625, 1.2294921875, -0.3427734375, -0.58056640625, 0.98095703125, 0.7763671875, -1.0859375, -0.98291015625, -0.152099609375, -0.041412353515625, -0.034912109375, -0.9169921875, -0.0609130859375, 0.475830078125, -0.447021484375, 0.11627197265625, 0.2098388671875, -0.093994140625, 0.287353515625, 0.1490478515625, 0.43603515625, -0.2152099609375, 0.2841796875, 1.0224609375, -0.32421875, -0.73583984375, -1.009765625, -0.391357421875, -0.33056640625, 0.309814453125, 0.72216796875, -0.2353515625, 0.367919921875, 0.70947265625, -0.08074951171875, 0.99365234375, -0.3037109375, -0.264404296875, 0.350341796875, -0.693359375, -0.60205078125, 0.0982666015625, 0.12646484375, -0.366455078125, 0.69287109375, -0.6328125, -0.104736328125, 0.287841796875, 0.1336669921875, -0.368408203125, -0.96923828125, -0.256591796875, -1.18359375, -0.421142578125, -0.484619140625, -0.91259765625, -0.06182861328125, 0.1951904296875, 0.220947265625, -0.75, 0.068359375, 0.57470703125, -0.343994140625, 0.849609375, -0.701171875, 0.006168365478515625, -0.46923828125, -0.45361328125, -0.6591796875, -0.08984375, -0.572265625, -0.11798095703125, -0.578125, 0.178955078125, -0.19287109375, 0.54833984375, -0.2646484375, 0.65673828125, -0.3447265625, -0.83642578125, 0.309326171875, 0.07177734375, -0.3017578125, 0.90771484375, 0.36279296875, 0.0504150390625, 0.46435546875, -0.1048583984375, -0.143310546875, -0.1290283203125, 0.74560546875, 0.482177734375, -0.2471923828125, -0.325439453125, -0.09912109375, 0.10516357421875, -1.205078125, 0.56201171875, -0.6123046875, 0.1883544921875, 0.2476806640625, -0.344970703125, 0.3076171875, 1.0625, -0.57958984375, 0.43603515625, 0.0296478271484375, 0.1580810546875, 0.255126953125, 0.27001953125, -0.09149169921875, 0.75732421875, -0.259033203125, -0.533203125, -0.12091064453125, 0.2939453125, -0.1246337890625, 0.4169921875, -0.289306640625, -1.1494140625, -1.0615234375, -0.10614013671875, -0.11297607421875, 0.2291259765625, 0.2073974609375, -0.3349609375, 0.0280914306640625, 0.204345703125, -0.94189453125, 0.262939453125, -1.0849609375, -0.96630859375, 0.77294921875, -0.1435546875, -0.36376953125, 0.185791015625, -0.2274169921875, -0.149658203125, 0.16943359375, 0.3134765625, -0.55224609375, 0.418212890625, -0.1572265625, 0.6708984375, -0.322509765625, -0.2193603515625, 0.0172119140625, 0.68701171875, -0.8984375, -0.363037109375, -0.382080078125, 0.83056640625, 0.1387939453125, -0.451416015625, -0.54345703125, 0.1373291015625, 0.2486572265625, 0.2144775390625, -0.45703125, 0.2027587890625, -0.04864501953125, 0.77734375, -1, 0.04998779296875, -0.0005469322204589844, 0.2152099609375, -0.00785064697265625, -0.38525390625, -0.748046875, 1.0185546875, 0.5517578125, 0.1409912109375, 0.6220703125, 0.00615692138671875, 0.51953125, -0.0023365020751953125, -0.0092620849609375, -0.291259765625, 0.732421875, 0.77734375, 0.7255859375, -0.158935546875, 0.369873046875, 0.833984375, 0.283935546875, -0.2022705078125, 0.35205078125, 0.0186004638671875, -0.1058349609375, 0.2724609375, -0.25537109375, -0.30322265625, -0.10986328125, -0.4287109375, 0.58935546875, -0.56494140625, -0.03546142578125, -0.337646484375, -0.7607421875, 0.82958984375, -0.481201171875, -0.2200927734375, 0.365234375, -0.1983642578125, 0.33837890625, 0.51025390625, -0.26953125, -0.323974609375, 1.1455078125, 0.81689453125, 0.5361328125, 0.767578125, 0.397705078125, 0.41748046875, -0.57177734375, 0.3154296875, 0.1077880859375, -0.07342529296875, -0.01004791259765625, -0.65478515625, -1.3046875, 0.56884765625, -0.2178955078125, -0.1402587890625, 0.35107421875, -0.7197265625, 0.2548828125, -0.5634765625, 1.1240234375, -0.5, 0.286376953125, 0.268310546875, -0.56396484375, -0.68603515625, 0.736328125, -0.2220458984375, 0.284912109375, 0.1376953125, 0.95703125, 0.06402587890625, 1.7529296875, 0.755859375, -0.197021484375, 0.1114501953125, 0.61865234375, -0.2646484375, -0.27490234375, -0.6142578125, -0.3671875, -0.0158843994140625, -0.33056640625, -0.7568359375, -0.1519775390625, 0.77685546875, 0.2099609375, -0.95068359375, -0.4013671875, 0.295166015625, -1.013671875, 0.55126953125, 0.1815185546875, 0.4482421875, 0.282958984375, -0.239501953125, -0.284912109375, -0.62548828125, 0.419189453125, -0.6240234375, 0.29150390625, -0.5654296875, -0.2705078125, -0.67578125, -0.55908203125, -0.360595703125, -0.07122802734375, -0.5234375, -0.70947265625, 0.634765625, 0.252197265625, 0.4775390625, 0.426025390625, -0.34326171875, 0.2335205078125, 0.83984375, 1.0341796875, -0.3134765625, 1.1640625, 0.359375, -0.007419586181640625, 0.0865478515625, -0.368896484375, 0.400146484375, 0.0029468536376953125, 0.332275390625, -0.58447265625, -0.1126708984375, -0.9677734375, -1.0576171875, 0.273681640625, 0.5, 0.19091796875, -0.849609375, -1.3076171875, -0.22314453125, -1.10546875, -0.380859375, -0.65625, 0.81298828125, -0.65478515625, -0.039306640625, 0.126708984375, -1.0302734375, 4.2109375, 0.83984375, 0.488037109375, 0.22998046875, 0.25634765625, 0.865234375, 0.359130859375, -0.41748046875, -0.232421875, -0.49462890625, 0.55419921875, -0.56982421875, 0.057159423828125, 1.0283203125, 0.51416015625, 0.36669921875, -0.33740234375, -0.2017822265625, 0.267822265625, -0.9462890625, -0.87841796875, 0.39111328125, 0.1849365234375, 0.392333984375, 0.2066650390625, 0.39404296875, 1.017578125, -0.62158203125, -0.342041015625, -0.77099609375, 0.21435546875, -0.333740234375, 0.95849609375, 0.266357421875, -0.0484619140625, 0.73388671875, -0.023712158203125, -0.52001953125, -0.01861572265625, 0.267578125, -0.1282958984375, 0.20068359375, 0.58642578125, -0.67041015625, -0.40380859375, 0.6826171875, -0.61669921875, 0.64404296875, 0.4716796875, -1.0615234375, 1.0244140625, -0.12841796875, 0.580078125, -0.77001953125, -0.66845703125, 0.2958984375, 0.1263427734375, 0.06915283203125, -0.346923828125, 0.54443359375, 0.529296875, 0.677734375, -0.156982421875, 0.671875, -1.060546875, 0.466552734375, -0.07196044921875, 0.52734375, -0.4521484375, 0.047576904296875, -0.445068359375, -0.397216796875, -0.332763671875, -0.67431640625, 0.58447265625, 0.126953125, -0.353759765625, 0.81787109375, 0.266845703125, -0.76318359375, 0.2056884765625, -0.4326171875, -0.03704833984375, -0.401611328125, 0.7001953125, 1.15234375, -0.505859375, 0.06396484375, -0.1915283203125, 0.63525390625, 0.61474609375, 0.8515625, -0.0909423828125, -0.654296875, -0.5185546875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Submitted Solution: ``` from sys import stdin, stdout # 0 1 2 3 4 5 6 7 8 9 # 9 8 7 6 5 4 3 2 1 (0) 9 # 1 2 3 4 5 6 7 8 (9) 8 # 8 7 6 5 4 3 2 (1) 7 # 2 3 4 5 6 7 (8) 6 # 7 6 5 4 3 (2) 5 # .......... t = int(stdin.readline()) for _ in range(t): n = int(stdin.readline()) a = stdin.readline().strip() b = stdin.readline().strip() ans = [] idx = 0 flip = False for i in range(n-1, -1, -1): if (not flip and a[idx] == b[i]) or (flip and a[idx] != b[i]): ans.append(1) ans.append(i+1) if flip: idx -= i else: idx += i flip = not flip stdout.write(str(len(ans)) + ' ') if len(ans) > 0: stdout.write(' '.join(map(str, ans)) + '\n') ``` Yes
105,447
[ 0.2313232421875, -0.31787109375, -0.12066650390625, 0.03607177734375, -0.58251953125, -0.60205078125, -0.09283447265625, -0.1060791015625, 0.037017822265625, 1.0498046875, 0.8037109375, -0.272216796875, 0.2149658203125, -0.9921875, -0.5654296875, 0.1834716796875, -0.2802734375, -0.70556640625, -0.236572265625, -0.57421875, -0.07647705078125, -0.17822265625, -1.345703125, 0.07904052734375, -0.479248046875, 0.71337890625, 0.43359375, -0.1470947265625, 0.89453125, 0.93603515625, -0.482421875, -0.5380859375, 0.75048828125, -0.89794921875, -0.350830078125, -0.425048828125, 0.697265625, -0.775390625, -0.243896484375, -0.44580078125, 0.395751953125, -0.2386474609375, 0.24267578125, -0.78466796875, -1.330078125, 0.049560546875, -0.2734375, -0.327880859375, -0.2406005859375, -0.34130859375, 0.03515625, -0.265380859375, 0.548828125, -0.07806396484375, 0.1416015625, 0.311767578125, 0.22216796875, -0.462646484375, -0.476318359375, 0.0830078125, 0.0271148681640625, 0.1256103515625, 0.16650390625, -0.75, 0.15576171875, 0.441162109375, -0.2015380859375, -0.380859375, -0.287109375, -0.81201171875, -0.278564453125, -0.0833740234375, -0.70166015625, -0.2203369140625, -0.10595703125, 0.1878662109375, 0.2100830078125, -0.0528564453125, -1.0556640625, 0.8701171875, -0.438232421875, 1.0693359375, 0.2435302734375, 0.18115234375, -0.55908203125, -0.458251953125, 0.11431884765625, 0.19384765625, 0.1806640625, -0.08880615234375, -0.298828125, 0.447998046875, -0.5947265625, -0.03204345703125, 0.402587890625, 0.65185546875, -0.341796875, 0.30908203125, 0.375732421875, 0.040435791015625, 0.6875, 1.0048828125, -0.263671875, 1.3271484375, -0.50732421875, -0.2003173828125, -0.035308837890625, 0.005298614501953125, -0.12127685546875, -0.04229736328125, -0.02093505859375, -0.31884765625, 0.7041015625, 0.34228515625, -0.3583984375, 0.71142578125, -0.06829833984375, 0.5234375, -0.87548828125, 0.296875, 0.6591796875, -0.2449951171875, 0.75244140625, -0.326171875, 0.0022296905517578125, -0.277587890625, -0.443603515625, 1.0126953125, -0.443603515625, -0.55224609375, 0.2288818359375, -0.0999755859375, -0.35009765625, 0.299072265625, -0.1019287109375, 0.677734375, -0.216064453125, 0.330078125, 0.646484375, -0.41064453125, 0.77392578125, -0.14111328125, -0.142822265625, 1.8525390625, 0.42431640625, 0.006198883056640625, 0.7802734375, 0.4541015625, -0.342529296875, 0.576171875, -0.935546875, 0.423828125, 0.064697265625, 0.214599609375, -0.2431640625, -0.0273895263671875, -0.37646484375, 0.475830078125, 0.233642578125, 0.1478271484375, -0.095947265625, 0.353515625, -0.058349609375, 0.857421875, -0.20361328125, 0.97412109375, -0.374755859375, -0.419677734375, -0.2734375, -0.51611328125, 0.31591796875, -0.228271484375, -0.256103515625, 0.70947265625, 0.6181640625, 1.12109375, 1.3271484375, -0.43310546875, 0.205810546875, 0.353759765625, -0.72607421875, 0.08990478515625, 0.63330078125, 0.94677734375, -0.12548828125, 0.28857421875, -0.0260162353515625, -0.291748046875, -0.38037109375, -0.791015625, -0.0230255126953125, 0.8330078125, -0.70556640625, 0.255615234375, 0.0205078125, 0.1834716796875, -0.7939453125, -0.2154541015625, -0.10772705078125, -0.80517578125, -0.427490234375, 0.483154296875, -0.28125, 0.580078125, -0.70654296875, -0.6357421875, 0.587890625, 1.2421875, -0.2017822265625, 0.477294921875, 0.45947265625, 0.2479248046875, -0.29248046875, 0.2095947265625, 0.2364501953125, -0.2237548828125, -0.463623046875, 0.95849609375, 0.35546875, -0.0755615234375, -0.060028076171875, 0.76171875, 0.49267578125, 0.3896484375, -0.430908203125, -0.00917816162109375, 0.487548828125, 1.3525390625, 0.088623046875, 0.75146484375, 0.208984375, 0.7626953125, 0.60302734375, 0.76953125, 0.39794921875, 0.126220703125, 0.91259765625, 0.76513671875, -0.142333984375, 0.4638671875, 0.388671875, 0.458984375, 0.29052734375, 0.6376953125, 0.2783203125, 0.1524658203125, 0.127685546875, -0.045654296875, -0.53125, 0.28759765625, -0.476318359375, 0.80029296875, -0.130859375, 0.352294921875, -0.310546875, -0.4775390625, 0.442626953125, 0.81884765625, -0.8564453125, -0.419677734375, 0.2005615234375, -0.016876220703125, 0.1234130859375, -0.141845703125, 0.37060546875, 0.2296142578125, 0.420654296875, 0.483642578125, -0.2490234375, -0.1297607421875, -1.0126953125, -0.87744140625, -0.9541015625, -0.52734375, -0.92431640625, -0.0131072998046875, -0.0140838623046875, -0.8173828125, 0.255859375, -0.625, -0.1304931640625, 0.254638671875, -0.67724609375, 0.73828125, -0.260986328125, 0.284423828125, -1.2666015625, 0.82080078125, 0.375244140625, 1.255859375, -0.73681640625, 0.204345703125, 0.0706787109375, -0.72119140625, 0.02783203125, -0.006366729736328125, 0.332275390625, 0.08929443359375, -0.625, -0.666015625, -0.7138671875, -0.146484375, -0.2919921875, 0.1483154296875, -0.51953125, 0.8896484375, 0.70166015625, -0.7470703125, 0.7236328125, 0.86865234375, -0.64892578125, 0.59716796875, 0.402099609375, 0.338623046875, -0.7099609375, 1.5361328125, 0.4423828125, 0.407470703125, -0.5009765625, -0.487060546875, -0.15966796875, -0.04290771484375, 0.184814453125, -0.5068359375, -0.5615234375, 0.5810546875, -0.0941162109375, -1.005859375, 0.3076171875, -0.974609375, -0.4951171875, -0.159423828125, -0.93505859375, 1.34375, 1.0771484375, 0.019683837890625, -0.0369873046875, -0.293212890625, -0.12841796875, 0.52978515625, 0.5615234375, -0.357666015625, -0.02264404296875, 0.89208984375, 0.262939453125, 0.1966552734375, 0.213134765625, -0.62646484375, -0.040924072265625, -0.19580078125, 0.33544921875, 0.57861328125, 0.1649169921875, 0.47802734375, 0.2154541015625, 0.5390625, -1.2890625, -0.1690673828125, -0.333740234375, 0.5888671875, 0.5400390625, 0.314697265625, 0.164306640625, -0.306884765625, -0.77685546875, -0.990234375, 0.11773681640625, 0.03692626953125, 0.76611328125, -0.57861328125, 0.681640625, -0.02069091796875, -0.47705078125, 0.7373046875, -0.693359375, 0.136474609375, 0.99169921875, -0.47509765625, 0.71826171875, -1.09375, 0.396484375, -0.00927734375, -0.2489013671875, 0.289306640625, 0.33447265625, 0.54443359375, -0.461181640625, -0.36328125, -0.6552734375, 0.046051025390625, 0.055328369140625, -0.40478515625, -0.054595947265625, -0.3125, -0.43505859375, -0.88818359375, 0.39404296875, 0.6796875, 0.89892578125, 0.04718017578125, 0.57666015625, 0.297607421875, 0.435302734375, 0.6484375, -0.060089111328125, 0.265380859375, -0.91845703125, 0.8583984375, 0.248779296875, -0.200927734375, -0.52099609375, -0.2242431640625, -0.1602783203125, 0.06341552734375, -0.24462890625, -0.2298583984375, -0.85986328125, 0.470458984375, -0.13916015625, 0.68115234375, -0.68896484375, -0.0239715576171875, -0.734375, 0.30322265625, 0.541015625, -0.89306640625, 0.4296875, -0.9453125, 0.4755859375, 0.5625, -0.2626953125, -0.3974609375, -0.53955078125, -0.8310546875, -0.80615234375, 0.258056640625, 1.0361328125, -0.2100830078125, 0.486083984375, -1.37890625, 0.416259765625, 0.3701171875, -0.91162109375, 0.044525146484375, -0.1873779296875, 0.389892578125, 0.1961669921875, 0.70947265625, -0.17822265625, -0.325927734375, -0.019561767578125, -1.2138671875, 0.477783203125, -0.65283203125, 0.52099609375, 0.1785888671875, -0.228759765625, 0.08428955078125, 0.41455078125, -0.12030029296875, 0.0587158203125, -0.1805419921875, 0.380859375, -1.0537109375, -0.8056640625, 0.5087890625, -0.12469482421875, -0.348388671875, 1.0234375, 0.0911865234375, -0.1744384765625, 0.1983642578125, 0.434814453125, -0.419189453125, 0.5498046875, -0.3310546875, 0.71923828125, -0.412109375, -0.6103515625, -0.5615234375, -0.273681640625, 0.74560546875, -0.130859375, -0.461669921875, -0.1856689453125, -1.15625, -0.0865478515625, 0.236328125, -0.50244140625, 0.2025146484375, 0.10101318359375, 0.252685546875, -0.23974609375, -0.12347412109375, -0.405029296875, -0.06292724609375, -0.49072265625, -0.6162109375, 0.58154296875, 0.38525390625, 0.60107421875, 0.0936279296875, -0.492431640625, -0.103759765625, 0.20263671875, -0.2008056640625, -0.6318359375, -0.1905517578125, -0.294677734375, -0.319091796875, -0.54052734375, 0.26611328125, -0.110595703125, 0.398193359375, 0.9208984375, -0.02374267578125, 0.46728515625, 0.3740234375, -0.830078125, 1.07421875, 0.300537109375, -0.859375, -0.193115234375, 0.37890625, -0.044677734375, 0.8046875, 0.310546875, -0.80712890625, -0.6064453125, -0.89404296875, 0.420654296875, -0.93505859375, -0.2252197265625, -1.009765625, -0.6435546875, -0.4296875, 0.70556640625, -0.198486328125, -0.65576171875, 0.147216796875, -1.0009765625, -0.0177001953125, -1.0146484375, -0.2293701171875, -0.767578125, -0.64990234375, -0.326171875, 1.033203125, -0.05706787109375, -0.032379150390625, 0.279541015625, 0.05706787109375, 0.1009521484375, 0.269775390625, -0.78125, -0.302001953125, 0.05523681640625, -0.004871368408203125, -0.345703125, -0.07684326171875, -0.8408203125, 0.66650390625, -0.84716796875, 0.2113037109375, -0.20654296875, -0.039825439453125, -0.30029296875, -0.2017822265625, 0.9814453125, -0.62255859375, 0.33544921875, -0.413818359375, 0.3798828125, 0.9736328125, -0.5322265625, -0.321044921875, -0.8896484375, -0.75439453125, -1.3583984375, 0.6083984375, -0.3466796875, 0.2578125, -0.677734375, -0.630859375, 1.001953125, -0.8212890625, 0.360107421875, 1.0810546875, 0.0269622802734375, 0.295166015625, -0.38037109375, 0.76123046875, 0.48193359375, -0.65087890625, 0.265380859375, 0.380126953125, -0.6337890625, -0.138427734375, -0.59716796875, -0.9638671875, -0.56396484375, 0.30029296875, 1.0654296875, -0.0552978515625, 0.5693359375, -0.50048828125, -1.1650390625, -0.310546875, 0.73876953125, 0.19970703125, 0.335693359375, 1.0693359375, 0.191162109375, -0.11407470703125, 0.325439453125, -0.62255859375, -0.175537109375, -0.30419921875, 1.22265625, -0.382080078125, -0.5947265625, 0.95068359375, 0.76025390625, -1.1064453125, -1.0537109375, -0.1424560546875, -0.03228759765625, -0.01140594482421875, -0.8994140625, -0.081787109375, 0.4970703125, -0.4140625, 0.070068359375, 0.278564453125, -0.07177734375, 0.344482421875, 0.1407470703125, 0.42724609375, -0.21142578125, 0.353515625, 1.0576171875, -0.33984375, -0.69140625, -0.99169921875, -0.375244140625, -0.358154296875, 0.2371826171875, 0.71630859375, -0.2509765625, 0.396484375, 0.662109375, -0.054534912109375, 1.087890625, -0.332275390625, -0.267333984375, 0.37646484375, -0.75927734375, -0.6484375, 0.109130859375, 0.1275634765625, -0.335205078125, 0.7607421875, -0.6298828125, -0.115478515625, 0.26953125, 0.185546875, -0.4169921875, -0.94482421875, -0.2269287109375, -1.1474609375, -0.416748046875, -0.4013671875, -0.869140625, -0.0012979507446289062, 0.1624755859375, 0.18603515625, -0.76513671875, 0.050323486328125, 0.46875, -0.3466796875, 0.83251953125, -0.716796875, 0.05841064453125, -0.47119140625, -0.40283203125, -0.640625, -0.07135009765625, -0.67578125, -0.189453125, -0.5146484375, 0.1513671875, -0.1485595703125, 0.4775390625, -0.2431640625, 0.6455078125, -0.4052734375, -0.80224609375, 0.30078125, 0.11309814453125, -0.2734375, 0.92578125, 0.40478515625, 0.060699462890625, 0.525390625, -0.07769775390625, -0.130859375, -0.1746826171875, 0.716796875, 0.51513671875, -0.1746826171875, -0.274658203125, -0.15576171875, 0.0909423828125, -1.12890625, 0.60498046875, -0.6103515625, 0.206298828125, 0.294189453125, -0.386962890625, 0.35546875, 1.041015625, -0.5380859375, 0.35791015625, 0.043426513671875, 0.15478515625, 0.235595703125, 0.21826171875, -0.11871337890625, 0.73681640625, -0.2388916015625, -0.53271484375, -0.069580078125, 0.326171875, -0.06927490234375, 0.406005859375, -0.276123046875, -1.1318359375, -1.123046875, -0.1337890625, -0.099609375, 0.177734375, 0.237548828125, -0.3046875, 0.035675048828125, 0.183837890625, -0.921875, 0.257568359375, -1.025390625, -0.9619140625, 0.7080078125, -0.1923828125, -0.406494140625, 0.145751953125, -0.301513671875, -0.15087890625, 0.1436767578125, 0.318115234375, -0.50439453125, 0.436767578125, -0.1361083984375, 0.6650390625, -0.322509765625, -0.128662109375, -0.00018990039825439453, 0.61865234375, -0.8876953125, -0.36669921875, -0.322021484375, 0.81494140625, 0.07525634765625, -0.52099609375, -0.60595703125, 0.1807861328125, 0.2071533203125, 0.2230224609375, -0.4833984375, 0.2340087890625, -0.03765869140625, 0.73583984375, -1.0283203125, 0.0750732421875, -0.0032711029052734375, 0.27783203125, -0.0797119140625, -0.37646484375, -0.77294921875, 1.041015625, 0.5263671875, 0.1571044921875, 0.6455078125, 0.02569580078125, 0.51953125, -0.01556396484375, 0.025726318359375, -0.324462890625, 0.646484375, 0.76220703125, 0.716796875, -0.1668701171875, 0.4130859375, 0.84130859375, 0.197509765625, -0.2430419921875, 0.330810546875, -0.00806427001953125, -0.1395263671875, 0.323974609375, -0.25634765625, -0.25634765625, -0.07470703125, -0.425048828125, 0.5556640625, -0.60546875, 0.02056884765625, -0.328857421875, -0.77880859375, 0.8232421875, -0.44091796875, -0.2105712890625, 0.37255859375, -0.18798828125, 0.343017578125, 0.53759765625, -0.192138671875, -0.330322265625, 1.13671875, 0.80029296875, 0.56640625, 0.7109375, 0.47998046875, 0.427734375, -0.54296875, 0.33984375, 0.1468505859375, -0.05816650390625, -0.00888824462890625, -0.61279296875, -1.3037109375, 0.57373046875, -0.1942138671875, -0.139892578125, 0.330078125, -0.68603515625, 0.267822265625, -0.55224609375, 1.1572265625, -0.50390625, 0.177001953125, 0.27880859375, -0.59912109375, -0.65576171875, 0.6875, -0.2049560546875, 0.26806640625, 0.1558837890625, 0.9111328125, 0.054046630859375, 1.751953125, 0.734375, -0.1922607421875, 0.052978515625, 0.60009765625, -0.266845703125, -0.311767578125, -0.58642578125, -0.309326171875, 0.013519287109375, -0.359375, -0.74267578125, -0.112548828125, 0.720703125, 0.2322998046875, -0.84912109375, -0.41259765625, 0.265869140625, -0.97216796875, 0.56982421875, 0.1912841796875, 0.477783203125, 0.2099609375, -0.216552734375, -0.274658203125, -0.67529296875, 0.351318359375, -0.6298828125, 0.3359375, -0.52685546875, -0.256103515625, -0.6796875, -0.52099609375, -0.355712890625, -0.06158447265625, -0.4970703125, -0.69921875, 0.64990234375, 0.222412109375, 0.444580078125, 0.443115234375, -0.346435546875, 0.3076171875, 0.76171875, 0.96728515625, -0.2919921875, 1.1474609375, 0.27197265625, -0.0728759765625, 0.08734130859375, -0.35009765625, 0.3974609375, -0.0246734619140625, 0.2724609375, -0.64013671875, -0.1258544921875, -0.9951171875, -1.041015625, 0.291259765625, 0.459228515625, 0.2548828125, -0.8291015625, -1.3046875, -0.2314453125, -1.1123046875, -0.3056640625, -0.732421875, 0.7412109375, -0.60546875, -0.038787841796875, 0.11212158203125, -1.001953125, 4.24609375, 0.833984375, 0.53271484375, 0.1954345703125, 0.243896484375, 0.8564453125, 0.330322265625, -0.445556640625, -0.273193359375, -0.5361328125, 0.59375, -0.5849609375, 0.025360107421875, 1.0302734375, 0.56494140625, 0.421142578125, -0.3125, -0.18212890625, 0.253173828125, -0.9716796875, -0.7958984375, 0.329345703125, 0.1148681640625, 0.361328125, 0.1961669921875, 0.447998046875, 0.978515625, -0.69580078125, -0.303955078125, -0.76171875, 0.24951171875, -0.3076171875, 0.96142578125, 0.195068359375, -0.0782470703125, 0.8232421875, -0.09375, -0.50830078125, 0.01454925537109375, 0.2177734375, -0.13818359375, 0.2191162109375, 0.58642578125, -0.66357421875, -0.4501953125, 0.73046875, -0.56591796875, 0.60107421875, 0.45751953125, -1.0400390625, 1.03125, -0.11376953125, 0.55126953125, -0.77734375, -0.599609375, 0.32861328125, 0.1497802734375, 0.059814453125, -0.36181640625, 0.5556640625, 0.55712890625, 0.66845703125, -0.0982666015625, 0.716796875, -1.0390625, 0.47412109375, -0.08453369140625, 0.5927734375, -0.473388671875, 0.004817962646484375, -0.449462890625, -0.34814453125, -0.314453125, -0.63037109375, 0.6064453125, 0.10467529296875, -0.314453125, 0.78759765625, 0.331787109375, -0.71142578125, 0.1881103515625, -0.413330078125, -0.07647705078125, -0.4580078125, 0.69921875, 1.1767578125, -0.46728515625, 0.09368896484375, -0.23095703125, 0.60888671875, 0.56494140625, 0.88427734375, -0.08233642578125, -0.640625, -0.54736328125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Submitted Solution: ``` #!/usr/bin/env python3 import sys input=sys.stdin.readline t=int(input()) for _ in range(t): n=int(input()) a=list(input()) b=list(input()) ans=[] l=0 r=n-1 for i in range(n-1,-1,-1): if a[i]!=b[i]: r=i break else: r=0 if l==r: if a[0]==b[0]: print(0) else: print(1,1) continue else: flip=False count=r while l!=r: if flip==False: if a[l]==b[count]: if a[l]=='0': a[l]='1' else: a[l]='0' ans.append(1) ans.append(count+1) else: ans.append(count+1) flip=True else: if a[r]!=b[count]: if a[r]=='0': a[r]='1' else: a[r]='0' ans.append(1) ans.append(count+1) else: ans.append(count+1) flip=False for i in range(count,-1,-1): if flip==True: if a[l+count-i]==b[i]: l=l+count-i count=i break else: if a[r-count+i]!=b[i]: r=r-count+i count=i break else: if flip==False: l=r else: r=l if flip==False: if a[l]!=b[0]: ans.append(1) else: if a[r]==b[0]: ans.append(1) ans=[len(ans)]+ans print(*ans) ``` Yes
105,448
[ 0.2705078125, -0.325927734375, -0.165771484375, 0.0802001953125, -0.53515625, -0.60205078125, -0.01837158203125, -0.10870361328125, 0.07830810546875, 1.048828125, 0.8232421875, -0.239501953125, 0.2099609375, -1.0263671875, -0.58203125, 0.1895751953125, -0.2861328125, -0.69189453125, -0.1802978515625, -0.5234375, -0.08978271484375, -0.171630859375, -1.369140625, 0.033355712890625, -0.492919921875, 0.794921875, 0.417724609375, -0.1279296875, 0.86767578125, 0.9619140625, -0.50244140625, -0.509765625, 0.78125, -0.88916015625, -0.33642578125, -0.375244140625, 0.7041015625, -0.73291015625, -0.2340087890625, -0.43798828125, 0.4189453125, -0.24169921875, 0.296142578125, -0.724609375, -1.373046875, 0.06451416015625, -0.2418212890625, -0.330810546875, -0.2041015625, -0.405029296875, 0.044464111328125, -0.288818359375, 0.6171875, -0.051513671875, 0.173828125, 0.316162109375, 0.2783203125, -0.426025390625, -0.477294921875, 0.10418701171875, 0.0175628662109375, 0.157470703125, 0.1923828125, -0.79736328125, 0.10052490234375, 0.40478515625, -0.2164306640625, -0.41357421875, -0.282958984375, -0.80517578125, -0.26611328125, -0.103271484375, -0.6943359375, -0.1385498046875, -0.0867919921875, 0.1787109375, 0.1334228515625, -0.114501953125, -1.0595703125, 0.88330078125, -0.418212890625, 1.0498046875, 0.279296875, 0.2156982421875, -0.5380859375, -0.4287109375, 0.1669921875, 0.2362060546875, 0.2291259765625, -0.0958251953125, -0.28515625, 0.458251953125, -0.58349609375, -0.0386962890625, 0.451904296875, 0.63330078125, -0.34326171875, 0.344482421875, 0.41015625, 0.05047607421875, 0.765625, 0.96044921875, -0.210693359375, 1.3662109375, -0.525390625, -0.2080078125, -0.051910400390625, 0.002536773681640625, -0.1214599609375, -0.07354736328125, -0.05108642578125, -0.362060546875, 0.6875, 0.27880859375, -0.311767578125, 0.71142578125, -0.10015869140625, 0.5517578125, -0.85693359375, 0.280029296875, 0.6494140625, -0.2452392578125, 0.77587890625, -0.2744140625, 0.0227203369140625, -0.2978515625, -0.48486328125, 1.041015625, -0.465576171875, -0.509765625, 0.22900390625, -0.0693359375, -0.384521484375, 0.29052734375, -0.153076171875, 0.599609375, -0.14892578125, 0.384765625, 0.6767578125, -0.447998046875, 0.79052734375, -0.1475830078125, -0.1126708984375, 1.826171875, 0.416259765625, -0.038909912109375, 0.81640625, 0.446533203125, -0.39794921875, 0.59375, -0.94921875, 0.40087890625, 0.0721435546875, 0.197509765625, -0.32666015625, 0.0011348724365234375, -0.378173828125, 0.473388671875, 0.2342529296875, 0.09954833984375, -0.05535888671875, 0.300048828125, -0.08050537109375, 0.84619140625, -0.21826171875, 0.958984375, -0.418212890625, -0.39794921875, -0.2431640625, -0.52783203125, 0.26416015625, -0.209716796875, -0.2607421875, 0.73095703125, 0.62060546875, 1.1513671875, 1.2568359375, -0.452880859375, 0.26513671875, 0.332275390625, -0.6630859375, 0.046722412109375, 0.60693359375, 0.91455078125, -0.2183837890625, 0.26708984375, -0.084716796875, -0.302978515625, -0.33056640625, -0.75830078125, -0.05682373046875, 0.83837890625, -0.7568359375, 0.277099609375, 0.09710693359375, 0.2099609375, -0.8203125, -0.1749267578125, -0.1138916015625, -0.85107421875, -0.40576171875, 0.5146484375, -0.299560546875, 0.61083984375, -0.72412109375, -0.6806640625, 0.53125, 1.1728515625, -0.239013671875, 0.5224609375, 0.431640625, 0.28564453125, -0.2724609375, 0.2041015625, 0.267578125, -0.182373046875, -0.49755859375, 0.9765625, 0.26416015625, -0.0396728515625, -0.08184814453125, 0.705078125, 0.49267578125, 0.422607421875, -0.4072265625, -0.0098114013671875, 0.505859375, 1.376953125, 0.06280517578125, 0.76806640625, 0.236572265625, 0.79833984375, 0.6494140625, 0.8046875, 0.438720703125, 0.1910400390625, 0.88671875, 0.755859375, -0.0831298828125, 0.3974609375, 0.36474609375, 0.460693359375, 0.3681640625, 0.646484375, 0.2744140625, 0.2093505859375, 0.11138916015625, -0.061981201171875, -0.50634765625, 0.3193359375, -0.437744140625, 0.75048828125, -0.1124267578125, 0.409423828125, -0.31201171875, -0.415771484375, 0.405517578125, 0.83349609375, -0.80908203125, -0.489013671875, 0.1826171875, 0.0582275390625, 0.10809326171875, -0.1512451171875, 0.365478515625, 0.227783203125, 0.46435546875, 0.489501953125, -0.2587890625, -0.1639404296875, -1.0751953125, -0.90234375, -0.98388671875, -0.52685546875, -0.9228515625, 0.02130126953125, 0.0689697265625, -0.830078125, 0.31103515625, -0.6279296875, -0.15966796875, 0.262451171875, -0.71728515625, 0.75146484375, -0.247314453125, 0.31494140625, -1.234375, 0.818359375, 0.3837890625, 1.181640625, -0.7646484375, 0.1776123046875, 0.08648681640625, -0.6923828125, 0.0269317626953125, 0.07977294921875, 0.333984375, 0.078369140625, -0.7119140625, -0.65576171875, -0.697265625, -0.1553955078125, -0.293212890625, 0.101806640625, -0.56982421875, 0.935546875, 0.716796875, -0.7509765625, 0.6943359375, 0.861328125, -0.69775390625, 0.626953125, 0.44921875, 0.398681640625, -0.70654296875, 1.5302734375, 0.45654296875, 0.420166015625, -0.480224609375, -0.427001953125, -0.1873779296875, -0.060211181640625, 0.19287109375, -0.52197265625, -0.58837890625, 0.552734375, -0.173583984375, -1.0615234375, 0.3408203125, -0.95849609375, -0.5380859375, -0.186279296875, -0.912109375, 1.3056640625, 1.0869140625, -0.0183868408203125, -0.01140594482421875, -0.31103515625, -0.1083984375, 0.52978515625, 0.5029296875, -0.333984375, -0.0220947265625, 0.8603515625, 0.260986328125, 0.21826171875, 0.1885986328125, -0.6064453125, -0.05792236328125, -0.1505126953125, 0.3076171875, 0.607421875, 0.152099609375, 0.451904296875, 0.1817626953125, 0.60888671875, -1.240234375, -0.19482421875, -0.375244140625, 0.56884765625, 0.51904296875, 0.409423828125, 0.1837158203125, -0.37353515625, -0.7841796875, -1.0302734375, 0.149169921875, 0.0218353271484375, 0.75830078125, -0.6005859375, 0.70849609375, 0.01071929931640625, -0.52685546875, 0.72705078125, -0.70263671875, 0.1485595703125, 0.96044921875, -0.499267578125, 0.7490234375, -1.0791015625, 0.423583984375, -0.0307464599609375, -0.1937255859375, 0.30224609375, 0.34912109375, 0.54296875, -0.466064453125, -0.367919921875, -0.5927734375, 0.0667724609375, 0.054412841796875, -0.36279296875, -0.05364990234375, -0.355224609375, -0.417724609375, -0.888671875, 0.422119140625, 0.69140625, 0.9140625, 0.0215301513671875, 0.56689453125, 0.342529296875, 0.39013671875, 0.6337890625, -0.043304443359375, 0.2381591796875, -0.91796875, 0.80517578125, 0.28369140625, -0.243408203125, -0.49853515625, -0.2359619140625, -0.2139892578125, 0.0182342529296875, -0.225341796875, -0.238037109375, -0.87841796875, 0.498291015625, -0.1524658203125, 0.75048828125, -0.64404296875, -0.0511474609375, -0.70947265625, 0.31884765625, 0.5341796875, -0.88818359375, 0.4697265625, -0.91015625, 0.478271484375, 0.580078125, -0.27197265625, -0.415283203125, -0.56591796875, -0.90283203125, -0.7568359375, 0.2276611328125, 1.0322265625, -0.233642578125, 0.5166015625, -1.408203125, 0.39501953125, 0.393310546875, -0.94091796875, 0.06494140625, -0.18115234375, 0.3955078125, 0.1915283203125, 0.74169921875, -0.223388671875, -0.304443359375, -0.01447296142578125, -1.208984375, 0.40966796875, -0.67724609375, 0.5166015625, 0.1668701171875, -0.2027587890625, 0.1136474609375, 0.384521484375, -0.11798095703125, 0.08111572265625, -0.2249755859375, 0.378662109375, -1.0576171875, -0.73828125, 0.5009765625, -0.08209228515625, -0.37890625, 1.021484375, 0.10247802734375, -0.1728515625, 0.1578369140625, 0.36865234375, -0.463623046875, 0.537109375, -0.27783203125, 0.7724609375, -0.48486328125, -0.58203125, -0.50146484375, -0.3076171875, 0.7255859375, -0.206298828125, -0.4423828125, -0.18408203125, -1.1640625, -0.10980224609375, 0.2181396484375, -0.5400390625, 0.209716796875, 0.1173095703125, 0.274169921875, -0.26220703125, -0.0965576171875, -0.43896484375, -0.07891845703125, -0.458984375, -0.61376953125, 0.60595703125, 0.391845703125, 0.56103515625, 0.1409912109375, -0.475341796875, -0.05230712890625, 0.1983642578125, -0.1397705078125, -0.6806640625, -0.257080078125, -0.28662109375, -0.307373046875, -0.5322265625, 0.2841796875, -0.12091064453125, 0.421142578125, 0.9853515625, -0.031768798828125, 0.54345703125, 0.275634765625, -0.83935546875, 1.1025390625, 0.300537109375, -0.84619140625, -0.271240234375, 0.42333984375, 0.014923095703125, 0.8349609375, 0.328857421875, -0.783203125, -0.65185546875, -0.88720703125, 0.405517578125, -0.9375, -0.2413330078125, -0.9736328125, -0.59130859375, -0.418212890625, 0.7080078125, -0.1732177734375, -0.669921875, 0.193115234375, -0.98193359375, -0.006275177001953125, -0.9658203125, -0.2318115234375, -0.7587890625, -0.59228515625, -0.34130859375, 0.970703125, -0.01050567626953125, -0.038543701171875, 0.306884765625, 0.06817626953125, 0.067138671875, 0.2275390625, -0.7802734375, -0.300537109375, 0.0545654296875, -0.04058837890625, -0.341796875, -0.06689453125, -0.78857421875, 0.64453125, -0.83740234375, 0.1953125, -0.153564453125, -0.0374755859375, -0.331298828125, -0.25146484375, 0.9833984375, -0.58935546875, 0.326416015625, -0.435791015625, 0.28173828125, 0.93603515625, -0.58251953125, -0.3349609375, -0.88818359375, -0.78076171875, -1.4130859375, 0.62646484375, -0.336181640625, 0.2491455078125, -0.673828125, -0.634765625, 1.0654296875, -0.755859375, 0.353271484375, 1.0595703125, 0.033355712890625, 0.35107421875, -0.359375, 0.6748046875, 0.456298828125, -0.60888671875, 0.240234375, 0.36865234375, -0.65234375, -0.1602783203125, -0.58349609375, -0.96630859375, -0.57373046875, 0.376708984375, 1.0322265625, -0.0631103515625, 0.5712890625, -0.452392578125, -1.1953125, -0.3095703125, 0.68212890625, 0.1893310546875, 0.31494140625, 1.0712890625, 0.2158203125, -0.16259765625, 0.295166015625, -0.5927734375, -0.25146484375, -0.291015625, 1.2353515625, -0.352783203125, -0.59228515625, 0.96484375, 0.77001953125, -1.0732421875, -0.99365234375, -0.1436767578125, -0.01092529296875, -0.00580596923828125, -0.9208984375, -0.037384033203125, 0.482177734375, -0.457275390625, 0.120849609375, 0.2236328125, -0.0855712890625, 0.29833984375, 0.1693115234375, 0.430908203125, -0.2147216796875, 0.306396484375, 1.044921875, -0.3671875, -0.7216796875, -0.99365234375, -0.39208984375, -0.309814453125, 0.2418212890625, 0.6875, -0.2391357421875, 0.340087890625, 0.66943359375, -0.051055908203125, 1.0380859375, -0.334228515625, -0.25244140625, 0.39013671875, -0.71826171875, -0.6025390625, 0.09735107421875, 0.1534423828125, -0.3935546875, 0.70703125, -0.62109375, -0.0704345703125, 0.266357421875, 0.138427734375, -0.466796875, -0.98583984375, -0.28271484375, -1.208984375, -0.40478515625, -0.449462890625, -0.89013671875, -0.032562255859375, 0.1669921875, 0.234619140625, -0.73193359375, 0.044036865234375, 0.5654296875, -0.353759765625, 0.81005859375, -0.6982421875, 0.030120849609375, -0.470458984375, -0.4287109375, -0.62255859375, -0.08758544921875, -0.61181640625, -0.16796875, -0.548828125, 0.188720703125, -0.1732177734375, 0.54833984375, -0.261962890625, 0.65966796875, -0.37255859375, -0.79443359375, 0.264404296875, 0.06927490234375, -0.251953125, 0.900390625, 0.360595703125, 0.06622314453125, 0.49658203125, -0.08349609375, -0.1375732421875, -0.2034912109375, 0.73828125, 0.47314453125, -0.2156982421875, -0.31298828125, -0.102294921875, 0.08319091796875, -1.1953125, 0.55126953125, -0.615234375, 0.2080078125, 0.27001953125, -0.3681640625, 0.357421875, 1.068359375, -0.6142578125, 0.390625, 0.042022705078125, 0.1475830078125, 0.255859375, 0.247314453125, -0.10479736328125, 0.70068359375, -0.255859375, -0.5615234375, -0.1220703125, 0.26416015625, -0.1317138671875, 0.3876953125, -0.2447509765625, -1.1552734375, -1.072265625, -0.135009765625, -0.10345458984375, 0.2454833984375, 0.231689453125, -0.269775390625, 0.029632568359375, 0.1873779296875, -0.93994140625, 0.27783203125, -1.08203125, -0.9208984375, 0.7626953125, -0.1544189453125, -0.37646484375, 0.1932373046875, -0.264404296875, -0.1590576171875, 0.1669921875, 0.35302734375, -0.55810546875, 0.43115234375, -0.14990234375, 0.6591796875, -0.3095703125, -0.1759033203125, -0.006359100341796875, 0.67529296875, -0.93017578125, -0.40087890625, -0.38916015625, 0.783203125, 0.09234619140625, -0.470947265625, -0.57421875, 0.1424560546875, 0.2279052734375, 0.2176513671875, -0.46435546875, 0.1842041015625, -0.06732177734375, 0.767578125, -1.01171875, 0.088134765625, 0.0038661956787109375, 0.2578125, -0.029327392578125, -0.392822265625, -0.74951171875, 1.0576171875, 0.55615234375, 0.11029052734375, 0.63330078125, 0.0143585205078125, 0.51611328125, -0.025390625, 0.016204833984375, -0.287841796875, 0.720703125, 0.75146484375, 0.6865234375, -0.169921875, 0.402587890625, 0.83642578125, 0.237548828125, -0.1824951171875, 0.390625, 0.007450103759765625, -0.09710693359375, 0.2919921875, -0.2392578125, -0.252197265625, -0.0943603515625, -0.4072265625, 0.51513671875, -0.5576171875, -0.0267791748046875, -0.2998046875, -0.755859375, 0.822265625, -0.45068359375, -0.2249755859375, 0.335205078125, -0.1971435546875, 0.354736328125, 0.50927734375, -0.265869140625, -0.314453125, 1.15625, 0.80712890625, 0.505859375, 0.74853515625, 0.444091796875, 0.400146484375, -0.5703125, 0.302490234375, 0.182373046875, -0.0770263671875, -0.01177215576171875, -0.6630859375, -1.2841796875, 0.60595703125, -0.171142578125, -0.1708984375, 0.3408203125, -0.72265625, 0.2471923828125, -0.56396484375, 1.1298828125, -0.52294921875, 0.2646484375, 0.267333984375, -0.572265625, -0.63232421875, 0.70263671875, -0.233154296875, 0.2890625, 0.1256103515625, 0.9072265625, 0.07012939453125, 1.7080078125, 0.740234375, -0.1688232421875, 0.050201416015625, 0.6171875, -0.25244140625, -0.311767578125, -0.57275390625, -0.372802734375, -0.02484130859375, -0.35107421875, -0.748046875, -0.190673828125, 0.74267578125, 0.2139892578125, -0.90966796875, -0.41015625, 0.27587890625, -0.99267578125, 0.53857421875, 0.1885986328125, 0.40869140625, 0.26806640625, -0.190673828125, -0.2939453125, -0.62744140625, 0.405029296875, -0.64599609375, 0.301025390625, -0.533203125, -0.2366943359375, -0.68017578125, -0.55419921875, -0.3662109375, -0.1058349609375, -0.5302734375, -0.72216796875, 0.6220703125, 0.265380859375, 0.461181640625, 0.446044921875, -0.355224609375, 0.288330078125, 0.8173828125, 0.97705078125, -0.30517578125, 1.1474609375, 0.341064453125, -0.0084075927734375, 0.0985107421875, -0.3740234375, 0.412353515625, -0.01076507568359375, 0.3369140625, -0.58544921875, -0.1156005859375, -1, -1.0400390625, 0.298828125, 0.448486328125, 0.2412109375, -0.8515625, -1.337890625, -0.25390625, -1.091796875, -0.324951171875, -0.7197265625, 0.81005859375, -0.6357421875, -0.039031982421875, 0.07879638671875, -1.015625, 4.234375, 0.83642578125, 0.5322265625, 0.27685546875, 0.258056640625, 0.8681640625, 0.401611328125, -0.415283203125, -0.2734375, -0.49365234375, 0.5693359375, -0.5439453125, 0.044677734375, 1.041015625, 0.529296875, 0.392578125, -0.31298828125, -0.1666259765625, 0.223388671875, -0.96533203125, -0.8486328125, 0.340576171875, 0.1920166015625, 0.40869140625, 0.222900390625, 0.389892578125, 1.0029296875, -0.66455078125, -0.337646484375, -0.771484375, 0.24658203125, -0.350341796875, 0.9775390625, 0.274169921875, -0.08245849609375, 0.77294921875, -0.025390625, -0.54296875, -0.01293182373046875, 0.2489013671875, -0.159423828125, 0.2266845703125, 0.6181640625, -0.6513671875, -0.44287109375, 0.67431640625, -0.59423828125, 0.60693359375, 0.4208984375, -1.0595703125, 1.0380859375, -0.1268310546875, 0.59375, -0.765625, -0.6328125, 0.30615234375, 0.1690673828125, 0.07415771484375, -0.352294921875, 0.564453125, 0.54248046875, 0.65771484375, -0.155517578125, 0.7060546875, -1.0498046875, 0.4609375, -0.09527587890625, 0.509765625, -0.45068359375, 0.0635986328125, -0.437744140625, -0.36083984375, -0.355712890625, -0.6845703125, 0.5830078125, 0.077392578125, -0.337646484375, 0.79296875, 0.3134765625, -0.71240234375, 0.1795654296875, -0.42822265625, -0.067138671875, -0.426513671875, 0.69677734375, 1.1513671875, -0.47216796875, 0.05426025390625, -0.216796875, 0.61083984375, 0.57958984375, 0.83251953125, -0.10662841796875, -0.662109375, -0.50830078125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Submitted Solution: ``` import sys #comment these out later #sys.stdin = open("in.in", "r") #sys.stdout = open("out.out", "w") inp = sys.stdin.read().split(); ii = 0 t = int(inp[ii]); ii += 1 for _ in range(t): toprint = [] n = int(inp[ii]); ii += 1 a = list(map(int, inp[ii])); ii += 1 b = list(map(int, inp[ii])); ii += 1 lead = a[0] for i in range(n-1, -1, -1): x = a[i] y = b[i] if lead == y: toprint.append(1) toprint.append(i + 1) lead = y else: toprint.append(i + 1) lead = y if toprint == []: print(0) else: print(" ".join(list(map(str, toprint)))) ``` No
105,449
[ 0.272705078125, -0.35498046875, -0.16455078125, 0.08221435546875, -0.5478515625, -0.595703125, -0.0207977294921875, -0.11090087890625, 0.0870361328125, 1.0556640625, 0.82568359375, -0.262451171875, 0.2144775390625, -1.0205078125, -0.5888671875, 0.2027587890625, -0.255615234375, -0.69384765625, -0.186279296875, -0.5205078125, -0.0877685546875, -0.1787109375, -1.3671875, 0.0308685302734375, -0.50048828125, 0.7939453125, 0.394287109375, -0.11663818359375, 0.87060546875, 0.95654296875, -0.52197265625, -0.51416015625, 0.76953125, -0.8798828125, -0.358154296875, -0.394287109375, 0.70263671875, -0.74609375, -0.2371826171875, -0.424072265625, 0.41455078125, -0.2646484375, 0.284423828125, -0.7294921875, -1.3671875, 0.054931640625, -0.23974609375, -0.342529296875, -0.19580078125, -0.387451171875, 0.052642822265625, -0.2861328125, 0.6015625, -0.06463623046875, 0.1600341796875, 0.32373046875, 0.260986328125, -0.442626953125, -0.491455078125, 0.09173583984375, 0.004276275634765625, 0.138427734375, 0.1990966796875, -0.779296875, 0.1109619140625, 0.3984375, -0.2059326171875, -0.4208984375, -0.291748046875, -0.81005859375, -0.2841796875, -0.1033935546875, -0.6962890625, -0.13720703125, -0.0860595703125, 0.1700439453125, 0.13720703125, -0.103759765625, -1.0576171875, 0.87939453125, -0.4150390625, 1.02734375, 0.28125, 0.2110595703125, -0.56298828125, -0.44287109375, 0.1605224609375, 0.2215576171875, 0.218505859375, -0.07025146484375, -0.29052734375, 0.464111328125, -0.576171875, -0.047271728515625, 0.447998046875, 0.64697265625, -0.340087890625, 0.346435546875, 0.39892578125, 0.05682373046875, 0.75, 0.97265625, -0.2166748046875, 1.3583984375, -0.52734375, -0.2080078125, -0.03594970703125, -0.0019664764404296875, -0.12457275390625, -0.0689697265625, -0.0426025390625, -0.343994140625, 0.66650390625, 0.29833984375, -0.33203125, 0.71875, -0.09698486328125, 0.55126953125, -0.83740234375, 0.2880859375, 0.6533203125, -0.2430419921875, 0.77734375, -0.288330078125, 0.00400543212890625, -0.31640625, -0.472900390625, 1.0322265625, -0.479248046875, -0.5400390625, 0.2242431640625, -0.04547119140625, -0.392578125, 0.302978515625, -0.143798828125, 0.59423828125, -0.1470947265625, 0.379150390625, 0.68505859375, -0.450439453125, 0.79248046875, -0.14892578125, -0.10009765625, 1.826171875, 0.408447265625, -0.037322998046875, 0.82080078125, 0.438232421875, -0.391845703125, 0.60546875, -0.95849609375, 0.39794921875, 0.090576171875, 0.2113037109375, -0.3154296875, -0.0154266357421875, -0.369873046875, 0.48095703125, 0.24609375, 0.10430908203125, -0.06610107421875, 0.310546875, -0.07012939453125, 0.83056640625, -0.21240234375, 0.94921875, -0.424560546875, -0.401123046875, -0.23876953125, -0.52294921875, 0.278076171875, -0.200927734375, -0.279541015625, 0.72265625, 0.61962890625, 1.1484375, 1.2548828125, -0.444091796875, 0.261474609375, 0.323486328125, -0.6796875, 0.057159423828125, 0.60693359375, 0.91455078125, -0.19921875, 0.26806640625, -0.072509765625, -0.3037109375, -0.34130859375, -0.76025390625, -0.049713134765625, 0.83544921875, -0.7568359375, 0.282470703125, 0.0863037109375, 0.2032470703125, -0.8037109375, -0.182373046875, -0.09912109375, -0.84423828125, -0.425537109375, 0.50244140625, -0.31103515625, 0.583984375, -0.73486328125, -0.671875, 0.5185546875, 1.1923828125, -0.21630859375, 0.5166015625, 0.46044921875, 0.283203125, -0.293212890625, 0.1944580078125, 0.27294921875, -0.2020263671875, -0.4873046875, 0.974609375, 0.270751953125, -0.033294677734375, -0.0704345703125, 0.71630859375, 0.484130859375, 0.402587890625, -0.382080078125, 0.012481689453125, 0.48095703125, 1.361328125, 0.0777587890625, 0.751953125, 0.2381591796875, 0.79345703125, 0.6357421875, 0.82177734375, 0.43115234375, 0.1873779296875, 0.8955078125, 0.75732421875, -0.09228515625, 0.419921875, 0.3544921875, 0.465087890625, 0.3486328125, 0.64453125, 0.26953125, 0.20263671875, 0.09912109375, -0.0557861328125, -0.5126953125, 0.28662109375, -0.417236328125, 0.7548828125, -0.128662109375, 0.40869140625, -0.31103515625, -0.421875, 0.398681640625, 0.81689453125, -0.826171875, -0.47216796875, 0.1917724609375, 0.05755615234375, 0.11090087890625, -0.1688232421875, 0.368896484375, 0.2371826171875, 0.456787109375, 0.476806640625, -0.265380859375, -0.146240234375, -1.076171875, -0.90087890625, -0.96533203125, -0.529296875, -0.9267578125, 0.037750244140625, 0.0687255859375, -0.82421875, 0.306884765625, -0.638671875, -0.1546630859375, 0.26025390625, -0.69580078125, 0.7451171875, -0.264404296875, 0.33984375, -1.2470703125, 0.828125, 0.388427734375, 1.1943359375, -0.76025390625, 0.1578369140625, 0.0968017578125, -0.69140625, 0.04364013671875, 0.07708740234375, 0.332275390625, 0.08526611328125, -0.72509765625, -0.65185546875, -0.6787109375, -0.166748046875, -0.288818359375, 0.0904541015625, -0.56787109375, 0.92822265625, 0.7109375, -0.744140625, 0.7158203125, 0.8779296875, -0.7138671875, 0.60595703125, 0.45361328125, 0.403076171875, -0.71435546875, 1.537109375, 0.452880859375, 0.414794921875, -0.46923828125, -0.433349609375, -0.1751708984375, -0.0537109375, 0.179931640625, -0.52099609375, -0.58837890625, 0.53662109375, -0.15478515625, -1.05078125, 0.344970703125, -0.94287109375, -0.52197265625, -0.1903076171875, -0.912109375, 1.330078125, 1.0859375, -0.0293731689453125, -0.015472412109375, -0.309326171875, -0.1099853515625, 0.53564453125, 0.51220703125, -0.333740234375, -0.012847900390625, 0.87451171875, 0.267578125, 0.230224609375, 0.2027587890625, -0.62109375, -0.043853759765625, -0.1680908203125, 0.310302734375, 0.59423828125, 0.127685546875, 0.45263671875, 0.180908203125, 0.6005859375, -1.2578125, -0.2093505859375, -0.387939453125, 0.56494140625, 0.53271484375, 0.398193359375, 0.176025390625, -0.34912109375, -0.78466796875, -1.0302734375, 0.1455078125, 0.0296173095703125, 0.7646484375, -0.595703125, 0.70068359375, 0.005828857421875, -0.5341796875, 0.724609375, -0.68798828125, 0.169189453125, 0.96875, -0.50439453125, 0.75048828125, -1.080078125, 0.4150390625, -0.00617218017578125, -0.19482421875, 0.292236328125, 0.333251953125, 0.54150390625, -0.462646484375, -0.370361328125, -0.5947265625, 0.07257080078125, 0.0513916015625, -0.36181640625, -0.06182861328125, -0.34375, -0.43017578125, -0.9111328125, 0.42529296875, 0.70654296875, 0.908203125, 0.0250396728515625, 0.57470703125, 0.323974609375, 0.396240234375, 0.64453125, -0.03851318359375, 0.252197265625, -0.91064453125, 0.81494140625, 0.276611328125, -0.2294921875, -0.51025390625, -0.2412109375, -0.20166015625, 0.0196685791015625, -0.2548828125, -0.2271728515625, -0.86279296875, 0.4990234375, -0.11761474609375, 0.75439453125, -0.64794921875, -0.053009033203125, -0.72021484375, 0.32421875, 0.5576171875, -0.88916015625, 0.460693359375, -0.9208984375, 0.48095703125, 0.5869140625, -0.268798828125, -0.419189453125, -0.5712890625, -0.89306640625, -0.77587890625, 0.2471923828125, 1.0390625, -0.2435302734375, 0.4990234375, -1.3984375, 0.400146484375, 0.394775390625, -0.9208984375, 0.0592041015625, -0.19384765625, 0.393310546875, 0.198974609375, 0.7470703125, -0.204345703125, -0.293212890625, -0.007904052734375, -1.2119140625, 0.41943359375, -0.69580078125, 0.5205078125, 0.1529541015625, -0.2012939453125, 0.10394287109375, 0.4013671875, -0.10516357421875, 0.077880859375, -0.224609375, 0.388427734375, -1.0888671875, -0.72216796875, 0.513671875, -0.080078125, -0.3759765625, 1.0224609375, 0.1046142578125, -0.1805419921875, 0.17431640625, 0.360107421875, -0.459716796875, 0.5380859375, -0.28271484375, 0.78271484375, -0.48046875, -0.57958984375, -0.5263671875, -0.31298828125, 0.736328125, -0.213623046875, -0.44384765625, -0.2005615234375, -1.1796875, -0.114501953125, 0.2337646484375, -0.53466796875, 0.2120361328125, 0.09869384765625, 0.27197265625, -0.2412109375, -0.09368896484375, -0.44384765625, -0.0677490234375, -0.458251953125, -0.60107421875, 0.61962890625, 0.40283203125, 0.57666015625, 0.1287841796875, -0.482177734375, -0.043914794921875, 0.216064453125, -0.150634765625, -0.68212890625, -0.249267578125, -0.29150390625, -0.289794921875, -0.5517578125, 0.297119140625, -0.11553955078125, 0.408447265625, 0.974609375, -0.0274658203125, 0.5400390625, 0.29052734375, -0.837890625, 1.1044921875, 0.29296875, -0.861328125, -0.276123046875, 0.416259765625, 0.0039005279541015625, 0.83837890625, 0.316162109375, -0.783203125, -0.6572265625, -0.88427734375, 0.41162109375, -0.91943359375, -0.2357177734375, -0.95849609375, -0.60693359375, -0.42138671875, 0.7109375, -0.1597900390625, -0.64404296875, 0.169677734375, -0.9697265625, 0.0030307769775390625, -0.982421875, -0.2186279296875, -0.7568359375, -0.5947265625, -0.335205078125, 1.015625, -0.01392364501953125, -0.04315185546875, 0.318115234375, 0.05352783203125, 0.06439208984375, 0.255859375, -0.791015625, -0.296875, 0.061553955078125, -0.04437255859375, -0.328857421875, -0.0611572265625, -0.79638671875, 0.6357421875, -0.83447265625, 0.2027587890625, -0.1607666015625, -0.02044677734375, -0.3369140625, -0.265380859375, 0.982421875, -0.599609375, 0.329345703125, -0.438232421875, 0.29541015625, 0.9287109375, -0.568359375, -0.334228515625, -0.89208984375, -0.7666015625, -1.42578125, 0.63232421875, -0.356201171875, 0.2435302734375, -0.6591796875, -0.63330078125, 1.0791015625, -0.76318359375, 0.360595703125, 1.087890625, 0.044647216796875, 0.3310546875, -0.358154296875, 0.6806640625, 0.468017578125, -0.63427734375, 0.2386474609375, 0.36962890625, -0.65673828125, -0.17138671875, -0.58984375, -0.984375, -0.56494140625, 0.339111328125, 1.029296875, -0.061126708984375, 0.58740234375, -0.458740234375, -1.1845703125, -0.3154296875, 0.68994140625, 0.1820068359375, 0.32763671875, 1.05859375, 0.2010498046875, -0.164306640625, 0.29541015625, -0.5947265625, -0.24560546875, -0.307373046875, 1.2314453125, -0.34912109375, -0.59521484375, 0.9609375, 0.7861328125, -1.0634765625, -1.0166015625, -0.1463623046875, 0.00023627281188964844, 0.005588531494140625, -0.927734375, -0.0391845703125, 0.453857421875, -0.46533203125, 0.1177978515625, 0.2183837890625, -0.0804443359375, 0.302001953125, 0.1707763671875, 0.431640625, -0.2242431640625, 0.301025390625, 1.0419921875, -0.38232421875, -0.73095703125, -0.99560546875, -0.38623046875, -0.322021484375, 0.244873046875, 0.7041015625, -0.252197265625, 0.3603515625, 0.6611328125, -0.031829833984375, 1.060546875, -0.336181640625, -0.253173828125, 0.368896484375, -0.72607421875, -0.6083984375, 0.0830078125, 0.1407470703125, -0.397705078125, 0.7177734375, -0.61181640625, -0.0732421875, 0.26318359375, 0.1318359375, -0.4560546875, -0.98779296875, -0.271240234375, -1.2041015625, -0.405517578125, -0.442138671875, -0.90234375, -0.03778076171875, 0.1763916015625, 0.2288818359375, -0.75048828125, 0.05047607421875, 0.5322265625, -0.356689453125, 0.79296875, -0.6943359375, 0.03387451171875, -0.468994140625, -0.4365234375, -0.63525390625, -0.0704345703125, -0.6083984375, -0.15380859375, -0.5498046875, 0.1776123046875, -0.1763916015625, 0.54443359375, -0.25927734375, 0.64501953125, -0.3857421875, -0.79541015625, 0.27490234375, 0.0640869140625, -0.257080078125, 0.91015625, 0.38525390625, 0.062255859375, 0.51416015625, -0.11370849609375, -0.1461181640625, -0.2186279296875, 0.72314453125, 0.47216796875, -0.2225341796875, -0.314453125, -0.12493896484375, 0.09710693359375, -1.1806640625, 0.5517578125, -0.6181640625, 0.2091064453125, 0.27001953125, -0.38037109375, 0.380615234375, 1.0498046875, -0.62353515625, 0.397705078125, 0.046356201171875, 0.1536865234375, 0.251708984375, 0.2626953125, -0.10498046875, 0.716796875, -0.245361328125, -0.55224609375, -0.11175537109375, 0.26611328125, -0.11907958984375, 0.405029296875, -0.258056640625, -1.146484375, -1.06640625, -0.1409912109375, -0.09918212890625, 0.252685546875, 0.2374267578125, -0.26708984375, 0.03680419921875, 0.1944580078125, -0.935546875, 0.28125, -1.078125, -0.93701171875, 0.75048828125, -0.159423828125, -0.39404296875, 0.191162109375, -0.267822265625, -0.1580810546875, 0.154541015625, 0.355712890625, -0.552734375, 0.440673828125, -0.1490478515625, 0.66259765625, -0.308837890625, -0.165283203125, 0.006343841552734375, 0.6630859375, -0.931640625, -0.405517578125, -0.379638671875, 0.80078125, 0.07781982421875, -0.47265625, -0.599609375, 0.154052734375, 0.209228515625, 0.2108154296875, -0.466796875, 0.1790771484375, -0.06573486328125, 0.76708984375, -1.0205078125, 0.08306884765625, -0.0025768280029296875, 0.25048828125, -0.0219268798828125, -0.39208984375, -0.74560546875, 1.048828125, 0.560546875, 0.10986328125, 0.64794921875, 0.0293731689453125, 0.51513671875, -0.02899169921875, 0.016082763671875, -0.293701171875, 0.716796875, 0.7626953125, 0.7080078125, -0.1663818359375, 0.40869140625, 0.83447265625, 0.2408447265625, -0.205078125, 0.403076171875, 0.03448486328125, -0.1141357421875, 0.321044921875, -0.259033203125, -0.252197265625, -0.09686279296875, -0.4033203125, 0.52685546875, -0.55859375, -0.0143280029296875, -0.3134765625, -0.7685546875, 0.7939453125, -0.439208984375, -0.222412109375, 0.33935546875, -0.1912841796875, 0.375244140625, 0.50390625, -0.251220703125, -0.319091796875, 1.1435546875, 0.81591796875, 0.5107421875, 0.75, 0.447509765625, 0.39111328125, -0.59521484375, 0.29736328125, 0.1729736328125, -0.071044921875, 0.0007457733154296875, -0.65185546875, -1.2900390625, 0.5927734375, -0.18115234375, -0.145263671875, 0.33203125, -0.7373046875, 0.260986328125, -0.5478515625, 1.1416015625, -0.52587890625, 0.2464599609375, 0.2841796875, -0.5576171875, -0.63623046875, 0.69921875, -0.234375, 0.27294921875, 0.1395263671875, 0.91259765625, 0.08599853515625, 1.7294921875, 0.73779296875, -0.1624755859375, 0.051300048828125, 0.599609375, -0.25244140625, -0.322021484375, -0.56591796875, -0.36328125, -0.0284271240234375, -0.33984375, -0.7607421875, -0.1580810546875, 0.7490234375, 0.2264404296875, -0.89208984375, -0.40234375, 0.27294921875, -0.9970703125, 0.533203125, 0.1990966796875, 0.421875, 0.27783203125, -0.1806640625, -0.298095703125, -0.63525390625, 0.41064453125, -0.65234375, 0.318603515625, -0.5263671875, -0.239501953125, -0.69580078125, -0.5556640625, -0.3681640625, -0.0897216796875, -0.5322265625, -0.72314453125, 0.638671875, 0.26806640625, 0.45751953125, 0.446044921875, -0.349609375, 0.278564453125, 0.8076171875, 0.970703125, -0.29248046875, 1.138671875, 0.331298828125, -0.0124969482421875, 0.09442138671875, -0.359619140625, 0.388671875, 0.006683349609375, 0.30615234375, -0.58544921875, -0.1334228515625, -0.9990234375, -1.029296875, 0.301025390625, 0.439697265625, 0.25146484375, -0.86083984375, -1.3193359375, -0.274658203125, -1.0869140625, -0.32861328125, -0.7236328125, 0.81298828125, -0.63134765625, -0.03070068359375, 0.0865478515625, -1.0048828125, 4.23046875, 0.83056640625, 0.52001953125, 0.2666015625, 0.262451171875, 0.86474609375, 0.393798828125, -0.42919921875, -0.266357421875, -0.53125, 0.5791015625, -0.54248046875, 0.05499267578125, 1.0517578125, 0.5185546875, 0.38427734375, -0.323486328125, -0.161865234375, 0.2305908203125, -0.9658203125, -0.8447265625, 0.34619140625, 0.167236328125, 0.402587890625, 0.2071533203125, 0.416259765625, 1.0234375, -0.65771484375, -0.3525390625, -0.77490234375, 0.2462158203125, -0.351806640625, 0.96875, 0.25732421875, -0.0723876953125, 0.77783203125, -0.035675048828125, -0.53369140625, -0.0013265609741210938, 0.257080078125, -0.1396484375, 0.2305908203125, 0.61181640625, -0.646484375, -0.45703125, 0.6826171875, -0.5869140625, 0.61181640625, 0.443359375, -1.0478515625, 1.041015625, -0.11724853515625, 0.57958984375, -0.74658203125, -0.625, 0.3037109375, 0.1668701171875, 0.07000732421875, -0.3583984375, 0.56103515625, 0.54736328125, 0.662109375, -0.1490478515625, 0.716796875, -1.03515625, 0.450439453125, -0.09197998046875, 0.50244140625, -0.469970703125, 0.04473876953125, -0.421142578125, -0.358642578125, -0.339111328125, -0.6611328125, 0.55322265625, 0.08001708984375, -0.329833984375, 0.79150390625, 0.30908203125, -0.716796875, 0.1864013671875, -0.423828125, -0.07745361328125, -0.42529296875, 0.7021484375, 1.146484375, -0.485107421875, 0.051544189453125, -0.2266845703125, 0.58984375, 0.58447265625, 0.83056640625, -0.0977783203125, -0.6474609375, -0.51416015625 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Submitted Solution: ``` from sys import stdin tt = int(input()) for loop in range(tt): n = int(input()) a = input() b = input() ans = [] x = 0 for i in range(n-1,-1,-1): if x == 0 and a[i] != b[i]: x ^= 1 ans.append(i+1) elif x == 1 and a[i] == b[i]: x ^= 1 ans.append(i+1) print (len(ans),*ans) ``` No
105,450
[ 0.2313232421875, -0.31787109375, -0.12066650390625, 0.03607177734375, -0.58251953125, -0.60205078125, -0.09283447265625, -0.1060791015625, 0.037017822265625, 1.0498046875, 0.8037109375, -0.272216796875, 0.2149658203125, -0.9921875, -0.5654296875, 0.1834716796875, -0.2802734375, -0.70556640625, -0.236572265625, -0.57421875, -0.07647705078125, -0.17822265625, -1.345703125, 0.07904052734375, -0.479248046875, 0.71337890625, 0.43359375, -0.1470947265625, 0.89453125, 0.93603515625, -0.482421875, -0.5380859375, 0.75048828125, -0.89794921875, -0.350830078125, -0.425048828125, 0.697265625, -0.775390625, -0.243896484375, -0.44580078125, 0.395751953125, -0.2386474609375, 0.24267578125, -0.78466796875, -1.330078125, 0.049560546875, -0.2734375, -0.327880859375, -0.2406005859375, -0.34130859375, 0.03515625, -0.265380859375, 0.548828125, -0.07806396484375, 0.1416015625, 0.311767578125, 0.22216796875, -0.462646484375, -0.476318359375, 0.0830078125, 0.0271148681640625, 0.1256103515625, 0.16650390625, -0.75, 0.15576171875, 0.441162109375, -0.2015380859375, -0.380859375, -0.287109375, -0.81201171875, -0.278564453125, -0.0833740234375, -0.70166015625, -0.2203369140625, -0.10595703125, 0.1878662109375, 0.2100830078125, -0.0528564453125, -1.0556640625, 0.8701171875, -0.438232421875, 1.0693359375, 0.2435302734375, 0.18115234375, -0.55908203125, -0.458251953125, 0.11431884765625, 0.19384765625, 0.1806640625, -0.08880615234375, -0.298828125, 0.447998046875, -0.5947265625, -0.03204345703125, 0.402587890625, 0.65185546875, -0.341796875, 0.30908203125, 0.375732421875, 0.040435791015625, 0.6875, 1.0048828125, -0.263671875, 1.3271484375, -0.50732421875, -0.2003173828125, -0.035308837890625, 0.005298614501953125, -0.12127685546875, -0.04229736328125, -0.02093505859375, -0.31884765625, 0.7041015625, 0.34228515625, -0.3583984375, 0.71142578125, -0.06829833984375, 0.5234375, -0.87548828125, 0.296875, 0.6591796875, -0.2449951171875, 0.75244140625, -0.326171875, 0.0022296905517578125, -0.277587890625, -0.443603515625, 1.0126953125, -0.443603515625, -0.55224609375, 0.2288818359375, -0.0999755859375, -0.35009765625, 0.299072265625, -0.1019287109375, 0.677734375, -0.216064453125, 0.330078125, 0.646484375, -0.41064453125, 0.77392578125, -0.14111328125, -0.142822265625, 1.8525390625, 0.42431640625, 0.006198883056640625, 0.7802734375, 0.4541015625, -0.342529296875, 0.576171875, -0.935546875, 0.423828125, 0.064697265625, 0.214599609375, -0.2431640625, -0.0273895263671875, -0.37646484375, 0.475830078125, 0.233642578125, 0.1478271484375, -0.095947265625, 0.353515625, -0.058349609375, 0.857421875, -0.20361328125, 0.97412109375, -0.374755859375, -0.419677734375, -0.2734375, -0.51611328125, 0.31591796875, -0.228271484375, -0.256103515625, 0.70947265625, 0.6181640625, 1.12109375, 1.3271484375, -0.43310546875, 0.205810546875, 0.353759765625, -0.72607421875, 0.08990478515625, 0.63330078125, 0.94677734375, -0.12548828125, 0.28857421875, -0.0260162353515625, -0.291748046875, -0.38037109375, -0.791015625, -0.0230255126953125, 0.8330078125, -0.70556640625, 0.255615234375, 0.0205078125, 0.1834716796875, -0.7939453125, -0.2154541015625, -0.10772705078125, -0.80517578125, -0.427490234375, 0.483154296875, -0.28125, 0.580078125, -0.70654296875, -0.6357421875, 0.587890625, 1.2421875, -0.2017822265625, 0.477294921875, 0.45947265625, 0.2479248046875, -0.29248046875, 0.2095947265625, 0.2364501953125, -0.2237548828125, -0.463623046875, 0.95849609375, 0.35546875, -0.0755615234375, -0.060028076171875, 0.76171875, 0.49267578125, 0.3896484375, -0.430908203125, -0.00917816162109375, 0.487548828125, 1.3525390625, 0.088623046875, 0.75146484375, 0.208984375, 0.7626953125, 0.60302734375, 0.76953125, 0.39794921875, 0.126220703125, 0.91259765625, 0.76513671875, -0.142333984375, 0.4638671875, 0.388671875, 0.458984375, 0.29052734375, 0.6376953125, 0.2783203125, 0.1524658203125, 0.127685546875, -0.045654296875, -0.53125, 0.28759765625, -0.476318359375, 0.80029296875, -0.130859375, 0.352294921875, -0.310546875, -0.4775390625, 0.442626953125, 0.81884765625, -0.8564453125, -0.419677734375, 0.2005615234375, -0.016876220703125, 0.1234130859375, -0.141845703125, 0.37060546875, 0.2296142578125, 0.420654296875, 0.483642578125, -0.2490234375, -0.1297607421875, -1.0126953125, -0.87744140625, -0.9541015625, -0.52734375, -0.92431640625, -0.0131072998046875, -0.0140838623046875, -0.8173828125, 0.255859375, -0.625, -0.1304931640625, 0.254638671875, -0.67724609375, 0.73828125, -0.260986328125, 0.284423828125, -1.2666015625, 0.82080078125, 0.375244140625, 1.255859375, -0.73681640625, 0.204345703125, 0.0706787109375, -0.72119140625, 0.02783203125, -0.006366729736328125, 0.332275390625, 0.08929443359375, -0.625, -0.666015625, -0.7138671875, -0.146484375, -0.2919921875, 0.1483154296875, -0.51953125, 0.8896484375, 0.70166015625, -0.7470703125, 0.7236328125, 0.86865234375, -0.64892578125, 0.59716796875, 0.402099609375, 0.338623046875, -0.7099609375, 1.5361328125, 0.4423828125, 0.407470703125, -0.5009765625, -0.487060546875, -0.15966796875, -0.04290771484375, 0.184814453125, -0.5068359375, -0.5615234375, 0.5810546875, -0.0941162109375, -1.005859375, 0.3076171875, -0.974609375, -0.4951171875, -0.159423828125, -0.93505859375, 1.34375, 1.0771484375, 0.019683837890625, -0.0369873046875, -0.293212890625, -0.12841796875, 0.52978515625, 0.5615234375, -0.357666015625, -0.02264404296875, 0.89208984375, 0.262939453125, 0.1966552734375, 0.213134765625, -0.62646484375, -0.040924072265625, -0.19580078125, 0.33544921875, 0.57861328125, 0.1649169921875, 0.47802734375, 0.2154541015625, 0.5390625, -1.2890625, -0.1690673828125, -0.333740234375, 0.5888671875, 0.5400390625, 0.314697265625, 0.164306640625, -0.306884765625, -0.77685546875, -0.990234375, 0.11773681640625, 0.03692626953125, 0.76611328125, -0.57861328125, 0.681640625, -0.02069091796875, -0.47705078125, 0.7373046875, -0.693359375, 0.136474609375, 0.99169921875, -0.47509765625, 0.71826171875, -1.09375, 0.396484375, -0.00927734375, -0.2489013671875, 0.289306640625, 0.33447265625, 0.54443359375, -0.461181640625, -0.36328125, -0.6552734375, 0.046051025390625, 0.055328369140625, -0.40478515625, -0.054595947265625, -0.3125, -0.43505859375, -0.88818359375, 0.39404296875, 0.6796875, 0.89892578125, 0.04718017578125, 0.57666015625, 0.297607421875, 0.435302734375, 0.6484375, -0.060089111328125, 0.265380859375, -0.91845703125, 0.8583984375, 0.248779296875, -0.200927734375, -0.52099609375, -0.2242431640625, -0.1602783203125, 0.06341552734375, -0.24462890625, -0.2298583984375, -0.85986328125, 0.470458984375, -0.13916015625, 0.68115234375, -0.68896484375, -0.0239715576171875, -0.734375, 0.30322265625, 0.541015625, -0.89306640625, 0.4296875, -0.9453125, 0.4755859375, 0.5625, -0.2626953125, -0.3974609375, -0.53955078125, -0.8310546875, -0.80615234375, 0.258056640625, 1.0361328125, -0.2100830078125, 0.486083984375, -1.37890625, 0.416259765625, 0.3701171875, -0.91162109375, 0.044525146484375, -0.1873779296875, 0.389892578125, 0.1961669921875, 0.70947265625, -0.17822265625, -0.325927734375, -0.019561767578125, -1.2138671875, 0.477783203125, -0.65283203125, 0.52099609375, 0.1785888671875, -0.228759765625, 0.08428955078125, 0.41455078125, -0.12030029296875, 0.0587158203125, -0.1805419921875, 0.380859375, -1.0537109375, -0.8056640625, 0.5087890625, -0.12469482421875, -0.348388671875, 1.0234375, 0.0911865234375, -0.1744384765625, 0.1983642578125, 0.434814453125, -0.419189453125, 0.5498046875, -0.3310546875, 0.71923828125, -0.412109375, -0.6103515625, -0.5615234375, -0.273681640625, 0.74560546875, -0.130859375, -0.461669921875, -0.1856689453125, -1.15625, -0.0865478515625, 0.236328125, -0.50244140625, 0.2025146484375, 0.10101318359375, 0.252685546875, -0.23974609375, -0.12347412109375, -0.405029296875, -0.06292724609375, -0.49072265625, -0.6162109375, 0.58154296875, 0.38525390625, 0.60107421875, 0.0936279296875, -0.492431640625, -0.103759765625, 0.20263671875, -0.2008056640625, -0.6318359375, -0.1905517578125, -0.294677734375, -0.319091796875, -0.54052734375, 0.26611328125, -0.110595703125, 0.398193359375, 0.9208984375, -0.02374267578125, 0.46728515625, 0.3740234375, -0.830078125, 1.07421875, 0.300537109375, -0.859375, -0.193115234375, 0.37890625, -0.044677734375, 0.8046875, 0.310546875, -0.80712890625, -0.6064453125, -0.89404296875, 0.420654296875, -0.93505859375, -0.2252197265625, -1.009765625, -0.6435546875, -0.4296875, 0.70556640625, -0.198486328125, -0.65576171875, 0.147216796875, -1.0009765625, -0.0177001953125, -1.0146484375, -0.2293701171875, -0.767578125, -0.64990234375, -0.326171875, 1.033203125, -0.05706787109375, -0.032379150390625, 0.279541015625, 0.05706787109375, 0.1009521484375, 0.269775390625, -0.78125, -0.302001953125, 0.05523681640625, -0.004871368408203125, -0.345703125, -0.07684326171875, -0.8408203125, 0.66650390625, -0.84716796875, 0.2113037109375, -0.20654296875, -0.039825439453125, -0.30029296875, -0.2017822265625, 0.9814453125, -0.62255859375, 0.33544921875, -0.413818359375, 0.3798828125, 0.9736328125, -0.5322265625, -0.321044921875, -0.8896484375, -0.75439453125, -1.3583984375, 0.6083984375, -0.3466796875, 0.2578125, -0.677734375, -0.630859375, 1.001953125, -0.8212890625, 0.360107421875, 1.0810546875, 0.0269622802734375, 0.295166015625, -0.38037109375, 0.76123046875, 0.48193359375, -0.65087890625, 0.265380859375, 0.380126953125, -0.6337890625, -0.138427734375, -0.59716796875, -0.9638671875, -0.56396484375, 0.30029296875, 1.0654296875, -0.0552978515625, 0.5693359375, -0.50048828125, -1.1650390625, -0.310546875, 0.73876953125, 0.19970703125, 0.335693359375, 1.0693359375, 0.191162109375, -0.11407470703125, 0.325439453125, -0.62255859375, -0.175537109375, -0.30419921875, 1.22265625, -0.382080078125, -0.5947265625, 0.95068359375, 0.76025390625, -1.1064453125, -1.0537109375, -0.1424560546875, -0.03228759765625, -0.01140594482421875, -0.8994140625, -0.081787109375, 0.4970703125, -0.4140625, 0.070068359375, 0.278564453125, -0.07177734375, 0.344482421875, 0.1407470703125, 0.42724609375, -0.21142578125, 0.353515625, 1.0576171875, -0.33984375, -0.69140625, -0.99169921875, -0.375244140625, -0.358154296875, 0.2371826171875, 0.71630859375, -0.2509765625, 0.396484375, 0.662109375, -0.054534912109375, 1.087890625, -0.332275390625, -0.267333984375, 0.37646484375, -0.75927734375, -0.6484375, 0.109130859375, 0.1275634765625, -0.335205078125, 0.7607421875, -0.6298828125, -0.115478515625, 0.26953125, 0.185546875, -0.4169921875, -0.94482421875, -0.2269287109375, -1.1474609375, -0.416748046875, -0.4013671875, -0.869140625, -0.0012979507446289062, 0.1624755859375, 0.18603515625, -0.76513671875, 0.050323486328125, 0.46875, -0.3466796875, 0.83251953125, -0.716796875, 0.05841064453125, -0.47119140625, -0.40283203125, -0.640625, -0.07135009765625, -0.67578125, -0.189453125, -0.5146484375, 0.1513671875, -0.1485595703125, 0.4775390625, -0.2431640625, 0.6455078125, -0.4052734375, -0.80224609375, 0.30078125, 0.11309814453125, -0.2734375, 0.92578125, 0.40478515625, 0.060699462890625, 0.525390625, -0.07769775390625, -0.130859375, -0.1746826171875, 0.716796875, 0.51513671875, -0.1746826171875, -0.274658203125, -0.15576171875, 0.0909423828125, -1.12890625, 0.60498046875, -0.6103515625, 0.206298828125, 0.294189453125, -0.386962890625, 0.35546875, 1.041015625, -0.5380859375, 0.35791015625, 0.043426513671875, 0.15478515625, 0.235595703125, 0.21826171875, -0.11871337890625, 0.73681640625, -0.2388916015625, -0.53271484375, -0.069580078125, 0.326171875, -0.06927490234375, 0.406005859375, -0.276123046875, -1.1318359375, -1.123046875, -0.1337890625, -0.099609375, 0.177734375, 0.237548828125, -0.3046875, 0.035675048828125, 0.183837890625, -0.921875, 0.257568359375, -1.025390625, -0.9619140625, 0.7080078125, -0.1923828125, -0.406494140625, 0.145751953125, -0.301513671875, -0.15087890625, 0.1436767578125, 0.318115234375, -0.50439453125, 0.436767578125, -0.1361083984375, 0.6650390625, -0.322509765625, -0.128662109375, -0.00018990039825439453, 0.61865234375, -0.8876953125, -0.36669921875, -0.322021484375, 0.81494140625, 0.07525634765625, -0.52099609375, -0.60595703125, 0.1807861328125, 0.2071533203125, 0.2230224609375, -0.4833984375, 0.2340087890625, -0.03765869140625, 0.73583984375, -1.0283203125, 0.0750732421875, -0.0032711029052734375, 0.27783203125, -0.0797119140625, -0.37646484375, -0.77294921875, 1.041015625, 0.5263671875, 0.1571044921875, 0.6455078125, 0.02569580078125, 0.51953125, -0.01556396484375, 0.025726318359375, -0.324462890625, 0.646484375, 0.76220703125, 0.716796875, -0.1668701171875, 0.4130859375, 0.84130859375, 0.197509765625, -0.2430419921875, 0.330810546875, -0.00806427001953125, -0.1395263671875, 0.323974609375, -0.25634765625, -0.25634765625, -0.07470703125, -0.425048828125, 0.5556640625, -0.60546875, 0.02056884765625, -0.328857421875, -0.77880859375, 0.8232421875, -0.44091796875, -0.2105712890625, 0.37255859375, -0.18798828125, 0.343017578125, 0.53759765625, -0.192138671875, -0.330322265625, 1.13671875, 0.80029296875, 0.56640625, 0.7109375, 0.47998046875, 0.427734375, -0.54296875, 0.33984375, 0.1468505859375, -0.05816650390625, -0.00888824462890625, -0.61279296875, -1.3037109375, 0.57373046875, -0.1942138671875, -0.139892578125, 0.330078125, -0.68603515625, 0.267822265625, -0.55224609375, 1.1572265625, -0.50390625, 0.177001953125, 0.27880859375, -0.59912109375, -0.65576171875, 0.6875, -0.2049560546875, 0.26806640625, 0.1558837890625, 0.9111328125, 0.054046630859375, 1.751953125, 0.734375, -0.1922607421875, 0.052978515625, 0.60009765625, -0.266845703125, -0.311767578125, -0.58642578125, -0.309326171875, 0.013519287109375, -0.359375, -0.74267578125, -0.112548828125, 0.720703125, 0.2322998046875, -0.84912109375, -0.41259765625, 0.265869140625, -0.97216796875, 0.56982421875, 0.1912841796875, 0.477783203125, 0.2099609375, -0.216552734375, -0.274658203125, -0.67529296875, 0.351318359375, -0.6298828125, 0.3359375, -0.52685546875, -0.256103515625, -0.6796875, -0.52099609375, -0.355712890625, -0.06158447265625, -0.4970703125, -0.69921875, 0.64990234375, 0.222412109375, 0.444580078125, 0.443115234375, -0.346435546875, 0.3076171875, 0.76171875, 0.96728515625, -0.2919921875, 1.1474609375, 0.27197265625, -0.0728759765625, 0.08734130859375, -0.35009765625, 0.3974609375, -0.0246734619140625, 0.2724609375, -0.64013671875, -0.1258544921875, -0.9951171875, -1.041015625, 0.291259765625, 0.459228515625, 0.2548828125, -0.8291015625, -1.3046875, -0.2314453125, -1.1123046875, -0.3056640625, -0.732421875, 0.7412109375, -0.60546875, -0.038787841796875, 0.11212158203125, -1.001953125, 4.24609375, 0.833984375, 0.53271484375, 0.1954345703125, 0.243896484375, 0.8564453125, 0.330322265625, -0.445556640625, -0.273193359375, -0.5361328125, 0.59375, -0.5849609375, 0.025360107421875, 1.0302734375, 0.56494140625, 0.421142578125, -0.3125, -0.18212890625, 0.253173828125, -0.9716796875, -0.7958984375, 0.329345703125, 0.1148681640625, 0.361328125, 0.1961669921875, 0.447998046875, 0.978515625, -0.69580078125, -0.303955078125, -0.76171875, 0.24951171875, -0.3076171875, 0.96142578125, 0.195068359375, -0.0782470703125, 0.8232421875, -0.09375, -0.50830078125, 0.01454925537109375, 0.2177734375, -0.13818359375, 0.2191162109375, 0.58642578125, -0.66357421875, -0.4501953125, 0.73046875, -0.56591796875, 0.60107421875, 0.45751953125, -1.0400390625, 1.03125, -0.11376953125, 0.55126953125, -0.77734375, -0.599609375, 0.32861328125, 0.1497802734375, 0.059814453125, -0.36181640625, 0.5556640625, 0.55712890625, 0.66845703125, -0.0982666015625, 0.716796875, -1.0390625, 0.47412109375, -0.08453369140625, 0.5927734375, -0.473388671875, 0.004817962646484375, -0.449462890625, -0.34814453125, -0.314453125, -0.63037109375, 0.6064453125, 0.10467529296875, -0.314453125, 0.78759765625, 0.331787109375, -0.71142578125, 0.1881103515625, -0.413330078125, -0.07647705078125, -0.4580078125, 0.69921875, 1.1767578125, -0.46728515625, 0.09368896484375, -0.23095703125, 0.60888671875, 0.56494140625, 0.88427734375, -0.08233642578125, -0.640625, -0.54736328125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Submitted Solution: ``` for _ in range(int(input())): n=int(input()) s=input() t=input() ans=0 A=[] for i in range(n-1,-1,-1): if ans%2==1 and t[i]!=s[i]: continue elif ans%2==0 and t[i]==s[i]: continue else: ans+=1 A.append(i+1) t=s print(ans,end=" ") for i in A: print(i,end=" ") print() ``` No
105,451
[ 0.25830078125, -0.380615234375, -0.14697265625, 0.08056640625, -0.5380859375, -0.60107421875, -0.016265869140625, -0.114013671875, 0.06341552734375, 1.0712890625, 0.8232421875, -0.25927734375, 0.194091796875, -1.02734375, -0.55810546875, 0.2159423828125, -0.304443359375, -0.708984375, -0.2147216796875, -0.5244140625, -0.0767822265625, -0.208251953125, -1.36328125, 0.039398193359375, -0.4755859375, 0.7744140625, 0.401123046875, -0.1304931640625, 0.83544921875, 0.974609375, -0.4716796875, -0.496337890625, 0.79248046875, -0.85986328125, -0.3701171875, -0.4013671875, 0.6708984375, -0.7607421875, -0.2056884765625, -0.39990234375, 0.4208984375, -0.2276611328125, 0.27099609375, -0.71435546875, -1.3818359375, 0.0606689453125, -0.25732421875, -0.33935546875, -0.215087890625, -0.3955078125, 0.04302978515625, -0.286376953125, 0.60888671875, -0.07373046875, 0.1480712890625, 0.303955078125, 0.2880859375, -0.467529296875, -0.50244140625, 0.0943603515625, -0.01345062255859375, 0.141357421875, 0.1904296875, -0.76123046875, 0.11614990234375, 0.384521484375, -0.190673828125, -0.4130859375, -0.26708984375, -0.81103515625, -0.293212890625, -0.10919189453125, -0.68701171875, -0.1417236328125, -0.09271240234375, 0.2008056640625, 0.1317138671875, -0.1026611328125, -1.064453125, 0.86962890625, -0.431396484375, 1.01171875, 0.2822265625, 0.200439453125, -0.57080078125, -0.4267578125, 0.1326904296875, 0.20849609375, 0.2210693359375, -0.09014892578125, -0.306396484375, 0.455078125, -0.57373046875, -0.03411865234375, 0.440185546875, 0.619140625, -0.374267578125, 0.32568359375, 0.4248046875, 0.0231170654296875, 0.751953125, 0.97802734375, -0.2183837890625, 1.3427734375, -0.53271484375, -0.19970703125, -0.060943603515625, 0.00574493408203125, -0.117919921875, -0.07879638671875, -0.05328369140625, -0.362060546875, 0.701171875, 0.26416015625, -0.3271484375, 0.703125, -0.07745361328125, 0.5478515625, -0.83154296875, 0.3193359375, 0.65771484375, -0.2230224609375, 0.8212890625, -0.2685546875, 0.035003662109375, -0.291259765625, -0.47802734375, 0.99267578125, -0.51171875, -0.4951171875, 0.2227783203125, -0.07733154296875, -0.400634765625, 0.31982421875, -0.13916015625, 0.595703125, -0.1600341796875, 0.389892578125, 0.68310546875, -0.40625, 0.8193359375, -0.139892578125, -0.12396240234375, 1.8037109375, 0.414306640625, -0.049591064453125, 0.80712890625, 0.466064453125, -0.372802734375, 0.55712890625, -0.97509765625, 0.42724609375, 0.08526611328125, 0.1907958984375, -0.255615234375, 0.00484466552734375, -0.3759765625, 0.42529296875, 0.2083740234375, 0.11517333984375, -0.09112548828125, 0.284912109375, -0.07415771484375, 0.83935546875, -0.1844482421875, 0.9521484375, -0.421875, -0.390869140625, -0.2357177734375, -0.5224609375, 0.27880859375, -0.202392578125, -0.2724609375, 0.73193359375, 0.6015625, 1.15234375, 1.2783203125, -0.454833984375, 0.25048828125, 0.321044921875, -0.666015625, 0.064697265625, 0.63037109375, 0.90478515625, -0.2149658203125, 0.2607421875, -0.067626953125, -0.27685546875, -0.346435546875, -0.75732421875, -0.0654296875, 0.82861328125, -0.703125, 0.271728515625, 0.0860595703125, 0.220458984375, -0.8017578125, -0.166259765625, -0.12322998046875, -0.85107421875, -0.410400390625, 0.4775390625, -0.28515625, 0.5791015625, -0.73388671875, -0.66552734375, 0.5224609375, 1.1943359375, -0.2298583984375, 0.4765625, 0.41357421875, 0.2462158203125, -0.28076171875, 0.232666015625, 0.24609375, -0.203125, -0.470458984375, 0.98486328125, 0.29296875, -0.022216796875, -0.08184814453125, 0.685546875, 0.477783203125, 0.43408203125, -0.380615234375, -0.00836944580078125, 0.431640625, 1.333984375, 0.057861328125, 0.78369140625, 0.2320556640625, 0.79736328125, 0.64208984375, 0.7958984375, 0.425537109375, 0.1522216796875, 0.86181640625, 0.7666015625, -0.095947265625, 0.402099609375, 0.344482421875, 0.480224609375, 0.3955078125, 0.6279296875, 0.24072265625, 0.243896484375, 0.118408203125, -0.059326171875, -0.485107421875, 0.322021484375, -0.4716796875, 0.7802734375, -0.1529541015625, 0.410888671875, -0.30517578125, -0.411865234375, 0.397705078125, 0.82666015625, -0.81298828125, -0.444580078125, 0.206787109375, 0.028045654296875, 0.1480712890625, -0.13818359375, 0.375244140625, 0.26708984375, 0.478759765625, 0.48974609375, -0.26123046875, -0.1591796875, -1.0537109375, -0.8798828125, -0.986328125, -0.498291015625, -0.88671875, 0.0275115966796875, 0.061065673828125, -0.80126953125, 0.312744140625, -0.6396484375, -0.159912109375, 0.276123046875, -0.72216796875, 0.76025390625, -0.251220703125, 0.30322265625, -1.2412109375, 0.787109375, 0.39794921875, 1.150390625, -0.76318359375, 0.1807861328125, 0.11065673828125, -0.7275390625, 0.0244598388671875, 0.069091796875, 0.353759765625, 0.0596923828125, -0.7119140625, -0.64697265625, -0.666015625, -0.1488037109375, -0.30419921875, 0.107666015625, -0.57275390625, 0.912109375, 0.740234375, -0.759765625, 0.6953125, 0.82568359375, -0.67236328125, 0.619140625, 0.447265625, 0.392333984375, -0.69189453125, 1.51171875, 0.46826171875, 0.432861328125, -0.48388671875, -0.4658203125, -0.2047119140625, -0.0919189453125, 0.161865234375, -0.49560546875, -0.5966796875, 0.54833984375, -0.1517333984375, -1.0625, 0.3310546875, -0.9423828125, -0.51611328125, -0.1964111328125, -0.8994140625, 1.302734375, 1.068359375, -0.01532745361328125, -0.01004791259765625, -0.307861328125, -0.106689453125, 0.53564453125, 0.5205078125, -0.30810546875, -0.00269317626953125, 0.8642578125, 0.28857421875, 0.2344970703125, 0.1876220703125, -0.58447265625, -0.06976318359375, -0.164794921875, 0.3193359375, 0.6044921875, 0.13330078125, 0.451416015625, 0.2064208984375, 0.611328125, -1.2177734375, -0.179443359375, -0.391845703125, 0.60546875, 0.50537109375, 0.399169921875, 0.166748046875, -0.35400390625, -0.79052734375, -1.0498046875, 0.1290283203125, 0.025360107421875, 0.7421875, -0.62255859375, 0.69970703125, 0.00518035888671875, -0.51025390625, 0.72265625, -0.6708984375, 0.1719970703125, 0.96142578125, -0.4697265625, 0.76611328125, -1.0712890625, 0.4248046875, -0.01280975341796875, -0.20556640625, 0.2939453125, 0.36328125, 0.53515625, -0.4443359375, -0.36181640625, -0.56396484375, 0.07177734375, 0.0220489501953125, -0.35693359375, -0.04644775390625, -0.364013671875, -0.420166015625, -0.89892578125, 0.440185546875, 0.69287109375, 0.91455078125, 0.05413818359375, 0.57275390625, 0.314453125, 0.371826171875, 0.63232421875, -0.0225830078125, 0.2344970703125, -0.91552734375, 0.83251953125, 0.256103515625, -0.2178955078125, -0.483642578125, -0.2279052734375, -0.191650390625, 0.01812744140625, -0.2257080078125, -0.2333984375, -0.88525390625, 0.4853515625, -0.1573486328125, 0.759765625, -0.619140625, -0.058349609375, -0.69873046875, 0.344970703125, 0.53759765625, -0.908203125, 0.4765625, -0.9140625, 0.478515625, 0.55029296875, -0.2666015625, -0.426513671875, -0.58544921875, -0.896484375, -0.767578125, 0.2279052734375, 1.005859375, -0.26123046875, 0.5205078125, -1.3994140625, 0.323974609375, 0.36474609375, -0.89990234375, 0.063232421875, -0.2020263671875, 0.392822265625, 0.192626953125, 0.7392578125, -0.2418212890625, -0.303466796875, -0.00872039794921875, -1.234375, 0.429931640625, -0.646484375, 0.521484375, 0.1446533203125, -0.210205078125, 0.1260986328125, 0.3798828125, -0.09930419921875, 0.0938720703125, -0.234619140625, 0.371337890625, -1.060546875, -0.75146484375, 0.50146484375, -0.0738525390625, -0.3701171875, 0.98779296875, 0.07427978515625, -0.1876220703125, 0.1600341796875, 0.35107421875, -0.443359375, 0.54296875, -0.24658203125, 0.76416015625, -0.49755859375, -0.56640625, -0.50390625, -0.33154296875, 0.73095703125, -0.257080078125, -0.43310546875, -0.219970703125, -1.15625, -0.11968994140625, 0.244140625, -0.5322265625, 0.228759765625, 0.119873046875, 0.239013671875, -0.26220703125, -0.09381103515625, -0.3798828125, -0.10968017578125, -0.456787109375, -0.62744140625, 0.6357421875, 0.37939453125, 0.55810546875, 0.142578125, -0.459716796875, -0.06292724609375, 0.1976318359375, -0.1322021484375, -0.66943359375, -0.2489013671875, -0.2734375, -0.306640625, -0.54541015625, 0.28125, -0.137451171875, 0.419189453125, 0.974609375, -0.02606201171875, 0.54541015625, 0.33056640625, -0.83154296875, 1.07421875, 0.29931640625, -0.81396484375, -0.287841796875, 0.4140625, -0.009979248046875, 0.81396484375, 0.317138671875, -0.76220703125, -0.623046875, -0.87841796875, 0.401123046875, -0.9140625, -0.2232666015625, -0.97705078125, -0.60888671875, -0.423828125, 0.66845703125, -0.1671142578125, -0.65185546875, 0.19580078125, -0.994140625, 0.052154541015625, -0.9580078125, -0.2259521484375, -0.7607421875, -0.59375, -0.337890625, 0.96484375, -0.03265380859375, -0.0311737060546875, 0.317626953125, 0.03424072265625, 0.096435546875, 0.209228515625, -0.7724609375, -0.2880859375, 0.0587158203125, -0.048980712890625, -0.31640625, -0.033782958984375, -0.7880859375, 0.66845703125, -0.81494140625, 0.189453125, -0.11962890625, -0.0226898193359375, -0.32958984375, -0.261962890625, 0.98779296875, -0.55224609375, 0.34326171875, -0.4345703125, 0.31201171875, 0.9140625, -0.60791015625, -0.3134765625, -0.88037109375, -0.74609375, -1.4169921875, 0.630859375, -0.34912109375, 0.228759765625, -0.63916015625, -0.6474609375, 1.09375, -0.75634765625, 0.34521484375, 1.08984375, 0.0447998046875, 0.351318359375, -0.3681640625, 0.66064453125, 0.46826171875, -0.60009765625, 0.25537109375, 0.34716796875, -0.63232421875, -0.1463623046875, -0.5517578125, -0.99267578125, -0.5556640625, 0.365234375, 1.0556640625, -0.05279541015625, 0.556640625, -0.4736328125, -1.201171875, -0.303955078125, 0.662109375, 0.1748046875, 0.297119140625, 1.0654296875, 0.2030029296875, -0.153564453125, 0.301025390625, -0.5751953125, -0.2308349609375, -0.295654296875, 1.2236328125, -0.37158203125, -0.58837890625, 0.9599609375, 0.7919921875, -1.0537109375, -0.96630859375, -0.1441650390625, -0.02972412109375, 0.04888916015625, -0.91259765625, -0.06463623046875, 0.478271484375, -0.450927734375, 0.12457275390625, 0.234619140625, -0.09295654296875, 0.3115234375, 0.165283203125, 0.428955078125, -0.236328125, 0.31494140625, 1.041015625, -0.371826171875, -0.740234375, -0.9990234375, -0.402099609375, -0.32568359375, 0.25537109375, 0.70654296875, -0.2548828125, 0.3271484375, 0.66162109375, -0.023651123046875, 0.98583984375, -0.30908203125, -0.2464599609375, 0.368408203125, -0.72119140625, -0.60595703125, 0.10687255859375, 0.141357421875, -0.37060546875, 0.7080078125, -0.59423828125, -0.0780029296875, 0.287353515625, 0.124755859375, -0.449462890625, -1.017578125, -0.2578125, -1.1796875, -0.441162109375, -0.40283203125, -0.89111328125, -0.0153656005859375, 0.176025390625, 0.23779296875, -0.7568359375, 0.053192138671875, 0.533203125, -0.361572265625, 0.79345703125, -0.6748046875, 0.03570556640625, -0.436279296875, -0.42578125, -0.63330078125, -0.08258056640625, -0.5927734375, -0.1368408203125, -0.58642578125, 0.1859130859375, -0.1705322265625, 0.52392578125, -0.28173828125, 0.681640625, -0.3583984375, -0.7919921875, 0.28466796875, 0.049468994140625, -0.27294921875, 0.9130859375, 0.362060546875, 0.049835205078125, 0.496826171875, -0.0689697265625, -0.146484375, -0.1802978515625, 0.73095703125, 0.494140625, -0.2327880859375, -0.298095703125, -0.11181640625, 0.08251953125, -1.1728515625, 0.56201171875, -0.64013671875, 0.2099609375, 0.2763671875, -0.351318359375, 0.360107421875, 1.0458984375, -0.60986328125, 0.392333984375, 0.035797119140625, 0.1427001953125, 0.257080078125, 0.258056640625, -0.11553955078125, 0.76416015625, -0.2261962890625, -0.56982421875, -0.09417724609375, 0.272705078125, -0.1317138671875, 0.38818359375, -0.249755859375, -1.1455078125, -1.0712890625, -0.1446533203125, -0.1392822265625, 0.253662109375, 0.2476806640625, -0.29150390625, 0.037872314453125, 0.1873779296875, -0.939453125, 0.26416015625, -1.080078125, -0.91943359375, 0.740234375, -0.1622314453125, -0.368408203125, 0.174072265625, -0.2880859375, -0.1524658203125, 0.148193359375, 0.343017578125, -0.59130859375, 0.451416015625, -0.161865234375, 0.6328125, -0.284912109375, -0.1976318359375, 0.01136016845703125, 0.68115234375, -0.921875, -0.3916015625, -0.391357421875, 0.79736328125, 0.08941650390625, -0.421142578125, -0.56591796875, 0.1175537109375, 0.21875, 0.22314453125, -0.4794921875, 0.14599609375, -0.057342529296875, 0.74365234375, -1.0478515625, 0.07830810546875, -0.023223876953125, 0.255126953125, -0.053741455078125, -0.384765625, -0.76953125, 1.0380859375, 0.541015625, 0.105224609375, 0.642578125, 0.0010137557983398438, 0.494140625, -0.05731201171875, 0.002849578857421875, -0.273681640625, 0.71337890625, 0.7626953125, 0.6982421875, -0.1275634765625, 0.388916015625, 0.80615234375, 0.2286376953125, -0.20068359375, 0.380615234375, 0.03326416015625, -0.1038818359375, 0.30029296875, -0.272705078125, -0.27001953125, -0.09814453125, -0.3837890625, 0.57373046875, -0.55810546875, -0.032501220703125, -0.287109375, -0.7705078125, 0.7900390625, -0.448486328125, -0.238525390625, 0.357177734375, -0.2171630859375, 0.36181640625, 0.50390625, -0.2529296875, -0.33544921875, 1.1611328125, 0.794921875, 0.50146484375, 0.73974609375, 0.442626953125, 0.404296875, -0.56787109375, 0.305908203125, 0.1639404296875, -0.07257080078125, -0.0217437744140625, -0.6787109375, -1.2666015625, 0.58447265625, -0.192138671875, -0.1568603515625, 0.34130859375, -0.6953125, 0.2281494140625, -0.5439453125, 1.123046875, -0.5390625, 0.263671875, 0.2978515625, -0.572265625, -0.642578125, 0.70361328125, -0.19677734375, 0.268310546875, 0.147216796875, 0.91650390625, 0.05023193359375, 1.7099609375, 0.7099609375, -0.1502685546875, 0.0341796875, 0.5927734375, -0.25732421875, -0.308837890625, -0.61279296875, -0.354736328125, -0.053741455078125, -0.340087890625, -0.720703125, -0.1832275390625, 0.72412109375, 0.218994140625, -0.896484375, -0.43115234375, 0.269775390625, -0.98388671875, 0.5400390625, 0.1658935546875, 0.399169921875, 0.293212890625, -0.20947265625, -0.30419921875, -0.6396484375, 0.40869140625, -0.6357421875, 0.314208984375, -0.54736328125, -0.2496337890625, -0.673828125, -0.541015625, -0.35400390625, -0.08135986328125, -0.5439453125, -0.7099609375, 0.61767578125, 0.270751953125, 0.48974609375, 0.436279296875, -0.357177734375, 0.26025390625, 0.82470703125, 0.97998046875, -0.283935546875, 1.1220703125, 0.31103515625, -0.01342010498046875, 0.10845947265625, -0.373779296875, 0.380615234375, 0.022857666015625, 0.322509765625, -0.56787109375, -0.136962890625, -0.97998046875, -1.017578125, 0.300048828125, 0.44091796875, 0.2244873046875, -0.84716796875, -1.3212890625, -0.2666015625, -1.0908203125, -0.30078125, -0.720703125, 0.810546875, -0.65869140625, -0.0193328857421875, 0.0643310546875, -0.97998046875, 4.265625, 0.8427734375, 0.482421875, 0.29833984375, 0.230712890625, 0.8486328125, 0.39794921875, -0.456298828125, -0.250732421875, -0.50390625, 0.58154296875, -0.55322265625, 0.0714111328125, 1.041015625, 0.5380859375, 0.381103515625, -0.320556640625, -0.166015625, 0.234130859375, -0.96435546875, -0.830078125, 0.373291015625, 0.1923828125, 0.378173828125, 0.2100830078125, 0.38134765625, 1.0009765625, -0.67724609375, -0.304443359375, -0.7841796875, 0.228271484375, -0.341796875, 0.97900390625, 0.279052734375, -0.05267333984375, 0.78076171875, -0.04095458984375, -0.51416015625, 0.03021240234375, 0.2332763671875, -0.1484375, 0.1973876953125, 0.59033203125, -0.6240234375, -0.4365234375, 0.65869140625, -0.59619140625, 0.58984375, 0.426513671875, -1.033203125, 1.0107421875, -0.1505126953125, 0.54345703125, -0.7314453125, -0.6611328125, 0.3154296875, 0.1728515625, 0.052520751953125, -0.356201171875, 0.6005859375, 0.53857421875, 0.64013671875, -0.1339111328125, 0.72314453125, -1.015625, 0.457763671875, -0.0792236328125, 0.51904296875, -0.434814453125, 0.035400390625, -0.405517578125, -0.3544921875, -0.348876953125, -0.671875, 0.568359375, 0.0782470703125, -0.339111328125, 0.810546875, 0.29296875, -0.74072265625, 0.2027587890625, -0.41162109375, -0.046234130859375, -0.401123046875, 0.70458984375, 1.158203125, -0.481201171875, 0.075439453125, -0.228271484375, 0.61474609375, 0.537109375, 0.830078125, -0.104736328125, -0.65283203125, -0.50830078125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. This is the hard version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved. There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix. For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001. Your task is to transform the string a into b in at most 2n operations. It can be proved that it is always possible. Input The first line contains a single integer t (1≀ t≀ 1000) β€” the number of test cases. Next 3t lines contain descriptions of test cases. The first line of each test case contains a single integer n (1≀ n≀ 10^5) β€” the length of the binary strings. The next two lines contain two binary strings a and b of length n. It is guaranteed that the sum of n across all test cases does not exceed 10^5. Output For each test case, output an integer k (0≀ k≀ 2n), followed by k integers p_1,…,p_k (1≀ p_i≀ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation. Example Input 5 2 01 10 5 01011 11100 2 01 01 10 0110011011 1000110100 1 0 1 Output 3 1 2 1 6 5 2 5 3 1 2 0 9 4 1 2 10 4 1 2 1 5 1 1 Note In the first test case, we have 01β†’ 11β†’ 00β†’ 10. In the second test case, we have 01011β†’ 00101β†’ 11101β†’ 01000β†’ 10100β†’ 00100β†’ 11100. In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged. Submitted Solution: ``` z,zz=input,lambda:list(map(int,z().split())) fast=lambda:stdin.readline().strip() zzz=lambda:[int(i) for i in fast().split()] szz,graph,mod,szzz=lambda:sorted(zz()),{},10**9+7,lambda:sorted(zzz()) from string import * from re import * from collections import * from queue import * from sys import * from collections import * from math import * from heapq import * from itertools import * from bisect import * from collections import Counter as cc from math import factorial as f from bisect import bisect as bs from bisect import bisect_left as bsl from itertools import accumulate as ac def lcd(xnum1,xnum2):return (xnum1*xnum2//gcd(xnum1,xnum2)) def prime(x): p=ceil(x**.5)+1 for i in range(2,p): if (x%i==0 and x!=2) or x==0:return 0 return 1 def dfs(u,visit,graph): visit[u]=1 for i in graph[u]: if not visit[i]: dfs(i,visit,graph) ###########################---Test-Case---################################# """ //If you Know me , Then you probably don't know me """ ###########################---START-CODING---############################## num=int(z()) for _ in range( num ): n=int(z()) T1=fast() T2=fast() ans=[] k=1 for i in T1: if i=='1': ans.append(k) k+=1 k=1 for i in T2: if i=='1': ans.append(k) k+=1 print(len(ans),*ans) ``` No
105,452
[ 0.271728515625, -0.346923828125, -0.1143798828125, 0.0311279296875, -0.60498046875, -0.60595703125, -0.07440185546875, -0.09918212890625, 0.044586181640625, 1.0625, 0.79931640625, -0.228515625, 0.22998046875, -0.98974609375, -0.578125, 0.2017822265625, -0.27294921875, -0.6796875, -0.1876220703125, -0.50732421875, -0.08770751953125, -0.211181640625, -1.3525390625, 0.06634521484375, -0.4775390625, 0.767578125, 0.36669921875, -0.158447265625, 0.8447265625, 0.9404296875, -0.548828125, -0.46044921875, 0.8134765625, -0.8583984375, -0.345703125, -0.390380859375, 0.68310546875, -0.74267578125, -0.24560546875, -0.45751953125, 0.40869140625, -0.259033203125, 0.241455078125, -0.67236328125, -1.43359375, 0.049774169921875, -0.264892578125, -0.327392578125, -0.2357177734375, -0.391845703125, 0.0701904296875, -0.26806640625, 0.6669921875, -0.04718017578125, 0.16015625, 0.27734375, 0.30029296875, -0.410400390625, -0.5302734375, 0.10406494140625, 0.006618499755859375, 0.1600341796875, 0.2105712890625, -0.7578125, 0.11126708984375, 0.393310546875, -0.214599609375, -0.38720703125, -0.319091796875, -0.78955078125, -0.30078125, -0.08795166015625, -0.6806640625, -0.153076171875, -0.1309814453125, 0.1885986328125, 0.1593017578125, -0.11517333984375, -1.0732421875, 0.8466796875, -0.4873046875, 0.99951171875, 0.2366943359375, 0.1619873046875, -0.486328125, -0.414306640625, 0.16943359375, 0.206787109375, 0.22314453125, -0.05084228515625, -0.343505859375, 0.458740234375, -0.6123046875, -0.03436279296875, 0.47119140625, 0.64501953125, -0.366943359375, 0.38720703125, 0.44140625, 0.0911865234375, 0.765625, 1.0048828125, -0.2159423828125, 1.375, -0.52978515625, -0.2158203125, -0.07867431640625, 0.0137939453125, -0.12481689453125, -0.056671142578125, -0.041168212890625, -0.37060546875, 0.63916015625, 0.30322265625, -0.330810546875, 0.701171875, -0.09326171875, 0.552734375, -0.85546875, 0.2239990234375, 0.64306640625, -0.2337646484375, 0.80029296875, -0.267578125, 0.01248931884765625, -0.3134765625, -0.490478515625, 1.0263671875, -0.471923828125, -0.52783203125, 0.251708984375, -0.061737060546875, -0.348876953125, 0.300537109375, -0.2069091796875, 0.59423828125, -0.17333984375, 0.364501953125, 0.64599609375, -0.39501953125, 0.822265625, -0.1395263671875, -0.1114501953125, 1.80859375, 0.43701171875, -0.063720703125, 0.76904296875, 0.41650390625, -0.377685546875, 0.57958984375, -0.96875, 0.408447265625, 0.0665283203125, 0.18408203125, -0.28125, 0.007709503173828125, -0.405029296875, 0.440185546875, 0.23291015625, 0.0872802734375, -0.0230255126953125, 0.286376953125, -0.080078125, 0.85595703125, -0.202392578125, 0.97900390625, -0.420654296875, -0.389892578125, -0.2437744140625, -0.513671875, 0.28515625, -0.20849609375, -0.220458984375, 0.7216796875, 0.6240234375, 1.1630859375, 1.2568359375, -0.4716796875, 0.26220703125, 0.349609375, -0.7109375, 0.0494384765625, 0.61962890625, 0.916015625, -0.19775390625, 0.2236328125, -0.08343505859375, -0.2474365234375, -0.314208984375, -0.70556640625, -0.036224365234375, 0.82080078125, -0.71142578125, 0.2335205078125, 0.08148193359375, 0.1939697265625, -0.82861328125, -0.1534423828125, -0.13720703125, -0.8232421875, -0.413818359375, 0.50341796875, -0.341796875, 0.58642578125, -0.71923828125, -0.62646484375, 0.52001953125, 1.1845703125, -0.18603515625, 0.50634765625, 0.466552734375, 0.31103515625, -0.2119140625, 0.2119140625, 0.265625, -0.21533203125, -0.490234375, 0.94677734375, 0.2822265625, -0.03167724609375, -0.0987548828125, 0.72216796875, 0.47021484375, 0.43212890625, -0.4326171875, -0.0062255859375, 0.459228515625, 1.380859375, 0.08197021484375, 0.7734375, 0.25439453125, 0.80126953125, 0.658203125, 0.85498046875, 0.458740234375, 0.1722412109375, 0.8837890625, 0.74951171875, -0.08502197265625, 0.374755859375, 0.352294921875, 0.44775390625, 0.391845703125, 0.63623046875, 0.265380859375, 0.25927734375, 0.1171875, -0.0443115234375, -0.521484375, 0.297607421875, -0.433837890625, 0.71630859375, -0.12017822265625, 0.40576171875, -0.30322265625, -0.4287109375, 0.373779296875, 0.828125, -0.8154296875, -0.439453125, 0.180419921875, 0.0491943359375, 0.184326171875, -0.150390625, 0.39892578125, 0.23681640625, 0.465576171875, 0.4501953125, -0.261474609375, -0.1466064453125, -1.033203125, -0.92138671875, -0.98486328125, -0.53857421875, -0.92529296875, 0.0628662109375, 0.036590576171875, -0.8076171875, 0.32177734375, -0.62158203125, -0.181884765625, 0.21923828125, -0.68505859375, 0.73779296875, -0.2181396484375, 0.330810546875, -1.283203125, 0.7607421875, 0.381591796875, 1.1337890625, -0.779296875, 0.2403564453125, 0.0657958984375, -0.72119140625, 0.019744873046875, 0.058197021484375, 0.342041015625, 0.09429931640625, -0.72802734375, -0.58984375, -0.67919921875, -0.0899658203125, -0.31298828125, 0.07244873046875, -0.56591796875, 0.962890625, 0.68212890625, -0.744140625, 0.68798828125, 0.884765625, -0.69287109375, 0.67578125, 0.481689453125, 0.372802734375, -0.705078125, 1.4873046875, 0.439453125, 0.403076171875, -0.45947265625, -0.412841796875, -0.21826171875, -0.07769775390625, 0.150146484375, -0.50390625, -0.5751953125, 0.50830078125, -0.1534423828125, -1.0517578125, 0.3486328125, -0.927734375, -0.52685546875, -0.230224609375, -0.8720703125, 1.3369140625, 1.1025390625, -0.09161376953125, -0.0268402099609375, -0.3046875, -0.1318359375, 0.50439453125, 0.49072265625, -0.359619140625, 0.0098876953125, 0.83984375, 0.32763671875, 0.2479248046875, 0.197998046875, -0.60791015625, -0.056884765625, -0.1259765625, 0.3330078125, 0.6064453125, 0.150634765625, 0.42529296875, 0.1802978515625, 0.6337890625, -1.220703125, -0.1927490234375, -0.396484375, 0.611328125, 0.494873046875, 0.419921875, 0.1868896484375, -0.371337890625, -0.80224609375, -1.03515625, 0.1427001953125, 0.0634765625, 0.77880859375, -0.61669921875, 0.69287109375, 0.0028285980224609375, -0.45703125, 0.71142578125, -0.654296875, 0.1712646484375, 0.93994140625, -0.529296875, 0.79052734375, -1.0732421875, 0.38330078125, 0.0292510986328125, -0.186767578125, 0.283203125, 0.33544921875, 0.59423828125, -0.390869140625, -0.371826171875, -0.5615234375, 0.11163330078125, 0.0609130859375, -0.39892578125, -0.078125, -0.348388671875, -0.458984375, -0.9033203125, 0.48681640625, 0.69091796875, 0.94873046875, -0.00408172607421875, 0.599609375, 0.306396484375, 0.384521484375, 0.6298828125, -0.037872314453125, 0.254638671875, -0.912109375, 0.8095703125, 0.267822265625, -0.2484130859375, -0.45068359375, -0.279052734375, -0.1754150390625, -0.006641387939453125, -0.1700439453125, -0.2301025390625, -0.8427734375, 0.51416015625, -0.180908203125, 0.7333984375, -0.669921875, -0.061370849609375, -0.70458984375, 0.31884765625, 0.5400390625, -0.912109375, 0.479248046875, -0.9560546875, 0.474853515625, 0.56884765625, -0.272216796875, -0.38623046875, -0.60302734375, -0.9013671875, -0.76806640625, 0.200927734375, 1.0205078125, -0.259521484375, 0.478515625, -1.3623046875, 0.41064453125, 0.417236328125, -0.9052734375, 0.08428955078125, -0.1688232421875, 0.423828125, 0.17724609375, 0.7578125, -0.248046875, -0.27685546875, -0.059295654296875, -1.2333984375, 0.42041015625, -0.61572265625, 0.56591796875, 0.13134765625, -0.226806640625, 0.10870361328125, 0.406982421875, -0.0762939453125, 0.0538330078125, -0.2197265625, 0.35791015625, -1.07421875, -0.75146484375, 0.492919921875, -0.056182861328125, -0.329345703125, 1.0234375, 0.07122802734375, -0.14697265625, 0.137451171875, 0.41796875, -0.4794921875, 0.54443359375, -0.26611328125, 0.7392578125, -0.436279296875, -0.5703125, -0.474609375, -0.292724609375, 0.72265625, -0.19873046875, -0.44873046875, -0.1907958984375, -1.154296875, -0.076904296875, 0.2353515625, -0.56982421875, 0.242919921875, 0.0780029296875, 0.2496337890625, -0.2607421875, -0.09014892578125, -0.421142578125, -0.1614990234375, -0.45263671875, -0.59521484375, 0.5849609375, 0.375732421875, 0.59423828125, 0.143310546875, -0.4560546875, -0.0811767578125, 0.193115234375, -0.1268310546875, -0.67626953125, -0.2548828125, -0.222412109375, -0.268798828125, -0.54248046875, 0.3173828125, -0.1429443359375, 0.415771484375, 0.99658203125, -0.0340576171875, 0.515625, 0.2978515625, -0.80224609375, 1.0712890625, 0.3466796875, -0.87255859375, -0.280517578125, 0.427734375, -0.0159454345703125, 0.83203125, 0.329833984375, -0.80712890625, -0.6591796875, -0.8759765625, 0.417724609375, -0.9228515625, -0.22509765625, -0.955078125, -0.5908203125, -0.463623046875, 0.6826171875, -0.162353515625, -0.6142578125, 0.1632080078125, -1.03125, 0.0227813720703125, -0.98486328125, -0.2042236328125, -0.75, -0.61474609375, -0.3701171875, 0.96875, 0.002315521240234375, -0.018310546875, 0.315185546875, 0.037261962890625, 0.07952880859375, 0.2078857421875, -0.748046875, -0.289306640625, 0.070068359375, -0.0474853515625, -0.2998046875, -0.061248779296875, -0.76220703125, 0.6748046875, -0.86181640625, 0.212890625, -0.1368408203125, -0.0692138671875, -0.354736328125, -0.228271484375, 1.0263671875, -0.5546875, 0.29150390625, -0.41357421875, 0.27099609375, 0.892578125, -0.6005859375, -0.37890625, -0.85595703125, -0.74658203125, -1.4345703125, 0.61767578125, -0.347412109375, 0.2437744140625, -0.68115234375, -0.65087890625, 1.013671875, -0.701171875, 0.307373046875, 1.0224609375, 0.01033782958984375, 0.336669921875, -0.36865234375, 0.69189453125, 0.450927734375, -0.61669921875, 0.280029296875, 0.374755859375, -0.64697265625, -0.133544921875, -0.5888671875, -1.0048828125, -0.5625, 0.359619140625, 1.037109375, -0.050323486328125, 0.52392578125, -0.486328125, -1.173828125, -0.326904296875, 0.65234375, 0.176025390625, 0.303955078125, 1.0419921875, 0.17724609375, -0.1422119140625, 0.2626953125, -0.595703125, -0.266845703125, -0.331298828125, 1.1884765625, -0.3134765625, -0.58837890625, 0.94384765625, 0.79345703125, -1.0380859375, -1.046875, -0.171630859375, -0.0306854248046875, 0.02496337890625, -0.9150390625, -0.011993408203125, 0.458740234375, -0.45068359375, 0.11737060546875, 0.207275390625, -0.09124755859375, 0.30859375, 0.177978515625, 0.40380859375, -0.26953125, 0.3544921875, 1.0283203125, -0.341796875, -0.73486328125, -0.9619140625, -0.373779296875, -0.35791015625, 0.232421875, 0.64453125, -0.269287109375, 0.335693359375, 0.68017578125, -0.0570068359375, 1.0478515625, -0.361572265625, -0.3095703125, 0.3759765625, -0.72119140625, -0.6103515625, 0.135498046875, 0.1142578125, -0.345703125, 0.69287109375, -0.64208984375, -0.107666015625, 0.2666015625, 0.08673095703125, -0.439453125, -1.005859375, -0.30517578125, -1.228515625, -0.439208984375, -0.4677734375, -0.91845703125, 0.01197052001953125, 0.2060546875, 0.21337890625, -0.71923828125, 0.06951904296875, 0.51904296875, -0.35986328125, 0.80908203125, -0.7216796875, 0.05438232421875, -0.43798828125, -0.438720703125, -0.58740234375, -0.08941650390625, -0.607421875, -0.1717529296875, -0.5595703125, 0.1546630859375, -0.149658203125, 0.53076171875, -0.2744140625, 0.6435546875, -0.34130859375, -0.80419921875, 0.26025390625, 0.057159423828125, -0.264404296875, 0.9140625, 0.3701171875, 0.09576416015625, 0.50146484375, -0.10552978515625, -0.17919921875, -0.1519775390625, 0.74853515625, 0.47900390625, -0.2213134765625, -0.279052734375, -0.07843017578125, 0.0880126953125, -1.2099609375, 0.5458984375, -0.66015625, 0.212890625, 0.2481689453125, -0.35791015625, 0.366943359375, 1.0234375, -0.5888671875, 0.3603515625, 0.07373046875, 0.1927490234375, 0.189453125, 0.2059326171875, -0.118896484375, 0.76611328125, -0.1727294921875, -0.55859375, -0.1053466796875, 0.2578125, -0.14892578125, 0.382568359375, -0.260498046875, -1.1171875, -1.0615234375, -0.1507568359375, -0.10101318359375, 0.2354736328125, 0.25048828125, -0.280517578125, 0.06634521484375, 0.1953125, -0.93408203125, 0.313232421875, -1.0615234375, -0.904296875, 0.6884765625, -0.1436767578125, -0.388671875, 0.187744140625, -0.257568359375, -0.11737060546875, 0.1715087890625, 0.35205078125, -0.53466796875, 0.369873046875, -0.1419677734375, 0.63330078125, -0.285888671875, -0.1900634765625, 0.0015506744384765625, 0.640625, -0.94140625, -0.39697265625, -0.375732421875, 0.787109375, 0.08905029296875, -0.5068359375, -0.5439453125, 0.1328125, 0.1761474609375, 0.200439453125, -0.483154296875, 0.16552734375, -0.034515380859375, 0.72705078125, -1.044921875, 0.09417724609375, 0.02276611328125, 0.2318115234375, -0.05743408203125, -0.398193359375, -0.74853515625, 1.005859375, 0.55419921875, 0.1392822265625, 0.57177734375, 0.0080718994140625, 0.474365234375, -0.057830810546875, -0.03375244140625, -0.2364501953125, 0.72412109375, 0.76171875, 0.7119140625, -0.165283203125, 0.385986328125, 0.8056640625, 0.230224609375, -0.220703125, 0.372314453125, 0.055572509765625, -0.06951904296875, 0.280029296875, -0.25634765625, -0.2095947265625, -0.10400390625, -0.4189453125, 0.53955078125, -0.541015625, -0.058929443359375, -0.296142578125, -0.77685546875, 0.83544921875, -0.439697265625, -0.227294921875, 0.342041015625, -0.15185546875, 0.371826171875, 0.53955078125, -0.251708984375, -0.309326171875, 1.15234375, 0.8232421875, 0.5048828125, 0.76416015625, 0.442626953125, 0.4208984375, -0.58740234375, 0.2958984375, 0.189697265625, -0.0667724609375, 0.007709503173828125, -0.64501953125, -1.244140625, 0.5673828125, -0.1890869140625, -0.1331787109375, 0.293701171875, -0.7294921875, 0.251220703125, -0.57421875, 1.107421875, -0.51513671875, 0.217529296875, 0.2327880859375, -0.529296875, -0.6220703125, 0.6904296875, -0.19580078125, 0.250732421875, 0.1776123046875, 0.86572265625, 0.08135986328125, 1.6962890625, 0.66455078125, -0.1451416015625, 0.06689453125, 0.5732421875, -0.26025390625, -0.28076171875, -0.560546875, -0.359375, -0.0634765625, -0.359130859375, -0.716796875, -0.1630859375, 0.75244140625, 0.217041015625, -0.93798828125, -0.43505859375, 0.285400390625, -0.94970703125, 0.56884765625, 0.1900634765625, 0.451904296875, 0.26025390625, -0.1915283203125, -0.256103515625, -0.66552734375, 0.410888671875, -0.7060546875, 0.2880859375, -0.51904296875, -0.2376708984375, -0.712890625, -0.56982421875, -0.323974609375, -0.063232421875, -0.5322265625, -0.7158203125, 0.625, 0.26611328125, 0.45263671875, 0.437744140625, -0.33740234375, 0.283935546875, 0.81689453125, 1.0234375, -0.320556640625, 1.14453125, 0.345947265625, -0.007038116455078125, 0.1484375, -0.367919921875, 0.426513671875, 0.01120758056640625, 0.351806640625, -0.52978515625, -0.1478271484375, -0.97216796875, -1.0478515625, 0.26171875, 0.40673828125, 0.2252197265625, -0.8232421875, -1.3251953125, -0.265869140625, -1.064453125, -0.33984375, -0.734375, 0.7841796875, -0.66162109375, -0.0504150390625, 0.11614990234375, -0.99853515625, 4.265625, 0.8203125, 0.462890625, 0.234130859375, 0.196533203125, 0.8955078125, 0.376220703125, -0.429443359375, -0.268310546875, -0.51708984375, 0.55126953125, -0.54931640625, 0.07135009765625, 1.0498046875, 0.50927734375, 0.392333984375, -0.323974609375, -0.142333984375, 0.2249755859375, -0.96728515625, -0.85205078125, 0.352783203125, 0.2119140625, 0.36328125, 0.23388671875, 0.4091796875, 1.017578125, -0.67236328125, -0.313232421875, -0.755859375, 0.2105712890625, -0.297119140625, 0.955078125, 0.26318359375, -0.10626220703125, 0.791015625, 0.0149993896484375, -0.5595703125, -0.040435791015625, 0.2705078125, -0.12359619140625, 0.2252197265625, 0.599609375, -0.65576171875, -0.42333984375, 0.689453125, -0.619140625, 0.60302734375, 0.412841796875, -1.046875, 1.0126953125, -0.091064453125, 0.55859375, -0.70166015625, -0.611328125, 0.3037109375, 0.162109375, 0.0821533203125, -0.327880859375, 0.54638671875, 0.59716796875, 0.6533203125, -0.16796875, 0.689453125, -1.02734375, 0.476318359375, -0.09039306640625, 0.53564453125, -0.43994140625, 0.06512451171875, -0.3974609375, -0.3857421875, -0.358642578125, -0.69384765625, 0.595703125, 0.12109375, -0.343017578125, 0.8212890625, 0.271728515625, -0.7216796875, 0.2122802734375, -0.406982421875, -0.057769775390625, -0.448486328125, 0.73828125, 1.1142578125, -0.467041015625, 0.059173583984375, -0.1917724609375, 0.62353515625, 0.572265625, 0.830078125, -0.10174560546875, -0.640625, -0.47607421875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Kawashiro Nitori is a girl who loves competitive programming. One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem. Given a string s and a parameter k, you need to check if there exist k+1 non-empty strings a_1,a_2...,a_{k+1}, such that $$$s=a_1+a_2+… +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+…+R(a_{1}).$$$ Here + represents concatenation. We define R(x) as a reversed string x. For example R(abcd) = dcba. Note that in the formula above the part R(a_{k+1}) is intentionally skipped. Input The input consists of multiple test cases. The first line contains a single integer t (1≀ t≀ 100) β€” the number of test cases. The description of the test cases follows. The first line of each test case description contains two integers n, k (1≀ n≀ 100, 0≀ k≀ ⌊ n/2 βŒ‹) β€” the length of the string s and the parameter k. The second line of each test case description contains a single string s of length n, consisting of lowercase English letters. Output For each test case, print "YES" (without quotes), if it is possible to find a_1,a_2,…,a_{k+1}, and "NO" (without quotes) otherwise. You can print letters in any case (upper or lower). Example Input 7 5 1 qwqwq 2 1 ab 3 1 ioi 4 2 icpc 22 0 dokidokiliteratureclub 19 8 imteamshanghaialice 6 3 aaaaaa Output YES NO YES NO YES NO NO Note In the first test case, one possible solution is a_1=qw and a_2=q. In the third test case, one possible solution is a_1=i and a_2=o. In the fifth test case, one possible solution is a_1=dokidokiliteratureclub. Tags: brute force, constructive algorithms, greedy, strings Correct Solution: ``` def solve(): n,k=map(int,input().split()) s=input() if k>=n/2: return "NO" for i in range(k): if s[i]!=s[-(i+1)]: return "NO" else: return "YES" for _ in range(int(input())): print(solve()) ```
105,478
[ 0.1292724609375, -0.415283203125, 0.1676025390625, 0.28759765625, -0.326416015625, -0.8193359375, -0.06884765625, 0.2174072265625, 0.068359375, 0.943359375, 0.9248046875, -0.09100341796875, 0.1741943359375, -0.7724609375, -0.41455078125, -0.08685302734375, -0.373046875, -0.71484375, -0.491943359375, 0.064453125, 0.259521484375, 0.0955810546875, -1.3671875, -0.06011962890625, -0.38720703125, 0.919921875, 0.430908203125, 0.07000732421875, 1.1767578125, 0.75341796875, -0.431640625, -0.405029296875, 0.6796875, -0.84912109375, -0.315673828125, -0.5546875, 0.642578125, -0.75634765625, -0.49462890625, -0.6015625, 0.2841796875, -0.442626953125, 0.289306640625, -0.822265625, -1.1923828125, 0.038848876953125, -0.7353515625, -0.32470703125, -0.370361328125, -0.6162109375, 0.25927734375, -0.251953125, 0.55712890625, 0.0167999267578125, -0.0799560546875, 0.0662841796875, -0.03289794921875, -0.140380859375, -0.609375, 0.0305023193359375, -0.037933349609375, -0.10675048828125, -0.1412353515625, -0.56201171875, -0.4658203125, -0.1138916015625, -0.1663818359375, -0.39404296875, -0.02117919921875, -1.044921875, -0.279296875, 0.214599609375, -1.015625, -0.39892578125, -0.08331298828125, -0.1756591796875, 0.60009765625, -0.2044677734375, -0.6123046875, 1.255859375, 0.0181884765625, 1.0927734375, 0.470947265625, 0.2379150390625, -0.63525390625, -0.87939453125, -0.033843994140625, 0.234130859375, 0.3125, 0.02728271484375, -0.232666015625, 0.5556640625, -0.55322265625, 0.01424407958984375, 0.384765625, 0.525390625, -0.06396484375, 0.1717529296875, 0.271240234375, -0.07354736328125, 0.98486328125, 0.90966796875, -0.57421875, 0.8662109375, -0.638671875, 0.0968017578125, 0.133056640625, 0.04229736328125, 0.08416748046875, -0.268310546875, -0.05047607421875, -0.361328125, 0.5458984375, 0.1376953125, -0.5625, 0.77197265625, -0.081787109375, 0.176025390625, -0.74609375, 0.1837158203125, 0.52197265625, 0.2044677734375, 0.54833984375, -0.0180511474609375, -0.018402099609375, -0.287841796875, -0.413330078125, 1.15625, -0.7744140625, 0.007465362548828125, 0.48193359375, -0.03607177734375, -0.24853515625, 0.360107421875, -0.1241455078125, 0.333740234375, -0.328369140625, 0.45703125, 0.59375, -0.59033203125, 0.79248046875, -0.1572265625, -0.134033203125, 1.404296875, 0.358642578125, 0.12744140625, 0.51953125, 0.477783203125, -0.95751953125, 0.479248046875, -0.99462890625, 0.35595703125, -0.0299530029296875, 0.2430419921875, -0.20361328125, 0.1143798828125, 0.018463134765625, 0.34375, 0.342041015625, 0.335693359375, -0.2403564453125, 0.28759765625, -0.4892578125, 0.86181640625, -0.5107421875, 0.97998046875, -0.2142333984375, -0.345458984375, -0.2403564453125, -0.67431640625, 0.25830078125, -0.1832275390625, -0.2305908203125, 0.85986328125, 0.53271484375, 0.91796875, 1.16015625, -0.174072265625, 0.53271484375, 0.42626953125, -0.345947265625, 0.3466796875, 0.447509765625, 0.51806640625, -0.0516357421875, 0.29931640625, 0.287353515625, -0.396728515625, -1.01953125, -0.470458984375, -0.16650390625, 0.5126953125, -0.88720703125, 0.137451171875, -0.02972412109375, 0.262939453125, -0.68603515625, -0.1683349609375, -0.1395263671875, -1.095703125, -0.16650390625, 0.4501953125, -0.284423828125, 0.430908203125, -0.419189453125, -0.463623046875, 0.497314453125, 1.21875, -0.1046142578125, 0.1741943359375, 0.107177734375, 0.428955078125, -0.41748046875, 0.236083984375, 0.10784912109375, -0.345947265625, -0.383544921875, 0.80078125, -0.359375, 0.1566162109375, -0.03289794921875, 0.83642578125, 0.25048828125, 0.64306640625, -0.150390625, -0.16162109375, 0.335205078125, 1.2080078125, -0.0089569091796875, 0.444091796875, 0.2587890625, 0.896484375, 0.41796875, 0.83056640625, 0.37646484375, 0.10247802734375, 0.66650390625, 1.2392578125, 0.54248046875, 0.453125, 0.1982421875, 0.2763671875, 0.45556640625, 0.429443359375, 0.294921875, 0.4130859375, -0.20068359375, -0.20849609375, -0.325927734375, 0.0031642913818359375, -0.1038818359375, 0.90478515625, 0.46337890625, 0.0887451171875, -0.64306640625, -0.45654296875, -0.1451416015625, 0.7392578125, -0.7548828125, -0.55810546875, 0.256103515625, 0.1485595703125, -0.053070068359375, -0.39111328125, 0.178955078125, 0.25537109375, 0.41259765625, 0.270263671875, -0.27294921875, -0.321044921875, -0.890625, -0.6845703125, -0.99755859375, -0.26708984375, -0.5673828125, 0.08837890625, 0.60986328125, -0.90625, -0.10394287109375, -0.1287841796875, -0.1517333984375, -0.0894775390625, -0.955078125, 0.59423828125, -0.1282958984375, 0.6328125, -0.900390625, 0.6806640625, 0.064697265625, 0.95068359375, -0.33935546875, -0.1981201171875, -0.075439453125, -0.490478515625, 0.1480712890625, 0.269287109375, 0.078369140625, -0.31689453125, -0.662109375, -0.61572265625, -0.310302734375, -0.1571044921875, 0.006450653076171875, 0.2406005859375, -0.242919921875, 0.76318359375, 0.224853515625, -0.299072265625, 0.459228515625, 1.060546875, -0.9521484375, 0.3134765625, 0.355224609375, 0.08770751953125, -0.82568359375, 1.3759765625, 0.4482421875, 0.0208740234375, -0.375244140625, -0.51904296875, -0.638671875, 0.0701904296875, 0.31103515625, -0.57666015625, -0.378662109375, 0.63671875, -0.160888671875, -1.0087890625, 0.158203125, -0.84326171875, -0.72705078125, 0.0232086181640625, -0.25341796875, 1.119140625, 0.7646484375, 0.1636962890625, -0.37158203125, -0.4306640625, -0.158203125, 0.407470703125, 0.341552734375, -0.262939453125, -0.443359375, 0.84912109375, 0.09344482421875, -0.0062103271484375, 0.006412506103515625, -0.32763671875, -0.337890625, -0.0504150390625, -0.0347900390625, 0.390625, 0.14501953125, 0.279296875, 0.456787109375, 0.66455078125, -1.0283203125, -0.2978515625, -0.22021484375, 0.7998046875, 0.30810546875, 0.6904296875, 0.2900390625, -0.572265625, -0.578125, -0.88330078125, 0.169677734375, 0.45556640625, 0.3740234375, -0.41259765625, 0.8525390625, 0.2939453125, -0.0716552734375, 0.56884765625, -0.68994140625, -0.38525390625, 1.384765625, -0.04266357421875, 0.92138671875, -0.58935546875, 0.203125, 0.09991455078125, 0.07781982421875, 0.5439453125, 0.185302734375, 0.5498046875, -0.410888671875, -0.673828125, -0.1768798828125, -0.002010345458984375, -0.0157318115234375, -0.391845703125, 0.2359619140625, -0.364013671875, -0.78466796875, -0.78173828125, 0.445068359375, 0.62109375, 0.8095703125, 0.305908203125, 0.55126953125, 0.485107421875, 0.56005859375, 0.62109375, -0.20263671875, 0.076904296875, -0.487060546875, 0.5185546875, -0.116943359375, -0.396240234375, -0.43994140625, 0.005977630615234375, -0.316650390625, -0.11419677734375, -0.118896484375, -0.474853515625, -0.466064453125, 0.32177734375, -0.291748046875, 0.41796875, -0.339111328125, -0.3388671875, -0.228271484375, 0.387939453125, 0.236083984375, -1.037109375, 0.38818359375, -0.8779296875, 0.80419921875, 0.29638671875, -0.341064453125, -0.615234375, -0.280029296875, -0.7568359375, -0.87548828125, -0.0863037109375, 0.61669921875, -0.11590576171875, 0.5078125, -1.421875, 0.428466796875, 0.29052734375, -0.282470703125, 0.25048828125, -0.252685546875, 0.1932373046875, 0.192626953125, 0.603515625, -0.5009765625, -0.71044921875, 0.056854248046875, -1.1337890625, 0.210205078125, -0.76318359375, 0.5673828125, 0.1153564453125, -0.29443359375, 0.052520751953125, 0.54541015625, -0.25927734375, 0.183349609375, -0.30615234375, 0.26220703125, -0.99658203125, -0.475830078125, 0.482177734375, 0.046661376953125, -0.44189453125, 1.064453125, -0.2425537109375, -0.366943359375, -0.049468994140625, 0.73681640625, -0.39111328125, 0.30859375, -0.521484375, 0.8974609375, -0.220947265625, -0.6689453125, -0.1671142578125, -0.859375, 1.0087890625, 0.041839599609375, -0.87451171875, -0.261474609375, -0.951171875, -0.044403076171875, 0.0576171875, -0.177490234375, 0.3857421875, -0.0024127960205078125, -0.019378662109375, -0.04754638671875, 0.020172119140625, -0.67041015625, 0.033355712890625, -0.5341796875, -0.447265625, -0.048187255859375, 0.7109375, 0.6962890625, 0.1552734375, -0.28125, 0.1434326171875, 0.1854248046875, -0.04205322265625, -0.467041015625, 0.1402587890625, -0.414306640625, -0.096923828125, -0.0010395050048828125, 0.759765625, 0.005908966064453125, 0.7421875, 0.74951171875, 0.260986328125, 0.7177734375, 0.351806640625, -0.72412109375, 1.09765625, 0.324462890625, -0.89794921875, -0.59326171875, 0.30908203125, -0.1268310546875, 0.64892578125, 0.1715087890625, -0.9404296875, -0.52099609375, -0.5693359375, 0.43896484375, -0.5244140625, -0.2352294921875, -1.158203125, 0.052642822265625, -0.245361328125, 0.2479248046875, 0.0836181640625, -0.261962890625, 0.173583984375, -0.814453125, 0.333251953125, -0.80615234375, -0.352294921875, -0.95654296875, -0.0955810546875, -0.0016775131225585938, 1.0400390625, 0.09014892578125, 0.619140625, -0.07159423828125, -0.20751953125, 0.423583984375, 0.14599609375, -0.93505859375, -0.54248046875, 0.190673828125, -0.0146026611328125, -0.143798828125, -0.1397705078125, -0.71923828125, 0.767578125, -0.72314453125, 0.32470703125, -0.272216796875, -0.353759765625, -0.2247314453125, -0.133056640625, 0.87109375, -0.418701171875, -0.2021484375, -0.2744140625, 0.27001953125, 0.55419921875, -0.387451171875, -0.436279296875, -0.81298828125, -0.1539306640625, -1.16796875, 0.55712890625, -0.55615234375, 0.0897216796875, -0.64501953125, -0.55615234375, 1.10546875, -0.76611328125, 0.41259765625, 1.2177734375, 0.34521484375, 0.439697265625, -0.92431640625, 0.57470703125, 0.6953125, -0.625, -0.419677734375, -0.039703369140625, -0.94140625, 0.282958984375, -0.11279296875, -0.92333984375, -0.7666015625, 0.13232421875, 1.1904296875, -0.30712890625, 0.74072265625, -0.0948486328125, -1.275390625, -0.90576171875, 0.912109375, -0.0653076171875, 0.24755859375, 0.4599609375, -0.12030029296875, -0.21337890625, -0.173583984375, -0.300048828125, -0.120849609375, -0.35498046875, 1.1513671875, -0.2498779296875, -0.7451171875, 0.97119140625, 0.697265625, -0.953125, -0.62646484375, 0.011016845703125, -0.2186279296875, -0.1285400390625, -0.280029296875, -0.1824951171875, 0.6328125, -0.9501953125, 0.2132568359375, 0.64990234375, -0.295654296875, 0.2137451171875, -0.09613037109375, 0.335693359375, -0.6787109375, 0.74658203125, 0.484375, -0.1451416015625, -0.318359375, -0.60400390625, -0.326171875, -0.55419921875, 0.09906005859375, 0.71875, -0.75390625, -0.04791259765625, 0.050811767578125, 0.1219482421875, 0.97998046875, -0.2034912109375, -0.5341796875, 0.342529296875, -0.609375, -0.63720703125, -0.05633544921875, 0.282470703125, -0.035888671875, 0.6845703125, -0.474609375, 0.08172607421875, 0.380126953125, 0.37353515625, -0.11572265625, -0.75732421875, -0.34912109375, -0.71044921875, -0.381103515625, -0.484619140625, -0.5703125, 0.0174407958984375, 0.473388671875, 0.136962890625, -0.5830078125, 0.033843994140625, 0.6328125, -0.177490234375, 0.8701171875, -0.66015625, 0.446044921875, -0.61474609375, -0.2369384765625, -0.2578125, -0.085693359375, -0.52099609375, -0.0120391845703125, -0.89599609375, 0.292724609375, -0.186767578125, 0.736328125, -0.1695556640625, 0.347900390625, -0.235107421875, -0.377685546875, 0.116455078125, -0.2318115234375, -0.371826171875, 0.85107421875, 0.2034912109375, -0.2169189453125, 0.168212890625, -0.68994140625, -0.4404296875, -0.27294921875, 0.424072265625, 0.708984375, -0.334228515625, -0.011810302734375, -0.18798828125, 0.2381591796875, -1.2978515625, 0.3056640625, 0.04779052734375, 0.03826904296875, 0.44482421875, -0.1019287109375, 0.61328125, 1.318359375, -0.50244140625, 0.38916015625, 0.1505126953125, -0.0616455078125, 0.55126953125, 0.418212890625, -0.01541900634765625, 0.306884765625, 0.287109375, -0.365478515625, -0.15478515625, 0.31787109375, 0.18310546875, 0.383056640625, 0.154541015625, -0.89599609375, -1.2451171875, -0.258544921875, 0.00899505615234375, 0.2430419921875, 0.1744384765625, -0.12274169921875, 0.1319580078125, 0.0361328125, -0.300048828125, 0.1820068359375, -1.0361328125, -0.82373046875, 0.27099609375, -0.276611328125, -0.58349609375, -0.2137451171875, -0.354248046875, -0.310302734375, 0.275146484375, 0.74072265625, -0.7744140625, 0.54736328125, -0.0152740478515625, 0.366943359375, 0.05303955078125, -0.755859375, 0.2117919921875, 0.489501953125, -0.76708984375, -0.576171875, 0.253173828125, 1.3251953125, 0.2783203125, -0.279296875, -0.436767578125, 0.37646484375, -0.07354736328125, 0.353515625, -0.5068359375, 0.23974609375, -0.419189453125, 0.251220703125, -0.86865234375, 0.256591796875, -0.305908203125, 0.235595703125, 0.326416015625, -0.64990234375, -0.4736328125, 0.53857421875, 0.55859375, -0.387939453125, 0.54345703125, 0.444580078125, 0.451904296875, 0.1878662109375, -0.07073974609375, -0.1324462890625, 0.54345703125, 0.7119140625, 0.58740234375, -0.154541015625, 0.49755859375, 0.87939453125, 0.019683837890625, -0.248779296875, 0.71240234375, 0.372802734375, -0.288330078125, 0.38427734375, -0.21875, 0.1690673828125, 0.1563720703125, -0.40673828125, 0.375244140625, -0.414306640625, 0.1903076171875, -0.21630859375, -0.5498046875, 0.998046875, -0.2322998046875, -0.1275634765625, -0.142822265625, -0.09197998046875, 0.15087890625, 0.5625, -0.212646484375, -0.1727294921875, 1.1201171875, 0.60009765625, 0.42236328125, 0.67626953125, 0.458251953125, 0.2978515625, -0.8330078125, 0.38427734375, 0.1748046875, -0.0168914794921875, -0.15771484375, -0.326416015625, -1.1376953125, 0.38720703125, -0.3955078125, -0.36376953125, 1.1181640625, -0.70654296875, 0.2044677734375, -0.284912109375, 0.49365234375, -0.6162109375, -0.124267578125, 0.1710205078125, -0.24755859375, -0.12481689453125, 1.03515625, -0.36767578125, 0.03155517578125, 0.351806640625, 0.88720703125, 0.0016193389892578125, 1.4296875, 0.66357421875, -0.2822265625, -0.1624755859375, 0.1468505859375, -0.293701171875, -0.5986328125, -0.315185546875, -0.43017578125, 0.08563232421875, -0.60009765625, -0.74658203125, -0.1756591796875, 0.86376953125, -0.025054931640625, -1.142578125, -0.0025844573974609375, 0.08770751953125, -0.84375, 0.281494140625, -0.01197052001953125, 0.427978515625, 0.1370849609375, -0.163330078125, 0.010498046875, -0.578125, 0.341796875, -0.78564453125, 0.1903076171875, -0.83154296875, -0.72412109375, -0.415283203125, -0.6171875, -0.26611328125, -0.34130859375, -0.041412353515625, -1.107421875, 0.71875, 0.233154296875, 0.2174072265625, 0.525390625, -0.39013671875, 0.12890625, 0.97900390625, 1.1904296875, -0.05841064453125, 0.81103515625, 0.266845703125, -0.09326171875, 0.53515625, -0.47314453125, 0.335205078125, 0.05413818359375, 0.1768798828125, -0.319580078125, 0.321533203125, -0.33056640625, -1.0966796875, 0.2529296875, 0.5927734375, 0.17431640625, -0.3486328125, -0.83544921875, -0.29248046875, -1.1455078125, -0.2091064453125, -0.79150390625, 0.8486328125, -0.564453125, 0.281494140625, -0.164794921875, -1.205078125, 4.42578125, 0.78955078125, 0.91552734375, 0.5009765625, 0.1563720703125, 1.080078125, 0.48193359375, -0.712890625, -0.2958984375, -0.37451171875, 0.65185546875, -0.60400390625, -0.07012939453125, 0.806640625, 0.046783447265625, 0.5009765625, -0.49365234375, 0.472900390625, 0.192626953125, -1.033203125, -0.7822265625, 0.389892578125, 0.07952880859375, 0.62353515625, -0.145263671875, 0.391845703125, 0.5048828125, -0.5439453125, -0.1864013671875, -0.60302734375, 0.264892578125, -0.6083984375, 0.77734375, -0.1566162109375, 0.00003886222839355469, 0.438232421875, -0.11859130859375, -0.85498046875, 0.01427459716796875, 0.128662109375, 0.1695556640625, 0.0284881591796875, 0.6181640625, -0.87255859375, 0.021881103515625, 0.1163330078125, -0.7490234375, 0.52734375, 0.303955078125, -1.375, 0.68701171875, -0.09857177734375, 0.369140625, -0.56201171875, -0.6337890625, 0.027496337890625, 0.11328125, 0.08782958984375, -0.23388671875, 0.1761474609375, 0.403076171875, 0.59619140625, -0.175537109375, 0.541015625, -0.86767578125, 1.01953125, -0.0528564453125, 0.2318115234375, -0.62646484375, -0.295654296875, -0.295166015625, -0.2213134765625, -0.417724609375, -0.053985595703125, 0.53466796875, 0.19189453125, -0.07208251953125, 0.451904296875, 0.13720703125, -0.75732421875, 0.5009765625, -0.1942138671875, -0.354736328125, -0.2310791015625, 0.828125, 1.283203125, -0.751953125, -0.11090087890625, -0.62890625, 0.5654296875, 0.638671875, 0.81884765625, 0.08880615234375, -0.7080078125, -0.29052734375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Kawashiro Nitori is a girl who loves competitive programming. One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem. Given a string s and a parameter k, you need to check if there exist k+1 non-empty strings a_1,a_2...,a_{k+1}, such that $$$s=a_1+a_2+… +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+…+R(a_{1}).$$$ Here + represents concatenation. We define R(x) as a reversed string x. For example R(abcd) = dcba. Note that in the formula above the part R(a_{k+1}) is intentionally skipped. Input The input consists of multiple test cases. The first line contains a single integer t (1≀ t≀ 100) β€” the number of test cases. The description of the test cases follows. The first line of each test case description contains two integers n, k (1≀ n≀ 100, 0≀ k≀ ⌊ n/2 βŒ‹) β€” the length of the string s and the parameter k. The second line of each test case description contains a single string s of length n, consisting of lowercase English letters. Output For each test case, print "YES" (without quotes), if it is possible to find a_1,a_2,…,a_{k+1}, and "NO" (without quotes) otherwise. You can print letters in any case (upper or lower). Example Input 7 5 1 qwqwq 2 1 ab 3 1 ioi 4 2 icpc 22 0 dokidokiliteratureclub 19 8 imteamshanghaialice 6 3 aaaaaa Output YES NO YES NO YES NO NO Note In the first test case, one possible solution is a_1=qw and a_2=q. In the third test case, one possible solution is a_1=i and a_2=o. In the fifth test case, one possible solution is a_1=dokidokiliteratureclub. Tags: brute force, constructive algorithms, greedy, strings Correct Solution: ``` def solve(n, k, s): if k == 0: return "YES" count = 0 if n%2: for i in range(n//2): if s[i] == s[-i-1]: count += 1 else: break if count >= k: return "YES" else: return "NO" else: for i in range(n//2 - 1): if s[i] == s[-i-1]: count += 1 else: break if count>=k: return "YES" else: return "NO" t = int(input()) for _ in range(t): n, k = map(int, input().split()) s = input() print(solve(n, k, s)) ```
105,479
[ 0.1292724609375, -0.415283203125, 0.1676025390625, 0.28759765625, -0.326416015625, -0.8193359375, -0.06884765625, 0.2174072265625, 0.068359375, 0.943359375, 0.9248046875, -0.09100341796875, 0.1741943359375, -0.7724609375, -0.41455078125, -0.08685302734375, -0.373046875, -0.71484375, -0.491943359375, 0.064453125, 0.259521484375, 0.0955810546875, -1.3671875, -0.06011962890625, -0.38720703125, 0.919921875, 0.430908203125, 0.07000732421875, 1.1767578125, 0.75341796875, -0.431640625, -0.405029296875, 0.6796875, -0.84912109375, -0.315673828125, -0.5546875, 0.642578125, -0.75634765625, -0.49462890625, -0.6015625, 0.2841796875, -0.442626953125, 0.289306640625, -0.822265625, -1.1923828125, 0.038848876953125, -0.7353515625, -0.32470703125, -0.370361328125, -0.6162109375, 0.25927734375, -0.251953125, 0.55712890625, 0.0167999267578125, -0.0799560546875, 0.0662841796875, -0.03289794921875, -0.140380859375, -0.609375, 0.0305023193359375, -0.037933349609375, -0.10675048828125, -0.1412353515625, -0.56201171875, -0.4658203125, -0.1138916015625, -0.1663818359375, -0.39404296875, -0.02117919921875, -1.044921875, -0.279296875, 0.214599609375, -1.015625, -0.39892578125, -0.08331298828125, -0.1756591796875, 0.60009765625, -0.2044677734375, -0.6123046875, 1.255859375, 0.0181884765625, 1.0927734375, 0.470947265625, 0.2379150390625, -0.63525390625, -0.87939453125, -0.033843994140625, 0.234130859375, 0.3125, 0.02728271484375, -0.232666015625, 0.5556640625, -0.55322265625, 0.01424407958984375, 0.384765625, 0.525390625, -0.06396484375, 0.1717529296875, 0.271240234375, -0.07354736328125, 0.98486328125, 0.90966796875, -0.57421875, 0.8662109375, -0.638671875, 0.0968017578125, 0.133056640625, 0.04229736328125, 0.08416748046875, -0.268310546875, -0.05047607421875, -0.361328125, 0.5458984375, 0.1376953125, -0.5625, 0.77197265625, -0.081787109375, 0.176025390625, -0.74609375, 0.1837158203125, 0.52197265625, 0.2044677734375, 0.54833984375, -0.0180511474609375, -0.018402099609375, -0.287841796875, -0.413330078125, 1.15625, -0.7744140625, 0.007465362548828125, 0.48193359375, -0.03607177734375, -0.24853515625, 0.360107421875, -0.1241455078125, 0.333740234375, -0.328369140625, 0.45703125, 0.59375, -0.59033203125, 0.79248046875, -0.1572265625, -0.134033203125, 1.404296875, 0.358642578125, 0.12744140625, 0.51953125, 0.477783203125, -0.95751953125, 0.479248046875, -0.99462890625, 0.35595703125, -0.0299530029296875, 0.2430419921875, -0.20361328125, 0.1143798828125, 0.018463134765625, 0.34375, 0.342041015625, 0.335693359375, -0.2403564453125, 0.28759765625, -0.4892578125, 0.86181640625, -0.5107421875, 0.97998046875, -0.2142333984375, -0.345458984375, -0.2403564453125, -0.67431640625, 0.25830078125, -0.1832275390625, -0.2305908203125, 0.85986328125, 0.53271484375, 0.91796875, 1.16015625, -0.174072265625, 0.53271484375, 0.42626953125, -0.345947265625, 0.3466796875, 0.447509765625, 0.51806640625, -0.0516357421875, 0.29931640625, 0.287353515625, -0.396728515625, -1.01953125, -0.470458984375, -0.16650390625, 0.5126953125, -0.88720703125, 0.137451171875, -0.02972412109375, 0.262939453125, -0.68603515625, -0.1683349609375, -0.1395263671875, -1.095703125, -0.16650390625, 0.4501953125, -0.284423828125, 0.430908203125, -0.419189453125, -0.463623046875, 0.497314453125, 1.21875, -0.1046142578125, 0.1741943359375, 0.107177734375, 0.428955078125, -0.41748046875, 0.236083984375, 0.10784912109375, -0.345947265625, -0.383544921875, 0.80078125, -0.359375, 0.1566162109375, -0.03289794921875, 0.83642578125, 0.25048828125, 0.64306640625, -0.150390625, -0.16162109375, 0.335205078125, 1.2080078125, -0.0089569091796875, 0.444091796875, 0.2587890625, 0.896484375, 0.41796875, 0.83056640625, 0.37646484375, 0.10247802734375, 0.66650390625, 1.2392578125, 0.54248046875, 0.453125, 0.1982421875, 0.2763671875, 0.45556640625, 0.429443359375, 0.294921875, 0.4130859375, -0.20068359375, -0.20849609375, -0.325927734375, 0.0031642913818359375, -0.1038818359375, 0.90478515625, 0.46337890625, 0.0887451171875, -0.64306640625, -0.45654296875, -0.1451416015625, 0.7392578125, -0.7548828125, -0.55810546875, 0.256103515625, 0.1485595703125, -0.053070068359375, -0.39111328125, 0.178955078125, 0.25537109375, 0.41259765625, 0.270263671875, -0.27294921875, -0.321044921875, -0.890625, -0.6845703125, -0.99755859375, -0.26708984375, -0.5673828125, 0.08837890625, 0.60986328125, -0.90625, -0.10394287109375, -0.1287841796875, -0.1517333984375, -0.0894775390625, -0.955078125, 0.59423828125, -0.1282958984375, 0.6328125, -0.900390625, 0.6806640625, 0.064697265625, 0.95068359375, -0.33935546875, -0.1981201171875, -0.075439453125, -0.490478515625, 0.1480712890625, 0.269287109375, 0.078369140625, -0.31689453125, -0.662109375, -0.61572265625, -0.310302734375, -0.1571044921875, 0.006450653076171875, 0.2406005859375, -0.242919921875, 0.76318359375, 0.224853515625, -0.299072265625, 0.459228515625, 1.060546875, -0.9521484375, 0.3134765625, 0.355224609375, 0.08770751953125, -0.82568359375, 1.3759765625, 0.4482421875, 0.0208740234375, -0.375244140625, -0.51904296875, -0.638671875, 0.0701904296875, 0.31103515625, -0.57666015625, -0.378662109375, 0.63671875, -0.160888671875, -1.0087890625, 0.158203125, -0.84326171875, -0.72705078125, 0.0232086181640625, -0.25341796875, 1.119140625, 0.7646484375, 0.1636962890625, -0.37158203125, -0.4306640625, -0.158203125, 0.407470703125, 0.341552734375, -0.262939453125, -0.443359375, 0.84912109375, 0.09344482421875, -0.0062103271484375, 0.006412506103515625, -0.32763671875, -0.337890625, -0.0504150390625, -0.0347900390625, 0.390625, 0.14501953125, 0.279296875, 0.456787109375, 0.66455078125, -1.0283203125, -0.2978515625, -0.22021484375, 0.7998046875, 0.30810546875, 0.6904296875, 0.2900390625, -0.572265625, -0.578125, -0.88330078125, 0.169677734375, 0.45556640625, 0.3740234375, -0.41259765625, 0.8525390625, 0.2939453125, -0.0716552734375, 0.56884765625, -0.68994140625, -0.38525390625, 1.384765625, -0.04266357421875, 0.92138671875, -0.58935546875, 0.203125, 0.09991455078125, 0.07781982421875, 0.5439453125, 0.185302734375, 0.5498046875, -0.410888671875, -0.673828125, -0.1768798828125, -0.002010345458984375, -0.0157318115234375, -0.391845703125, 0.2359619140625, -0.364013671875, -0.78466796875, -0.78173828125, 0.445068359375, 0.62109375, 0.8095703125, 0.305908203125, 0.55126953125, 0.485107421875, 0.56005859375, 0.62109375, -0.20263671875, 0.076904296875, -0.487060546875, 0.5185546875, -0.116943359375, -0.396240234375, -0.43994140625, 0.005977630615234375, -0.316650390625, -0.11419677734375, -0.118896484375, -0.474853515625, -0.466064453125, 0.32177734375, -0.291748046875, 0.41796875, -0.339111328125, -0.3388671875, -0.228271484375, 0.387939453125, 0.236083984375, -1.037109375, 0.38818359375, -0.8779296875, 0.80419921875, 0.29638671875, -0.341064453125, -0.615234375, -0.280029296875, -0.7568359375, -0.87548828125, -0.0863037109375, 0.61669921875, -0.11590576171875, 0.5078125, -1.421875, 0.428466796875, 0.29052734375, -0.282470703125, 0.25048828125, -0.252685546875, 0.1932373046875, 0.192626953125, 0.603515625, -0.5009765625, -0.71044921875, 0.056854248046875, -1.1337890625, 0.210205078125, -0.76318359375, 0.5673828125, 0.1153564453125, -0.29443359375, 0.052520751953125, 0.54541015625, -0.25927734375, 0.183349609375, -0.30615234375, 0.26220703125, -0.99658203125, -0.475830078125, 0.482177734375, 0.046661376953125, -0.44189453125, 1.064453125, -0.2425537109375, -0.366943359375, -0.049468994140625, 0.73681640625, -0.39111328125, 0.30859375, -0.521484375, 0.8974609375, -0.220947265625, -0.6689453125, -0.1671142578125, -0.859375, 1.0087890625, 0.041839599609375, -0.87451171875, -0.261474609375, -0.951171875, -0.044403076171875, 0.0576171875, -0.177490234375, 0.3857421875, -0.0024127960205078125, -0.019378662109375, -0.04754638671875, 0.020172119140625, -0.67041015625, 0.033355712890625, -0.5341796875, -0.447265625, -0.048187255859375, 0.7109375, 0.6962890625, 0.1552734375, -0.28125, 0.1434326171875, 0.1854248046875, -0.04205322265625, -0.467041015625, 0.1402587890625, -0.414306640625, -0.096923828125, -0.0010395050048828125, 0.759765625, 0.005908966064453125, 0.7421875, 0.74951171875, 0.260986328125, 0.7177734375, 0.351806640625, -0.72412109375, 1.09765625, 0.324462890625, -0.89794921875, -0.59326171875, 0.30908203125, -0.1268310546875, 0.64892578125, 0.1715087890625, -0.9404296875, -0.52099609375, -0.5693359375, 0.43896484375, -0.5244140625, -0.2352294921875, -1.158203125, 0.052642822265625, -0.245361328125, 0.2479248046875, 0.0836181640625, -0.261962890625, 0.173583984375, -0.814453125, 0.333251953125, -0.80615234375, -0.352294921875, -0.95654296875, -0.0955810546875, -0.0016775131225585938, 1.0400390625, 0.09014892578125, 0.619140625, -0.07159423828125, -0.20751953125, 0.423583984375, 0.14599609375, -0.93505859375, -0.54248046875, 0.190673828125, -0.0146026611328125, -0.143798828125, -0.1397705078125, -0.71923828125, 0.767578125, -0.72314453125, 0.32470703125, -0.272216796875, -0.353759765625, -0.2247314453125, -0.133056640625, 0.87109375, -0.418701171875, -0.2021484375, -0.2744140625, 0.27001953125, 0.55419921875, -0.387451171875, -0.436279296875, -0.81298828125, -0.1539306640625, -1.16796875, 0.55712890625, -0.55615234375, 0.0897216796875, -0.64501953125, -0.55615234375, 1.10546875, -0.76611328125, 0.41259765625, 1.2177734375, 0.34521484375, 0.439697265625, -0.92431640625, 0.57470703125, 0.6953125, -0.625, -0.419677734375, -0.039703369140625, -0.94140625, 0.282958984375, -0.11279296875, -0.92333984375, -0.7666015625, 0.13232421875, 1.1904296875, -0.30712890625, 0.74072265625, -0.0948486328125, -1.275390625, -0.90576171875, 0.912109375, -0.0653076171875, 0.24755859375, 0.4599609375, -0.12030029296875, -0.21337890625, -0.173583984375, -0.300048828125, -0.120849609375, -0.35498046875, 1.1513671875, -0.2498779296875, -0.7451171875, 0.97119140625, 0.697265625, -0.953125, -0.62646484375, 0.011016845703125, -0.2186279296875, -0.1285400390625, -0.280029296875, -0.1824951171875, 0.6328125, -0.9501953125, 0.2132568359375, 0.64990234375, -0.295654296875, 0.2137451171875, -0.09613037109375, 0.335693359375, -0.6787109375, 0.74658203125, 0.484375, -0.1451416015625, -0.318359375, -0.60400390625, -0.326171875, -0.55419921875, 0.09906005859375, 0.71875, -0.75390625, -0.04791259765625, 0.050811767578125, 0.1219482421875, 0.97998046875, -0.2034912109375, -0.5341796875, 0.342529296875, -0.609375, -0.63720703125, -0.05633544921875, 0.282470703125, -0.035888671875, 0.6845703125, -0.474609375, 0.08172607421875, 0.380126953125, 0.37353515625, -0.11572265625, -0.75732421875, -0.34912109375, -0.71044921875, -0.381103515625, -0.484619140625, -0.5703125, 0.0174407958984375, 0.473388671875, 0.136962890625, -0.5830078125, 0.033843994140625, 0.6328125, -0.177490234375, 0.8701171875, -0.66015625, 0.446044921875, -0.61474609375, -0.2369384765625, -0.2578125, -0.085693359375, -0.52099609375, -0.0120391845703125, -0.89599609375, 0.292724609375, -0.186767578125, 0.736328125, -0.1695556640625, 0.347900390625, -0.235107421875, -0.377685546875, 0.116455078125, -0.2318115234375, -0.371826171875, 0.85107421875, 0.2034912109375, -0.2169189453125, 0.168212890625, -0.68994140625, -0.4404296875, -0.27294921875, 0.424072265625, 0.708984375, -0.334228515625, -0.011810302734375, -0.18798828125, 0.2381591796875, -1.2978515625, 0.3056640625, 0.04779052734375, 0.03826904296875, 0.44482421875, -0.1019287109375, 0.61328125, 1.318359375, -0.50244140625, 0.38916015625, 0.1505126953125, -0.0616455078125, 0.55126953125, 0.418212890625, -0.01541900634765625, 0.306884765625, 0.287109375, -0.365478515625, -0.15478515625, 0.31787109375, 0.18310546875, 0.383056640625, 0.154541015625, -0.89599609375, -1.2451171875, -0.258544921875, 0.00899505615234375, 0.2430419921875, 0.1744384765625, -0.12274169921875, 0.1319580078125, 0.0361328125, -0.300048828125, 0.1820068359375, -1.0361328125, -0.82373046875, 0.27099609375, -0.276611328125, -0.58349609375, -0.2137451171875, -0.354248046875, -0.310302734375, 0.275146484375, 0.74072265625, -0.7744140625, 0.54736328125, -0.0152740478515625, 0.366943359375, 0.05303955078125, -0.755859375, 0.2117919921875, 0.489501953125, -0.76708984375, -0.576171875, 0.253173828125, 1.3251953125, 0.2783203125, -0.279296875, -0.436767578125, 0.37646484375, -0.07354736328125, 0.353515625, -0.5068359375, 0.23974609375, -0.419189453125, 0.251220703125, -0.86865234375, 0.256591796875, -0.305908203125, 0.235595703125, 0.326416015625, -0.64990234375, -0.4736328125, 0.53857421875, 0.55859375, -0.387939453125, 0.54345703125, 0.444580078125, 0.451904296875, 0.1878662109375, -0.07073974609375, -0.1324462890625, 0.54345703125, 0.7119140625, 0.58740234375, -0.154541015625, 0.49755859375, 0.87939453125, 0.019683837890625, -0.248779296875, 0.71240234375, 0.372802734375, -0.288330078125, 0.38427734375, -0.21875, 0.1690673828125, 0.1563720703125, -0.40673828125, 0.375244140625, -0.414306640625, 0.1903076171875, -0.21630859375, -0.5498046875, 0.998046875, -0.2322998046875, -0.1275634765625, -0.142822265625, -0.09197998046875, 0.15087890625, 0.5625, -0.212646484375, -0.1727294921875, 1.1201171875, 0.60009765625, 0.42236328125, 0.67626953125, 0.458251953125, 0.2978515625, -0.8330078125, 0.38427734375, 0.1748046875, -0.0168914794921875, -0.15771484375, -0.326416015625, -1.1376953125, 0.38720703125, -0.3955078125, -0.36376953125, 1.1181640625, -0.70654296875, 0.2044677734375, -0.284912109375, 0.49365234375, -0.6162109375, -0.124267578125, 0.1710205078125, -0.24755859375, -0.12481689453125, 1.03515625, -0.36767578125, 0.03155517578125, 0.351806640625, 0.88720703125, 0.0016193389892578125, 1.4296875, 0.66357421875, -0.2822265625, -0.1624755859375, 0.1468505859375, -0.293701171875, -0.5986328125, -0.315185546875, -0.43017578125, 0.08563232421875, -0.60009765625, -0.74658203125, -0.1756591796875, 0.86376953125, -0.025054931640625, -1.142578125, -0.0025844573974609375, 0.08770751953125, -0.84375, 0.281494140625, -0.01197052001953125, 0.427978515625, 0.1370849609375, -0.163330078125, 0.010498046875, -0.578125, 0.341796875, -0.78564453125, 0.1903076171875, -0.83154296875, -0.72412109375, -0.415283203125, -0.6171875, -0.26611328125, -0.34130859375, -0.041412353515625, -1.107421875, 0.71875, 0.233154296875, 0.2174072265625, 0.525390625, -0.39013671875, 0.12890625, 0.97900390625, 1.1904296875, -0.05841064453125, 0.81103515625, 0.266845703125, -0.09326171875, 0.53515625, -0.47314453125, 0.335205078125, 0.05413818359375, 0.1768798828125, -0.319580078125, 0.321533203125, -0.33056640625, -1.0966796875, 0.2529296875, 0.5927734375, 0.17431640625, -0.3486328125, -0.83544921875, -0.29248046875, -1.1455078125, -0.2091064453125, -0.79150390625, 0.8486328125, -0.564453125, 0.281494140625, -0.164794921875, -1.205078125, 4.42578125, 0.78955078125, 0.91552734375, 0.5009765625, 0.1563720703125, 1.080078125, 0.48193359375, -0.712890625, -0.2958984375, -0.37451171875, 0.65185546875, -0.60400390625, -0.07012939453125, 0.806640625, 0.046783447265625, 0.5009765625, -0.49365234375, 0.472900390625, 0.192626953125, -1.033203125, -0.7822265625, 0.389892578125, 0.07952880859375, 0.62353515625, -0.145263671875, 0.391845703125, 0.5048828125, -0.5439453125, -0.1864013671875, -0.60302734375, 0.264892578125, -0.6083984375, 0.77734375, -0.1566162109375, 0.00003886222839355469, 0.438232421875, -0.11859130859375, -0.85498046875, 0.01427459716796875, 0.128662109375, 0.1695556640625, 0.0284881591796875, 0.6181640625, -0.87255859375, 0.021881103515625, 0.1163330078125, -0.7490234375, 0.52734375, 0.303955078125, -1.375, 0.68701171875, -0.09857177734375, 0.369140625, -0.56201171875, -0.6337890625, 0.027496337890625, 0.11328125, 0.08782958984375, -0.23388671875, 0.1761474609375, 0.403076171875, 0.59619140625, -0.175537109375, 0.541015625, -0.86767578125, 1.01953125, -0.0528564453125, 0.2318115234375, -0.62646484375, -0.295654296875, -0.295166015625, -0.2213134765625, -0.417724609375, -0.053985595703125, 0.53466796875, 0.19189453125, -0.07208251953125, 0.451904296875, 0.13720703125, -0.75732421875, 0.5009765625, -0.1942138671875, -0.354736328125, -0.2310791015625, 0.828125, 1.283203125, -0.751953125, -0.11090087890625, -0.62890625, 0.5654296875, 0.638671875, 0.81884765625, 0.08880615234375, -0.7080078125, -0.29052734375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Kawashiro Nitori is a girl who loves competitive programming. One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem. Given a string s and a parameter k, you need to check if there exist k+1 non-empty strings a_1,a_2...,a_{k+1}, such that $$$s=a_1+a_2+… +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+…+R(a_{1}).$$$ Here + represents concatenation. We define R(x) as a reversed string x. For example R(abcd) = dcba. Note that in the formula above the part R(a_{k+1}) is intentionally skipped. Input The input consists of multiple test cases. The first line contains a single integer t (1≀ t≀ 100) β€” the number of test cases. The description of the test cases follows. The first line of each test case description contains two integers n, k (1≀ n≀ 100, 0≀ k≀ ⌊ n/2 βŒ‹) β€” the length of the string s and the parameter k. The second line of each test case description contains a single string s of length n, consisting of lowercase English letters. Output For each test case, print "YES" (without quotes), if it is possible to find a_1,a_2,…,a_{k+1}, and "NO" (without quotes) otherwise. You can print letters in any case (upper or lower). Example Input 7 5 1 qwqwq 2 1 ab 3 1 ioi 4 2 icpc 22 0 dokidokiliteratureclub 19 8 imteamshanghaialice 6 3 aaaaaa Output YES NO YES NO YES NO NO Note In the first test case, one possible solution is a_1=qw and a_2=q. In the third test case, one possible solution is a_1=i and a_2=o. In the fifth test case, one possible solution is a_1=dokidokiliteratureclub. Tags: brute force, constructive algorithms, greedy, strings Correct Solution: ``` t = int(input()) for _ in range(t): n,k = map(int,input().split()) s = input() if 2*k==n: print("NO") continue if k==0: print("YES") continue if s[:k]==s[-k:][::-1]: print("YES") else: print("NO") ```
105,480
[ 0.1292724609375, -0.415283203125, 0.1676025390625, 0.28759765625, -0.326416015625, -0.8193359375, -0.06884765625, 0.2174072265625, 0.068359375, 0.943359375, 0.9248046875, -0.09100341796875, 0.1741943359375, -0.7724609375, -0.41455078125, -0.08685302734375, -0.373046875, -0.71484375, -0.491943359375, 0.064453125, 0.259521484375, 0.0955810546875, -1.3671875, -0.06011962890625, -0.38720703125, 0.919921875, 0.430908203125, 0.07000732421875, 1.1767578125, 0.75341796875, -0.431640625, -0.405029296875, 0.6796875, -0.84912109375, -0.315673828125, -0.5546875, 0.642578125, -0.75634765625, -0.49462890625, -0.6015625, 0.2841796875, -0.442626953125, 0.289306640625, -0.822265625, -1.1923828125, 0.038848876953125, -0.7353515625, -0.32470703125, -0.370361328125, -0.6162109375, 0.25927734375, -0.251953125, 0.55712890625, 0.0167999267578125, -0.0799560546875, 0.0662841796875, -0.03289794921875, -0.140380859375, -0.609375, 0.0305023193359375, -0.037933349609375, -0.10675048828125, -0.1412353515625, -0.56201171875, -0.4658203125, -0.1138916015625, -0.1663818359375, -0.39404296875, -0.02117919921875, -1.044921875, -0.279296875, 0.214599609375, -1.015625, -0.39892578125, -0.08331298828125, -0.1756591796875, 0.60009765625, -0.2044677734375, -0.6123046875, 1.255859375, 0.0181884765625, 1.0927734375, 0.470947265625, 0.2379150390625, -0.63525390625, -0.87939453125, -0.033843994140625, 0.234130859375, 0.3125, 0.02728271484375, -0.232666015625, 0.5556640625, -0.55322265625, 0.01424407958984375, 0.384765625, 0.525390625, -0.06396484375, 0.1717529296875, 0.271240234375, -0.07354736328125, 0.98486328125, 0.90966796875, -0.57421875, 0.8662109375, -0.638671875, 0.0968017578125, 0.133056640625, 0.04229736328125, 0.08416748046875, -0.268310546875, -0.05047607421875, -0.361328125, 0.5458984375, 0.1376953125, -0.5625, 0.77197265625, -0.081787109375, 0.176025390625, -0.74609375, 0.1837158203125, 0.52197265625, 0.2044677734375, 0.54833984375, -0.0180511474609375, -0.018402099609375, -0.287841796875, -0.413330078125, 1.15625, -0.7744140625, 0.007465362548828125, 0.48193359375, -0.03607177734375, -0.24853515625, 0.360107421875, -0.1241455078125, 0.333740234375, -0.328369140625, 0.45703125, 0.59375, -0.59033203125, 0.79248046875, -0.1572265625, -0.134033203125, 1.404296875, 0.358642578125, 0.12744140625, 0.51953125, 0.477783203125, -0.95751953125, 0.479248046875, -0.99462890625, 0.35595703125, -0.0299530029296875, 0.2430419921875, -0.20361328125, 0.1143798828125, 0.018463134765625, 0.34375, 0.342041015625, 0.335693359375, -0.2403564453125, 0.28759765625, -0.4892578125, 0.86181640625, -0.5107421875, 0.97998046875, -0.2142333984375, -0.345458984375, -0.2403564453125, -0.67431640625, 0.25830078125, -0.1832275390625, -0.2305908203125, 0.85986328125, 0.53271484375, 0.91796875, 1.16015625, -0.174072265625, 0.53271484375, 0.42626953125, -0.345947265625, 0.3466796875, 0.447509765625, 0.51806640625, -0.0516357421875, 0.29931640625, 0.287353515625, -0.396728515625, -1.01953125, -0.470458984375, -0.16650390625, 0.5126953125, -0.88720703125, 0.137451171875, -0.02972412109375, 0.262939453125, -0.68603515625, -0.1683349609375, -0.1395263671875, -1.095703125, -0.16650390625, 0.4501953125, -0.284423828125, 0.430908203125, -0.419189453125, -0.463623046875, 0.497314453125, 1.21875, -0.1046142578125, 0.1741943359375, 0.107177734375, 0.428955078125, -0.41748046875, 0.236083984375, 0.10784912109375, -0.345947265625, -0.383544921875, 0.80078125, -0.359375, 0.1566162109375, -0.03289794921875, 0.83642578125, 0.25048828125, 0.64306640625, -0.150390625, -0.16162109375, 0.335205078125, 1.2080078125, -0.0089569091796875, 0.444091796875, 0.2587890625, 0.896484375, 0.41796875, 0.83056640625, 0.37646484375, 0.10247802734375, 0.66650390625, 1.2392578125, 0.54248046875, 0.453125, 0.1982421875, 0.2763671875, 0.45556640625, 0.429443359375, 0.294921875, 0.4130859375, -0.20068359375, -0.20849609375, -0.325927734375, 0.0031642913818359375, -0.1038818359375, 0.90478515625, 0.46337890625, 0.0887451171875, -0.64306640625, -0.45654296875, -0.1451416015625, 0.7392578125, -0.7548828125, -0.55810546875, 0.256103515625, 0.1485595703125, -0.053070068359375, -0.39111328125, 0.178955078125, 0.25537109375, 0.41259765625, 0.270263671875, -0.27294921875, -0.321044921875, -0.890625, -0.6845703125, -0.99755859375, -0.26708984375, -0.5673828125, 0.08837890625, 0.60986328125, -0.90625, -0.10394287109375, -0.1287841796875, -0.1517333984375, -0.0894775390625, -0.955078125, 0.59423828125, -0.1282958984375, 0.6328125, -0.900390625, 0.6806640625, 0.064697265625, 0.95068359375, -0.33935546875, -0.1981201171875, -0.075439453125, -0.490478515625, 0.1480712890625, 0.269287109375, 0.078369140625, -0.31689453125, -0.662109375, -0.61572265625, -0.310302734375, -0.1571044921875, 0.006450653076171875, 0.2406005859375, -0.242919921875, 0.76318359375, 0.224853515625, -0.299072265625, 0.459228515625, 1.060546875, -0.9521484375, 0.3134765625, 0.355224609375, 0.08770751953125, -0.82568359375, 1.3759765625, 0.4482421875, 0.0208740234375, -0.375244140625, -0.51904296875, -0.638671875, 0.0701904296875, 0.31103515625, -0.57666015625, -0.378662109375, 0.63671875, -0.160888671875, -1.0087890625, 0.158203125, -0.84326171875, -0.72705078125, 0.0232086181640625, -0.25341796875, 1.119140625, 0.7646484375, 0.1636962890625, -0.37158203125, -0.4306640625, -0.158203125, 0.407470703125, 0.341552734375, -0.262939453125, -0.443359375, 0.84912109375, 0.09344482421875, -0.0062103271484375, 0.006412506103515625, -0.32763671875, -0.337890625, -0.0504150390625, -0.0347900390625, 0.390625, 0.14501953125, 0.279296875, 0.456787109375, 0.66455078125, -1.0283203125, -0.2978515625, -0.22021484375, 0.7998046875, 0.30810546875, 0.6904296875, 0.2900390625, -0.572265625, -0.578125, -0.88330078125, 0.169677734375, 0.45556640625, 0.3740234375, -0.41259765625, 0.8525390625, 0.2939453125, -0.0716552734375, 0.56884765625, -0.68994140625, -0.38525390625, 1.384765625, -0.04266357421875, 0.92138671875, -0.58935546875, 0.203125, 0.09991455078125, 0.07781982421875, 0.5439453125, 0.185302734375, 0.5498046875, -0.410888671875, -0.673828125, -0.1768798828125, -0.002010345458984375, -0.0157318115234375, -0.391845703125, 0.2359619140625, -0.364013671875, -0.78466796875, -0.78173828125, 0.445068359375, 0.62109375, 0.8095703125, 0.305908203125, 0.55126953125, 0.485107421875, 0.56005859375, 0.62109375, -0.20263671875, 0.076904296875, -0.487060546875, 0.5185546875, -0.116943359375, -0.396240234375, -0.43994140625, 0.005977630615234375, -0.316650390625, -0.11419677734375, -0.118896484375, -0.474853515625, -0.466064453125, 0.32177734375, -0.291748046875, 0.41796875, -0.339111328125, -0.3388671875, -0.228271484375, 0.387939453125, 0.236083984375, -1.037109375, 0.38818359375, -0.8779296875, 0.80419921875, 0.29638671875, -0.341064453125, -0.615234375, -0.280029296875, -0.7568359375, -0.87548828125, -0.0863037109375, 0.61669921875, -0.11590576171875, 0.5078125, -1.421875, 0.428466796875, 0.29052734375, -0.282470703125, 0.25048828125, -0.252685546875, 0.1932373046875, 0.192626953125, 0.603515625, -0.5009765625, -0.71044921875, 0.056854248046875, -1.1337890625, 0.210205078125, -0.76318359375, 0.5673828125, 0.1153564453125, -0.29443359375, 0.052520751953125, 0.54541015625, -0.25927734375, 0.183349609375, -0.30615234375, 0.26220703125, -0.99658203125, -0.475830078125, 0.482177734375, 0.046661376953125, -0.44189453125, 1.064453125, -0.2425537109375, -0.366943359375, -0.049468994140625, 0.73681640625, -0.39111328125, 0.30859375, -0.521484375, 0.8974609375, -0.220947265625, -0.6689453125, -0.1671142578125, -0.859375, 1.0087890625, 0.041839599609375, -0.87451171875, -0.261474609375, -0.951171875, -0.044403076171875, 0.0576171875, -0.177490234375, 0.3857421875, -0.0024127960205078125, -0.019378662109375, -0.04754638671875, 0.020172119140625, -0.67041015625, 0.033355712890625, -0.5341796875, -0.447265625, -0.048187255859375, 0.7109375, 0.6962890625, 0.1552734375, -0.28125, 0.1434326171875, 0.1854248046875, -0.04205322265625, -0.467041015625, 0.1402587890625, -0.414306640625, -0.096923828125, -0.0010395050048828125, 0.759765625, 0.005908966064453125, 0.7421875, 0.74951171875, 0.260986328125, 0.7177734375, 0.351806640625, -0.72412109375, 1.09765625, 0.324462890625, -0.89794921875, -0.59326171875, 0.30908203125, -0.1268310546875, 0.64892578125, 0.1715087890625, -0.9404296875, -0.52099609375, -0.5693359375, 0.43896484375, -0.5244140625, -0.2352294921875, -1.158203125, 0.052642822265625, -0.245361328125, 0.2479248046875, 0.0836181640625, -0.261962890625, 0.173583984375, -0.814453125, 0.333251953125, -0.80615234375, -0.352294921875, -0.95654296875, -0.0955810546875, -0.0016775131225585938, 1.0400390625, 0.09014892578125, 0.619140625, -0.07159423828125, -0.20751953125, 0.423583984375, 0.14599609375, -0.93505859375, -0.54248046875, 0.190673828125, -0.0146026611328125, -0.143798828125, -0.1397705078125, -0.71923828125, 0.767578125, -0.72314453125, 0.32470703125, -0.272216796875, -0.353759765625, -0.2247314453125, -0.133056640625, 0.87109375, -0.418701171875, -0.2021484375, -0.2744140625, 0.27001953125, 0.55419921875, -0.387451171875, -0.436279296875, -0.81298828125, -0.1539306640625, -1.16796875, 0.55712890625, -0.55615234375, 0.0897216796875, -0.64501953125, -0.55615234375, 1.10546875, -0.76611328125, 0.41259765625, 1.2177734375, 0.34521484375, 0.439697265625, -0.92431640625, 0.57470703125, 0.6953125, -0.625, -0.419677734375, -0.039703369140625, -0.94140625, 0.282958984375, -0.11279296875, -0.92333984375, -0.7666015625, 0.13232421875, 1.1904296875, -0.30712890625, 0.74072265625, -0.0948486328125, -1.275390625, -0.90576171875, 0.912109375, -0.0653076171875, 0.24755859375, 0.4599609375, -0.12030029296875, -0.21337890625, -0.173583984375, -0.300048828125, -0.120849609375, -0.35498046875, 1.1513671875, -0.2498779296875, -0.7451171875, 0.97119140625, 0.697265625, -0.953125, -0.62646484375, 0.011016845703125, -0.2186279296875, -0.1285400390625, -0.280029296875, -0.1824951171875, 0.6328125, -0.9501953125, 0.2132568359375, 0.64990234375, -0.295654296875, 0.2137451171875, -0.09613037109375, 0.335693359375, -0.6787109375, 0.74658203125, 0.484375, -0.1451416015625, -0.318359375, -0.60400390625, -0.326171875, -0.55419921875, 0.09906005859375, 0.71875, -0.75390625, -0.04791259765625, 0.050811767578125, 0.1219482421875, 0.97998046875, -0.2034912109375, -0.5341796875, 0.342529296875, -0.609375, -0.63720703125, -0.05633544921875, 0.282470703125, -0.035888671875, 0.6845703125, -0.474609375, 0.08172607421875, 0.380126953125, 0.37353515625, -0.11572265625, -0.75732421875, -0.34912109375, -0.71044921875, -0.381103515625, -0.484619140625, -0.5703125, 0.0174407958984375, 0.473388671875, 0.136962890625, -0.5830078125, 0.033843994140625, 0.6328125, -0.177490234375, 0.8701171875, -0.66015625, 0.446044921875, -0.61474609375, -0.2369384765625, -0.2578125, -0.085693359375, -0.52099609375, -0.0120391845703125, -0.89599609375, 0.292724609375, -0.186767578125, 0.736328125, -0.1695556640625, 0.347900390625, -0.235107421875, -0.377685546875, 0.116455078125, -0.2318115234375, -0.371826171875, 0.85107421875, 0.2034912109375, -0.2169189453125, 0.168212890625, -0.68994140625, -0.4404296875, -0.27294921875, 0.424072265625, 0.708984375, -0.334228515625, -0.011810302734375, -0.18798828125, 0.2381591796875, -1.2978515625, 0.3056640625, 0.04779052734375, 0.03826904296875, 0.44482421875, -0.1019287109375, 0.61328125, 1.318359375, -0.50244140625, 0.38916015625, 0.1505126953125, -0.0616455078125, 0.55126953125, 0.418212890625, -0.01541900634765625, 0.306884765625, 0.287109375, -0.365478515625, -0.15478515625, 0.31787109375, 0.18310546875, 0.383056640625, 0.154541015625, -0.89599609375, -1.2451171875, -0.258544921875, 0.00899505615234375, 0.2430419921875, 0.1744384765625, -0.12274169921875, 0.1319580078125, 0.0361328125, -0.300048828125, 0.1820068359375, -1.0361328125, -0.82373046875, 0.27099609375, -0.276611328125, -0.58349609375, -0.2137451171875, -0.354248046875, -0.310302734375, 0.275146484375, 0.74072265625, -0.7744140625, 0.54736328125, -0.0152740478515625, 0.366943359375, 0.05303955078125, -0.755859375, 0.2117919921875, 0.489501953125, -0.76708984375, -0.576171875, 0.253173828125, 1.3251953125, 0.2783203125, -0.279296875, -0.436767578125, 0.37646484375, -0.07354736328125, 0.353515625, -0.5068359375, 0.23974609375, -0.419189453125, 0.251220703125, -0.86865234375, 0.256591796875, -0.305908203125, 0.235595703125, 0.326416015625, -0.64990234375, -0.4736328125, 0.53857421875, 0.55859375, -0.387939453125, 0.54345703125, 0.444580078125, 0.451904296875, 0.1878662109375, -0.07073974609375, -0.1324462890625, 0.54345703125, 0.7119140625, 0.58740234375, -0.154541015625, 0.49755859375, 0.87939453125, 0.019683837890625, -0.248779296875, 0.71240234375, 0.372802734375, -0.288330078125, 0.38427734375, -0.21875, 0.1690673828125, 0.1563720703125, -0.40673828125, 0.375244140625, -0.414306640625, 0.1903076171875, -0.21630859375, -0.5498046875, 0.998046875, -0.2322998046875, -0.1275634765625, -0.142822265625, -0.09197998046875, 0.15087890625, 0.5625, -0.212646484375, -0.1727294921875, 1.1201171875, 0.60009765625, 0.42236328125, 0.67626953125, 0.458251953125, 0.2978515625, -0.8330078125, 0.38427734375, 0.1748046875, -0.0168914794921875, -0.15771484375, -0.326416015625, -1.1376953125, 0.38720703125, -0.3955078125, -0.36376953125, 1.1181640625, -0.70654296875, 0.2044677734375, -0.284912109375, 0.49365234375, -0.6162109375, -0.124267578125, 0.1710205078125, -0.24755859375, -0.12481689453125, 1.03515625, -0.36767578125, 0.03155517578125, 0.351806640625, 0.88720703125, 0.0016193389892578125, 1.4296875, 0.66357421875, -0.2822265625, -0.1624755859375, 0.1468505859375, -0.293701171875, -0.5986328125, -0.315185546875, -0.43017578125, 0.08563232421875, -0.60009765625, -0.74658203125, -0.1756591796875, 0.86376953125, -0.025054931640625, -1.142578125, -0.0025844573974609375, 0.08770751953125, -0.84375, 0.281494140625, -0.01197052001953125, 0.427978515625, 0.1370849609375, -0.163330078125, 0.010498046875, -0.578125, 0.341796875, -0.78564453125, 0.1903076171875, -0.83154296875, -0.72412109375, -0.415283203125, -0.6171875, -0.26611328125, -0.34130859375, -0.041412353515625, -1.107421875, 0.71875, 0.233154296875, 0.2174072265625, 0.525390625, -0.39013671875, 0.12890625, 0.97900390625, 1.1904296875, -0.05841064453125, 0.81103515625, 0.266845703125, -0.09326171875, 0.53515625, -0.47314453125, 0.335205078125, 0.05413818359375, 0.1768798828125, -0.319580078125, 0.321533203125, -0.33056640625, -1.0966796875, 0.2529296875, 0.5927734375, 0.17431640625, -0.3486328125, -0.83544921875, -0.29248046875, -1.1455078125, -0.2091064453125, -0.79150390625, 0.8486328125, -0.564453125, 0.281494140625, -0.164794921875, -1.205078125, 4.42578125, 0.78955078125, 0.91552734375, 0.5009765625, 0.1563720703125, 1.080078125, 0.48193359375, -0.712890625, -0.2958984375, -0.37451171875, 0.65185546875, -0.60400390625, -0.07012939453125, 0.806640625, 0.046783447265625, 0.5009765625, -0.49365234375, 0.472900390625, 0.192626953125, -1.033203125, -0.7822265625, 0.389892578125, 0.07952880859375, 0.62353515625, -0.145263671875, 0.391845703125, 0.5048828125, -0.5439453125, -0.1864013671875, -0.60302734375, 0.264892578125, -0.6083984375, 0.77734375, -0.1566162109375, 0.00003886222839355469, 0.438232421875, -0.11859130859375, -0.85498046875, 0.01427459716796875, 0.128662109375, 0.1695556640625, 0.0284881591796875, 0.6181640625, -0.87255859375, 0.021881103515625, 0.1163330078125, -0.7490234375, 0.52734375, 0.303955078125, -1.375, 0.68701171875, -0.09857177734375, 0.369140625, -0.56201171875, -0.6337890625, 0.027496337890625, 0.11328125, 0.08782958984375, -0.23388671875, 0.1761474609375, 0.403076171875, 0.59619140625, -0.175537109375, 0.541015625, -0.86767578125, 1.01953125, -0.0528564453125, 0.2318115234375, -0.62646484375, -0.295654296875, -0.295166015625, -0.2213134765625, -0.417724609375, -0.053985595703125, 0.53466796875, 0.19189453125, -0.07208251953125, 0.451904296875, 0.13720703125, -0.75732421875, 0.5009765625, -0.1942138671875, -0.354736328125, -0.2310791015625, 0.828125, 1.283203125, -0.751953125, -0.11090087890625, -0.62890625, 0.5654296875, 0.638671875, 0.81884765625, 0.08880615234375, -0.7080078125, -0.29052734375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Kawashiro Nitori is a girl who loves competitive programming. One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem. Given a string s and a parameter k, you need to check if there exist k+1 non-empty strings a_1,a_2...,a_{k+1}, such that $$$s=a_1+a_2+… +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+…+R(a_{1}).$$$ Here + represents concatenation. We define R(x) as a reversed string x. For example R(abcd) = dcba. Note that in the formula above the part R(a_{k+1}) is intentionally skipped. Input The input consists of multiple test cases. The first line contains a single integer t (1≀ t≀ 100) β€” the number of test cases. The description of the test cases follows. The first line of each test case description contains two integers n, k (1≀ n≀ 100, 0≀ k≀ ⌊ n/2 βŒ‹) β€” the length of the string s and the parameter k. The second line of each test case description contains a single string s of length n, consisting of lowercase English letters. Output For each test case, print "YES" (without quotes), if it is possible to find a_1,a_2,…,a_{k+1}, and "NO" (without quotes) otherwise. You can print letters in any case (upper or lower). Example Input 7 5 1 qwqwq 2 1 ab 3 1 ioi 4 2 icpc 22 0 dokidokiliteratureclub 19 8 imteamshanghaialice 6 3 aaaaaa Output YES NO YES NO YES NO NO Note In the first test case, one possible solution is a_1=qw and a_2=q. In the third test case, one possible solution is a_1=i and a_2=o. In the fifth test case, one possible solution is a_1=dokidokiliteratureclub. Tags: brute force, constructive algorithms, greedy, strings Correct Solution: ``` for _ in range(int(input())): n, k = map(int, input().split()) S = input() print() if k == 0: print("YES") continue elif S[:k] == (S[::-1])[:k]: if n//2 >= k + 1 - n%2: print("YES") continue print("NO") ```
105,481
[ 0.1292724609375, -0.415283203125, 0.1676025390625, 0.28759765625, -0.326416015625, -0.8193359375, -0.06884765625, 0.2174072265625, 0.068359375, 0.943359375, 0.9248046875, -0.09100341796875, 0.1741943359375, -0.7724609375, -0.41455078125, -0.08685302734375, -0.373046875, -0.71484375, -0.491943359375, 0.064453125, 0.259521484375, 0.0955810546875, -1.3671875, -0.06011962890625, -0.38720703125, 0.919921875, 0.430908203125, 0.07000732421875, 1.1767578125, 0.75341796875, -0.431640625, -0.405029296875, 0.6796875, -0.84912109375, -0.315673828125, -0.5546875, 0.642578125, -0.75634765625, -0.49462890625, -0.6015625, 0.2841796875, -0.442626953125, 0.289306640625, -0.822265625, -1.1923828125, 0.038848876953125, -0.7353515625, -0.32470703125, -0.370361328125, -0.6162109375, 0.25927734375, -0.251953125, 0.55712890625, 0.0167999267578125, -0.0799560546875, 0.0662841796875, -0.03289794921875, -0.140380859375, -0.609375, 0.0305023193359375, -0.037933349609375, -0.10675048828125, -0.1412353515625, -0.56201171875, -0.4658203125, -0.1138916015625, -0.1663818359375, -0.39404296875, -0.02117919921875, -1.044921875, -0.279296875, 0.214599609375, -1.015625, -0.39892578125, -0.08331298828125, -0.1756591796875, 0.60009765625, -0.2044677734375, -0.6123046875, 1.255859375, 0.0181884765625, 1.0927734375, 0.470947265625, 0.2379150390625, -0.63525390625, -0.87939453125, -0.033843994140625, 0.234130859375, 0.3125, 0.02728271484375, -0.232666015625, 0.5556640625, -0.55322265625, 0.01424407958984375, 0.384765625, 0.525390625, -0.06396484375, 0.1717529296875, 0.271240234375, -0.07354736328125, 0.98486328125, 0.90966796875, -0.57421875, 0.8662109375, -0.638671875, 0.0968017578125, 0.133056640625, 0.04229736328125, 0.08416748046875, -0.268310546875, -0.05047607421875, -0.361328125, 0.5458984375, 0.1376953125, -0.5625, 0.77197265625, -0.081787109375, 0.176025390625, -0.74609375, 0.1837158203125, 0.52197265625, 0.2044677734375, 0.54833984375, -0.0180511474609375, -0.018402099609375, -0.287841796875, -0.413330078125, 1.15625, -0.7744140625, 0.007465362548828125, 0.48193359375, -0.03607177734375, -0.24853515625, 0.360107421875, -0.1241455078125, 0.333740234375, -0.328369140625, 0.45703125, 0.59375, -0.59033203125, 0.79248046875, -0.1572265625, -0.134033203125, 1.404296875, 0.358642578125, 0.12744140625, 0.51953125, 0.477783203125, -0.95751953125, 0.479248046875, -0.99462890625, 0.35595703125, -0.0299530029296875, 0.2430419921875, -0.20361328125, 0.1143798828125, 0.018463134765625, 0.34375, 0.342041015625, 0.335693359375, -0.2403564453125, 0.28759765625, -0.4892578125, 0.86181640625, -0.5107421875, 0.97998046875, -0.2142333984375, -0.345458984375, -0.2403564453125, -0.67431640625, 0.25830078125, -0.1832275390625, -0.2305908203125, 0.85986328125, 0.53271484375, 0.91796875, 1.16015625, -0.174072265625, 0.53271484375, 0.42626953125, -0.345947265625, 0.3466796875, 0.447509765625, 0.51806640625, -0.0516357421875, 0.29931640625, 0.287353515625, -0.396728515625, -1.01953125, -0.470458984375, -0.16650390625, 0.5126953125, -0.88720703125, 0.137451171875, -0.02972412109375, 0.262939453125, -0.68603515625, -0.1683349609375, -0.1395263671875, -1.095703125, -0.16650390625, 0.4501953125, -0.284423828125, 0.430908203125, -0.419189453125, -0.463623046875, 0.497314453125, 1.21875, -0.1046142578125, 0.1741943359375, 0.107177734375, 0.428955078125, -0.41748046875, 0.236083984375, 0.10784912109375, -0.345947265625, -0.383544921875, 0.80078125, -0.359375, 0.1566162109375, -0.03289794921875, 0.83642578125, 0.25048828125, 0.64306640625, -0.150390625, -0.16162109375, 0.335205078125, 1.2080078125, -0.0089569091796875, 0.444091796875, 0.2587890625, 0.896484375, 0.41796875, 0.83056640625, 0.37646484375, 0.10247802734375, 0.66650390625, 1.2392578125, 0.54248046875, 0.453125, 0.1982421875, 0.2763671875, 0.45556640625, 0.429443359375, 0.294921875, 0.4130859375, -0.20068359375, -0.20849609375, -0.325927734375, 0.0031642913818359375, -0.1038818359375, 0.90478515625, 0.46337890625, 0.0887451171875, -0.64306640625, -0.45654296875, -0.1451416015625, 0.7392578125, -0.7548828125, -0.55810546875, 0.256103515625, 0.1485595703125, -0.053070068359375, -0.39111328125, 0.178955078125, 0.25537109375, 0.41259765625, 0.270263671875, -0.27294921875, -0.321044921875, -0.890625, -0.6845703125, -0.99755859375, -0.26708984375, -0.5673828125, 0.08837890625, 0.60986328125, -0.90625, -0.10394287109375, -0.1287841796875, -0.1517333984375, -0.0894775390625, -0.955078125, 0.59423828125, -0.1282958984375, 0.6328125, -0.900390625, 0.6806640625, 0.064697265625, 0.95068359375, -0.33935546875, -0.1981201171875, -0.075439453125, -0.490478515625, 0.1480712890625, 0.269287109375, 0.078369140625, -0.31689453125, -0.662109375, -0.61572265625, -0.310302734375, -0.1571044921875, 0.006450653076171875, 0.2406005859375, -0.242919921875, 0.76318359375, 0.224853515625, -0.299072265625, 0.459228515625, 1.060546875, -0.9521484375, 0.3134765625, 0.355224609375, 0.08770751953125, -0.82568359375, 1.3759765625, 0.4482421875, 0.0208740234375, -0.375244140625, -0.51904296875, -0.638671875, 0.0701904296875, 0.31103515625, -0.57666015625, -0.378662109375, 0.63671875, -0.160888671875, -1.0087890625, 0.158203125, -0.84326171875, -0.72705078125, 0.0232086181640625, -0.25341796875, 1.119140625, 0.7646484375, 0.1636962890625, -0.37158203125, -0.4306640625, -0.158203125, 0.407470703125, 0.341552734375, -0.262939453125, -0.443359375, 0.84912109375, 0.09344482421875, -0.0062103271484375, 0.006412506103515625, -0.32763671875, -0.337890625, -0.0504150390625, -0.0347900390625, 0.390625, 0.14501953125, 0.279296875, 0.456787109375, 0.66455078125, -1.0283203125, -0.2978515625, -0.22021484375, 0.7998046875, 0.30810546875, 0.6904296875, 0.2900390625, -0.572265625, -0.578125, -0.88330078125, 0.169677734375, 0.45556640625, 0.3740234375, -0.41259765625, 0.8525390625, 0.2939453125, -0.0716552734375, 0.56884765625, -0.68994140625, -0.38525390625, 1.384765625, -0.04266357421875, 0.92138671875, -0.58935546875, 0.203125, 0.09991455078125, 0.07781982421875, 0.5439453125, 0.185302734375, 0.5498046875, -0.410888671875, -0.673828125, -0.1768798828125, -0.002010345458984375, -0.0157318115234375, -0.391845703125, 0.2359619140625, -0.364013671875, -0.78466796875, -0.78173828125, 0.445068359375, 0.62109375, 0.8095703125, 0.305908203125, 0.55126953125, 0.485107421875, 0.56005859375, 0.62109375, -0.20263671875, 0.076904296875, -0.487060546875, 0.5185546875, -0.116943359375, -0.396240234375, -0.43994140625, 0.005977630615234375, -0.316650390625, -0.11419677734375, -0.118896484375, -0.474853515625, -0.466064453125, 0.32177734375, -0.291748046875, 0.41796875, -0.339111328125, -0.3388671875, -0.228271484375, 0.387939453125, 0.236083984375, -1.037109375, 0.38818359375, -0.8779296875, 0.80419921875, 0.29638671875, -0.341064453125, -0.615234375, -0.280029296875, -0.7568359375, -0.87548828125, -0.0863037109375, 0.61669921875, -0.11590576171875, 0.5078125, -1.421875, 0.428466796875, 0.29052734375, -0.282470703125, 0.25048828125, -0.252685546875, 0.1932373046875, 0.192626953125, 0.603515625, -0.5009765625, -0.71044921875, 0.056854248046875, -1.1337890625, 0.210205078125, -0.76318359375, 0.5673828125, 0.1153564453125, -0.29443359375, 0.052520751953125, 0.54541015625, -0.25927734375, 0.183349609375, -0.30615234375, 0.26220703125, -0.99658203125, -0.475830078125, 0.482177734375, 0.046661376953125, -0.44189453125, 1.064453125, -0.2425537109375, -0.366943359375, -0.049468994140625, 0.73681640625, -0.39111328125, 0.30859375, -0.521484375, 0.8974609375, -0.220947265625, -0.6689453125, -0.1671142578125, -0.859375, 1.0087890625, 0.041839599609375, -0.87451171875, -0.261474609375, -0.951171875, -0.044403076171875, 0.0576171875, -0.177490234375, 0.3857421875, -0.0024127960205078125, -0.019378662109375, -0.04754638671875, 0.020172119140625, -0.67041015625, 0.033355712890625, -0.5341796875, -0.447265625, -0.048187255859375, 0.7109375, 0.6962890625, 0.1552734375, -0.28125, 0.1434326171875, 0.1854248046875, -0.04205322265625, -0.467041015625, 0.1402587890625, -0.414306640625, -0.096923828125, -0.0010395050048828125, 0.759765625, 0.005908966064453125, 0.7421875, 0.74951171875, 0.260986328125, 0.7177734375, 0.351806640625, -0.72412109375, 1.09765625, 0.324462890625, -0.89794921875, -0.59326171875, 0.30908203125, -0.1268310546875, 0.64892578125, 0.1715087890625, -0.9404296875, -0.52099609375, -0.5693359375, 0.43896484375, -0.5244140625, -0.2352294921875, -1.158203125, 0.052642822265625, -0.245361328125, 0.2479248046875, 0.0836181640625, -0.261962890625, 0.173583984375, -0.814453125, 0.333251953125, -0.80615234375, -0.352294921875, -0.95654296875, -0.0955810546875, -0.0016775131225585938, 1.0400390625, 0.09014892578125, 0.619140625, -0.07159423828125, -0.20751953125, 0.423583984375, 0.14599609375, -0.93505859375, -0.54248046875, 0.190673828125, -0.0146026611328125, -0.143798828125, -0.1397705078125, -0.71923828125, 0.767578125, -0.72314453125, 0.32470703125, -0.272216796875, -0.353759765625, -0.2247314453125, -0.133056640625, 0.87109375, -0.418701171875, -0.2021484375, -0.2744140625, 0.27001953125, 0.55419921875, -0.387451171875, -0.436279296875, -0.81298828125, -0.1539306640625, -1.16796875, 0.55712890625, -0.55615234375, 0.0897216796875, -0.64501953125, -0.55615234375, 1.10546875, -0.76611328125, 0.41259765625, 1.2177734375, 0.34521484375, 0.439697265625, -0.92431640625, 0.57470703125, 0.6953125, -0.625, -0.419677734375, -0.039703369140625, -0.94140625, 0.282958984375, -0.11279296875, -0.92333984375, -0.7666015625, 0.13232421875, 1.1904296875, -0.30712890625, 0.74072265625, -0.0948486328125, -1.275390625, -0.90576171875, 0.912109375, -0.0653076171875, 0.24755859375, 0.4599609375, -0.12030029296875, -0.21337890625, -0.173583984375, -0.300048828125, -0.120849609375, -0.35498046875, 1.1513671875, -0.2498779296875, -0.7451171875, 0.97119140625, 0.697265625, -0.953125, -0.62646484375, 0.011016845703125, -0.2186279296875, -0.1285400390625, -0.280029296875, -0.1824951171875, 0.6328125, -0.9501953125, 0.2132568359375, 0.64990234375, -0.295654296875, 0.2137451171875, -0.09613037109375, 0.335693359375, -0.6787109375, 0.74658203125, 0.484375, -0.1451416015625, -0.318359375, -0.60400390625, -0.326171875, -0.55419921875, 0.09906005859375, 0.71875, -0.75390625, -0.04791259765625, 0.050811767578125, 0.1219482421875, 0.97998046875, -0.2034912109375, -0.5341796875, 0.342529296875, -0.609375, -0.63720703125, -0.05633544921875, 0.282470703125, -0.035888671875, 0.6845703125, -0.474609375, 0.08172607421875, 0.380126953125, 0.37353515625, -0.11572265625, -0.75732421875, -0.34912109375, -0.71044921875, -0.381103515625, -0.484619140625, -0.5703125, 0.0174407958984375, 0.473388671875, 0.136962890625, -0.5830078125, 0.033843994140625, 0.6328125, -0.177490234375, 0.8701171875, -0.66015625, 0.446044921875, -0.61474609375, -0.2369384765625, -0.2578125, -0.085693359375, -0.52099609375, -0.0120391845703125, -0.89599609375, 0.292724609375, -0.186767578125, 0.736328125, -0.1695556640625, 0.347900390625, -0.235107421875, -0.377685546875, 0.116455078125, -0.2318115234375, -0.371826171875, 0.85107421875, 0.2034912109375, -0.2169189453125, 0.168212890625, -0.68994140625, -0.4404296875, -0.27294921875, 0.424072265625, 0.708984375, -0.334228515625, -0.011810302734375, -0.18798828125, 0.2381591796875, -1.2978515625, 0.3056640625, 0.04779052734375, 0.03826904296875, 0.44482421875, -0.1019287109375, 0.61328125, 1.318359375, -0.50244140625, 0.38916015625, 0.1505126953125, -0.0616455078125, 0.55126953125, 0.418212890625, -0.01541900634765625, 0.306884765625, 0.287109375, -0.365478515625, -0.15478515625, 0.31787109375, 0.18310546875, 0.383056640625, 0.154541015625, -0.89599609375, -1.2451171875, -0.258544921875, 0.00899505615234375, 0.2430419921875, 0.1744384765625, -0.12274169921875, 0.1319580078125, 0.0361328125, -0.300048828125, 0.1820068359375, -1.0361328125, -0.82373046875, 0.27099609375, -0.276611328125, -0.58349609375, -0.2137451171875, -0.354248046875, -0.310302734375, 0.275146484375, 0.74072265625, -0.7744140625, 0.54736328125, -0.0152740478515625, 0.366943359375, 0.05303955078125, -0.755859375, 0.2117919921875, 0.489501953125, -0.76708984375, -0.576171875, 0.253173828125, 1.3251953125, 0.2783203125, -0.279296875, -0.436767578125, 0.37646484375, -0.07354736328125, 0.353515625, -0.5068359375, 0.23974609375, -0.419189453125, 0.251220703125, -0.86865234375, 0.256591796875, -0.305908203125, 0.235595703125, 0.326416015625, -0.64990234375, -0.4736328125, 0.53857421875, 0.55859375, -0.387939453125, 0.54345703125, 0.444580078125, 0.451904296875, 0.1878662109375, -0.07073974609375, -0.1324462890625, 0.54345703125, 0.7119140625, 0.58740234375, -0.154541015625, 0.49755859375, 0.87939453125, 0.019683837890625, -0.248779296875, 0.71240234375, 0.372802734375, -0.288330078125, 0.38427734375, -0.21875, 0.1690673828125, 0.1563720703125, -0.40673828125, 0.375244140625, -0.414306640625, 0.1903076171875, -0.21630859375, -0.5498046875, 0.998046875, -0.2322998046875, -0.1275634765625, -0.142822265625, -0.09197998046875, 0.15087890625, 0.5625, -0.212646484375, -0.1727294921875, 1.1201171875, 0.60009765625, 0.42236328125, 0.67626953125, 0.458251953125, 0.2978515625, -0.8330078125, 0.38427734375, 0.1748046875, -0.0168914794921875, -0.15771484375, -0.326416015625, -1.1376953125, 0.38720703125, -0.3955078125, -0.36376953125, 1.1181640625, -0.70654296875, 0.2044677734375, -0.284912109375, 0.49365234375, -0.6162109375, -0.124267578125, 0.1710205078125, -0.24755859375, -0.12481689453125, 1.03515625, -0.36767578125, 0.03155517578125, 0.351806640625, 0.88720703125, 0.0016193389892578125, 1.4296875, 0.66357421875, -0.2822265625, -0.1624755859375, 0.1468505859375, -0.293701171875, -0.5986328125, -0.315185546875, -0.43017578125, 0.08563232421875, -0.60009765625, -0.74658203125, -0.1756591796875, 0.86376953125, -0.025054931640625, -1.142578125, -0.0025844573974609375, 0.08770751953125, -0.84375, 0.281494140625, -0.01197052001953125, 0.427978515625, 0.1370849609375, -0.163330078125, 0.010498046875, -0.578125, 0.341796875, -0.78564453125, 0.1903076171875, -0.83154296875, -0.72412109375, -0.415283203125, -0.6171875, -0.26611328125, -0.34130859375, -0.041412353515625, -1.107421875, 0.71875, 0.233154296875, 0.2174072265625, 0.525390625, -0.39013671875, 0.12890625, 0.97900390625, 1.1904296875, -0.05841064453125, 0.81103515625, 0.266845703125, -0.09326171875, 0.53515625, -0.47314453125, 0.335205078125, 0.05413818359375, 0.1768798828125, -0.319580078125, 0.321533203125, -0.33056640625, -1.0966796875, 0.2529296875, 0.5927734375, 0.17431640625, -0.3486328125, -0.83544921875, -0.29248046875, -1.1455078125, -0.2091064453125, -0.79150390625, 0.8486328125, -0.564453125, 0.281494140625, -0.164794921875, -1.205078125, 4.42578125, 0.78955078125, 0.91552734375, 0.5009765625, 0.1563720703125, 1.080078125, 0.48193359375, -0.712890625, -0.2958984375, -0.37451171875, 0.65185546875, -0.60400390625, -0.07012939453125, 0.806640625, 0.046783447265625, 0.5009765625, -0.49365234375, 0.472900390625, 0.192626953125, -1.033203125, -0.7822265625, 0.389892578125, 0.07952880859375, 0.62353515625, -0.145263671875, 0.391845703125, 0.5048828125, -0.5439453125, -0.1864013671875, -0.60302734375, 0.264892578125, -0.6083984375, 0.77734375, -0.1566162109375, 0.00003886222839355469, 0.438232421875, -0.11859130859375, -0.85498046875, 0.01427459716796875, 0.128662109375, 0.1695556640625, 0.0284881591796875, 0.6181640625, -0.87255859375, 0.021881103515625, 0.1163330078125, -0.7490234375, 0.52734375, 0.303955078125, -1.375, 0.68701171875, -0.09857177734375, 0.369140625, -0.56201171875, -0.6337890625, 0.027496337890625, 0.11328125, 0.08782958984375, -0.23388671875, 0.1761474609375, 0.403076171875, 0.59619140625, -0.175537109375, 0.541015625, -0.86767578125, 1.01953125, -0.0528564453125, 0.2318115234375, -0.62646484375, -0.295654296875, -0.295166015625, -0.2213134765625, -0.417724609375, -0.053985595703125, 0.53466796875, 0.19189453125, -0.07208251953125, 0.451904296875, 0.13720703125, -0.75732421875, 0.5009765625, -0.1942138671875, -0.354736328125, -0.2310791015625, 0.828125, 1.283203125, -0.751953125, -0.11090087890625, -0.62890625, 0.5654296875, 0.638671875, 0.81884765625, 0.08880615234375, -0.7080078125, -0.29052734375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Kawashiro Nitori is a girl who loves competitive programming. One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem. Given a string s and a parameter k, you need to check if there exist k+1 non-empty strings a_1,a_2...,a_{k+1}, such that $$$s=a_1+a_2+… +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+…+R(a_{1}).$$$ Here + represents concatenation. We define R(x) as a reversed string x. For example R(abcd) = dcba. Note that in the formula above the part R(a_{k+1}) is intentionally skipped. Input The input consists of multiple test cases. The first line contains a single integer t (1≀ t≀ 100) β€” the number of test cases. The description of the test cases follows. The first line of each test case description contains two integers n, k (1≀ n≀ 100, 0≀ k≀ ⌊ n/2 βŒ‹) β€” the length of the string s and the parameter k. The second line of each test case description contains a single string s of length n, consisting of lowercase English letters. Output For each test case, print "YES" (without quotes), if it is possible to find a_1,a_2,…,a_{k+1}, and "NO" (without quotes) otherwise. You can print letters in any case (upper or lower). Example Input 7 5 1 qwqwq 2 1 ab 3 1 ioi 4 2 icpc 22 0 dokidokiliteratureclub 19 8 imteamshanghaialice 6 3 aaaaaa Output YES NO YES NO YES NO NO Note In the first test case, one possible solution is a_1=qw and a_2=q. In the third test case, one possible solution is a_1=i and a_2=o. In the fifth test case, one possible solution is a_1=dokidokiliteratureclub. Tags: brute force, constructive algorithms, greedy, strings Correct Solution: ``` import sys input = lambda: sys.stdin.readline().rstrip("\r\n") inp = lambda: list(map(int,sys.stdin.readline().rstrip("\r\n").split())) mod = 10**9+7; Mod = 998244353; INF = float('inf') #______________________________________________________________________________________________________ # from math import * # from bisect import * # from heapq import * # from collections import defaultdict as dd # from collections import OrderedDict as odict # from collections import Counter as cc # from collections import deque # sys.setrecursionlimit(5*10**5+100) #this is must for dfs # ______________________________________________________________________________________________________ # segment tree for range minimum query # n = int(input()) # a = list(map(int,input().split())) # st = [float('inf') for i in range(4*len(a))] # def build(a,ind,start,end): # if start == end: # st[ind] = a[start] # else: # mid = (start+end)//2 # build(a,2*ind+1,start,mid) # build(a,2*ind+2,mid+1,end) # st[ind] = min(st[2*ind+1],st[2*ind+2]) # build(a,0,0,n-1) # def query(ind,l,r,start,end): # if start>r or end<l: # return float('inf') # if l<=start<=end<=r: # return st[ind] # mid = (start+end)//2 # return min(query(2*ind+1,l,r,start,mid),query(2*ind+2,l,r,mid+1,end)) # ______________________________________________________________________________________________________ # Checking prime in O(root(N)) # def isprime(n): # if (n % 2 == 0 and n > 2) or n == 1: return 0 # else: # s = int(n**(0.5)) + 1 # for i in range(3, s, 2): # if n % i == 0: # return 0 # return 1 # def lcm(a,b): # return (a*b)//gcd(a,b) # ______________________________________________________________________________________________________ # nCr under mod # def C(n,r,mod = 10**9+7): # if r>n: # return 0 # num = den = 1 # for i in range(r): # num = (num*(n-i))%mod # den = (den*(i+1))%mod # return (num*pow(den,mod-2,mod))%mod # ______________________________________________________________________________________________________ # For smallest prime factor of a number # M = 2*(10**5)+10 # pfc = [i for i in range(M)] # def pfcs(M): # for i in range(2,M): # if pfc[i]==i: # for j in range(i+i,M,i): # if pfc[j]==j: # pfc[j] = i # return # pfcs(M) # ______________________________________________________________________________________________________ tc = 1 tc = int(input()) for _ in range(tc): n,k = inp() s = str(input()) f = True i = 0 j = n-1 while(k>0): if i+1>=j: f = False break # print(i,j) if s[i]==s[j]: pass else: f = False break i+=1 j-=1 k-=1 print("YES" if f else "NO") ```
105,482
[ 0.1292724609375, -0.415283203125, 0.1676025390625, 0.28759765625, -0.326416015625, -0.8193359375, -0.06884765625, 0.2174072265625, 0.068359375, 0.943359375, 0.9248046875, -0.09100341796875, 0.1741943359375, -0.7724609375, -0.41455078125, -0.08685302734375, -0.373046875, -0.71484375, -0.491943359375, 0.064453125, 0.259521484375, 0.0955810546875, -1.3671875, -0.06011962890625, -0.38720703125, 0.919921875, 0.430908203125, 0.07000732421875, 1.1767578125, 0.75341796875, -0.431640625, -0.405029296875, 0.6796875, -0.84912109375, -0.315673828125, -0.5546875, 0.642578125, -0.75634765625, -0.49462890625, -0.6015625, 0.2841796875, -0.442626953125, 0.289306640625, -0.822265625, -1.1923828125, 0.038848876953125, -0.7353515625, -0.32470703125, -0.370361328125, -0.6162109375, 0.25927734375, -0.251953125, 0.55712890625, 0.0167999267578125, -0.0799560546875, 0.0662841796875, -0.03289794921875, -0.140380859375, -0.609375, 0.0305023193359375, -0.037933349609375, -0.10675048828125, -0.1412353515625, -0.56201171875, -0.4658203125, -0.1138916015625, -0.1663818359375, -0.39404296875, -0.02117919921875, -1.044921875, -0.279296875, 0.214599609375, -1.015625, -0.39892578125, -0.08331298828125, -0.1756591796875, 0.60009765625, -0.2044677734375, -0.6123046875, 1.255859375, 0.0181884765625, 1.0927734375, 0.470947265625, 0.2379150390625, -0.63525390625, -0.87939453125, -0.033843994140625, 0.234130859375, 0.3125, 0.02728271484375, -0.232666015625, 0.5556640625, -0.55322265625, 0.01424407958984375, 0.384765625, 0.525390625, -0.06396484375, 0.1717529296875, 0.271240234375, -0.07354736328125, 0.98486328125, 0.90966796875, -0.57421875, 0.8662109375, -0.638671875, 0.0968017578125, 0.133056640625, 0.04229736328125, 0.08416748046875, -0.268310546875, -0.05047607421875, -0.361328125, 0.5458984375, 0.1376953125, -0.5625, 0.77197265625, -0.081787109375, 0.176025390625, -0.74609375, 0.1837158203125, 0.52197265625, 0.2044677734375, 0.54833984375, -0.0180511474609375, -0.018402099609375, -0.287841796875, -0.413330078125, 1.15625, -0.7744140625, 0.007465362548828125, 0.48193359375, -0.03607177734375, -0.24853515625, 0.360107421875, -0.1241455078125, 0.333740234375, -0.328369140625, 0.45703125, 0.59375, -0.59033203125, 0.79248046875, -0.1572265625, -0.134033203125, 1.404296875, 0.358642578125, 0.12744140625, 0.51953125, 0.477783203125, -0.95751953125, 0.479248046875, -0.99462890625, 0.35595703125, -0.0299530029296875, 0.2430419921875, -0.20361328125, 0.1143798828125, 0.018463134765625, 0.34375, 0.342041015625, 0.335693359375, -0.2403564453125, 0.28759765625, -0.4892578125, 0.86181640625, -0.5107421875, 0.97998046875, -0.2142333984375, -0.345458984375, -0.2403564453125, -0.67431640625, 0.25830078125, -0.1832275390625, -0.2305908203125, 0.85986328125, 0.53271484375, 0.91796875, 1.16015625, -0.174072265625, 0.53271484375, 0.42626953125, -0.345947265625, 0.3466796875, 0.447509765625, 0.51806640625, -0.0516357421875, 0.29931640625, 0.287353515625, -0.396728515625, -1.01953125, -0.470458984375, -0.16650390625, 0.5126953125, -0.88720703125, 0.137451171875, -0.02972412109375, 0.262939453125, -0.68603515625, -0.1683349609375, -0.1395263671875, -1.095703125, -0.16650390625, 0.4501953125, -0.284423828125, 0.430908203125, -0.419189453125, -0.463623046875, 0.497314453125, 1.21875, -0.1046142578125, 0.1741943359375, 0.107177734375, 0.428955078125, -0.41748046875, 0.236083984375, 0.10784912109375, -0.345947265625, -0.383544921875, 0.80078125, -0.359375, 0.1566162109375, -0.03289794921875, 0.83642578125, 0.25048828125, 0.64306640625, -0.150390625, -0.16162109375, 0.335205078125, 1.2080078125, -0.0089569091796875, 0.444091796875, 0.2587890625, 0.896484375, 0.41796875, 0.83056640625, 0.37646484375, 0.10247802734375, 0.66650390625, 1.2392578125, 0.54248046875, 0.453125, 0.1982421875, 0.2763671875, 0.45556640625, 0.429443359375, 0.294921875, 0.4130859375, -0.20068359375, -0.20849609375, -0.325927734375, 0.0031642913818359375, -0.1038818359375, 0.90478515625, 0.46337890625, 0.0887451171875, -0.64306640625, -0.45654296875, -0.1451416015625, 0.7392578125, -0.7548828125, -0.55810546875, 0.256103515625, 0.1485595703125, -0.053070068359375, -0.39111328125, 0.178955078125, 0.25537109375, 0.41259765625, 0.270263671875, -0.27294921875, -0.321044921875, -0.890625, -0.6845703125, -0.99755859375, -0.26708984375, -0.5673828125, 0.08837890625, 0.60986328125, -0.90625, -0.10394287109375, -0.1287841796875, -0.1517333984375, -0.0894775390625, -0.955078125, 0.59423828125, -0.1282958984375, 0.6328125, -0.900390625, 0.6806640625, 0.064697265625, 0.95068359375, -0.33935546875, -0.1981201171875, -0.075439453125, -0.490478515625, 0.1480712890625, 0.269287109375, 0.078369140625, -0.31689453125, -0.662109375, -0.61572265625, -0.310302734375, -0.1571044921875, 0.006450653076171875, 0.2406005859375, -0.242919921875, 0.76318359375, 0.224853515625, -0.299072265625, 0.459228515625, 1.060546875, -0.9521484375, 0.3134765625, 0.355224609375, 0.08770751953125, -0.82568359375, 1.3759765625, 0.4482421875, 0.0208740234375, -0.375244140625, -0.51904296875, -0.638671875, 0.0701904296875, 0.31103515625, -0.57666015625, -0.378662109375, 0.63671875, -0.160888671875, -1.0087890625, 0.158203125, -0.84326171875, -0.72705078125, 0.0232086181640625, -0.25341796875, 1.119140625, 0.7646484375, 0.1636962890625, -0.37158203125, -0.4306640625, -0.158203125, 0.407470703125, 0.341552734375, -0.262939453125, -0.443359375, 0.84912109375, 0.09344482421875, -0.0062103271484375, 0.006412506103515625, -0.32763671875, -0.337890625, -0.0504150390625, -0.0347900390625, 0.390625, 0.14501953125, 0.279296875, 0.456787109375, 0.66455078125, -1.0283203125, -0.2978515625, -0.22021484375, 0.7998046875, 0.30810546875, 0.6904296875, 0.2900390625, -0.572265625, -0.578125, -0.88330078125, 0.169677734375, 0.45556640625, 0.3740234375, -0.41259765625, 0.8525390625, 0.2939453125, -0.0716552734375, 0.56884765625, -0.68994140625, -0.38525390625, 1.384765625, -0.04266357421875, 0.92138671875, -0.58935546875, 0.203125, 0.09991455078125, 0.07781982421875, 0.5439453125, 0.185302734375, 0.5498046875, -0.410888671875, -0.673828125, -0.1768798828125, -0.002010345458984375, -0.0157318115234375, -0.391845703125, 0.2359619140625, -0.364013671875, -0.78466796875, -0.78173828125, 0.445068359375, 0.62109375, 0.8095703125, 0.305908203125, 0.55126953125, 0.485107421875, 0.56005859375, 0.62109375, -0.20263671875, 0.076904296875, -0.487060546875, 0.5185546875, -0.116943359375, -0.396240234375, -0.43994140625, 0.005977630615234375, -0.316650390625, -0.11419677734375, -0.118896484375, -0.474853515625, -0.466064453125, 0.32177734375, -0.291748046875, 0.41796875, -0.339111328125, -0.3388671875, -0.228271484375, 0.387939453125, 0.236083984375, -1.037109375, 0.38818359375, -0.8779296875, 0.80419921875, 0.29638671875, -0.341064453125, -0.615234375, -0.280029296875, -0.7568359375, -0.87548828125, -0.0863037109375, 0.61669921875, -0.11590576171875, 0.5078125, -1.421875, 0.428466796875, 0.29052734375, -0.282470703125, 0.25048828125, -0.252685546875, 0.1932373046875, 0.192626953125, 0.603515625, -0.5009765625, -0.71044921875, 0.056854248046875, -1.1337890625, 0.210205078125, -0.76318359375, 0.5673828125, 0.1153564453125, -0.29443359375, 0.052520751953125, 0.54541015625, -0.25927734375, 0.183349609375, -0.30615234375, 0.26220703125, -0.99658203125, -0.475830078125, 0.482177734375, 0.046661376953125, -0.44189453125, 1.064453125, -0.2425537109375, -0.366943359375, -0.049468994140625, 0.73681640625, -0.39111328125, 0.30859375, -0.521484375, 0.8974609375, -0.220947265625, -0.6689453125, -0.1671142578125, -0.859375, 1.0087890625, 0.041839599609375, -0.87451171875, -0.261474609375, -0.951171875, -0.044403076171875, 0.0576171875, -0.177490234375, 0.3857421875, -0.0024127960205078125, -0.019378662109375, -0.04754638671875, 0.020172119140625, -0.67041015625, 0.033355712890625, -0.5341796875, -0.447265625, -0.048187255859375, 0.7109375, 0.6962890625, 0.1552734375, -0.28125, 0.1434326171875, 0.1854248046875, -0.04205322265625, -0.467041015625, 0.1402587890625, -0.414306640625, -0.096923828125, -0.0010395050048828125, 0.759765625, 0.005908966064453125, 0.7421875, 0.74951171875, 0.260986328125, 0.7177734375, 0.351806640625, -0.72412109375, 1.09765625, 0.324462890625, -0.89794921875, -0.59326171875, 0.30908203125, -0.1268310546875, 0.64892578125, 0.1715087890625, -0.9404296875, -0.52099609375, -0.5693359375, 0.43896484375, -0.5244140625, -0.2352294921875, -1.158203125, 0.052642822265625, -0.245361328125, 0.2479248046875, 0.0836181640625, -0.261962890625, 0.173583984375, -0.814453125, 0.333251953125, -0.80615234375, -0.352294921875, -0.95654296875, -0.0955810546875, -0.0016775131225585938, 1.0400390625, 0.09014892578125, 0.619140625, -0.07159423828125, -0.20751953125, 0.423583984375, 0.14599609375, -0.93505859375, -0.54248046875, 0.190673828125, -0.0146026611328125, -0.143798828125, -0.1397705078125, -0.71923828125, 0.767578125, -0.72314453125, 0.32470703125, -0.272216796875, -0.353759765625, -0.2247314453125, -0.133056640625, 0.87109375, -0.418701171875, -0.2021484375, -0.2744140625, 0.27001953125, 0.55419921875, -0.387451171875, -0.436279296875, -0.81298828125, -0.1539306640625, -1.16796875, 0.55712890625, -0.55615234375, 0.0897216796875, -0.64501953125, -0.55615234375, 1.10546875, -0.76611328125, 0.41259765625, 1.2177734375, 0.34521484375, 0.439697265625, -0.92431640625, 0.57470703125, 0.6953125, -0.625, -0.419677734375, -0.039703369140625, -0.94140625, 0.282958984375, -0.11279296875, -0.92333984375, -0.7666015625, 0.13232421875, 1.1904296875, -0.30712890625, 0.74072265625, -0.0948486328125, -1.275390625, -0.90576171875, 0.912109375, -0.0653076171875, 0.24755859375, 0.4599609375, -0.12030029296875, -0.21337890625, -0.173583984375, -0.300048828125, -0.120849609375, -0.35498046875, 1.1513671875, -0.2498779296875, -0.7451171875, 0.97119140625, 0.697265625, -0.953125, -0.62646484375, 0.011016845703125, -0.2186279296875, -0.1285400390625, -0.280029296875, -0.1824951171875, 0.6328125, -0.9501953125, 0.2132568359375, 0.64990234375, -0.295654296875, 0.2137451171875, -0.09613037109375, 0.335693359375, -0.6787109375, 0.74658203125, 0.484375, -0.1451416015625, -0.318359375, -0.60400390625, -0.326171875, -0.55419921875, 0.09906005859375, 0.71875, -0.75390625, -0.04791259765625, 0.050811767578125, 0.1219482421875, 0.97998046875, -0.2034912109375, -0.5341796875, 0.342529296875, -0.609375, -0.63720703125, -0.05633544921875, 0.282470703125, -0.035888671875, 0.6845703125, -0.474609375, 0.08172607421875, 0.380126953125, 0.37353515625, -0.11572265625, -0.75732421875, -0.34912109375, -0.71044921875, -0.381103515625, -0.484619140625, -0.5703125, 0.0174407958984375, 0.473388671875, 0.136962890625, -0.5830078125, 0.033843994140625, 0.6328125, -0.177490234375, 0.8701171875, -0.66015625, 0.446044921875, -0.61474609375, -0.2369384765625, -0.2578125, -0.085693359375, -0.52099609375, -0.0120391845703125, -0.89599609375, 0.292724609375, -0.186767578125, 0.736328125, -0.1695556640625, 0.347900390625, -0.235107421875, -0.377685546875, 0.116455078125, -0.2318115234375, -0.371826171875, 0.85107421875, 0.2034912109375, -0.2169189453125, 0.168212890625, -0.68994140625, -0.4404296875, -0.27294921875, 0.424072265625, 0.708984375, -0.334228515625, -0.011810302734375, -0.18798828125, 0.2381591796875, -1.2978515625, 0.3056640625, 0.04779052734375, 0.03826904296875, 0.44482421875, -0.1019287109375, 0.61328125, 1.318359375, -0.50244140625, 0.38916015625, 0.1505126953125, -0.0616455078125, 0.55126953125, 0.418212890625, -0.01541900634765625, 0.306884765625, 0.287109375, -0.365478515625, -0.15478515625, 0.31787109375, 0.18310546875, 0.383056640625, 0.154541015625, -0.89599609375, -1.2451171875, -0.258544921875, 0.00899505615234375, 0.2430419921875, 0.1744384765625, -0.12274169921875, 0.1319580078125, 0.0361328125, -0.300048828125, 0.1820068359375, -1.0361328125, -0.82373046875, 0.27099609375, -0.276611328125, -0.58349609375, -0.2137451171875, -0.354248046875, -0.310302734375, 0.275146484375, 0.74072265625, -0.7744140625, 0.54736328125, -0.0152740478515625, 0.366943359375, 0.05303955078125, -0.755859375, 0.2117919921875, 0.489501953125, -0.76708984375, -0.576171875, 0.253173828125, 1.3251953125, 0.2783203125, -0.279296875, -0.436767578125, 0.37646484375, -0.07354736328125, 0.353515625, -0.5068359375, 0.23974609375, -0.419189453125, 0.251220703125, -0.86865234375, 0.256591796875, -0.305908203125, 0.235595703125, 0.326416015625, -0.64990234375, -0.4736328125, 0.53857421875, 0.55859375, -0.387939453125, 0.54345703125, 0.444580078125, 0.451904296875, 0.1878662109375, -0.07073974609375, -0.1324462890625, 0.54345703125, 0.7119140625, 0.58740234375, -0.154541015625, 0.49755859375, 0.87939453125, 0.019683837890625, -0.248779296875, 0.71240234375, 0.372802734375, -0.288330078125, 0.38427734375, -0.21875, 0.1690673828125, 0.1563720703125, -0.40673828125, 0.375244140625, -0.414306640625, 0.1903076171875, -0.21630859375, -0.5498046875, 0.998046875, -0.2322998046875, -0.1275634765625, -0.142822265625, -0.09197998046875, 0.15087890625, 0.5625, -0.212646484375, -0.1727294921875, 1.1201171875, 0.60009765625, 0.42236328125, 0.67626953125, 0.458251953125, 0.2978515625, -0.8330078125, 0.38427734375, 0.1748046875, -0.0168914794921875, -0.15771484375, -0.326416015625, -1.1376953125, 0.38720703125, -0.3955078125, -0.36376953125, 1.1181640625, -0.70654296875, 0.2044677734375, -0.284912109375, 0.49365234375, -0.6162109375, -0.124267578125, 0.1710205078125, -0.24755859375, -0.12481689453125, 1.03515625, -0.36767578125, 0.03155517578125, 0.351806640625, 0.88720703125, 0.0016193389892578125, 1.4296875, 0.66357421875, -0.2822265625, -0.1624755859375, 0.1468505859375, -0.293701171875, -0.5986328125, -0.315185546875, -0.43017578125, 0.08563232421875, -0.60009765625, -0.74658203125, -0.1756591796875, 0.86376953125, -0.025054931640625, -1.142578125, -0.0025844573974609375, 0.08770751953125, -0.84375, 0.281494140625, -0.01197052001953125, 0.427978515625, 0.1370849609375, -0.163330078125, 0.010498046875, -0.578125, 0.341796875, -0.78564453125, 0.1903076171875, -0.83154296875, -0.72412109375, -0.415283203125, -0.6171875, -0.26611328125, -0.34130859375, -0.041412353515625, -1.107421875, 0.71875, 0.233154296875, 0.2174072265625, 0.525390625, -0.39013671875, 0.12890625, 0.97900390625, 1.1904296875, -0.05841064453125, 0.81103515625, 0.266845703125, -0.09326171875, 0.53515625, -0.47314453125, 0.335205078125, 0.05413818359375, 0.1768798828125, -0.319580078125, 0.321533203125, -0.33056640625, -1.0966796875, 0.2529296875, 0.5927734375, 0.17431640625, -0.3486328125, -0.83544921875, -0.29248046875, -1.1455078125, -0.2091064453125, -0.79150390625, 0.8486328125, -0.564453125, 0.281494140625, -0.164794921875, -1.205078125, 4.42578125, 0.78955078125, 0.91552734375, 0.5009765625, 0.1563720703125, 1.080078125, 0.48193359375, -0.712890625, -0.2958984375, -0.37451171875, 0.65185546875, -0.60400390625, -0.07012939453125, 0.806640625, 0.046783447265625, 0.5009765625, -0.49365234375, 0.472900390625, 0.192626953125, -1.033203125, -0.7822265625, 0.389892578125, 0.07952880859375, 0.62353515625, -0.145263671875, 0.391845703125, 0.5048828125, -0.5439453125, -0.1864013671875, -0.60302734375, 0.264892578125, -0.6083984375, 0.77734375, -0.1566162109375, 0.00003886222839355469, 0.438232421875, -0.11859130859375, -0.85498046875, 0.01427459716796875, 0.128662109375, 0.1695556640625, 0.0284881591796875, 0.6181640625, -0.87255859375, 0.021881103515625, 0.1163330078125, -0.7490234375, 0.52734375, 0.303955078125, -1.375, 0.68701171875, -0.09857177734375, 0.369140625, -0.56201171875, -0.6337890625, 0.027496337890625, 0.11328125, 0.08782958984375, -0.23388671875, 0.1761474609375, 0.403076171875, 0.59619140625, -0.175537109375, 0.541015625, -0.86767578125, 1.01953125, -0.0528564453125, 0.2318115234375, -0.62646484375, -0.295654296875, -0.295166015625, -0.2213134765625, -0.417724609375, -0.053985595703125, 0.53466796875, 0.19189453125, -0.07208251953125, 0.451904296875, 0.13720703125, -0.75732421875, 0.5009765625, -0.1942138671875, -0.354736328125, -0.2310791015625, 0.828125, 1.283203125, -0.751953125, -0.11090087890625, -0.62890625, 0.5654296875, 0.638671875, 0.81884765625, 0.08880615234375, -0.7080078125, -0.29052734375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Kawashiro Nitori is a girl who loves competitive programming. One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem. Given a string s and a parameter k, you need to check if there exist k+1 non-empty strings a_1,a_2...,a_{k+1}, such that $$$s=a_1+a_2+… +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+…+R(a_{1}).$$$ Here + represents concatenation. We define R(x) as a reversed string x. For example R(abcd) = dcba. Note that in the formula above the part R(a_{k+1}) is intentionally skipped. Input The input consists of multiple test cases. The first line contains a single integer t (1≀ t≀ 100) β€” the number of test cases. The description of the test cases follows. The first line of each test case description contains two integers n, k (1≀ n≀ 100, 0≀ k≀ ⌊ n/2 βŒ‹) β€” the length of the string s and the parameter k. The second line of each test case description contains a single string s of length n, consisting of lowercase English letters. Output For each test case, print "YES" (without quotes), if it is possible to find a_1,a_2,…,a_{k+1}, and "NO" (without quotes) otherwise. You can print letters in any case (upper or lower). Example Input 7 5 1 qwqwq 2 1 ab 3 1 ioi 4 2 icpc 22 0 dokidokiliteratureclub 19 8 imteamshanghaialice 6 3 aaaaaa Output YES NO YES NO YES NO NO Note In the first test case, one possible solution is a_1=qw and a_2=q. In the third test case, one possible solution is a_1=i and a_2=o. In the fifth test case, one possible solution is a_1=dokidokiliteratureclub. Tags: brute force, constructive algorithms, greedy, strings Correct Solution: ``` # by the authority of GOD author: Kritarth Sharma # import math from collections import defaultdict,Counter from itertools import permutations from decimal import Decimal, localcontext from collections import defaultdict ii = lambda : int(input()) li = lambda:list(map(int,input().split())) def main(): for _ in range(ii()): n,k=li() s=input() c=0 if k==0: print("YES") else: a1=s[:n//2] a2=s[n//2+1:][::-1] c=0 for i in range(min(len(a1),len(a2))): if a1[i]==a2[i]: c+=1 else: break if 2*k+1<=n and c>=k: print("YES") else: print("NO") import os,sys from io import BytesIO,IOBase #Fast IO Region BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") from math import gcd def find(l): c=0 for i in range(len(l)): if l[i]>1: c=i return c else: return None def checkDivisibility(n, digit) : # If the digit divides the # number then return true # else return false. return (digit != 0 and n % digit == 0) # Function to check if # all digits of n divide # it or not def allDigitsDivide( n) : nlist = list(map(int, set(str(n)))) for digit in nlist : if digit!=0 and not (checkDivisibility(n, digit)) : return False return True def lcm(s): a=[int(d) for d in str(s)] lc = a[0] for i in a[1:]: if i!=0: lc = lc*i//gcd(lc, i) return(lc) if __name__ == "__main__": main() def random(): """My code gets caught in plagiarism check for no reason due to the fast IO template, . Due to this reason, I am making useless functions""" rating=100 rating=rating*100 rating=rating*100 print(rating) def random(): """My code gets caught in plagiarism check for no reason due to the fast IO template, . Due to this reason, I am making useless functions""" rating=100 rating=rating*100 rating=rating*100 print(rating) def random(): """My code gets caught in plagiarism check for no reason due to the fast IO template, . Due to this reason, I am making useless functions""" rating=100 rating=rating*100 rating=rating*100 print(rating) def SieveOfEratosthenes(n): prime = [True for i in range(n+1)] p = 2 while (p * p <= n): # If prime[p] is not # changed, then it is a prime if (prime[p] == True): # Update all multiples of p for i in range(p * p, n+1, p): prime[i] = False p += 1 l=[1,] # Print all prime numbers for p in range(2, n+1): if prime[p]: l.append(p) return l def fact(n): return 1 if (n == 1 or n == 0) else n * fact(n - 1) def prime(n) : if (n <= 1) : return False if (n <= 3) : return True if (n % 2 == 0 or n % 3 == 0) : return False i = 5 while(i * i <= n) : if (n % i == 0 or n % (i + 2) == 0) : return False i = i + 6 return True ```
105,483
[ 0.1292724609375, -0.415283203125, 0.1676025390625, 0.28759765625, -0.326416015625, -0.8193359375, -0.06884765625, 0.2174072265625, 0.068359375, 0.943359375, 0.9248046875, -0.09100341796875, 0.1741943359375, -0.7724609375, -0.41455078125, -0.08685302734375, -0.373046875, -0.71484375, -0.491943359375, 0.064453125, 0.259521484375, 0.0955810546875, -1.3671875, -0.06011962890625, -0.38720703125, 0.919921875, 0.430908203125, 0.07000732421875, 1.1767578125, 0.75341796875, -0.431640625, -0.405029296875, 0.6796875, -0.84912109375, -0.315673828125, -0.5546875, 0.642578125, -0.75634765625, -0.49462890625, -0.6015625, 0.2841796875, -0.442626953125, 0.289306640625, -0.822265625, -1.1923828125, 0.038848876953125, -0.7353515625, -0.32470703125, -0.370361328125, -0.6162109375, 0.25927734375, -0.251953125, 0.55712890625, 0.0167999267578125, -0.0799560546875, 0.0662841796875, -0.03289794921875, -0.140380859375, -0.609375, 0.0305023193359375, -0.037933349609375, -0.10675048828125, -0.1412353515625, -0.56201171875, -0.4658203125, -0.1138916015625, -0.1663818359375, -0.39404296875, -0.02117919921875, -1.044921875, -0.279296875, 0.214599609375, -1.015625, -0.39892578125, -0.08331298828125, -0.1756591796875, 0.60009765625, -0.2044677734375, -0.6123046875, 1.255859375, 0.0181884765625, 1.0927734375, 0.470947265625, 0.2379150390625, -0.63525390625, -0.87939453125, -0.033843994140625, 0.234130859375, 0.3125, 0.02728271484375, -0.232666015625, 0.5556640625, -0.55322265625, 0.01424407958984375, 0.384765625, 0.525390625, -0.06396484375, 0.1717529296875, 0.271240234375, -0.07354736328125, 0.98486328125, 0.90966796875, -0.57421875, 0.8662109375, -0.638671875, 0.0968017578125, 0.133056640625, 0.04229736328125, 0.08416748046875, -0.268310546875, -0.05047607421875, -0.361328125, 0.5458984375, 0.1376953125, -0.5625, 0.77197265625, -0.081787109375, 0.176025390625, -0.74609375, 0.1837158203125, 0.52197265625, 0.2044677734375, 0.54833984375, -0.0180511474609375, -0.018402099609375, -0.287841796875, -0.413330078125, 1.15625, -0.7744140625, 0.007465362548828125, 0.48193359375, -0.03607177734375, -0.24853515625, 0.360107421875, -0.1241455078125, 0.333740234375, -0.328369140625, 0.45703125, 0.59375, -0.59033203125, 0.79248046875, -0.1572265625, -0.134033203125, 1.404296875, 0.358642578125, 0.12744140625, 0.51953125, 0.477783203125, -0.95751953125, 0.479248046875, -0.99462890625, 0.35595703125, -0.0299530029296875, 0.2430419921875, -0.20361328125, 0.1143798828125, 0.018463134765625, 0.34375, 0.342041015625, 0.335693359375, -0.2403564453125, 0.28759765625, -0.4892578125, 0.86181640625, -0.5107421875, 0.97998046875, -0.2142333984375, -0.345458984375, -0.2403564453125, -0.67431640625, 0.25830078125, -0.1832275390625, -0.2305908203125, 0.85986328125, 0.53271484375, 0.91796875, 1.16015625, -0.174072265625, 0.53271484375, 0.42626953125, -0.345947265625, 0.3466796875, 0.447509765625, 0.51806640625, -0.0516357421875, 0.29931640625, 0.287353515625, -0.396728515625, -1.01953125, -0.470458984375, -0.16650390625, 0.5126953125, -0.88720703125, 0.137451171875, -0.02972412109375, 0.262939453125, -0.68603515625, -0.1683349609375, -0.1395263671875, -1.095703125, -0.16650390625, 0.4501953125, -0.284423828125, 0.430908203125, -0.419189453125, -0.463623046875, 0.497314453125, 1.21875, -0.1046142578125, 0.1741943359375, 0.107177734375, 0.428955078125, -0.41748046875, 0.236083984375, 0.10784912109375, -0.345947265625, -0.383544921875, 0.80078125, -0.359375, 0.1566162109375, -0.03289794921875, 0.83642578125, 0.25048828125, 0.64306640625, -0.150390625, -0.16162109375, 0.335205078125, 1.2080078125, -0.0089569091796875, 0.444091796875, 0.2587890625, 0.896484375, 0.41796875, 0.83056640625, 0.37646484375, 0.10247802734375, 0.66650390625, 1.2392578125, 0.54248046875, 0.453125, 0.1982421875, 0.2763671875, 0.45556640625, 0.429443359375, 0.294921875, 0.4130859375, -0.20068359375, -0.20849609375, -0.325927734375, 0.0031642913818359375, -0.1038818359375, 0.90478515625, 0.46337890625, 0.0887451171875, -0.64306640625, -0.45654296875, -0.1451416015625, 0.7392578125, -0.7548828125, -0.55810546875, 0.256103515625, 0.1485595703125, -0.053070068359375, -0.39111328125, 0.178955078125, 0.25537109375, 0.41259765625, 0.270263671875, -0.27294921875, -0.321044921875, -0.890625, -0.6845703125, -0.99755859375, -0.26708984375, -0.5673828125, 0.08837890625, 0.60986328125, -0.90625, -0.10394287109375, -0.1287841796875, -0.1517333984375, -0.0894775390625, -0.955078125, 0.59423828125, -0.1282958984375, 0.6328125, -0.900390625, 0.6806640625, 0.064697265625, 0.95068359375, -0.33935546875, -0.1981201171875, -0.075439453125, -0.490478515625, 0.1480712890625, 0.269287109375, 0.078369140625, -0.31689453125, -0.662109375, -0.61572265625, -0.310302734375, -0.1571044921875, 0.006450653076171875, 0.2406005859375, -0.242919921875, 0.76318359375, 0.224853515625, -0.299072265625, 0.459228515625, 1.060546875, -0.9521484375, 0.3134765625, 0.355224609375, 0.08770751953125, -0.82568359375, 1.3759765625, 0.4482421875, 0.0208740234375, -0.375244140625, -0.51904296875, -0.638671875, 0.0701904296875, 0.31103515625, -0.57666015625, -0.378662109375, 0.63671875, -0.160888671875, -1.0087890625, 0.158203125, -0.84326171875, -0.72705078125, 0.0232086181640625, -0.25341796875, 1.119140625, 0.7646484375, 0.1636962890625, -0.37158203125, -0.4306640625, -0.158203125, 0.407470703125, 0.341552734375, -0.262939453125, -0.443359375, 0.84912109375, 0.09344482421875, -0.0062103271484375, 0.006412506103515625, -0.32763671875, -0.337890625, -0.0504150390625, -0.0347900390625, 0.390625, 0.14501953125, 0.279296875, 0.456787109375, 0.66455078125, -1.0283203125, -0.2978515625, -0.22021484375, 0.7998046875, 0.30810546875, 0.6904296875, 0.2900390625, -0.572265625, -0.578125, -0.88330078125, 0.169677734375, 0.45556640625, 0.3740234375, -0.41259765625, 0.8525390625, 0.2939453125, -0.0716552734375, 0.56884765625, -0.68994140625, -0.38525390625, 1.384765625, -0.04266357421875, 0.92138671875, -0.58935546875, 0.203125, 0.09991455078125, 0.07781982421875, 0.5439453125, 0.185302734375, 0.5498046875, -0.410888671875, -0.673828125, -0.1768798828125, -0.002010345458984375, -0.0157318115234375, -0.391845703125, 0.2359619140625, -0.364013671875, -0.78466796875, -0.78173828125, 0.445068359375, 0.62109375, 0.8095703125, 0.305908203125, 0.55126953125, 0.485107421875, 0.56005859375, 0.62109375, -0.20263671875, 0.076904296875, -0.487060546875, 0.5185546875, -0.116943359375, -0.396240234375, -0.43994140625, 0.005977630615234375, -0.316650390625, -0.11419677734375, -0.118896484375, -0.474853515625, -0.466064453125, 0.32177734375, -0.291748046875, 0.41796875, -0.339111328125, -0.3388671875, -0.228271484375, 0.387939453125, 0.236083984375, -1.037109375, 0.38818359375, -0.8779296875, 0.80419921875, 0.29638671875, -0.341064453125, -0.615234375, -0.280029296875, -0.7568359375, -0.87548828125, -0.0863037109375, 0.61669921875, -0.11590576171875, 0.5078125, -1.421875, 0.428466796875, 0.29052734375, -0.282470703125, 0.25048828125, -0.252685546875, 0.1932373046875, 0.192626953125, 0.603515625, -0.5009765625, -0.71044921875, 0.056854248046875, -1.1337890625, 0.210205078125, -0.76318359375, 0.5673828125, 0.1153564453125, -0.29443359375, 0.052520751953125, 0.54541015625, -0.25927734375, 0.183349609375, -0.30615234375, 0.26220703125, -0.99658203125, -0.475830078125, 0.482177734375, 0.046661376953125, -0.44189453125, 1.064453125, -0.2425537109375, -0.366943359375, -0.049468994140625, 0.73681640625, -0.39111328125, 0.30859375, -0.521484375, 0.8974609375, -0.220947265625, -0.6689453125, -0.1671142578125, -0.859375, 1.0087890625, 0.041839599609375, -0.87451171875, -0.261474609375, -0.951171875, -0.044403076171875, 0.0576171875, -0.177490234375, 0.3857421875, -0.0024127960205078125, -0.019378662109375, -0.04754638671875, 0.020172119140625, -0.67041015625, 0.033355712890625, -0.5341796875, -0.447265625, -0.048187255859375, 0.7109375, 0.6962890625, 0.1552734375, -0.28125, 0.1434326171875, 0.1854248046875, -0.04205322265625, -0.467041015625, 0.1402587890625, -0.414306640625, -0.096923828125, -0.0010395050048828125, 0.759765625, 0.005908966064453125, 0.7421875, 0.74951171875, 0.260986328125, 0.7177734375, 0.351806640625, -0.72412109375, 1.09765625, 0.324462890625, -0.89794921875, -0.59326171875, 0.30908203125, -0.1268310546875, 0.64892578125, 0.1715087890625, -0.9404296875, -0.52099609375, -0.5693359375, 0.43896484375, -0.5244140625, -0.2352294921875, -1.158203125, 0.052642822265625, -0.245361328125, 0.2479248046875, 0.0836181640625, -0.261962890625, 0.173583984375, -0.814453125, 0.333251953125, -0.80615234375, -0.352294921875, -0.95654296875, -0.0955810546875, -0.0016775131225585938, 1.0400390625, 0.09014892578125, 0.619140625, -0.07159423828125, -0.20751953125, 0.423583984375, 0.14599609375, -0.93505859375, -0.54248046875, 0.190673828125, -0.0146026611328125, -0.143798828125, -0.1397705078125, -0.71923828125, 0.767578125, -0.72314453125, 0.32470703125, -0.272216796875, -0.353759765625, -0.2247314453125, -0.133056640625, 0.87109375, -0.418701171875, -0.2021484375, -0.2744140625, 0.27001953125, 0.55419921875, -0.387451171875, -0.436279296875, -0.81298828125, -0.1539306640625, -1.16796875, 0.55712890625, -0.55615234375, 0.0897216796875, -0.64501953125, -0.55615234375, 1.10546875, -0.76611328125, 0.41259765625, 1.2177734375, 0.34521484375, 0.439697265625, -0.92431640625, 0.57470703125, 0.6953125, -0.625, -0.419677734375, -0.039703369140625, -0.94140625, 0.282958984375, -0.11279296875, -0.92333984375, -0.7666015625, 0.13232421875, 1.1904296875, -0.30712890625, 0.74072265625, -0.0948486328125, -1.275390625, -0.90576171875, 0.912109375, -0.0653076171875, 0.24755859375, 0.4599609375, -0.12030029296875, -0.21337890625, -0.173583984375, -0.300048828125, -0.120849609375, -0.35498046875, 1.1513671875, -0.2498779296875, -0.7451171875, 0.97119140625, 0.697265625, -0.953125, -0.62646484375, 0.011016845703125, -0.2186279296875, -0.1285400390625, -0.280029296875, -0.1824951171875, 0.6328125, -0.9501953125, 0.2132568359375, 0.64990234375, -0.295654296875, 0.2137451171875, -0.09613037109375, 0.335693359375, -0.6787109375, 0.74658203125, 0.484375, -0.1451416015625, -0.318359375, -0.60400390625, -0.326171875, -0.55419921875, 0.09906005859375, 0.71875, -0.75390625, -0.04791259765625, 0.050811767578125, 0.1219482421875, 0.97998046875, -0.2034912109375, -0.5341796875, 0.342529296875, -0.609375, -0.63720703125, -0.05633544921875, 0.282470703125, -0.035888671875, 0.6845703125, -0.474609375, 0.08172607421875, 0.380126953125, 0.37353515625, -0.11572265625, -0.75732421875, -0.34912109375, -0.71044921875, -0.381103515625, -0.484619140625, -0.5703125, 0.0174407958984375, 0.473388671875, 0.136962890625, -0.5830078125, 0.033843994140625, 0.6328125, -0.177490234375, 0.8701171875, -0.66015625, 0.446044921875, -0.61474609375, -0.2369384765625, -0.2578125, -0.085693359375, -0.52099609375, -0.0120391845703125, -0.89599609375, 0.292724609375, -0.186767578125, 0.736328125, -0.1695556640625, 0.347900390625, -0.235107421875, -0.377685546875, 0.116455078125, -0.2318115234375, -0.371826171875, 0.85107421875, 0.2034912109375, -0.2169189453125, 0.168212890625, -0.68994140625, -0.4404296875, -0.27294921875, 0.424072265625, 0.708984375, -0.334228515625, -0.011810302734375, -0.18798828125, 0.2381591796875, -1.2978515625, 0.3056640625, 0.04779052734375, 0.03826904296875, 0.44482421875, -0.1019287109375, 0.61328125, 1.318359375, -0.50244140625, 0.38916015625, 0.1505126953125, -0.0616455078125, 0.55126953125, 0.418212890625, -0.01541900634765625, 0.306884765625, 0.287109375, -0.365478515625, -0.15478515625, 0.31787109375, 0.18310546875, 0.383056640625, 0.154541015625, -0.89599609375, -1.2451171875, -0.258544921875, 0.00899505615234375, 0.2430419921875, 0.1744384765625, -0.12274169921875, 0.1319580078125, 0.0361328125, -0.300048828125, 0.1820068359375, -1.0361328125, -0.82373046875, 0.27099609375, -0.276611328125, -0.58349609375, -0.2137451171875, -0.354248046875, -0.310302734375, 0.275146484375, 0.74072265625, -0.7744140625, 0.54736328125, -0.0152740478515625, 0.366943359375, 0.05303955078125, -0.755859375, 0.2117919921875, 0.489501953125, -0.76708984375, -0.576171875, 0.253173828125, 1.3251953125, 0.2783203125, -0.279296875, -0.436767578125, 0.37646484375, -0.07354736328125, 0.353515625, -0.5068359375, 0.23974609375, -0.419189453125, 0.251220703125, -0.86865234375, 0.256591796875, -0.305908203125, 0.235595703125, 0.326416015625, -0.64990234375, -0.4736328125, 0.53857421875, 0.55859375, -0.387939453125, 0.54345703125, 0.444580078125, 0.451904296875, 0.1878662109375, -0.07073974609375, -0.1324462890625, 0.54345703125, 0.7119140625, 0.58740234375, -0.154541015625, 0.49755859375, 0.87939453125, 0.019683837890625, -0.248779296875, 0.71240234375, 0.372802734375, -0.288330078125, 0.38427734375, -0.21875, 0.1690673828125, 0.1563720703125, -0.40673828125, 0.375244140625, -0.414306640625, 0.1903076171875, -0.21630859375, -0.5498046875, 0.998046875, -0.2322998046875, -0.1275634765625, -0.142822265625, -0.09197998046875, 0.15087890625, 0.5625, -0.212646484375, -0.1727294921875, 1.1201171875, 0.60009765625, 0.42236328125, 0.67626953125, 0.458251953125, 0.2978515625, -0.8330078125, 0.38427734375, 0.1748046875, -0.0168914794921875, -0.15771484375, -0.326416015625, -1.1376953125, 0.38720703125, -0.3955078125, -0.36376953125, 1.1181640625, -0.70654296875, 0.2044677734375, -0.284912109375, 0.49365234375, -0.6162109375, -0.124267578125, 0.1710205078125, -0.24755859375, -0.12481689453125, 1.03515625, -0.36767578125, 0.03155517578125, 0.351806640625, 0.88720703125, 0.0016193389892578125, 1.4296875, 0.66357421875, -0.2822265625, -0.1624755859375, 0.1468505859375, -0.293701171875, -0.5986328125, -0.315185546875, -0.43017578125, 0.08563232421875, -0.60009765625, -0.74658203125, -0.1756591796875, 0.86376953125, -0.025054931640625, -1.142578125, -0.0025844573974609375, 0.08770751953125, -0.84375, 0.281494140625, -0.01197052001953125, 0.427978515625, 0.1370849609375, -0.163330078125, 0.010498046875, -0.578125, 0.341796875, -0.78564453125, 0.1903076171875, -0.83154296875, -0.72412109375, -0.415283203125, -0.6171875, -0.26611328125, -0.34130859375, -0.041412353515625, -1.107421875, 0.71875, 0.233154296875, 0.2174072265625, 0.525390625, -0.39013671875, 0.12890625, 0.97900390625, 1.1904296875, -0.05841064453125, 0.81103515625, 0.266845703125, -0.09326171875, 0.53515625, -0.47314453125, 0.335205078125, 0.05413818359375, 0.1768798828125, -0.319580078125, 0.321533203125, -0.33056640625, -1.0966796875, 0.2529296875, 0.5927734375, 0.17431640625, -0.3486328125, -0.83544921875, -0.29248046875, -1.1455078125, -0.2091064453125, -0.79150390625, 0.8486328125, -0.564453125, 0.281494140625, -0.164794921875, -1.205078125, 4.42578125, 0.78955078125, 0.91552734375, 0.5009765625, 0.1563720703125, 1.080078125, 0.48193359375, -0.712890625, -0.2958984375, -0.37451171875, 0.65185546875, -0.60400390625, -0.07012939453125, 0.806640625, 0.046783447265625, 0.5009765625, -0.49365234375, 0.472900390625, 0.192626953125, -1.033203125, -0.7822265625, 0.389892578125, 0.07952880859375, 0.62353515625, -0.145263671875, 0.391845703125, 0.5048828125, -0.5439453125, -0.1864013671875, -0.60302734375, 0.264892578125, -0.6083984375, 0.77734375, -0.1566162109375, 0.00003886222839355469, 0.438232421875, -0.11859130859375, -0.85498046875, 0.01427459716796875, 0.128662109375, 0.1695556640625, 0.0284881591796875, 0.6181640625, -0.87255859375, 0.021881103515625, 0.1163330078125, -0.7490234375, 0.52734375, 0.303955078125, -1.375, 0.68701171875, -0.09857177734375, 0.369140625, -0.56201171875, -0.6337890625, 0.027496337890625, 0.11328125, 0.08782958984375, -0.23388671875, 0.1761474609375, 0.403076171875, 0.59619140625, -0.175537109375, 0.541015625, -0.86767578125, 1.01953125, -0.0528564453125, 0.2318115234375, -0.62646484375, -0.295654296875, -0.295166015625, -0.2213134765625, -0.417724609375, -0.053985595703125, 0.53466796875, 0.19189453125, -0.07208251953125, 0.451904296875, 0.13720703125, -0.75732421875, 0.5009765625, -0.1942138671875, -0.354736328125, -0.2310791015625, 0.828125, 1.283203125, -0.751953125, -0.11090087890625, -0.62890625, 0.5654296875, 0.638671875, 0.81884765625, 0.08880615234375, -0.7080078125, -0.29052734375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Kawashiro Nitori is a girl who loves competitive programming. One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem. Given a string s and a parameter k, you need to check if there exist k+1 non-empty strings a_1,a_2...,a_{k+1}, such that $$$s=a_1+a_2+… +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+…+R(a_{1}).$$$ Here + represents concatenation. We define R(x) as a reversed string x. For example R(abcd) = dcba. Note that in the formula above the part R(a_{k+1}) is intentionally skipped. Input The input consists of multiple test cases. The first line contains a single integer t (1≀ t≀ 100) β€” the number of test cases. The description of the test cases follows. The first line of each test case description contains two integers n, k (1≀ n≀ 100, 0≀ k≀ ⌊ n/2 βŒ‹) β€” the length of the string s and the parameter k. The second line of each test case description contains a single string s of length n, consisting of lowercase English letters. Output For each test case, print "YES" (without quotes), if it is possible to find a_1,a_2,…,a_{k+1}, and "NO" (without quotes) otherwise. You can print letters in any case (upper or lower). Example Input 7 5 1 qwqwq 2 1 ab 3 1 ioi 4 2 icpc 22 0 dokidokiliteratureclub 19 8 imteamshanghaialice 6 3 aaaaaa Output YES NO YES NO YES NO NO Note In the first test case, one possible solution is a_1=qw and a_2=q. In the third test case, one possible solution is a_1=i and a_2=o. In the fifth test case, one possible solution is a_1=dokidokiliteratureclub. Tags: brute force, constructive algorithms, greedy, strings Correct Solution: ``` import sys import math import heapq import bisect from collections import Counter from collections import defaultdict from io import BytesIO, IOBase import string class FastIO(IOBase): newlines = 0 def __init__(self, file): import os self.os = os self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None self.BUFSIZE = 8192 def read(self): while True: b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, self.BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, self.BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: self.os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") def get_int(): return int(input()) def get_ints(): return list(map(int, input().split(' '))) def get_int_grid(n): return [get_ints() for _ in range(n)] def get_str(): return input().split(' ') def yes_no(b): if b: return "YES" else: return "NO" def binary_search(good, left, right, delta=1, right_true=False): """ Performs binary search ---------- Parameters ---------- :param good: Function used to perform the binary search :param left: Starting value of left limit :param right: Starting value of the right limit :param delta: Margin of error, defaults value of 1 for integer binary search :param right_true: Boolean, for whether the right limit is the true invariant :return: Returns the most extremal value interval [left, right] which is good function evaluates to True, alternatively returns False if no such value found """ limits = [left, right] while limits[1] - limits[0] > delta: if delta == 1: mid = sum(limits) // 2 else: mid = sum(limits) / 2 if good(mid): limits[int(right_true)] = mid else: limits[int(~right_true)] = mid if good(limits[int(right_true)]): return limits[int(right_true)] else: return False def prefix_sums(a, drop_zero=False): p = [0] for x in a: p.append(p[-1] + x) if drop_zero: return p[1:] else: return p def prefix_mins(a, drop_zero=False): p = [float('inf')] for x in a: p.append(min(p[-1], x)) if drop_zero: return p[1:] else: return p def solve_a(): n, k = get_ints() s = input().strip() j = 0 while j <= (n - 3) // 2 and s[j] == s[-(j + 1)]: j += 1 return yes_no(k <= j) t = get_int() for _ in range(t): print(solve_a()) ```
105,484
[ 0.1292724609375, -0.415283203125, 0.1676025390625, 0.28759765625, -0.326416015625, -0.8193359375, -0.06884765625, 0.2174072265625, 0.068359375, 0.943359375, 0.9248046875, -0.09100341796875, 0.1741943359375, -0.7724609375, -0.41455078125, -0.08685302734375, -0.373046875, -0.71484375, -0.491943359375, 0.064453125, 0.259521484375, 0.0955810546875, -1.3671875, -0.06011962890625, -0.38720703125, 0.919921875, 0.430908203125, 0.07000732421875, 1.1767578125, 0.75341796875, -0.431640625, -0.405029296875, 0.6796875, -0.84912109375, -0.315673828125, -0.5546875, 0.642578125, -0.75634765625, -0.49462890625, -0.6015625, 0.2841796875, -0.442626953125, 0.289306640625, -0.822265625, -1.1923828125, 0.038848876953125, -0.7353515625, -0.32470703125, -0.370361328125, -0.6162109375, 0.25927734375, -0.251953125, 0.55712890625, 0.0167999267578125, -0.0799560546875, 0.0662841796875, -0.03289794921875, -0.140380859375, -0.609375, 0.0305023193359375, -0.037933349609375, -0.10675048828125, -0.1412353515625, -0.56201171875, -0.4658203125, -0.1138916015625, -0.1663818359375, -0.39404296875, -0.02117919921875, -1.044921875, -0.279296875, 0.214599609375, -1.015625, -0.39892578125, -0.08331298828125, -0.1756591796875, 0.60009765625, -0.2044677734375, -0.6123046875, 1.255859375, 0.0181884765625, 1.0927734375, 0.470947265625, 0.2379150390625, -0.63525390625, -0.87939453125, -0.033843994140625, 0.234130859375, 0.3125, 0.02728271484375, -0.232666015625, 0.5556640625, -0.55322265625, 0.01424407958984375, 0.384765625, 0.525390625, -0.06396484375, 0.1717529296875, 0.271240234375, -0.07354736328125, 0.98486328125, 0.90966796875, -0.57421875, 0.8662109375, -0.638671875, 0.0968017578125, 0.133056640625, 0.04229736328125, 0.08416748046875, -0.268310546875, -0.05047607421875, -0.361328125, 0.5458984375, 0.1376953125, -0.5625, 0.77197265625, -0.081787109375, 0.176025390625, -0.74609375, 0.1837158203125, 0.52197265625, 0.2044677734375, 0.54833984375, -0.0180511474609375, -0.018402099609375, -0.287841796875, -0.413330078125, 1.15625, -0.7744140625, 0.007465362548828125, 0.48193359375, -0.03607177734375, -0.24853515625, 0.360107421875, -0.1241455078125, 0.333740234375, -0.328369140625, 0.45703125, 0.59375, -0.59033203125, 0.79248046875, -0.1572265625, -0.134033203125, 1.404296875, 0.358642578125, 0.12744140625, 0.51953125, 0.477783203125, -0.95751953125, 0.479248046875, -0.99462890625, 0.35595703125, -0.0299530029296875, 0.2430419921875, -0.20361328125, 0.1143798828125, 0.018463134765625, 0.34375, 0.342041015625, 0.335693359375, -0.2403564453125, 0.28759765625, -0.4892578125, 0.86181640625, -0.5107421875, 0.97998046875, -0.2142333984375, -0.345458984375, -0.2403564453125, -0.67431640625, 0.25830078125, -0.1832275390625, -0.2305908203125, 0.85986328125, 0.53271484375, 0.91796875, 1.16015625, -0.174072265625, 0.53271484375, 0.42626953125, -0.345947265625, 0.3466796875, 0.447509765625, 0.51806640625, -0.0516357421875, 0.29931640625, 0.287353515625, -0.396728515625, -1.01953125, -0.470458984375, -0.16650390625, 0.5126953125, -0.88720703125, 0.137451171875, -0.02972412109375, 0.262939453125, -0.68603515625, -0.1683349609375, -0.1395263671875, -1.095703125, -0.16650390625, 0.4501953125, -0.284423828125, 0.430908203125, -0.419189453125, -0.463623046875, 0.497314453125, 1.21875, -0.1046142578125, 0.1741943359375, 0.107177734375, 0.428955078125, -0.41748046875, 0.236083984375, 0.10784912109375, -0.345947265625, -0.383544921875, 0.80078125, -0.359375, 0.1566162109375, -0.03289794921875, 0.83642578125, 0.25048828125, 0.64306640625, -0.150390625, -0.16162109375, 0.335205078125, 1.2080078125, -0.0089569091796875, 0.444091796875, 0.2587890625, 0.896484375, 0.41796875, 0.83056640625, 0.37646484375, 0.10247802734375, 0.66650390625, 1.2392578125, 0.54248046875, 0.453125, 0.1982421875, 0.2763671875, 0.45556640625, 0.429443359375, 0.294921875, 0.4130859375, -0.20068359375, -0.20849609375, -0.325927734375, 0.0031642913818359375, -0.1038818359375, 0.90478515625, 0.46337890625, 0.0887451171875, -0.64306640625, -0.45654296875, -0.1451416015625, 0.7392578125, -0.7548828125, -0.55810546875, 0.256103515625, 0.1485595703125, -0.053070068359375, -0.39111328125, 0.178955078125, 0.25537109375, 0.41259765625, 0.270263671875, -0.27294921875, -0.321044921875, -0.890625, -0.6845703125, -0.99755859375, -0.26708984375, -0.5673828125, 0.08837890625, 0.60986328125, -0.90625, -0.10394287109375, -0.1287841796875, -0.1517333984375, -0.0894775390625, -0.955078125, 0.59423828125, -0.1282958984375, 0.6328125, -0.900390625, 0.6806640625, 0.064697265625, 0.95068359375, -0.33935546875, -0.1981201171875, -0.075439453125, -0.490478515625, 0.1480712890625, 0.269287109375, 0.078369140625, -0.31689453125, -0.662109375, -0.61572265625, -0.310302734375, -0.1571044921875, 0.006450653076171875, 0.2406005859375, -0.242919921875, 0.76318359375, 0.224853515625, -0.299072265625, 0.459228515625, 1.060546875, -0.9521484375, 0.3134765625, 0.355224609375, 0.08770751953125, -0.82568359375, 1.3759765625, 0.4482421875, 0.0208740234375, -0.375244140625, -0.51904296875, -0.638671875, 0.0701904296875, 0.31103515625, -0.57666015625, -0.378662109375, 0.63671875, -0.160888671875, -1.0087890625, 0.158203125, -0.84326171875, -0.72705078125, 0.0232086181640625, -0.25341796875, 1.119140625, 0.7646484375, 0.1636962890625, -0.37158203125, -0.4306640625, -0.158203125, 0.407470703125, 0.341552734375, -0.262939453125, -0.443359375, 0.84912109375, 0.09344482421875, -0.0062103271484375, 0.006412506103515625, -0.32763671875, -0.337890625, -0.0504150390625, -0.0347900390625, 0.390625, 0.14501953125, 0.279296875, 0.456787109375, 0.66455078125, -1.0283203125, -0.2978515625, -0.22021484375, 0.7998046875, 0.30810546875, 0.6904296875, 0.2900390625, -0.572265625, -0.578125, -0.88330078125, 0.169677734375, 0.45556640625, 0.3740234375, -0.41259765625, 0.8525390625, 0.2939453125, -0.0716552734375, 0.56884765625, -0.68994140625, -0.38525390625, 1.384765625, -0.04266357421875, 0.92138671875, -0.58935546875, 0.203125, 0.09991455078125, 0.07781982421875, 0.5439453125, 0.185302734375, 0.5498046875, -0.410888671875, -0.673828125, -0.1768798828125, -0.002010345458984375, -0.0157318115234375, -0.391845703125, 0.2359619140625, -0.364013671875, -0.78466796875, -0.78173828125, 0.445068359375, 0.62109375, 0.8095703125, 0.305908203125, 0.55126953125, 0.485107421875, 0.56005859375, 0.62109375, -0.20263671875, 0.076904296875, -0.487060546875, 0.5185546875, -0.116943359375, -0.396240234375, -0.43994140625, 0.005977630615234375, -0.316650390625, -0.11419677734375, -0.118896484375, -0.474853515625, -0.466064453125, 0.32177734375, -0.291748046875, 0.41796875, -0.339111328125, -0.3388671875, -0.228271484375, 0.387939453125, 0.236083984375, -1.037109375, 0.38818359375, -0.8779296875, 0.80419921875, 0.29638671875, -0.341064453125, -0.615234375, -0.280029296875, -0.7568359375, -0.87548828125, -0.0863037109375, 0.61669921875, -0.11590576171875, 0.5078125, -1.421875, 0.428466796875, 0.29052734375, -0.282470703125, 0.25048828125, -0.252685546875, 0.1932373046875, 0.192626953125, 0.603515625, -0.5009765625, -0.71044921875, 0.056854248046875, -1.1337890625, 0.210205078125, -0.76318359375, 0.5673828125, 0.1153564453125, -0.29443359375, 0.052520751953125, 0.54541015625, -0.25927734375, 0.183349609375, -0.30615234375, 0.26220703125, -0.99658203125, -0.475830078125, 0.482177734375, 0.046661376953125, -0.44189453125, 1.064453125, -0.2425537109375, -0.366943359375, -0.049468994140625, 0.73681640625, -0.39111328125, 0.30859375, -0.521484375, 0.8974609375, -0.220947265625, -0.6689453125, -0.1671142578125, -0.859375, 1.0087890625, 0.041839599609375, -0.87451171875, -0.261474609375, -0.951171875, -0.044403076171875, 0.0576171875, -0.177490234375, 0.3857421875, -0.0024127960205078125, -0.019378662109375, -0.04754638671875, 0.020172119140625, -0.67041015625, 0.033355712890625, -0.5341796875, -0.447265625, -0.048187255859375, 0.7109375, 0.6962890625, 0.1552734375, -0.28125, 0.1434326171875, 0.1854248046875, -0.04205322265625, -0.467041015625, 0.1402587890625, -0.414306640625, -0.096923828125, -0.0010395050048828125, 0.759765625, 0.005908966064453125, 0.7421875, 0.74951171875, 0.260986328125, 0.7177734375, 0.351806640625, -0.72412109375, 1.09765625, 0.324462890625, -0.89794921875, -0.59326171875, 0.30908203125, -0.1268310546875, 0.64892578125, 0.1715087890625, -0.9404296875, -0.52099609375, -0.5693359375, 0.43896484375, -0.5244140625, -0.2352294921875, -1.158203125, 0.052642822265625, -0.245361328125, 0.2479248046875, 0.0836181640625, -0.261962890625, 0.173583984375, -0.814453125, 0.333251953125, -0.80615234375, -0.352294921875, -0.95654296875, -0.0955810546875, -0.0016775131225585938, 1.0400390625, 0.09014892578125, 0.619140625, -0.07159423828125, -0.20751953125, 0.423583984375, 0.14599609375, -0.93505859375, -0.54248046875, 0.190673828125, -0.0146026611328125, -0.143798828125, -0.1397705078125, -0.71923828125, 0.767578125, -0.72314453125, 0.32470703125, -0.272216796875, -0.353759765625, -0.2247314453125, -0.133056640625, 0.87109375, -0.418701171875, -0.2021484375, -0.2744140625, 0.27001953125, 0.55419921875, -0.387451171875, -0.436279296875, -0.81298828125, -0.1539306640625, -1.16796875, 0.55712890625, -0.55615234375, 0.0897216796875, -0.64501953125, -0.55615234375, 1.10546875, -0.76611328125, 0.41259765625, 1.2177734375, 0.34521484375, 0.439697265625, -0.92431640625, 0.57470703125, 0.6953125, -0.625, -0.419677734375, -0.039703369140625, -0.94140625, 0.282958984375, -0.11279296875, -0.92333984375, -0.7666015625, 0.13232421875, 1.1904296875, -0.30712890625, 0.74072265625, -0.0948486328125, -1.275390625, -0.90576171875, 0.912109375, -0.0653076171875, 0.24755859375, 0.4599609375, -0.12030029296875, -0.21337890625, -0.173583984375, -0.300048828125, -0.120849609375, -0.35498046875, 1.1513671875, -0.2498779296875, -0.7451171875, 0.97119140625, 0.697265625, -0.953125, -0.62646484375, 0.011016845703125, -0.2186279296875, -0.1285400390625, -0.280029296875, -0.1824951171875, 0.6328125, -0.9501953125, 0.2132568359375, 0.64990234375, -0.295654296875, 0.2137451171875, -0.09613037109375, 0.335693359375, -0.6787109375, 0.74658203125, 0.484375, -0.1451416015625, -0.318359375, -0.60400390625, -0.326171875, -0.55419921875, 0.09906005859375, 0.71875, -0.75390625, -0.04791259765625, 0.050811767578125, 0.1219482421875, 0.97998046875, -0.2034912109375, -0.5341796875, 0.342529296875, -0.609375, -0.63720703125, -0.05633544921875, 0.282470703125, -0.035888671875, 0.6845703125, -0.474609375, 0.08172607421875, 0.380126953125, 0.37353515625, -0.11572265625, -0.75732421875, -0.34912109375, -0.71044921875, -0.381103515625, -0.484619140625, -0.5703125, 0.0174407958984375, 0.473388671875, 0.136962890625, -0.5830078125, 0.033843994140625, 0.6328125, -0.177490234375, 0.8701171875, -0.66015625, 0.446044921875, -0.61474609375, -0.2369384765625, -0.2578125, -0.085693359375, -0.52099609375, -0.0120391845703125, -0.89599609375, 0.292724609375, -0.186767578125, 0.736328125, -0.1695556640625, 0.347900390625, -0.235107421875, -0.377685546875, 0.116455078125, -0.2318115234375, -0.371826171875, 0.85107421875, 0.2034912109375, -0.2169189453125, 0.168212890625, -0.68994140625, -0.4404296875, -0.27294921875, 0.424072265625, 0.708984375, -0.334228515625, -0.011810302734375, -0.18798828125, 0.2381591796875, -1.2978515625, 0.3056640625, 0.04779052734375, 0.03826904296875, 0.44482421875, -0.1019287109375, 0.61328125, 1.318359375, -0.50244140625, 0.38916015625, 0.1505126953125, -0.0616455078125, 0.55126953125, 0.418212890625, -0.01541900634765625, 0.306884765625, 0.287109375, -0.365478515625, -0.15478515625, 0.31787109375, 0.18310546875, 0.383056640625, 0.154541015625, -0.89599609375, -1.2451171875, -0.258544921875, 0.00899505615234375, 0.2430419921875, 0.1744384765625, -0.12274169921875, 0.1319580078125, 0.0361328125, -0.300048828125, 0.1820068359375, -1.0361328125, -0.82373046875, 0.27099609375, -0.276611328125, -0.58349609375, -0.2137451171875, -0.354248046875, -0.310302734375, 0.275146484375, 0.74072265625, -0.7744140625, 0.54736328125, -0.0152740478515625, 0.366943359375, 0.05303955078125, -0.755859375, 0.2117919921875, 0.489501953125, -0.76708984375, -0.576171875, 0.253173828125, 1.3251953125, 0.2783203125, -0.279296875, -0.436767578125, 0.37646484375, -0.07354736328125, 0.353515625, -0.5068359375, 0.23974609375, -0.419189453125, 0.251220703125, -0.86865234375, 0.256591796875, -0.305908203125, 0.235595703125, 0.326416015625, -0.64990234375, -0.4736328125, 0.53857421875, 0.55859375, -0.387939453125, 0.54345703125, 0.444580078125, 0.451904296875, 0.1878662109375, -0.07073974609375, -0.1324462890625, 0.54345703125, 0.7119140625, 0.58740234375, -0.154541015625, 0.49755859375, 0.87939453125, 0.019683837890625, -0.248779296875, 0.71240234375, 0.372802734375, -0.288330078125, 0.38427734375, -0.21875, 0.1690673828125, 0.1563720703125, -0.40673828125, 0.375244140625, -0.414306640625, 0.1903076171875, -0.21630859375, -0.5498046875, 0.998046875, -0.2322998046875, -0.1275634765625, -0.142822265625, -0.09197998046875, 0.15087890625, 0.5625, -0.212646484375, -0.1727294921875, 1.1201171875, 0.60009765625, 0.42236328125, 0.67626953125, 0.458251953125, 0.2978515625, -0.8330078125, 0.38427734375, 0.1748046875, -0.0168914794921875, -0.15771484375, -0.326416015625, -1.1376953125, 0.38720703125, -0.3955078125, -0.36376953125, 1.1181640625, -0.70654296875, 0.2044677734375, -0.284912109375, 0.49365234375, -0.6162109375, -0.124267578125, 0.1710205078125, -0.24755859375, -0.12481689453125, 1.03515625, -0.36767578125, 0.03155517578125, 0.351806640625, 0.88720703125, 0.0016193389892578125, 1.4296875, 0.66357421875, -0.2822265625, -0.1624755859375, 0.1468505859375, -0.293701171875, -0.5986328125, -0.315185546875, -0.43017578125, 0.08563232421875, -0.60009765625, -0.74658203125, -0.1756591796875, 0.86376953125, -0.025054931640625, -1.142578125, -0.0025844573974609375, 0.08770751953125, -0.84375, 0.281494140625, -0.01197052001953125, 0.427978515625, 0.1370849609375, -0.163330078125, 0.010498046875, -0.578125, 0.341796875, -0.78564453125, 0.1903076171875, -0.83154296875, -0.72412109375, -0.415283203125, -0.6171875, -0.26611328125, -0.34130859375, -0.041412353515625, -1.107421875, 0.71875, 0.233154296875, 0.2174072265625, 0.525390625, -0.39013671875, 0.12890625, 0.97900390625, 1.1904296875, -0.05841064453125, 0.81103515625, 0.266845703125, -0.09326171875, 0.53515625, -0.47314453125, 0.335205078125, 0.05413818359375, 0.1768798828125, -0.319580078125, 0.321533203125, -0.33056640625, -1.0966796875, 0.2529296875, 0.5927734375, 0.17431640625, -0.3486328125, -0.83544921875, -0.29248046875, -1.1455078125, -0.2091064453125, -0.79150390625, 0.8486328125, -0.564453125, 0.281494140625, -0.164794921875, -1.205078125, 4.42578125, 0.78955078125, 0.91552734375, 0.5009765625, 0.1563720703125, 1.080078125, 0.48193359375, -0.712890625, -0.2958984375, -0.37451171875, 0.65185546875, -0.60400390625, -0.07012939453125, 0.806640625, 0.046783447265625, 0.5009765625, -0.49365234375, 0.472900390625, 0.192626953125, -1.033203125, -0.7822265625, 0.389892578125, 0.07952880859375, 0.62353515625, -0.145263671875, 0.391845703125, 0.5048828125, -0.5439453125, -0.1864013671875, -0.60302734375, 0.264892578125, -0.6083984375, 0.77734375, -0.1566162109375, 0.00003886222839355469, 0.438232421875, -0.11859130859375, -0.85498046875, 0.01427459716796875, 0.128662109375, 0.1695556640625, 0.0284881591796875, 0.6181640625, -0.87255859375, 0.021881103515625, 0.1163330078125, -0.7490234375, 0.52734375, 0.303955078125, -1.375, 0.68701171875, -0.09857177734375, 0.369140625, -0.56201171875, -0.6337890625, 0.027496337890625, 0.11328125, 0.08782958984375, -0.23388671875, 0.1761474609375, 0.403076171875, 0.59619140625, -0.175537109375, 0.541015625, -0.86767578125, 1.01953125, -0.0528564453125, 0.2318115234375, -0.62646484375, -0.295654296875, -0.295166015625, -0.2213134765625, -0.417724609375, -0.053985595703125, 0.53466796875, 0.19189453125, -0.07208251953125, 0.451904296875, 0.13720703125, -0.75732421875, 0.5009765625, -0.1942138671875, -0.354736328125, -0.2310791015625, 0.828125, 1.283203125, -0.751953125, -0.11090087890625, -0.62890625, 0.5654296875, 0.638671875, 0.81884765625, 0.08880615234375, -0.7080078125, -0.29052734375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Kawashiro Nitori is a girl who loves competitive programming. One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem. Given a string s and a parameter k, you need to check if there exist k+1 non-empty strings a_1,a_2...,a_{k+1}, such that $$$s=a_1+a_2+… +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+…+R(a_{1}).$$$ Here + represents concatenation. We define R(x) as a reversed string x. For example R(abcd) = dcba. Note that in the formula above the part R(a_{k+1}) is intentionally skipped. Input The input consists of multiple test cases. The first line contains a single integer t (1≀ t≀ 100) β€” the number of test cases. The description of the test cases follows. The first line of each test case description contains two integers n, k (1≀ n≀ 100, 0≀ k≀ ⌊ n/2 βŒ‹) β€” the length of the string s and the parameter k. The second line of each test case description contains a single string s of length n, consisting of lowercase English letters. Output For each test case, print "YES" (without quotes), if it is possible to find a_1,a_2,…,a_{k+1}, and "NO" (without quotes) otherwise. You can print letters in any case (upper or lower). Example Input 7 5 1 qwqwq 2 1 ab 3 1 ioi 4 2 icpc 22 0 dokidokiliteratureclub 19 8 imteamshanghaialice 6 3 aaaaaa Output YES NO YES NO YES NO NO Note In the first test case, one possible solution is a_1=qw and a_2=q. In the third test case, one possible solution is a_1=i and a_2=o. In the fifth test case, one possible solution is a_1=dokidokiliteratureclub. Tags: brute force, constructive algorithms, greedy, strings Correct Solution: ``` t=int(input()) for z in range(t): n,k=[int(q)for q in input().split()] s=input() a=s[:k]+s[n-k:] if k==n/2: print("NO") elif k==0 or a==a[::-1]: print("YES") else: print("NO") ```
105,485
[ 0.1292724609375, -0.415283203125, 0.1676025390625, 0.28759765625, -0.326416015625, -0.8193359375, -0.06884765625, 0.2174072265625, 0.068359375, 0.943359375, 0.9248046875, -0.09100341796875, 0.1741943359375, -0.7724609375, -0.41455078125, -0.08685302734375, -0.373046875, -0.71484375, -0.491943359375, 0.064453125, 0.259521484375, 0.0955810546875, -1.3671875, -0.06011962890625, -0.38720703125, 0.919921875, 0.430908203125, 0.07000732421875, 1.1767578125, 0.75341796875, -0.431640625, -0.405029296875, 0.6796875, -0.84912109375, -0.315673828125, -0.5546875, 0.642578125, -0.75634765625, -0.49462890625, -0.6015625, 0.2841796875, -0.442626953125, 0.289306640625, -0.822265625, -1.1923828125, 0.038848876953125, -0.7353515625, -0.32470703125, -0.370361328125, -0.6162109375, 0.25927734375, -0.251953125, 0.55712890625, 0.0167999267578125, -0.0799560546875, 0.0662841796875, -0.03289794921875, -0.140380859375, -0.609375, 0.0305023193359375, -0.037933349609375, -0.10675048828125, -0.1412353515625, -0.56201171875, -0.4658203125, -0.1138916015625, -0.1663818359375, -0.39404296875, -0.02117919921875, -1.044921875, -0.279296875, 0.214599609375, -1.015625, -0.39892578125, -0.08331298828125, -0.1756591796875, 0.60009765625, -0.2044677734375, -0.6123046875, 1.255859375, 0.0181884765625, 1.0927734375, 0.470947265625, 0.2379150390625, -0.63525390625, -0.87939453125, -0.033843994140625, 0.234130859375, 0.3125, 0.02728271484375, -0.232666015625, 0.5556640625, -0.55322265625, 0.01424407958984375, 0.384765625, 0.525390625, -0.06396484375, 0.1717529296875, 0.271240234375, -0.07354736328125, 0.98486328125, 0.90966796875, -0.57421875, 0.8662109375, -0.638671875, 0.0968017578125, 0.133056640625, 0.04229736328125, 0.08416748046875, -0.268310546875, -0.05047607421875, -0.361328125, 0.5458984375, 0.1376953125, -0.5625, 0.77197265625, -0.081787109375, 0.176025390625, -0.74609375, 0.1837158203125, 0.52197265625, 0.2044677734375, 0.54833984375, -0.0180511474609375, -0.018402099609375, -0.287841796875, -0.413330078125, 1.15625, -0.7744140625, 0.007465362548828125, 0.48193359375, -0.03607177734375, -0.24853515625, 0.360107421875, -0.1241455078125, 0.333740234375, -0.328369140625, 0.45703125, 0.59375, -0.59033203125, 0.79248046875, -0.1572265625, -0.134033203125, 1.404296875, 0.358642578125, 0.12744140625, 0.51953125, 0.477783203125, -0.95751953125, 0.479248046875, -0.99462890625, 0.35595703125, -0.0299530029296875, 0.2430419921875, -0.20361328125, 0.1143798828125, 0.018463134765625, 0.34375, 0.342041015625, 0.335693359375, -0.2403564453125, 0.28759765625, -0.4892578125, 0.86181640625, -0.5107421875, 0.97998046875, -0.2142333984375, -0.345458984375, -0.2403564453125, -0.67431640625, 0.25830078125, -0.1832275390625, -0.2305908203125, 0.85986328125, 0.53271484375, 0.91796875, 1.16015625, -0.174072265625, 0.53271484375, 0.42626953125, -0.345947265625, 0.3466796875, 0.447509765625, 0.51806640625, -0.0516357421875, 0.29931640625, 0.287353515625, -0.396728515625, -1.01953125, -0.470458984375, -0.16650390625, 0.5126953125, -0.88720703125, 0.137451171875, -0.02972412109375, 0.262939453125, -0.68603515625, -0.1683349609375, -0.1395263671875, -1.095703125, -0.16650390625, 0.4501953125, -0.284423828125, 0.430908203125, -0.419189453125, -0.463623046875, 0.497314453125, 1.21875, -0.1046142578125, 0.1741943359375, 0.107177734375, 0.428955078125, -0.41748046875, 0.236083984375, 0.10784912109375, -0.345947265625, -0.383544921875, 0.80078125, -0.359375, 0.1566162109375, -0.03289794921875, 0.83642578125, 0.25048828125, 0.64306640625, -0.150390625, -0.16162109375, 0.335205078125, 1.2080078125, -0.0089569091796875, 0.444091796875, 0.2587890625, 0.896484375, 0.41796875, 0.83056640625, 0.37646484375, 0.10247802734375, 0.66650390625, 1.2392578125, 0.54248046875, 0.453125, 0.1982421875, 0.2763671875, 0.45556640625, 0.429443359375, 0.294921875, 0.4130859375, -0.20068359375, -0.20849609375, -0.325927734375, 0.0031642913818359375, -0.1038818359375, 0.90478515625, 0.46337890625, 0.0887451171875, -0.64306640625, -0.45654296875, -0.1451416015625, 0.7392578125, -0.7548828125, -0.55810546875, 0.256103515625, 0.1485595703125, -0.053070068359375, -0.39111328125, 0.178955078125, 0.25537109375, 0.41259765625, 0.270263671875, -0.27294921875, -0.321044921875, -0.890625, -0.6845703125, -0.99755859375, -0.26708984375, -0.5673828125, 0.08837890625, 0.60986328125, -0.90625, -0.10394287109375, -0.1287841796875, -0.1517333984375, -0.0894775390625, -0.955078125, 0.59423828125, -0.1282958984375, 0.6328125, -0.900390625, 0.6806640625, 0.064697265625, 0.95068359375, -0.33935546875, -0.1981201171875, -0.075439453125, -0.490478515625, 0.1480712890625, 0.269287109375, 0.078369140625, -0.31689453125, -0.662109375, -0.61572265625, -0.310302734375, -0.1571044921875, 0.006450653076171875, 0.2406005859375, -0.242919921875, 0.76318359375, 0.224853515625, -0.299072265625, 0.459228515625, 1.060546875, -0.9521484375, 0.3134765625, 0.355224609375, 0.08770751953125, -0.82568359375, 1.3759765625, 0.4482421875, 0.0208740234375, -0.375244140625, -0.51904296875, -0.638671875, 0.0701904296875, 0.31103515625, -0.57666015625, -0.378662109375, 0.63671875, -0.160888671875, -1.0087890625, 0.158203125, -0.84326171875, -0.72705078125, 0.0232086181640625, -0.25341796875, 1.119140625, 0.7646484375, 0.1636962890625, -0.37158203125, -0.4306640625, -0.158203125, 0.407470703125, 0.341552734375, -0.262939453125, -0.443359375, 0.84912109375, 0.09344482421875, -0.0062103271484375, 0.006412506103515625, -0.32763671875, -0.337890625, -0.0504150390625, -0.0347900390625, 0.390625, 0.14501953125, 0.279296875, 0.456787109375, 0.66455078125, -1.0283203125, -0.2978515625, -0.22021484375, 0.7998046875, 0.30810546875, 0.6904296875, 0.2900390625, -0.572265625, -0.578125, -0.88330078125, 0.169677734375, 0.45556640625, 0.3740234375, -0.41259765625, 0.8525390625, 0.2939453125, -0.0716552734375, 0.56884765625, -0.68994140625, -0.38525390625, 1.384765625, -0.04266357421875, 0.92138671875, -0.58935546875, 0.203125, 0.09991455078125, 0.07781982421875, 0.5439453125, 0.185302734375, 0.5498046875, -0.410888671875, -0.673828125, -0.1768798828125, -0.002010345458984375, -0.0157318115234375, -0.391845703125, 0.2359619140625, -0.364013671875, -0.78466796875, -0.78173828125, 0.445068359375, 0.62109375, 0.8095703125, 0.305908203125, 0.55126953125, 0.485107421875, 0.56005859375, 0.62109375, -0.20263671875, 0.076904296875, -0.487060546875, 0.5185546875, -0.116943359375, -0.396240234375, -0.43994140625, 0.005977630615234375, -0.316650390625, -0.11419677734375, -0.118896484375, -0.474853515625, -0.466064453125, 0.32177734375, -0.291748046875, 0.41796875, -0.339111328125, -0.3388671875, -0.228271484375, 0.387939453125, 0.236083984375, -1.037109375, 0.38818359375, -0.8779296875, 0.80419921875, 0.29638671875, -0.341064453125, -0.615234375, -0.280029296875, -0.7568359375, -0.87548828125, -0.0863037109375, 0.61669921875, -0.11590576171875, 0.5078125, -1.421875, 0.428466796875, 0.29052734375, -0.282470703125, 0.25048828125, -0.252685546875, 0.1932373046875, 0.192626953125, 0.603515625, -0.5009765625, -0.71044921875, 0.056854248046875, -1.1337890625, 0.210205078125, -0.76318359375, 0.5673828125, 0.1153564453125, -0.29443359375, 0.052520751953125, 0.54541015625, -0.25927734375, 0.183349609375, -0.30615234375, 0.26220703125, -0.99658203125, -0.475830078125, 0.482177734375, 0.046661376953125, -0.44189453125, 1.064453125, -0.2425537109375, -0.366943359375, -0.049468994140625, 0.73681640625, -0.39111328125, 0.30859375, -0.521484375, 0.8974609375, -0.220947265625, -0.6689453125, -0.1671142578125, -0.859375, 1.0087890625, 0.041839599609375, -0.87451171875, -0.261474609375, -0.951171875, -0.044403076171875, 0.0576171875, -0.177490234375, 0.3857421875, -0.0024127960205078125, -0.019378662109375, -0.04754638671875, 0.020172119140625, -0.67041015625, 0.033355712890625, -0.5341796875, -0.447265625, -0.048187255859375, 0.7109375, 0.6962890625, 0.1552734375, -0.28125, 0.1434326171875, 0.1854248046875, -0.04205322265625, -0.467041015625, 0.1402587890625, -0.414306640625, -0.096923828125, -0.0010395050048828125, 0.759765625, 0.005908966064453125, 0.7421875, 0.74951171875, 0.260986328125, 0.7177734375, 0.351806640625, -0.72412109375, 1.09765625, 0.324462890625, -0.89794921875, -0.59326171875, 0.30908203125, -0.1268310546875, 0.64892578125, 0.1715087890625, -0.9404296875, -0.52099609375, -0.5693359375, 0.43896484375, -0.5244140625, -0.2352294921875, -1.158203125, 0.052642822265625, -0.245361328125, 0.2479248046875, 0.0836181640625, -0.261962890625, 0.173583984375, -0.814453125, 0.333251953125, -0.80615234375, -0.352294921875, -0.95654296875, -0.0955810546875, -0.0016775131225585938, 1.0400390625, 0.09014892578125, 0.619140625, -0.07159423828125, -0.20751953125, 0.423583984375, 0.14599609375, -0.93505859375, -0.54248046875, 0.190673828125, -0.0146026611328125, -0.143798828125, -0.1397705078125, -0.71923828125, 0.767578125, -0.72314453125, 0.32470703125, -0.272216796875, -0.353759765625, -0.2247314453125, -0.133056640625, 0.87109375, -0.418701171875, -0.2021484375, -0.2744140625, 0.27001953125, 0.55419921875, -0.387451171875, -0.436279296875, -0.81298828125, -0.1539306640625, -1.16796875, 0.55712890625, -0.55615234375, 0.0897216796875, -0.64501953125, -0.55615234375, 1.10546875, -0.76611328125, 0.41259765625, 1.2177734375, 0.34521484375, 0.439697265625, -0.92431640625, 0.57470703125, 0.6953125, -0.625, -0.419677734375, -0.039703369140625, -0.94140625, 0.282958984375, -0.11279296875, -0.92333984375, -0.7666015625, 0.13232421875, 1.1904296875, -0.30712890625, 0.74072265625, -0.0948486328125, -1.275390625, -0.90576171875, 0.912109375, -0.0653076171875, 0.24755859375, 0.4599609375, -0.12030029296875, -0.21337890625, -0.173583984375, -0.300048828125, -0.120849609375, -0.35498046875, 1.1513671875, -0.2498779296875, -0.7451171875, 0.97119140625, 0.697265625, -0.953125, -0.62646484375, 0.011016845703125, -0.2186279296875, -0.1285400390625, -0.280029296875, -0.1824951171875, 0.6328125, -0.9501953125, 0.2132568359375, 0.64990234375, -0.295654296875, 0.2137451171875, -0.09613037109375, 0.335693359375, -0.6787109375, 0.74658203125, 0.484375, -0.1451416015625, -0.318359375, -0.60400390625, -0.326171875, -0.55419921875, 0.09906005859375, 0.71875, -0.75390625, -0.04791259765625, 0.050811767578125, 0.1219482421875, 0.97998046875, -0.2034912109375, -0.5341796875, 0.342529296875, -0.609375, -0.63720703125, -0.05633544921875, 0.282470703125, -0.035888671875, 0.6845703125, -0.474609375, 0.08172607421875, 0.380126953125, 0.37353515625, -0.11572265625, -0.75732421875, -0.34912109375, -0.71044921875, -0.381103515625, -0.484619140625, -0.5703125, 0.0174407958984375, 0.473388671875, 0.136962890625, -0.5830078125, 0.033843994140625, 0.6328125, -0.177490234375, 0.8701171875, -0.66015625, 0.446044921875, -0.61474609375, -0.2369384765625, -0.2578125, -0.085693359375, -0.52099609375, -0.0120391845703125, -0.89599609375, 0.292724609375, -0.186767578125, 0.736328125, -0.1695556640625, 0.347900390625, -0.235107421875, -0.377685546875, 0.116455078125, -0.2318115234375, -0.371826171875, 0.85107421875, 0.2034912109375, -0.2169189453125, 0.168212890625, -0.68994140625, -0.4404296875, -0.27294921875, 0.424072265625, 0.708984375, -0.334228515625, -0.011810302734375, -0.18798828125, 0.2381591796875, -1.2978515625, 0.3056640625, 0.04779052734375, 0.03826904296875, 0.44482421875, -0.1019287109375, 0.61328125, 1.318359375, -0.50244140625, 0.38916015625, 0.1505126953125, -0.0616455078125, 0.55126953125, 0.418212890625, -0.01541900634765625, 0.306884765625, 0.287109375, -0.365478515625, -0.15478515625, 0.31787109375, 0.18310546875, 0.383056640625, 0.154541015625, -0.89599609375, -1.2451171875, -0.258544921875, 0.00899505615234375, 0.2430419921875, 0.1744384765625, -0.12274169921875, 0.1319580078125, 0.0361328125, -0.300048828125, 0.1820068359375, -1.0361328125, -0.82373046875, 0.27099609375, -0.276611328125, -0.58349609375, -0.2137451171875, -0.354248046875, -0.310302734375, 0.275146484375, 0.74072265625, -0.7744140625, 0.54736328125, -0.0152740478515625, 0.366943359375, 0.05303955078125, -0.755859375, 0.2117919921875, 0.489501953125, -0.76708984375, -0.576171875, 0.253173828125, 1.3251953125, 0.2783203125, -0.279296875, -0.436767578125, 0.37646484375, -0.07354736328125, 0.353515625, -0.5068359375, 0.23974609375, -0.419189453125, 0.251220703125, -0.86865234375, 0.256591796875, -0.305908203125, 0.235595703125, 0.326416015625, -0.64990234375, -0.4736328125, 0.53857421875, 0.55859375, -0.387939453125, 0.54345703125, 0.444580078125, 0.451904296875, 0.1878662109375, -0.07073974609375, -0.1324462890625, 0.54345703125, 0.7119140625, 0.58740234375, -0.154541015625, 0.49755859375, 0.87939453125, 0.019683837890625, -0.248779296875, 0.71240234375, 0.372802734375, -0.288330078125, 0.38427734375, -0.21875, 0.1690673828125, 0.1563720703125, -0.40673828125, 0.375244140625, -0.414306640625, 0.1903076171875, -0.21630859375, -0.5498046875, 0.998046875, -0.2322998046875, -0.1275634765625, -0.142822265625, -0.09197998046875, 0.15087890625, 0.5625, -0.212646484375, -0.1727294921875, 1.1201171875, 0.60009765625, 0.42236328125, 0.67626953125, 0.458251953125, 0.2978515625, -0.8330078125, 0.38427734375, 0.1748046875, -0.0168914794921875, -0.15771484375, -0.326416015625, -1.1376953125, 0.38720703125, -0.3955078125, -0.36376953125, 1.1181640625, -0.70654296875, 0.2044677734375, -0.284912109375, 0.49365234375, -0.6162109375, -0.124267578125, 0.1710205078125, -0.24755859375, -0.12481689453125, 1.03515625, -0.36767578125, 0.03155517578125, 0.351806640625, 0.88720703125, 0.0016193389892578125, 1.4296875, 0.66357421875, -0.2822265625, -0.1624755859375, 0.1468505859375, -0.293701171875, -0.5986328125, -0.315185546875, -0.43017578125, 0.08563232421875, -0.60009765625, -0.74658203125, -0.1756591796875, 0.86376953125, -0.025054931640625, -1.142578125, -0.0025844573974609375, 0.08770751953125, -0.84375, 0.281494140625, -0.01197052001953125, 0.427978515625, 0.1370849609375, -0.163330078125, 0.010498046875, -0.578125, 0.341796875, -0.78564453125, 0.1903076171875, -0.83154296875, -0.72412109375, -0.415283203125, -0.6171875, -0.26611328125, -0.34130859375, -0.041412353515625, -1.107421875, 0.71875, 0.233154296875, 0.2174072265625, 0.525390625, -0.39013671875, 0.12890625, 0.97900390625, 1.1904296875, -0.05841064453125, 0.81103515625, 0.266845703125, -0.09326171875, 0.53515625, -0.47314453125, 0.335205078125, 0.05413818359375, 0.1768798828125, -0.319580078125, 0.321533203125, -0.33056640625, -1.0966796875, 0.2529296875, 0.5927734375, 0.17431640625, -0.3486328125, -0.83544921875, -0.29248046875, -1.1455078125, -0.2091064453125, -0.79150390625, 0.8486328125, -0.564453125, 0.281494140625, -0.164794921875, -1.205078125, 4.42578125, 0.78955078125, 0.91552734375, 0.5009765625, 0.1563720703125, 1.080078125, 0.48193359375, -0.712890625, -0.2958984375, -0.37451171875, 0.65185546875, -0.60400390625, -0.07012939453125, 0.806640625, 0.046783447265625, 0.5009765625, -0.49365234375, 0.472900390625, 0.192626953125, -1.033203125, -0.7822265625, 0.389892578125, 0.07952880859375, 0.62353515625, -0.145263671875, 0.391845703125, 0.5048828125, -0.5439453125, -0.1864013671875, -0.60302734375, 0.264892578125, -0.6083984375, 0.77734375, -0.1566162109375, 0.00003886222839355469, 0.438232421875, -0.11859130859375, -0.85498046875, 0.01427459716796875, 0.128662109375, 0.1695556640625, 0.0284881591796875, 0.6181640625, -0.87255859375, 0.021881103515625, 0.1163330078125, -0.7490234375, 0.52734375, 0.303955078125, -1.375, 0.68701171875, -0.09857177734375, 0.369140625, -0.56201171875, -0.6337890625, 0.027496337890625, 0.11328125, 0.08782958984375, -0.23388671875, 0.1761474609375, 0.403076171875, 0.59619140625, -0.175537109375, 0.541015625, -0.86767578125, 1.01953125, -0.0528564453125, 0.2318115234375, -0.62646484375, -0.295654296875, -0.295166015625, -0.2213134765625, -0.417724609375, -0.053985595703125, 0.53466796875, 0.19189453125, -0.07208251953125, 0.451904296875, 0.13720703125, -0.75732421875, 0.5009765625, -0.1942138671875, -0.354736328125, -0.2310791015625, 0.828125, 1.283203125, -0.751953125, -0.11090087890625, -0.62890625, 0.5654296875, 0.638671875, 0.81884765625, 0.08880615234375, -0.7080078125, -0.29052734375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Let's introduce the designation <image>, where x is a string, n is a positive integer and operation " + " is the string concatenation operation. For example, [abc, 2] = abcabc. We'll say that string s can be obtained from string t, if we can remove some characters from string t and obtain string s. For example, strings ab and aсba can be obtained from string xacbac, and strings bx and aaa cannot be obtained from it. Sereja has two strings, w = [a, b] and q = [c, d]. He wants to find such maximum integer p (p > 0), that [q, p] can be obtained from string w. Input The first line contains two integers b, d (1 ≀ b, d ≀ 107). The second line contains string a. The third line contains string c. The given strings are not empty and consist of lowercase English letters. Their lengths do not exceed 100. Output In a single line print an integer β€” the largest number p. If the required value of p doesn't exist, print 0. Examples Input 10 3 abab bab Output 3 Tags: binary search, dfs and similar, strings Correct Solution: ``` b, p = map(int, input().split()) s1 = input() s2 = input() cnt = [0] * len(s2) nxt = [0] * len(s2) for i in range(len(s2)): pos = i for j in range(len(s1)): if s1[j] == s2[pos]: pos += 1 if pos == len(s2): cnt[i] += 1 pos = 0 nxt[i] = pos ans = 0 poss = 0 for i in range(b): ans += cnt[poss] poss = nxt[poss] print(ans // p) ```
105,560
[ 0.357177734375, -0.334228515625, -0.0699462890625, 0.57373046875, -0.1422119140625, -0.59130859375, -0.2108154296875, 0.04388427734375, 0.599609375, 0.70654296875, 0.88037109375, -0.045867919921875, -0.059326171875, -0.9892578125, -0.5068359375, -0.02459716796875, -0.501953125, -0.49267578125, -0.031982421875, -0.1002197265625, -0.103271484375, -0.0309906005859375, -1.4833984375, -0.01490020751953125, -0.274169921875, 0.71923828125, 0.6005859375, -0.0024662017822265625, 0.63671875, 1.4521484375, -0.521484375, -0.490478515625, 0.5869140625, -0.89111328125, -0.3984375, -0.36376953125, 0.6435546875, -0.88037109375, -0.29443359375, -0.14697265625, 0.1392822265625, -0.666015625, 0.64501953125, -0.84765625, -1.51171875, -0.07110595703125, -0.452392578125, -0.265869140625, -0.183837890625, -0.85986328125, -0.196533203125, -0.274658203125, 0.8134765625, 0.19287109375, -0.07611083984375, 0.1893310546875, 0.173828125, -0.29736328125, -0.71533203125, 0.382080078125, 0.269775390625, -0.08477783203125, 0.0572509765625, -0.59423828125, -0.47216796875, 0.068359375, -0.11297607421875, -0.33447265625, 0.1068115234375, -0.9189453125, -0.2015380859375, 0.2734375, -0.74755859375, -0.332763671875, -0.195556640625, 0.06060791015625, 0.219482421875, -0.29541015625, -0.40478515625, 1.15234375, 0.06695556640625, 1.01953125, 0.14697265625, 0.39453125, -0.385986328125, -0.5654296875, -0.2061767578125, 0.119873046875, 0.053680419921875, -0.04986572265625, -0.312255859375, 0.6943359375, -0.62353515625, 0.2607421875, 0.6484375, 0.40087890625, -0.50439453125, -0.087158203125, 0.54443359375, 0.185546875, 0.465576171875, 0.82763671875, -0.477294921875, 0.962890625, -0.2353515625, 0.0997314453125, 0.0885009765625, 0.09686279296875, 0.0257720947265625, -0.2008056640625, -0.20068359375, -0.296142578125, 0.814453125, -0.339599609375, -0.289306640625, 0.97509765625, 0.4189453125, 0.369873046875, -0.6552734375, 0.497314453125, 0.1634521484375, 0.1512451171875, 0.955078125, 0.0283355712890625, -0.06500244140625, -0.4365234375, -0.416015625, 0.95068359375, -0.56005859375, -0.007442474365234375, 0.34130859375, 0.1116943359375, -0.169189453125, 0.53515625, -0.1673583984375, 0.65673828125, -0.31689453125, 0.55908203125, 0.337890625, -0.55224609375, 0.77001953125, -0.5224609375, 0.2425537109375, 1.513671875, 0.65185546875, 0.25830078125, 0.91748046875, 0.190673828125, -0.72705078125, 0.07965087890625, -1.2275390625, 0.7119140625, 0.10986328125, 0.39208984375, -0.2021484375, 0.335693359375, -0.2142333984375, 0.059722900390625, 0.25390625, 0.212646484375, -0.210205078125, 0.2470703125, -0.470458984375, 0.7412109375, -0.3896484375, 0.6162109375, -0.194580078125, 0.1510009765625, -0.2208251953125, -0.5341796875, 0.227783203125, -0.1357421875, -0.2125244140625, 0.99853515625, 0.485595703125, 1.177734375, 0.88134765625, -0.1165771484375, 0.353515625, 0.24072265625, -0.3330078125, 0.249267578125, 0.033782958984375, 0.8671875, 0.3671875, 0.6318359375, 0.08447265625, -0.0889892578125, -0.472900390625, -0.68701171875, -0.045379638671875, 0.79150390625, -0.55908203125, 0.190673828125, -0.26708984375, 0.416015625, -0.9521484375, -0.2100830078125, -0.5556640625, -0.78466796875, -0.3271484375, 0.395263671875, 0.0413818359375, 0.2366943359375, -0.86865234375, -0.67822265625, 0.7548828125, 1.0537109375, -0.337158203125, -0.11865234375, 0.468994140625, 0.05718994140625, 0.0105133056640625, 0.269287109375, 0.1107177734375, -0.23583984375, -0.7138671875, 0.7265625, -0.1114501953125, -0.030487060546875, -0.10321044921875, 0.90771484375, 0.442138671875, 0.8759765625, 0.047210693359375, -0.1907958984375, 0.66650390625, 0.953125, -0.1917724609375, 0.56298828125, 0.323486328125, 1.0029296875, 0.65478515625, 0.64306640625, 0.437255859375, 0.189453125, 0.4677734375, 0.71630859375, 0.2369384765625, 0.09295654296875, 0.1300048828125, 0.552734375, 0.2371826171875, 0.28662109375, 0.254638671875, 0.76904296875, -0.160888671875, -0.03387451171875, -0.256591796875, 0.090087890625, -0.288330078125, 0.724609375, 0.1995849609375, 0.3447265625, -0.650390625, -0.353515625, 0.58837890625, 1.009765625, -0.73193359375, -0.5654296875, -0.0943603515625, 0.0887451171875, -0.4111328125, 0.140869140625, 0.1724853515625, 0.3994140625, 0.326416015625, 0.310546875, -0.65478515625, -0.55908203125, -0.8955078125, -0.587890625, -0.7978515625, -0.291015625, -0.64453125, -0.2578125, 0.35009765625, -0.62548828125, -0.10931396484375, -0.346923828125, -0.332275390625, 0.26708984375, -0.86328125, 0.5185546875, -0.332275390625, 0.32470703125, -0.646484375, 0.53076171875, 0.51171875, 1.0791015625, -0.478759765625, -0.01300048828125, -0.09320068359375, -0.701171875, 0.12384033203125, 0.1544189453125, 0.497802734375, 0.06988525390625, -0.480224609375, -0.6435546875, -0.69921875, 0.1275634765625, -0.37060546875, 0.449951171875, -0.294189453125, 0.720703125, 0.6005859375, -0.2294921875, 0.48486328125, 0.94384765625, -0.85107421875, 0.3056640625, 0.37646484375, 0.12066650390625, -0.76708984375, 1.2392578125, 0.478515625, 0.173095703125, -0.58984375, -0.14990234375, -0.3955078125, 0.2125244140625, 0.23095703125, -0.7275390625, -0.3466796875, 0.5673828125, -0.1832275390625, -0.68994140625, 0.65185546875, -0.7978515625, -0.54150390625, -0.1436767578125, -0.367919921875, 0.76904296875, 0.81298828125, 0.284912109375, -0.419189453125, -0.1673583984375, 0.0190582275390625, 0.438232421875, 0.488037109375, -0.3984375, -0.353271484375, 0.92138671875, 0.0474853515625, -0.3076171875, -0.134033203125, 0.10076904296875, -0.208251953125, 0.09454345703125, 0.1141357421875, 0.8330078125, 0.250732421875, 0.318359375, 0.51171875, 0.56591796875, -0.830078125, -0.24658203125, -0.273681640625, 0.572265625, 0.50244140625, 0.30322265625, 0.297607421875, -0.3876953125, -0.283447265625, -0.908203125, 0.451904296875, 0.4306640625, 0.9306640625, -0.71044921875, 0.74169921875, 0.50634765625, -0.48046875, 0.66845703125, -0.6630859375, -0.08233642578125, 1.232421875, -0.14990234375, 0.8330078125, -0.414306640625, 0.302490234375, 0.1766357421875, 0.10418701171875, 0.513671875, 0.2066650390625, 0.41357421875, -0.638671875, -0.208984375, -0.59716796875, -0.386962890625, -0.047088623046875, -0.64599609375, 0.395751953125, -0.325439453125, -0.38720703125, -0.8427734375, 0.51220703125, 0.716796875, 0.44287109375, -0.00514984130859375, 0.494140625, 0.41943359375, 0.5, 0.62890625, -0.302001953125, -0.047210693359375, -0.408203125, 0.8037109375, 0.087646484375, -0.39013671875, -0.7607421875, -0.293701171875, -0.136962890625, -0.07464599609375, -0.357421875, -0.282958984375, -0.6923828125, 0.412109375, -0.2178955078125, 0.61181640625, -0.369140625, -0.2021484375, -0.41650390625, 0.48974609375, 0.291748046875, -1.015625, 0.313720703125, -0.76220703125, 0.464599609375, 0.0299072265625, -0.2159423828125, -0.283935546875, -0.46337890625, -0.62548828125, -0.72607421875, -0.1729736328125, 1.0732421875, -0.2432861328125, 0.4404296875, -1.2451171875, 0.174072265625, 0.31201171875, -0.1859130859375, 0.1776123046875, -0.138671875, 0.408447265625, 0.2142333984375, 0.83447265625, -0.75830078125, -0.9013671875, 0.0217132568359375, -1.3193359375, 0.66259765625, -0.673828125, 0.2095947265625, 0.42919921875, -0.15576171875, -0.412841796875, 0.11383056640625, -0.20263671875, 0.085205078125, -0.364013671875, 0.447998046875, -0.7724609375, -0.371826171875, 0.50244140625, -0.446044921875, -0.5126953125, 0.96484375, -0.07879638671875, -0.10693359375, 0.10308837890625, 0.693359375, -0.83203125, 0.3447265625, -0.57861328125, 0.83203125, -0.60693359375, -0.67138671875, -0.33642578125, -0.619140625, 0.9892578125, 0.134521484375, -0.9931640625, -0.08746337890625, -1.16796875, 0.0712890625, 0.14404296875, -0.423828125, 0.2529296875, 0.337158203125, -0.38720703125, -0.032073974609375, -0.07159423828125, -0.38037109375, -0.5615234375, -0.463134765625, -0.055328369140625, 0.363037109375, -0.030029296875, 0.89990234375, 0.22119140625, -0.367919921875, 0.325927734375, 0.0012445449829101562, 0.006572723388671875, -0.50439453125, -0.1900634765625, -0.459716796875, -0.08184814453125, -0.227294921875, 0.255126953125, -0.23486328125, 0.43115234375, 0.76611328125, 0.08795166015625, 0.450439453125, 0.39453125, -0.611328125, 1.0751953125, 0.1470947265625, -0.84912109375, -0.56201171875, 0.666015625, -0.042816162109375, 0.55078125, 0.445556640625, -1.1572265625, -0.74072265625, -0.69189453125, 0.39208984375, -0.425537109375, -0.12237548828125, -1.201171875, -0.3388671875, -0.347412109375, 0.39111328125, 0.15185546875, -0.54931640625, 0.07879638671875, -0.76123046875, 0.0904541015625, -1.015625, -0.264892578125, -0.9248046875, -0.432373046875, -0.08917236328125, 0.74462890625, -0.008880615234375, 0.278564453125, -0.1419677734375, -0.328369140625, 0.7216796875, -0.166015625, -0.51904296875, -0.423583984375, 0.0235137939453125, 0.287353515625, -0.1142578125, 0.045379638671875, -0.254150390625, 0.75439453125, -0.79736328125, 0.47021484375, -0.179443359375, -0.39404296875, -0.315185546875, 0.044525146484375, 1.1533203125, -0.5830078125, -0.05743408203125, -0.21923828125, 0.32373046875, 0.5771484375, -0.320068359375, -0.84228515625, -0.5654296875, -0.62890625, -0.9267578125, 0.5703125, -0.327392578125, -0.08447265625, -0.68017578125, 0.1785888671875, 0.9345703125, -0.7529296875, 0.464599609375, 1.2880859375, 0.236083984375, 0.296875, -0.6005859375, 0.5908203125, 0.55810546875, -0.7880859375, 0.0035724639892578125, -0.01064300537109375, -0.6044921875, 0.1231689453125, -0.57568359375, -1.2041015625, -0.45166015625, 0.23681640625, 1.3134765625, -0.406494140625, 0.81201171875, -0.148681640625, -1.1484375, -0.77880859375, 0.759765625, 0.1573486328125, 0.362548828125, 0.96484375, -0.066162109375, -0.2237548828125, -0.47509765625, -0.2294921875, -0.32568359375, -0.458984375, 1.0146484375, -0.291259765625, -0.392822265625, 0.72509765625, 0.91064453125, -0.72900390625, -0.93994140625, 0.09527587890625, -0.2430419921875, -0.74658203125, -0.488525390625, 0.21630859375, 0.79541015625, -0.70703125, 0.082763671875, 0.658203125, -0.102783203125, 0.4140625, -0.389404296875, 0.0823974609375, -0.5146484375, 0.380859375, 0.67236328125, -0.1959228515625, -0.38623046875, -0.8935546875, -0.2347412109375, -0.280029296875, -0.22509765625, 0.85986328125, -0.262451171875, 0.22216796875, 0.1806640625, -0.057281494140625, 0.59228515625, -0.261474609375, -0.51220703125, 0.381591796875, -0.88427734375, -0.482421875, 0.263916015625, 0.529296875, -0.0823974609375, 0.51416015625, -0.48583984375, -0.050933837890625, 0.44384765625, 0.2568359375, -0.40673828125, -0.8427734375, -0.107177734375, -1.109375, -0.78076171875, -0.90185546875, -0.55078125, -0.31005859375, 0.0023784637451171875, -0.04443359375, -0.53662109375, -0.1298828125, 0.240966796875, -0.8349609375, 0.95751953125, -0.68408203125, 0.267333984375, -0.5859375, -0.5625, -0.73193359375, -0.1204833984375, -0.264404296875, -0.004119873046875, -0.740234375, 0.413818359375, -0.38623046875, 0.515625, -0.38134765625, 0.525390625, -0.5107421875, -0.912109375, 0.2275390625, 0.049041748046875, -0.07464599609375, 0.90576171875, 0.5771484375, -0.2056884765625, -0.0212860107421875, -0.142578125, -0.23291015625, -0.56982421875, 0.92138671875, 0.552734375, -0.07061767578125, -0.157470703125, -0.1217041015625, 0.017120361328125, -1.1337890625, 0.30810546875, -0.279541015625, 0.30859375, 0.282958984375, -0.041534423828125, 0.63720703125, 1.244140625, -0.5283203125, 0.387451171875, -0.206787109375, 0.10589599609375, 0.64013671875, 0.4248046875, -0.3818359375, 0.2340087890625, -0.1630859375, -0.253662109375, 0.024566650390625, 0.37744140625, 0.040252685546875, 0.1585693359375, 0.05364990234375, -0.75732421875, -0.7197265625, -0.60986328125, 0.234130859375, 0.1282958984375, 0.1204833984375, -0.392333984375, -0.012176513671875, 0.134521484375, -0.325439453125, 0.128173828125, -1.111328125, -1.0029296875, 0.6435546875, -0.023681640625, -0.98046875, 0.1197509765625, -0.31103515625, -0.19384765625, 0.135009765625, 0.47216796875, -0.433837890625, 0.626953125, -0.2088623046875, 0.470703125, -0.1961669921875, -0.42041015625, 0.04827880859375, 0.33203125, -0.64794921875, -0.78515625, 0.17333984375, 0.87451171875, 0.326171875, -0.35400390625, -0.344970703125, 0.39013671875, -0.11529541015625, 0.34326171875, -0.59228515625, 0.1375732421875, -0.52099609375, 0.2064208984375, -0.67041015625, 0.06060791015625, -0.54052734375, 0.350830078125, 0.3916015625, -0.433349609375, -0.6708984375, 0.80078125, 0.60498046875, -0.1903076171875, 0.32373046875, 0.212158203125, 0.6337890625, 0.3857421875, -0.4208984375, -0.11920166015625, 0.783203125, 0.48291015625, 0.8740234375, -0.292724609375, 0.1629638671875, 0.88330078125, -0.066162109375, -0.480712890625, 0.1832275390625, 0.231689453125, -0.00991058349609375, 0.331298828125, 0.105224609375, -0.3759765625, -0.287841796875, -0.83447265625, 0.358154296875, -0.289306640625, -0.142578125, 0.01326751708984375, -0.7158203125, 0.705078125, -0.396484375, -0.38134765625, 0.327880859375, -0.378662109375, 0.271240234375, 0.63232421875, -0.2362060546875, -0.378173828125, 0.9150390625, 0.8623046875, 0.83984375, 0.8076171875, 0.308837890625, 0.55517578125, -0.344482421875, 0.1566162109375, -0.2122802734375, 0.1998291015625, -0.22412109375, -0.6435546875, -0.953125, 0.16748046875, -0.21484375, -0.404296875, 0.69091796875, -0.260986328125, 0.12408447265625, -0.2374267578125, 0.6533203125, -0.63232421875, -0.044647216796875, 0.275390625, -0.6162109375, -0.40966796875, 0.755859375, -0.189453125, 0.1356201171875, 0.060791015625, 1.1064453125, -0.080078125, 1.4990234375, 0.6494140625, -0.3798828125, 0.01001739501953125, 0.54443359375, -0.345947265625, -0.65185546875, -0.62548828125, -0.397216796875, 0.2271728515625, -0.61328125, -0.484130859375, -0.1231689453125, 0.7080078125, 0.409423828125, -0.98486328125, -0.274658203125, 0.2205810546875, -0.8232421875, 0.0230255126953125, 0.39306640625, 0.283203125, -0.0931396484375, -0.1812744140625, -0.2022705078125, -0.68896484375, 0.71484375, -0.89306640625, 0.2010498046875, -0.60693359375, -0.53369140625, -0.168701171875, -0.54150390625, -0.1678466796875, -0.2474365234375, -0.160888671875, -0.7373046875, 0.3740234375, 0.423095703125, 0.64013671875, 0.342529296875, -0.07965087890625, 0.180419921875, 1.11328125, 1.1630859375, 0.0791015625, 0.74267578125, 0.1829833984375, -0.1622314453125, 0.4716796875, -0.6513671875, 0.50537109375, 0.144287109375, 0.457275390625, -0.353271484375, 0.5263671875, -0.939453125, -1.21875, 0.09906005859375, 0.74755859375, 0.509765625, -0.7275390625, -0.9111328125, 0.016143798828125, -1.361328125, -0.3583984375, -0.348876953125, 0.6796875, -0.517578125, -0.1531982421875, -0.12408447265625, -1.322265625, 4.35546875, 0.67333984375, 1.0234375, 0.88330078125, 0.245849609375, 0.892578125, 0.54052734375, -0.328125, -0.309326171875, -0.393310546875, 0.72119140625, -0.255126953125, -0.0109405517578125, 0.93701171875, 0.50537109375, 0.1549072265625, -0.315185546875, 0.1375732421875, 0.0697021484375, -0.859375, -0.7216796875, 0.6025390625, -0.07244873046875, 1.1611328125, -0.166015625, 0.111083984375, 0.436279296875, -0.6845703125, -0.476318359375, -0.53369140625, 0.312255859375, -0.47802734375, 1.08203125, 0.0477294921875, -0.1512451171875, 0.6328125, 0.08087158203125, -0.52587890625, -0.239990234375, 0.221435546875, 0.04241943359375, -0.25048828125, 0.6416015625, -0.9716796875, -0.41796875, 0.302734375, -1.0205078125, 0.6396484375, 0.0205078125, -1.1630859375, 0.52099609375, -0.3642578125, 0.09771728515625, -0.99169921875, -0.487548828125, 0.159912109375, -0.16796875, -0.146240234375, -0.281494140625, 0.69921875, 0.66064453125, 0.5517578125, 0.13818359375, 0.461181640625, -1.0517578125, 0.8173828125, -0.3349609375, 0.95263671875, -0.70703125, -0.052459716796875, 0.004467010498046875, -0.5693359375, -0.12481689453125, -0.489990234375, 0.53369140625, 0.305908203125, -0.257568359375, 0.6337890625, 0.55126953125, -0.6845703125, 0.145751953125, 0.2069091796875, -0.4833984375, -0.48486328125, 0.56396484375, 1.1513671875, -0.8515625, -0.1129150390625, -0.427490234375, 0.5830078125, 0.771484375, 0.609375, -0.148193359375, -0.390625, -0.1136474609375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's introduce the designation <image>, where x is a string, n is a positive integer and operation " + " is the string concatenation operation. For example, [abc, 2] = abcabc. We'll say that string s can be obtained from string t, if we can remove some characters from string t and obtain string s. For example, strings ab and aсba can be obtained from string xacbac, and strings bx and aaa cannot be obtained from it. Sereja has two strings, w = [a, b] and q = [c, d]. He wants to find such maximum integer p (p > 0), that [q, p] can be obtained from string w. Input The first line contains two integers b, d (1 ≀ b, d ≀ 107). The second line contains string a. The third line contains string c. The given strings are not empty and consist of lowercase English letters. Their lengths do not exceed 100. Output In a single line print an integer β€” the largest number p. If the required value of p doesn't exist, print 0. Examples Input 10 3 abab bab Output 3 Submitted Solution: ``` b, p = map(int, input().split()) s1 = input() s2 = input() cnt = 0 pos = 0 flag = True while flag: for i in range(len(s1)): if s1[i] == s2[pos]: pos += 1 if i == len(s1) - 1: cnt += 1 if pos == len(s2): flag = False break ans = b // cnt // p print(ans) ``` No
105,561
[ 0.404541015625, -0.373291015625, -0.10821533203125, 0.54833984375, -0.38232421875, -0.5517578125, -0.34619140625, 0.25634765625, 0.433837890625, 0.7294921875, 0.72509765625, -0.06927490234375, -0.07183837890625, -1.037109375, -0.58544921875, -0.04400634765625, -0.494140625, -0.63818359375, 0.1195068359375, -0.236572265625, -0.1025390625, -0.06732177734375, -1.4052734375, 0.052459716796875, -0.2607421875, 0.70703125, 0.72412109375, -0.0472412109375, 0.62255859375, 1.2998046875, -0.52490234375, -0.44873046875, 0.53271484375, -0.79541015625, -0.328125, -0.53125, 0.74609375, -0.88916015625, -0.413330078125, -0.412109375, -0.0193634033203125, -0.61572265625, 0.56982421875, -0.6943359375, -1.6279296875, -0.1409912109375, -0.197998046875, -0.26904296875, -0.223388671875, -0.87255859375, -0.260498046875, -0.2449951171875, 0.8076171875, 0.06976318359375, 0.01407623291015625, 0.26318359375, 0.23583984375, -0.3828125, -0.73193359375, 0.287841796875, 0.296630859375, 0.0120697021484375, -0.051544189453125, -0.70849609375, -0.5283203125, 0.267333984375, -0.06719970703125, -0.326171875, 0.2432861328125, -0.7919921875, -0.336669921875, 0.1295166015625, -0.791015625, -0.22412109375, -0.21240234375, 0.11712646484375, 0.22705078125, 0.034881591796875, -0.5654296875, 1.283203125, 0.003875732421875, 1.1533203125, 0.1495361328125, 0.29345703125, -0.50341796875, -0.52978515625, 0.008270263671875, 0.037628173828125, 0.1571044921875, -0.09552001953125, -0.424072265625, 0.446533203125, -0.58642578125, 0.08905029296875, 0.6357421875, 0.36865234375, -0.4228515625, 0.00002491474151611328, 0.454833984375, 0.216552734375, 0.5107421875, 0.7158203125, -0.47802734375, 1.05078125, -0.422607421875, 0.0018177032470703125, 0.2266845703125, 0.11285400390625, 0.0718994140625, -0.303466796875, -0.2037353515625, -0.2415771484375, 0.71435546875, -0.3251953125, -0.383056640625, 0.87451171875, 0.295166015625, 0.437255859375, -0.6357421875, 0.4189453125, 0.1893310546875, 0.13134765625, 0.88330078125, 0.08038330078125, 0.01354217529296875, -0.49560546875, -0.52734375, 0.91650390625, -0.6748046875, -0.134765625, 0.280517578125, 0.103759765625, -0.42529296875, 0.60009765625, -0.32763671875, 0.689453125, -0.1810302734375, 0.474609375, 0.356201171875, -0.59130859375, 0.76708984375, -0.46875, 0.2880859375, 1.6650390625, 0.485107421875, 0.1190185546875, 0.5947265625, 0.322021484375, -0.73876953125, 0.2135009765625, -1.2919921875, 0.53759765625, -0.0609130859375, 0.2099609375, -0.364013671875, 0.45361328125, -0.1741943359375, 0.1856689453125, 0.49560546875, 0.158935546875, -0.26416015625, 0.32080078125, -0.66845703125, 0.59912109375, -0.434814453125, 0.52783203125, -0.1676025390625, 0.1014404296875, -0.1497802734375, -0.422119140625, 0.172607421875, -0.2060546875, 0.09832763671875, 1.1416015625, 0.6611328125, 1.23046875, 0.869140625, -0.0703125, 0.337890625, 0.252685546875, -0.462890625, 0.308837890625, 0.023590087890625, 0.7744140625, 0.2607421875, 0.76416015625, -0.09478759765625, 0.00572967529296875, -0.2174072265625, -0.80615234375, 0.01348114013671875, 0.95166015625, -0.654296875, 0.30322265625, -0.375244140625, 0.284423828125, -0.939453125, -0.279296875, -0.3876953125, -0.93798828125, -0.47705078125, 0.320068359375, 0.16943359375, 0.353271484375, -0.85791015625, -0.8232421875, 0.71240234375, 1.095703125, -0.2958984375, 0.07720947265625, 0.50048828125, 0.09136962890625, 0.007579803466796875, -0.038116455078125, 0.307861328125, -0.1920166015625, -0.6875, 0.4375, -0.0276947021484375, 0.00124359130859375, -0.095458984375, 0.90185546875, 0.34375, 0.9033203125, -0.132080078125, -0.3291015625, 0.67236328125, 0.974609375, -0.270751953125, 0.685546875, 0.3515625, 1.0546875, 0.63232421875, 0.73095703125, 0.435546875, 0.229736328125, 0.70068359375, 0.64208984375, -0.0714111328125, 0.0002541542053222656, 0.046905517578125, 0.732421875, 0.1270751953125, 0.454833984375, 0.408935546875, 0.74658203125, -0.2227783203125, -0.08319091796875, -0.251220703125, 0.225830078125, -0.318359375, 0.78125, 0.2152099609375, 0.50537109375, -0.61328125, -0.2335205078125, 0.54150390625, 0.8662109375, -0.68408203125, -0.78466796875, -0.1475830078125, 0.05865478515625, -0.415283203125, 0.312255859375, 0.0892333984375, 0.31298828125, 0.32421875, 0.32177734375, -0.472900390625, -0.59130859375, -0.7578125, -0.68310546875, -0.9609375, -0.344970703125, -0.7802734375, -0.265869140625, 0.288330078125, -0.626953125, -0.1614990234375, -0.370849609375, -0.330078125, 0.15673828125, -0.71923828125, 0.5810546875, -0.34033203125, 0.22265625, -0.5927734375, 0.408935546875, 0.54052734375, 1.01953125, -0.50439453125, -0.0054168701171875, -0.17236328125, -0.46484375, 0.2196044921875, 0.09039306640625, 0.460205078125, 0.253662109375, -0.51611328125, -0.81982421875, -0.71044921875, 0.0875244140625, -0.40673828125, 0.2369384765625, -0.306640625, 0.9150390625, 0.44140625, -0.490966796875, 0.55859375, 1.0263671875, -0.85693359375, 0.440185546875, 0.3271484375, 0.3095703125, -0.65771484375, 1.32421875, 0.43310546875, 0.293701171875, -0.5517578125, -0.2802734375, -0.343505859375, 0.236328125, 0.1298828125, -0.70849609375, -0.50048828125, 0.60009765625, -0.1993408203125, -0.69287109375, 0.78564453125, -0.91259765625, -0.5654296875, -0.177734375, -0.7236328125, 0.8134765625, 0.86865234375, 0.38818359375, -0.37158203125, -0.303466796875, -0.060546875, 0.326904296875, 0.6015625, -0.6904296875, -0.34326171875, 1.037109375, 0.0197601318359375, -0.10858154296875, -0.00852203369140625, 0.091064453125, -0.25048828125, 0.045318603515625, 0.079833984375, 0.9248046875, 0.2410888671875, 0.43017578125, 0.2939453125, 0.6123046875, -1.013671875, -0.2012939453125, -0.374267578125, 0.552734375, 0.50146484375, 0.33740234375, 0.4384765625, -0.2081298828125, -0.509765625, -0.9052734375, 0.4013671875, 0.367431640625, 0.96142578125, -0.490234375, 0.80908203125, 0.32958984375, -0.62060546875, 0.81494140625, -0.763671875, 0.10162353515625, 1.263671875, -0.08465576171875, 0.73046875, -0.65576171875, 0.300048828125, 0.12042236328125, -0.1668701171875, 0.47509765625, 0.1634521484375, 0.599609375, -0.442138671875, -0.1358642578125, -0.60546875, -0.2227783203125, -0.03216552734375, -0.72216796875, 0.268310546875, -0.4306640625, -0.51220703125, -0.919921875, 0.57568359375, 0.62060546875, 0.4912109375, -0.02313232421875, 0.495361328125, 0.396240234375, 0.410888671875, 0.689453125, -0.19580078125, -0.07452392578125, -0.42919921875, 1.0634765625, 0.2122802734375, -0.431396484375, -0.59912109375, -0.3271484375, -0.133056640625, -0.04132080078125, -0.34765625, -0.10809326171875, -0.85009765625, 0.53076171875, -0.139404296875, 0.5546875, -0.60888671875, -0.0479736328125, -0.47265625, 0.46728515625, 0.2763671875, -1.044921875, 0.2724609375, -0.85009765625, 0.392822265625, 0.1925048828125, -0.2103271484375, -0.319580078125, -0.333984375, -0.95068359375, -0.896484375, -0.2047119140625, 1.08203125, -0.375, 0.2626953125, -1.34375, 0.302490234375, 0.54150390625, -0.401611328125, 0.320068359375, -0.283203125, 0.34033203125, 0.1649169921875, 0.57763671875, -0.67333984375, -0.80224609375, -0.101806640625, -1.2861328125, 0.5244140625, -0.5576171875, 0.45654296875, 0.50537109375, -0.2059326171875, -0.296630859375, 0.2291259765625, -0.1680908203125, 0.06488037109375, -0.2958984375, 0.58740234375, -0.8798828125, -0.462158203125, 0.420166015625, -0.33935546875, -0.66455078125, 0.9921875, -0.06732177734375, -0.20751953125, 0.075439453125, 0.67431640625, -0.78466796875, 0.46728515625, -0.476318359375, 0.73095703125, -0.4716796875, -0.57080078125, -0.20556640625, -0.57470703125, 0.978515625, -0.022125244140625, -0.95166015625, 0.034698486328125, -1.21484375, -0.042022705078125, 0.08514404296875, -0.58056640625, 0.2322998046875, 0.364990234375, -0.41552734375, 0.09210205078125, -0.026123046875, -0.40283203125, -0.55615234375, -0.386962890625, -0.171630859375, 0.29833984375, -0.1534423828125, 0.86669921875, 0.315673828125, -0.34521484375, 0.25927734375, -0.263916015625, -0.123046875, -0.5341796875, -0.133544921875, -0.50537109375, -0.1646728515625, -0.2166748046875, 0.379638671875, -0.1517333984375, 0.455322265625, 0.65869140625, 0.09844970703125, 0.5625, 0.381103515625, -0.7265625, 1.2705078125, 0.11260986328125, -1.0478515625, -0.31591796875, 0.837890625, -0.00843048095703125, 0.61474609375, 0.2281494140625, -1.0947265625, -0.67529296875, -0.80322265625, 0.525390625, -0.67236328125, -0.1890869140625, -1.265625, -0.375244140625, -0.31787109375, 0.457275390625, 0.01186370849609375, -0.26708984375, 0.267333984375, -0.78515625, 0.2449951171875, -1.0849609375, -0.371826171875, -1.0693359375, -0.231689453125, -0.313232421875, 0.90771484375, 0.068359375, 0.298828125, -0.1173095703125, -0.055206298828125, 0.498291015625, -0.1513671875, -0.56640625, -0.462646484375, 0.058319091796875, 0.21044921875, -0.07122802734375, -0.033050537109375, -0.291748046875, 0.7021484375, -0.84423828125, 0.57080078125, -0.05078125, -0.321533203125, -0.161865234375, -0.0236053466796875, 1.212890625, -0.58642578125, 0.0173492431640625, -0.355224609375, 0.269775390625, 0.68115234375, -0.342041015625, -0.65966796875, -0.470458984375, -0.60107421875, -1.0546875, 0.5712890625, -0.2252197265625, -0.054718017578125, -0.82861328125, 0.162353515625, 1.048828125, -0.81005859375, 0.54833984375, 1.3017578125, 0.2479248046875, 0.2396240234375, -0.607421875, 0.66748046875, 0.712890625, -0.771484375, -0.00301361083984375, -0.10107421875, -0.85400390625, 0.176513671875, -0.67431640625, -1.271484375, -0.54248046875, 0.1929931640625, 1.1357421875, -0.30126953125, 0.92724609375, -0.1356201171875, -1.337890625, -0.5302734375, 0.77099609375, 0.043853759765625, 0.20166015625, 1.029296875, -0.11553955078125, -0.302734375, -0.267333984375, -0.41845703125, -0.40673828125, -0.38037109375, 1.03515625, -0.619140625, -0.2418212890625, 0.98095703125, 0.89599609375, -1.0224609375, -1.1083984375, -0.2220458984375, -0.2454833984375, -0.4365234375, -0.56640625, 0.165771484375, 0.826171875, -0.63037109375, 0.08050537109375, 0.59814453125, -0.052520751953125, 0.44482421875, -0.27294921875, 0.182373046875, -0.55908203125, 0.29541015625, 0.8056640625, -0.2288818359375, -0.5888671875, -0.92724609375, -0.024627685546875, -0.2001953125, -0.117431640625, 0.8251953125, -0.251953125, 0.329833984375, 0.420166015625, -0.101806640625, 0.58251953125, -0.42724609375, -0.250244140625, 0.296142578125, -0.86279296875, -0.436767578125, 0.07489013671875, 0.5283203125, -0.00506591796875, 0.5986328125, -0.4736328125, -0.152587890625, 0.427978515625, 0.33056640625, -0.247314453125, -0.57373046875, -0.181640625, -1.181640625, -0.81640625, -0.80615234375, -0.5205078125, -0.07257080078125, 0.12646484375, 0.12310791015625, -0.484375, 0.0125885009765625, 0.35888671875, -0.9384765625, 1.0126953125, -0.69775390625, 0.2169189453125, -0.42138671875, -0.533203125, -0.74755859375, -0.1470947265625, -0.440185546875, -0.330322265625, -0.44921875, 0.424072265625, -0.41064453125, 0.3056640625, -0.35009765625, 0.646484375, -0.2220458984375, -0.63330078125, 0.2100830078125, 0.09490966796875, -0.1402587890625, 1.080078125, 0.4287109375, -0.1939697265625, -0.0178985595703125, -0.2271728515625, -0.2086181640625, -0.335693359375, 1.07421875, 0.45751953125, 0.053253173828125, -0.2021484375, 0.005035400390625, -0.08984375, -1.0205078125, 0.2232666015625, -0.26806640625, 0.406494140625, 0.181396484375, 0.0112457275390625, 0.52587890625, 1.25, -0.76025390625, 0.541015625, -0.08697509765625, 0.174072265625, 0.65576171875, 0.474853515625, -0.39990234375, 0.421875, -0.09857177734375, -0.37109375, 0.08843994140625, 0.38427734375, 0.220703125, 0.21923828125, -0.0716552734375, -0.865234375, -0.845703125, -0.5341796875, 0.181640625, 0.201171875, 0.28662109375, -0.388916015625, 0.00905609130859375, 0.1419677734375, -0.51708984375, 0.09429931640625, -1.2578125, -0.91796875, 0.64892578125, 0.01367950439453125, -1.0146484375, 0.1937255859375, -0.1875, -0.01385498046875, 0.1622314453125, 0.260009765625, -0.4130859375, 0.434814453125, -0.166259765625, 0.45263671875, -0.158935546875, -0.388427734375, 0.0044403076171875, 0.408447265625, -0.80859375, -0.73583984375, 0.1134033203125, 0.95751953125, 0.186767578125, -0.473876953125, -0.289794921875, 0.388916015625, -0.10223388671875, 0.18701171875, -0.55908203125, 0.03570556640625, -0.311767578125, 0.2529296875, -0.73291015625, -0.02142333984375, -0.5419921875, 0.227783203125, 0.1380615234375, -0.4091796875, -0.66064453125, 0.79443359375, 0.7236328125, -0.006320953369140625, 0.42919921875, 0.05694580078125, 0.76318359375, 0.5576171875, -0.313720703125, -0.21435546875, 0.65673828125, 0.63916015625, 0.89892578125, -0.1898193359375, 0.413818359375, 0.8896484375, -0.09844970703125, -0.295654296875, 0.345703125, 0.1263427734375, -0.045196533203125, 0.345947265625, -0.01349639892578125, -0.297119140625, -0.09259033203125, -0.80126953125, 0.269775390625, -0.3837890625, -0.10699462890625, 0.11761474609375, -0.59228515625, 0.8525390625, -0.442138671875, -0.37451171875, 0.201904296875, -0.49560546875, 0.4287109375, 0.533203125, -0.09930419921875, -0.28564453125, 0.95947265625, 1.0478515625, 0.91650390625, 0.7001953125, 0.36181640625, 0.389892578125, -0.53955078125, 0.047088623046875, -0.055267333984375, 0.1907958984375, -0.243896484375, -0.56396484375, -1.0595703125, 0.3203125, 0.02099609375, -0.0303497314453125, 0.3984375, -0.340576171875, 0.01497650146484375, -0.415771484375, 0.70556640625, -0.77685546875, -0.07855224609375, 0.431884765625, -0.5185546875, -0.29736328125, 0.7470703125, -0.0821533203125, 0.10870361328125, 0.16650390625, 1.166015625, 0.0036945343017578125, 1.60546875, 0.751953125, -0.322509765625, 0.12225341796875, 0.73828125, -0.34326171875, -0.60400390625, -0.493896484375, -0.419189453125, 0.10943603515625, -0.58349609375, -0.52880859375, -0.2125244140625, 0.81396484375, 0.460693359375, -0.89404296875, -0.444580078125, 0.152099609375, -0.7490234375, 0.1787109375, 0.194580078125, 0.37548828125, 0.08099365234375, -0.121826171875, -0.3203125, -0.638671875, 0.79150390625, -0.58154296875, 0.2376708984375, -0.57861328125, -0.38330078125, -0.332275390625, -0.4775390625, -0.1446533203125, -0.1845703125, -0.314453125, -0.7001953125, 0.48046875, 0.443359375, 0.5322265625, 0.186767578125, -0.211181640625, 0.135009765625, 1.162109375, 1.28515625, 0.00421905517578125, 0.8115234375, 0.232177734375, -0.148681640625, 0.2298583984375, -0.55322265625, 0.53955078125, 0.32421875, 0.368896484375, -0.51611328125, 0.4482421875, -1.078125, -1.11328125, -0.0135650634765625, 0.69677734375, 0.29931640625, -0.77978515625, -1.1435546875, -0.2391357421875, -1.1640625, -0.2386474609375, -0.3740234375, 0.76416015625, -0.477294921875, -0.17333984375, -0.0838623046875, -1.232421875, 4.25390625, 0.59130859375, 0.78759765625, 0.65625, 0.314453125, 0.88916015625, 0.501953125, -0.456787109375, -0.12396240234375, -0.55322265625, 0.7490234375, -0.27294921875, 0.0184326171875, 1.021484375, 0.630859375, 0.2919921875, -0.296875, -0.1580810546875, 0.2294921875, -0.89013671875, -0.72509765625, 0.544921875, 0.12103271484375, 0.87353515625, -0.148681640625, 0.29150390625, 0.630859375, -0.76953125, -0.54150390625, -0.5380859375, 0.339111328125, -0.32763671875, 1.0771484375, 0.0263824462890625, -0.2216796875, 0.84033203125, 0.1920166015625, -0.55224609375, -0.11798095703125, 0.324951171875, -0.03662109375, -0.166015625, 0.6181640625, -0.927734375, -0.4111328125, 0.414794921875, -0.94775390625, 0.73974609375, 0.0838623046875, -1.2294921875, 0.56591796875, -0.1884765625, 0.047332763671875, -0.76611328125, -0.470458984375, 0.209716796875, -0.0760498046875, -0.10809326171875, -0.27587890625, 0.72900390625, 0.541015625, 0.50341796875, 0.06298828125, 0.74169921875, -1.130859375, 0.83056640625, -0.1873779296875, 0.79541015625, -0.85498046875, -0.0474853515625, -0.051300048828125, -0.65771484375, -0.270751953125, -0.54833984375, 0.404052734375, 0.394775390625, -0.1834716796875, 0.51953125, 0.59033203125, -0.67041015625, 0.1151123046875, 0.06231689453125, -0.4189453125, -0.61962890625, 0.49267578125, 1.1630859375, -0.9677734375, -0.237060546875, -0.405517578125, 0.55224609375, 0.828125, 0.7060546875, -0.0615234375, -0.52783203125, -0.32421875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's introduce the designation <image>, where x is a string, n is a positive integer and operation " + " is the string concatenation operation. For example, [abc, 2] = abcabc. We'll say that string s can be obtained from string t, if we can remove some characters from string t and obtain string s. For example, strings ab and aсba can be obtained from string xacbac, and strings bx and aaa cannot be obtained from it. Sereja has two strings, w = [a, b] and q = [c, d]. He wants to find such maximum integer p (p > 0), that [q, p] can be obtained from string w. Input The first line contains two integers b, d (1 ≀ b, d ≀ 107). The second line contains string a. The third line contains string c. The given strings are not empty and consist of lowercase English letters. Their lengths do not exceed 100. Output In a single line print an integer β€” the largest number p. If the required value of p doesn't exist, print 0. Examples Input 10 3 abab bab Output 3 Submitted Solution: ``` import math def a_can_from_b(a, b): pt = 0 for chr in a: try: while b[pt] != chr: pt += 1 except IndexError: return False return True class CodeforcesTask314BSolution: def __init__(self): self.result = '' self.b_d = [] self.a = '' self.c = '' def read_input(self): self.b_d = [int(x) for x in input().split(" ")] self.a = input() self.c = input() def process_task(self): left = 1 right = math.ceil(self.b_d[0] / self.b_d[1]) while right - left > 1: mid = left + (right - left) // 2 #print(left, right, mid) if a_can_from_b(self.c * (self.b_d[1] * mid), self.a * self.b_d[0]): left = mid else: right = mid if not a_can_from_b(self.c * (self.b_d[1] * left), self.a * self.b_d[0]): left -= 1 self.result = str(left) def get_result(self): return self.result if __name__ == "__main__": Solution = CodeforcesTask314BSolution() Solution.read_input() Solution.process_task() print(Solution.get_result()) ``` No
105,562
[ 0.380126953125, -0.285888671875, -0.09039306640625, 0.6484375, -0.358642578125, -0.448974609375, -0.308349609375, 0.2003173828125, 0.39501953125, 0.73193359375, 0.73828125, -0.1591796875, 0.003627777099609375, -1.0546875, -0.5361328125, -0.06243896484375, -0.453369140625, -0.54931640625, 0.032562255859375, -0.155517578125, -0.0474853515625, -0.1300048828125, -1.28515625, 0.10064697265625, -0.343017578125, 0.63671875, 0.7783203125, -0.018768310546875, 0.578125, 1.3525390625, -0.59765625, -0.61962890625, 0.5517578125, -0.76708984375, -0.388671875, -0.5771484375, 0.8359375, -0.95166015625, -0.41943359375, -0.389892578125, -0.022186279296875, -0.552734375, 0.52197265625, -0.63916015625, -1.6630859375, -0.125, -0.2330322265625, -0.233154296875, -0.2491455078125, -0.7138671875, -0.20703125, -0.2042236328125, 0.76904296875, -0.05889892578125, 0.1082763671875, 0.1998291015625, 0.26416015625, -0.393310546875, -0.650390625, 0.2332763671875, 0.1390380859375, 0.0276641845703125, -0.036041259765625, -0.62890625, -0.409912109375, 0.316162109375, -0.196044921875, -0.286865234375, 0.2138671875, -0.7041015625, -0.28076171875, 0.1771240234375, -0.78955078125, -0.229248046875, -0.3017578125, 0.06890869140625, 0.08978271484375, -0.04705810546875, -0.427734375, 1.330078125, 0.04437255859375, 1.158203125, 0.259033203125, 0.35546875, -0.375244140625, -0.452880859375, 0.03460693359375, 0.05828857421875, 0.09552001953125, -0.045989990234375, -0.298095703125, 0.5166015625, -0.7626953125, 0.10052490234375, 0.65283203125, 0.412353515625, -0.3154296875, -0.045745849609375, 0.407958984375, 0.275634765625, 0.45458984375, 0.71337890625, -0.541015625, 1.0302734375, -0.3974609375, 0.04937744140625, 0.2958984375, 0.11712646484375, 0.043701171875, -0.27294921875, -0.284912109375, -0.326416015625, 0.70166015625, -0.409423828125, -0.388671875, 0.7939453125, 0.30322265625, 0.544921875, -0.578125, 0.341064453125, 0.1839599609375, 0.11895751953125, 0.85791015625, 0.08843994140625, 0.022308349609375, -0.434814453125, -0.3837890625, 0.88720703125, -0.5703125, -0.07684326171875, 0.249755859375, 0.0174713134765625, -0.426513671875, 0.6513671875, -0.427978515625, 0.71826171875, -0.1241455078125, 0.3984375, 0.355712890625, -0.5654296875, 0.75927734375, -0.473876953125, 0.2763671875, 1.6162109375, 0.4443359375, 0.060394287109375, 0.619140625, 0.306640625, -0.8251953125, 0.11810302734375, -1.2509765625, 0.48974609375, -0.01125335693359375, 0.287109375, -0.29150390625, 0.44384765625, -0.240234375, 0.384033203125, 0.356201171875, 0.1046142578125, -0.1993408203125, 0.3857421875, -0.65380859375, 0.494140625, -0.3212890625, 0.3759765625, -0.145263671875, 0.035736083984375, -0.1768798828125, -0.361328125, 0.2286376953125, -0.06353759765625, 0.0311737060546875, 1.0341796875, 0.6298828125, 1.107421875, 0.83203125, -0.046966552734375, 0.248779296875, 0.254150390625, -0.495361328125, 0.303955078125, 0.08917236328125, 0.76904296875, 0.31591796875, 0.625, -0.100341796875, 0.029388427734375, -0.261474609375, -0.697265625, 0.04840087890625, 0.916015625, -0.61962890625, 0.31787109375, -0.347900390625, 0.309814453125, -0.9501953125, -0.33447265625, -0.3486328125, -0.89599609375, -0.4716796875, 0.4736328125, 0.06890869140625, 0.30419921875, -0.8203125, -0.7578125, 0.8701171875, 1.14453125, -0.299072265625, 0.024261474609375, 0.307861328125, 0.01131439208984375, 0.033233642578125, -0.042144775390625, 0.283935546875, -0.2490234375, -0.65869140625, 0.533203125, -0.026611328125, -0.00984954833984375, -0.08624267578125, 0.8876953125, 0.37353515625, 1.021484375, -0.192138671875, -0.347900390625, 0.6552734375, 1.0107421875, -0.271484375, 0.576171875, 0.442138671875, 1.0087890625, 0.5693359375, 0.6171875, 0.4111328125, 0.2257080078125, 0.61376953125, 0.701171875, 0.0606689453125, -0.007450103759765625, -0.09039306640625, 0.748046875, 0.115478515625, 0.459716796875, 0.46533203125, 0.7333984375, -0.315673828125, -0.162109375, -0.2978515625, 0.15576171875, -0.3369140625, 0.66845703125, 0.2357177734375, 0.48095703125, -0.6962890625, -0.3203125, 0.4013671875, 0.85009765625, -0.7255859375, -0.75146484375, 0.017059326171875, 0.0858154296875, -0.4677734375, 0.318603515625, 0.11712646484375, 0.2174072265625, 0.3232421875, 0.283203125, -0.496826171875, -0.6611328125, -0.76513671875, -0.80126953125, -0.9189453125, -0.374755859375, -0.73486328125, -0.297119140625, 0.159423828125, -0.6669921875, 0.032379150390625, -0.2890625, -0.2744140625, 0.18994140625, -0.720703125, 0.56396484375, -0.48193359375, 0.283447265625, -0.53076171875, 0.39306640625, 0.6171875, 0.99609375, -0.5078125, -0.0240020751953125, -0.197998046875, -0.498779296875, 0.263916015625, -0.01052093505859375, 0.46728515625, 0.1217041015625, -0.4208984375, -0.72802734375, -0.65283203125, 0.08831787109375, -0.4326171875, 0.2388916015625, -0.244384765625, 0.79931640625, 0.46435546875, -0.599609375, 0.68115234375, 1.021484375, -0.76953125, 0.451904296875, 0.258544921875, 0.2724609375, -0.607421875, 1.251953125, 0.427978515625, 0.2142333984375, -0.50830078125, -0.28955078125, -0.411376953125, 0.1636962890625, 0.150146484375, -0.697265625, -0.495361328125, 0.61328125, -0.304443359375, -0.62841796875, 0.73681640625, -0.935546875, -0.6064453125, -0.28125, -0.748046875, 0.81787109375, 0.91455078125, 0.316650390625, -0.43603515625, -0.1978759765625, -0.0257568359375, 0.4296875, 0.54736328125, -0.658203125, -0.30712890625, 0.8916015625, 0.09783935546875, -0.18017578125, 0.06793212890625, -0.007709503173828125, -0.24267578125, -0.0224609375, 0.06195068359375, 0.9423828125, 0.20361328125, 0.60595703125, 0.31103515625, 0.701171875, -0.947265625, -0.249755859375, -0.421142578125, 0.6337890625, 0.462158203125, 0.203125, 0.308837890625, -0.251708984375, -0.51220703125, -0.91015625, 0.29443359375, 0.3017578125, 0.912109375, -0.5048828125, 0.80419921875, 0.1942138671875, -0.56787109375, 0.79443359375, -0.7236328125, 0.2381591796875, 1.28515625, -0.07733154296875, 0.701171875, -0.6259765625, 0.3251953125, 0.062408447265625, -0.0281219482421875, 0.4462890625, 0.2022705078125, 0.56787109375, -0.41552734375, -0.021392822265625, -0.53515625, -0.2430419921875, 0.0675048828125, -0.6904296875, 0.272216796875, -0.42333984375, -0.458984375, -0.9619140625, 0.51171875, 0.59521484375, 0.44580078125, -0.036895751953125, 0.453857421875, 0.364501953125, 0.43505859375, 0.75341796875, -0.3466796875, -0.1697998046875, -0.39501953125, 1.0439453125, 0.1590576171875, -0.34521484375, -0.58447265625, -0.2208251953125, -0.14697265625, -0.0733642578125, -0.39404296875, 0.0250701904296875, -0.87548828125, 0.53857421875, -0.04302978515625, 0.5126953125, -0.583984375, -0.1376953125, -0.576171875, 0.384033203125, 0.279541015625, -1.1103515625, 0.2578125, -0.92529296875, 0.329833984375, 0.22705078125, -0.21044921875, -0.339599609375, -0.384033203125, -0.9853515625, -0.96044921875, -0.2420654296875, 1.087890625, -0.342529296875, 0.1927490234375, -1.373046875, 0.358642578125, 0.45654296875, -0.41064453125, 0.2626953125, -0.213623046875, 0.269775390625, 0.2081298828125, 0.640625, -0.77197265625, -0.7880859375, -0.1575927734375, -1.267578125, 0.5869140625, -0.53857421875, 0.396484375, 0.52294921875, -0.2008056640625, -0.273193359375, 0.307373046875, -0.166259765625, 0.10906982421875, -0.36669921875, 0.50830078125, -0.89404296875, -0.58203125, 0.379638671875, -0.42578125, -0.5810546875, 0.93994140625, -0.126708984375, -0.2159423828125, 0.06768798828125, 0.47509765625, -0.7412109375, 0.469482421875, -0.485595703125, 0.7099609375, -0.3818359375, -0.65185546875, -0.28125, -0.58056640625, 1.0146484375, 0.0665283203125, -0.99853515625, 0.058929443359375, -1.07421875, -0.0288848876953125, 0.185791015625, -0.62939453125, 0.253173828125, 0.313232421875, -0.52490234375, 0.053985595703125, 0.022552490234375, -0.457763671875, -0.493408203125, -0.29736328125, -0.1591796875, 0.279052734375, -0.107421875, 0.82763671875, 0.3759765625, -0.260498046875, 0.292724609375, -0.240478515625, -0.12310791015625, -0.60791015625, -0.184814453125, -0.4892578125, -0.2783203125, -0.2685546875, 0.42626953125, -0.28076171875, 0.497802734375, 0.6796875, 0.08001708984375, 0.5419921875, 0.360107421875, -0.65283203125, 1.2509765625, 0.1890869140625, -1.02734375, -0.398193359375, 0.81591796875, 0.000583648681640625, 0.53173828125, 0.1458740234375, -1.2197265625, -0.55810546875, -0.84130859375, 0.556640625, -0.70947265625, -0.1597900390625, -1.2490234375, -0.403564453125, -0.382080078125, 0.51171875, 0.0887451171875, -0.216064453125, 0.32275390625, -0.7607421875, 0.2176513671875, -1.1279296875, -0.396484375, -0.95947265625, -0.2037353515625, -0.2822265625, 0.9716796875, 0.1273193359375, 0.364013671875, -0.189453125, -0.041900634765625, 0.54296875, -0.1199951171875, -0.49658203125, -0.461181640625, 0.1279296875, 0.2001953125, -0.03173828125, 0.08953857421875, -0.34423828125, 0.7109375, -0.8291015625, 0.5478515625, -0.016693115234375, -0.314697265625, -0.09979248046875, 0.08074951171875, 1.2802734375, -0.66259765625, 0.03173828125, -0.406005859375, 0.32275390625, 0.59765625, -0.255859375, -0.6669921875, -0.393310546875, -0.75439453125, -1.095703125, 0.57470703125, -0.2354736328125, -0.014678955078125, -0.77880859375, 0.1497802734375, 1.02734375, -0.8203125, 0.47509765625, 1.232421875, 0.28369140625, 0.1876220703125, -0.57568359375, 0.623046875, 0.70556640625, -0.75146484375, -0.028656005859375, -0.0081787109375, -0.673828125, 0.15576171875, -0.576171875, -1.18359375, -0.58984375, 0.1444091796875, 1.171875, -0.3837890625, 1.001953125, -0.1600341796875, -1.2177734375, -0.471435546875, 0.65966796875, 0.10400390625, 0.321533203125, 1.021484375, -0.12347412109375, -0.36669921875, -0.187255859375, -0.50390625, -0.453369140625, -0.34619140625, 1.123046875, -0.5966796875, -0.1942138671875, 0.96728515625, 0.966796875, -0.9697265625, -0.95849609375, -0.1898193359375, -0.20849609375, -0.412353515625, -0.541015625, 0.09368896484375, 0.70751953125, -0.59814453125, 0.0302276611328125, 0.52099609375, -0.10089111328125, 0.355712890625, -0.29296875, 0.173828125, -0.54736328125, 0.251953125, 0.8828125, -0.260009765625, -0.52880859375, -0.89306640625, -0.0208740234375, -0.26025390625, -0.097900390625, 0.849609375, -0.366943359375, 0.35498046875, 0.39990234375, -0.17724609375, 0.5947265625, -0.369384765625, -0.00994110107421875, 0.391357421875, -0.865234375, -0.5380859375, 0.0875244140625, 0.43310546875, 0.1351318359375, 0.52587890625, -0.5673828125, 0.006023406982421875, 0.4453125, 0.270263671875, -0.219482421875, -0.46484375, -0.195556640625, -1.17578125, -0.9013671875, -0.87158203125, -0.47705078125, -0.054351806640625, 0.1781005859375, 0.054107666015625, -0.52490234375, 0.0003364086151123047, 0.419921875, -0.80859375, 1.001953125, -0.70556640625, 0.2476806640625, -0.420166015625, -0.59619140625, -0.7265625, -0.2431640625, -0.46728515625, -0.240966796875, -0.501953125, 0.424072265625, -0.50341796875, 0.353271484375, -0.32666015625, 0.60546875, -0.2200927734375, -0.69287109375, 0.272705078125, 0.0946044921875, -0.2086181640625, 1.0400390625, 0.376708984375, -0.189453125, 0.049774169921875, -0.2666015625, -0.1783447265625, -0.245849609375, 1.080078125, 0.54541015625, 0.056640625, -0.2127685546875, 0.0509033203125, -0.1507568359375, -1.1025390625, 0.355224609375, -0.2061767578125, 0.475341796875, 0.281982421875, -0.0333251953125, 0.63037109375, 1.1669921875, -0.72021484375, 0.45068359375, -0.06573486328125, 0.193359375, 0.62548828125, 0.422607421875, -0.28759765625, 0.284423828125, -0.10528564453125, -0.448974609375, 0.01259613037109375, 0.359375, 0.1871337890625, 0.1630859375, -0.0615234375, -0.81103515625, -0.9150390625, -0.47998046875, 0.06939697265625, 0.1842041015625, 0.346435546875, -0.3095703125, 0.022857666015625, 0.190673828125, -0.55859375, 0.0736083984375, -1.19921875, -0.916015625, 0.609375, -0.1397705078125, -1.107421875, 0.1302490234375, -0.140625, -0.08331298828125, 0.11273193359375, 0.238525390625, -0.379150390625, 0.492919921875, -0.18603515625, 0.406982421875, -0.0902099609375, -0.399658203125, -0.006771087646484375, 0.53076171875, -0.76318359375, -0.7958984375, 0.1868896484375, 0.990234375, 0.18798828125, -0.5048828125, -0.345947265625, 0.320556640625, -0.0013294219970703125, 0.2235107421875, -0.51513671875, 0.124267578125, -0.375, 0.344482421875, -0.7041015625, 0.046844482421875, -0.46875, 0.1429443359375, 0.076904296875, -0.441650390625, -0.6689453125, 0.8134765625, 0.67138671875, 0.0316162109375, 0.373779296875, 0.09429931640625, 0.7099609375, 0.491943359375, -0.36669921875, -0.2491455078125, 0.65234375, 0.64306640625, 0.81201171875, -0.2454833984375, 0.46630859375, 0.89990234375, 0.05621337890625, -0.171875, 0.32373046875, 0.1544189453125, -0.054473876953125, 0.203125, -0.02154541015625, -0.255126953125, -0.1915283203125, -0.80224609375, 0.277099609375, -0.4345703125, -0.1060791015625, 0.056243896484375, -0.6669921875, 0.80029296875, -0.4697265625, -0.311279296875, 0.11712646484375, -0.466064453125, 0.39013671875, 0.53125, -0.10211181640625, -0.333251953125, 1.0244140625, 1.068359375, 0.93115234375, 0.67919921875, 0.40869140625, 0.357177734375, -0.5283203125, 0.0931396484375, -0.025726318359375, 0.279296875, -0.2822265625, -0.5439453125, -1.02734375, 0.268798828125, -0.05621337890625, -0.0810546875, 0.35009765625, -0.21875, 0.00931549072265625, -0.31689453125, 0.67431640625, -0.7626953125, -0.2041015625, 0.44384765625, -0.470703125, -0.378662109375, 0.76611328125, -0.099365234375, 0.039825439453125, 0.206787109375, 1.0732421875, -0.054718017578125, 1.6591796875, 0.67724609375, -0.38525390625, 0.1492919921875, 0.73974609375, -0.40283203125, -0.6923828125, -0.57568359375, -0.4228515625, 0.1429443359375, -0.60107421875, -0.47265625, -0.1790771484375, 0.69921875, 0.44287109375, -0.87646484375, -0.357421875, 0.068603515625, -0.66552734375, 0.1495361328125, 0.25, 0.433837890625, 0.05267333984375, -0.1669921875, -0.272705078125, -0.68017578125, 0.73095703125, -0.56201171875, 0.243408203125, -0.6064453125, -0.29296875, -0.272705078125, -0.505859375, -0.13720703125, -0.187255859375, -0.263427734375, -0.6650390625, 0.41064453125, 0.5625, 0.53466796875, 0.073486328125, -0.1944580078125, 0.10888671875, 1.1181640625, 1.1875, -0.04608154296875, 0.87451171875, 0.24169921875, -0.12164306640625, 0.2147216796875, -0.4365234375, 0.458740234375, 0.25048828125, 0.2486572265625, -0.49658203125, 0.45947265625, -1.0595703125, -1.068359375, 0.1319580078125, 0.60791015625, 0.34912109375, -0.73583984375, -1.2080078125, -0.23193359375, -1.1982421875, -0.1199951171875, -0.40185546875, 0.75390625, -0.29248046875, -0.2003173828125, -0.06268310546875, -1.185546875, 4.32421875, 0.62744140625, 0.8623046875, 0.53857421875, 0.357666015625, 0.943359375, 0.51953125, -0.490478515625, -0.1541748046875, -0.53515625, 0.6513671875, -0.306884765625, 0.041473388671875, 0.99365234375, 0.56591796875, 0.269287109375, -0.2880859375, -0.16552734375, 0.162353515625, -0.94189453125, -0.73876953125, 0.5322265625, -0.01416015625, 0.87841796875, -0.131591796875, 0.233154296875, 0.6162109375, -0.75927734375, -0.59619140625, -0.54541015625, 0.326171875, -0.276611328125, 1.048828125, 0.01995849609375, -0.17236328125, 0.8564453125, 0.197021484375, -0.5, -0.131591796875, 0.26953125, -0.001861572265625, -0.149658203125, 0.65185546875, -0.912109375, -0.32421875, 0.402099609375, -1.0166015625, 0.6806640625, 0.09552001953125, -1.0888671875, 0.50634765625, -0.260009765625, 0.15771484375, -0.73388671875, -0.350341796875, 0.176513671875, -0.1336669921875, -0.0816650390625, -0.2330322265625, 0.60595703125, 0.494140625, 0.51123046875, 0.0849609375, 0.76416015625, -1.0791015625, 0.80908203125, -0.006946563720703125, 0.81494140625, -0.7294921875, 0.0257110595703125, -0.09417724609375, -0.607421875, -0.258544921875, -0.50244140625, 0.39306640625, 0.42138671875, -0.09661865234375, 0.5361328125, 0.5341796875, -0.5830078125, 0.325927734375, 0.035614013671875, -0.42919921875, -0.546875, 0.5595703125, 1.16796875, -0.97509765625, -0.227783203125, -0.373046875, 0.56787109375, 0.85595703125, 0.787109375, -0.1055908203125, -0.5185546875, -0.263427734375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's introduce the designation <image>, where x is a string, n is a positive integer and operation " + " is the string concatenation operation. For example, [abc, 2] = abcabc. We'll say that string s can be obtained from string t, if we can remove some characters from string t and obtain string s. For example, strings ab and aсba can be obtained from string xacbac, and strings bx and aaa cannot be obtained from it. Sereja has two strings, w = [a, b] and q = [c, d]. He wants to find such maximum integer p (p > 0), that [q, p] can be obtained from string w. Input The first line contains two integers b, d (1 ≀ b, d ≀ 107). The second line contains string a. The third line contains string c. The given strings are not empty and consist of lowercase English letters. Their lengths do not exceed 100. Output In a single line print an integer β€” the largest number p. If the required value of p doesn't exist, print 0. Examples Input 10 3 abab bab Output 3 Submitted Solution: ``` b, p = map(int, input().split()) s1 = input() s2 = input() cnt = 0 pos = 0 flag = True while flag and cnt < b: for i in range(len(s1)): if i == 0: cnt += 1 if s1[i] == s2[pos]: pos += 1 if pos == len(s2): flag = False break if flag == False: ans = b // cnt // p else: ans = 0 print(ans) ``` No
105,563
[ 0.432373046875, -0.400390625, -0.11627197265625, 0.5498046875, -0.373779296875, -0.5498046875, -0.302978515625, 0.24365234375, 0.437255859375, 0.7431640625, 0.744140625, -0.07806396484375, -0.075927734375, -1.048828125, -0.55224609375, -0.061920166015625, -0.46826171875, -0.6357421875, 0.10223388671875, -0.258544921875, -0.105224609375, -0.07666015625, -1.4189453125, 0.054351806640625, -0.27880859375, 0.70556640625, 0.7333984375, -0.0526123046875, 0.6416015625, 1.29296875, -0.52197265625, -0.470703125, 0.53515625, -0.8212890625, -0.32568359375, -0.560546875, 0.7783203125, -0.89208984375, -0.422607421875, -0.417724609375, -0.04095458984375, -0.58837890625, 0.5849609375, -0.72998046875, -1.640625, -0.1331787109375, -0.2119140625, -0.27392578125, -0.213134765625, -0.8525390625, -0.25048828125, -0.2462158203125, 0.80615234375, 0.0367431640625, 0.01483917236328125, 0.2464599609375, 0.25, -0.370849609375, -0.7099609375, 0.252685546875, 0.302490234375, 0.021209716796875, -0.033966064453125, -0.7197265625, -0.564453125, 0.25146484375, -0.04937744140625, -0.336669921875, 0.22900390625, -0.806640625, -0.342041015625, 0.1163330078125, -0.8017578125, -0.236083984375, -0.20458984375, 0.10101318359375, 0.2314453125, 0.029754638671875, -0.59912109375, 1.3017578125, 0.00894927978515625, 1.1533203125, 0.1768798828125, 0.299072265625, -0.485595703125, -0.491455078125, 0.009552001953125, 0.035858154296875, 0.12469482421875, -0.09814453125, -0.4111328125, 0.427490234375, -0.59619140625, 0.09039306640625, 0.5966796875, 0.328369140625, -0.3818359375, -0.005496978759765625, 0.463623046875, 0.21533203125, 0.50048828125, 0.681640625, -0.5087890625, 1.01953125, -0.423095703125, -0.00858306884765625, 0.1956787109375, 0.10748291015625, 0.07720947265625, -0.2900390625, -0.2015380859375, -0.267578125, 0.732421875, -0.318115234375, -0.39404296875, 0.84814453125, 0.3046875, 0.42138671875, -0.626953125, 0.444580078125, 0.19921875, 0.1396484375, 0.89404296875, 0.088134765625, 0.032867431640625, -0.492919921875, -0.52197265625, 0.92333984375, -0.693359375, -0.1392822265625, 0.285888671875, 0.0850830078125, -0.432861328125, 0.60107421875, -0.319091796875, 0.68212890625, -0.1666259765625, 0.45703125, 0.3837890625, -0.58837890625, 0.7587890625, -0.48583984375, 0.30126953125, 1.6552734375, 0.47314453125, 0.11541748046875, 0.60498046875, 0.334228515625, -0.7080078125, 0.212646484375, -1.29296875, 0.5244140625, -0.0389404296875, 0.2025146484375, -0.35400390625, 0.4365234375, -0.14697265625, 0.2042236328125, 0.483154296875, 0.1666259765625, -0.2486572265625, 0.3310546875, -0.673828125, 0.58349609375, -0.417724609375, 0.53271484375, -0.152099609375, 0.114013671875, -0.1688232421875, -0.4404296875, 0.1746826171875, -0.1832275390625, 0.10357666015625, 1.1240234375, 0.63037109375, 1.2373046875, 0.8701171875, -0.06378173828125, 0.3447265625, 0.2469482421875, -0.4560546875, 0.2841796875, 0.00750732421875, 0.826171875, 0.25341796875, 0.75341796875, -0.08526611328125, -0.0015039443969726562, -0.2227783203125, -0.81298828125, 0.00571441650390625, 0.94921875, -0.63720703125, 0.335693359375, -0.364013671875, 0.2890625, -0.93603515625, -0.255859375, -0.4111328125, -0.931640625, -0.489501953125, 0.311279296875, 0.1651611328125, 0.353759765625, -0.849609375, -0.82275390625, 0.74072265625, 1.0810546875, -0.29541015625, 0.04998779296875, 0.4921875, 0.1082763671875, 0.022918701171875, -0.034759521484375, 0.302734375, -0.2161865234375, -0.6953125, 0.4638671875, -0.02734375, -0.010986328125, -0.08984375, 0.89013671875, 0.33837890625, 0.9189453125, -0.13134765625, -0.30078125, 0.63720703125, 0.9775390625, -0.263916015625, 0.67431640625, 0.3544921875, 1.05078125, 0.619140625, 0.748046875, 0.438232421875, 0.2281494140625, 0.69921875, 0.6640625, -0.063232421875, 0.01084136962890625, 0.03485107421875, 0.7314453125, 0.12432861328125, 0.489013671875, 0.39306640625, 0.73046875, -0.224609375, -0.093017578125, -0.234375, 0.212890625, -0.344482421875, 0.78125, 0.1998291015625, 0.5244140625, -0.61376953125, -0.21826171875, 0.54541015625, 0.85986328125, -0.697265625, -0.7705078125, -0.1358642578125, 0.042999267578125, -0.441162109375, 0.271240234375, 0.0953369140625, 0.3193359375, 0.285400390625, 0.3125, -0.487548828125, -0.59814453125, -0.75146484375, -0.70068359375, -0.9697265625, -0.337646484375, -0.779296875, -0.271240234375, 0.27197265625, -0.64404296875, -0.182861328125, -0.35888671875, -0.3388671875, 0.1455078125, -0.71484375, 0.576171875, -0.350830078125, 0.213134765625, -0.537109375, 0.403564453125, 0.55517578125, 1, -0.515625, 0.0264434814453125, -0.1671142578125, -0.447265625, 0.2410888671875, 0.06756591796875, 0.441650390625, 0.251708984375, -0.50244140625, -0.81982421875, -0.7197265625, 0.10589599609375, -0.39697265625, 0.2298583984375, -0.3212890625, 0.88525390625, 0.42578125, -0.49609375, 0.54931640625, 1.02734375, -0.8583984375, 0.441650390625, 0.32470703125, 0.298828125, -0.67236328125, 1.3134765625, 0.431640625, 0.29931640625, -0.57470703125, -0.288330078125, -0.367919921875, 0.26220703125, 0.1314697265625, -0.69384765625, -0.485595703125, 0.6005859375, -0.2239990234375, -0.6865234375, 0.796875, -0.91015625, -0.58544921875, -0.1978759765625, -0.71337890625, 0.81591796875, 0.82373046875, 0.423095703125, -0.353515625, -0.32568359375, -0.04400634765625, 0.350830078125, 0.5712890625, -0.69677734375, -0.331787109375, 1.0185546875, 0.0311737060546875, -0.09344482421875, -0.013702392578125, 0.07177734375, -0.252685546875, 0.0005097389221191406, 0.08917236328125, 0.951171875, 0.2281494140625, 0.40625, 0.3193359375, 0.63330078125, -1.041015625, -0.1990966796875, -0.357666015625, 0.52490234375, 0.476806640625, 0.339599609375, 0.432373046875, -0.18505859375, -0.51318359375, -0.89892578125, 0.384033203125, 0.35400390625, 0.9599609375, -0.4814453125, 0.8203125, 0.307373046875, -0.654296875, 0.81298828125, -0.7626953125, 0.0709228515625, 1.2421875, -0.056976318359375, 0.73583984375, -0.64697265625, 0.29443359375, 0.1199951171875, -0.1737060546875, 0.461181640625, 0.15087890625, 0.57666015625, -0.45703125, -0.150146484375, -0.61083984375, -0.222412109375, -0.04193115234375, -0.71630859375, 0.2413330078125, -0.394775390625, -0.52001953125, -0.93359375, 0.58056640625, 0.5849609375, 0.515625, 0.028656005859375, 0.53369140625, 0.403564453125, 0.44091796875, 0.68798828125, -0.20263671875, -0.055023193359375, -0.4150390625, 1.04296875, 0.23095703125, -0.44384765625, -0.6005859375, -0.299072265625, -0.1407470703125, -0.0205078125, -0.3701171875, -0.1171875, -0.87646484375, 0.5302734375, -0.152099609375, 0.54150390625, -0.61474609375, -0.060882568359375, -0.4755859375, 0.468017578125, 0.31103515625, -1.0908203125, 0.298828125, -0.8525390625, 0.40673828125, 0.183349609375, -0.1990966796875, -0.324462890625, -0.33642578125, -0.97802734375, -0.93212890625, -0.21240234375, 1.0625, -0.37841796875, 0.265869140625, -1.33203125, 0.275390625, 0.5478515625, -0.39453125, 0.342529296875, -0.31103515625, 0.3271484375, 0.1480712890625, 0.56884765625, -0.7197265625, -0.7783203125, -0.09417724609375, -1.2744140625, 0.499267578125, -0.580078125, 0.472900390625, 0.5146484375, -0.19140625, -0.287841796875, 0.25048828125, -0.1422119140625, 0.0704345703125, -0.287841796875, 0.62109375, -0.87744140625, -0.451416015625, 0.409912109375, -0.3095703125, -0.67138671875, 1.0048828125, -0.08294677734375, -0.1783447265625, 0.036041259765625, 0.6591796875, -0.8291015625, 0.457275390625, -0.491943359375, 0.7490234375, -0.442626953125, -0.58447265625, -0.2086181640625, -0.56103515625, 0.9912109375, -0.0161590576171875, -0.97607421875, -0.0103759765625, -1.2451171875, -0.03765869140625, 0.08807373046875, -0.5654296875, 0.24267578125, 0.365966796875, -0.387451171875, 0.07373046875, -0.039794921875, -0.374267578125, -0.55517578125, -0.36767578125, -0.155029296875, 0.29541015625, -0.1270751953125, 0.86328125, 0.320068359375, -0.328125, 0.253662109375, -0.250244140625, -0.0919189453125, -0.51953125, -0.1453857421875, -0.501953125, -0.16455078125, -0.2088623046875, 0.371826171875, -0.1898193359375, 0.453857421875, 0.67626953125, 0.07025146484375, 0.56982421875, 0.404052734375, -0.75390625, 1.2626953125, 0.0948486328125, -1.0302734375, -0.328125, 0.8330078125, -0.02569580078125, 0.61572265625, 0.22998046875, -1.09765625, -0.67138671875, -0.79931640625, 0.52685546875, -0.654296875, -0.2064208984375, -1.2646484375, -0.375732421875, -0.309814453125, 0.456787109375, 0.016510009765625, -0.29736328125, 0.2469482421875, -0.79248046875, 0.1998291015625, -1.0986328125, -0.365478515625, -1.0791015625, -0.2335205078125, -0.276611328125, 0.91357421875, 0.06201171875, 0.287841796875, -0.11279296875, -0.040771484375, 0.484619140625, -0.1357421875, -0.56005859375, -0.455322265625, 0.049163818359375, 0.2303466796875, -0.06805419921875, -0.04498291015625, -0.290283203125, 0.66845703125, -0.841796875, 0.5732421875, -0.045166015625, -0.297119140625, -0.151611328125, -0.0181732177734375, 1.2138671875, -0.59521484375, 0.07293701171875, -0.337890625, 0.28955078125, 0.6728515625, -0.339599609375, -0.634765625, -0.450439453125, -0.56640625, -1.0595703125, 0.5615234375, -0.2147216796875, -0.0394287109375, -0.83447265625, 0.12841796875, 1.068359375, -0.79052734375, 0.54443359375, 1.296875, 0.235107421875, 0.186279296875, -0.61474609375, 0.6376953125, 0.72314453125, -0.73828125, 0.0323486328125, -0.08306884765625, -0.8779296875, 0.2083740234375, -0.65625, -1.2578125, -0.5419921875, 0.1878662109375, 1.1357421875, -0.304931640625, 0.9228515625, -0.1153564453125, -1.3330078125, -0.49755859375, 0.7744140625, 0.048736572265625, 0.1993408203125, 1.02734375, -0.1114501953125, -0.261962890625, -0.2626953125, -0.4130859375, -0.384765625, -0.3408203125, 1.056640625, -0.62939453125, -0.247314453125, 0.966796875, 0.88330078125, -1.02734375, -1.0771484375, -0.2037353515625, -0.2376708984375, -0.43115234375, -0.5537109375, 0.1878662109375, 0.79248046875, -0.62939453125, 0.1009521484375, 0.5947265625, -0.047149658203125, 0.459228515625, -0.3134765625, 0.166015625, -0.56787109375, 0.309814453125, 0.80712890625, -0.2296142578125, -0.5751953125, -0.9091796875, -0.0164642333984375, -0.211181640625, -0.07952880859375, 0.83349609375, -0.2100830078125, 0.35205078125, 0.3994140625, -0.11602783203125, 0.60302734375, -0.40087890625, -0.271728515625, 0.271240234375, -0.89501953125, -0.440673828125, 0.0587158203125, 0.53173828125, -0.032196044921875, 0.6025390625, -0.50146484375, -0.1551513671875, 0.423095703125, 0.310302734375, -0.21630859375, -0.58203125, -0.1715087890625, -1.173828125, -0.826171875, -0.82568359375, -0.53125, -0.0760498046875, 0.1378173828125, 0.10455322265625, -0.472412109375, -0.0014591217041015625, 0.36669921875, -0.92236328125, 1.00390625, -0.6845703125, 0.1881103515625, -0.44677734375, -0.483154296875, -0.734375, -0.11065673828125, -0.455078125, -0.32177734375, -0.457275390625, 0.44873046875, -0.40380859375, 0.305908203125, -0.3271484375, 0.65234375, -0.216064453125, -0.64599609375, 0.2305908203125, 0.105224609375, -0.134521484375, 1.0869140625, 0.42822265625, -0.208740234375, -0.01285552978515625, -0.21826171875, -0.1763916015625, -0.29638671875, 1.0341796875, 0.47802734375, 0.04931640625, -0.1888427734375, 0.00489044189453125, -0.08563232421875, -0.998046875, 0.2274169921875, -0.298095703125, 0.39453125, 0.1854248046875, 0.001232147216796875, 0.51953125, 1.2548828125, -0.7353515625, 0.5126953125, -0.077392578125, 0.2061767578125, 0.64892578125, 0.47119140625, -0.385986328125, 0.430908203125, -0.1514892578125, -0.335205078125, 0.093994140625, 0.409912109375, 0.192138671875, 0.2210693359375, -0.043121337890625, -0.869140625, -0.865234375, -0.52197265625, 0.165771484375, 0.231689453125, 0.2958984375, -0.392578125, 0.0220947265625, 0.1531982421875, -0.4912109375, 0.1046142578125, -1.2783203125, -0.9091796875, 0.6337890625, 0.014312744140625, -1.025390625, 0.18896484375, -0.19482421875, 0.00765228271484375, 0.2095947265625, 0.23876953125, -0.4296875, 0.414794921875, -0.1573486328125, 0.478759765625, -0.1478271484375, -0.390380859375, 0.0011348724365234375, 0.378662109375, -0.82177734375, -0.78125, 0.1287841796875, 0.93896484375, 0.154296875, -0.51171875, -0.28857421875, 0.397216796875, -0.093994140625, 0.198486328125, -0.55859375, 0.054534912109375, -0.326904296875, 0.267578125, -0.72998046875, -0.052001953125, -0.55126953125, 0.211181640625, 0.1378173828125, -0.39306640625, -0.6689453125, 0.7998046875, 0.7724609375, -0.0194549560546875, 0.427734375, 0.06353759765625, 0.7861328125, 0.55859375, -0.32275390625, -0.1895751953125, 0.68896484375, 0.61767578125, 0.89599609375, -0.18603515625, 0.40478515625, 0.84521484375, -0.1060791015625, -0.278564453125, 0.335693359375, 0.1298828125, -0.04608154296875, 0.360107421875, -0.006744384765625, -0.30029296875, -0.09954833984375, -0.79052734375, 0.2783203125, -0.38427734375, -0.10662841796875, 0.0772705078125, -0.59765625, 0.83984375, -0.4619140625, -0.387451171875, 0.19091796875, -0.458251953125, 0.4248046875, 0.564453125, -0.1043701171875, -0.272216796875, 0.9638671875, 1.0869140625, 0.88134765625, 0.69384765625, 0.3271484375, 0.368896484375, -0.56982421875, 0.0758056640625, -0.050933837890625, 0.216552734375, -0.24072265625, -0.55517578125, -1.080078125, 0.34375, 0.01546478271484375, -0.07354736328125, 0.385498046875, -0.33740234375, 0.042938232421875, -0.38037109375, 0.7080078125, -0.7919921875, -0.08282470703125, 0.427001953125, -0.5390625, -0.28759765625, 0.7548828125, -0.0836181640625, 0.09783935546875, 0.17236328125, 1.173828125, 0.003559112548828125, 1.6015625, 0.77099609375, -0.3349609375, 0.1275634765625, 0.6982421875, -0.298583984375, -0.603515625, -0.467529296875, -0.409423828125, 0.1173095703125, -0.5908203125, -0.52490234375, -0.2030029296875, 0.81298828125, 0.46826171875, -0.892578125, -0.449951171875, 0.1597900390625, -0.76416015625, 0.19970703125, 0.1507568359375, 0.364501953125, 0.0958251953125, -0.11077880859375, -0.30029296875, -0.64697265625, 0.79736328125, -0.57861328125, 0.2303466796875, -0.6005859375, -0.390869140625, -0.339111328125, -0.468017578125, -0.1380615234375, -0.184326171875, -0.314453125, -0.6904296875, 0.49072265625, 0.4638671875, 0.5107421875, 0.1976318359375, -0.2056884765625, 0.133544921875, 1.1552734375, 1.2646484375, 0.039398193359375, 0.79931640625, 0.250732421875, -0.1612548828125, 0.211181640625, -0.5546875, 0.54541015625, 0.33154296875, 0.34814453125, -0.51123046875, 0.4423828125, -1.076171875, -1.111328125, -0.0208282470703125, 0.68359375, 0.28125, -0.78125, -1.15234375, -0.25927734375, -1.173828125, -0.2454833984375, -0.37255859375, 0.76806640625, -0.4638671875, -0.1636962890625, -0.09326171875, -1.22265625, 4.2578125, 0.578125, 0.7978515625, 0.6650390625, 0.332763671875, 0.888671875, 0.488037109375, -0.452880859375, -0.12335205078125, -0.5703125, 0.74267578125, -0.315185546875, 0.0021724700927734375, 1.0166015625, 0.62890625, 0.28857421875, -0.27392578125, -0.1549072265625, 0.2337646484375, -0.865234375, -0.73046875, 0.54736328125, 0.1416015625, 0.865234375, -0.1766357421875, 0.29833984375, 0.65869140625, -0.7880859375, -0.54150390625, -0.55859375, 0.341552734375, -0.33203125, 1.0791015625, 0.008148193359375, -0.2015380859375, 0.83740234375, 0.1470947265625, -0.55322265625, -0.1021728515625, 0.32470703125, -0.0216827392578125, -0.151123046875, 0.599609375, -0.91357421875, -0.397216796875, 0.442138671875, -0.95654296875, 0.708984375, 0.09442138671875, -1.236328125, 0.5966796875, -0.188232421875, 0.0416259765625, -0.75439453125, -0.44384765625, 0.215087890625, -0.0611572265625, -0.07672119140625, -0.258056640625, 0.7509765625, 0.5185546875, 0.5283203125, -0.004730224609375, 0.755859375, -1.138671875, 0.81689453125, -0.1961669921875, 0.78564453125, -0.85302734375, -0.06536865234375, -0.0633544921875, -0.65380859375, -0.259521484375, -0.52294921875, 0.3857421875, 0.400390625, -0.1868896484375, 0.51904296875, 0.587890625, -0.66796875, 0.135009765625, 0.07733154296875, -0.425537109375, -0.60791015625, 0.53271484375, 1.150390625, -0.96826171875, -0.2252197265625, -0.443115234375, 0.5751953125, 0.83154296875, 0.6982421875, -0.040374755859375, -0.52685546875, -0.31005859375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's introduce the designation <image>, where x is a string, n is a positive integer and operation " + " is the string concatenation operation. For example, [abc, 2] = abcabc. We'll say that string s can be obtained from string t, if we can remove some characters from string t and obtain string s. For example, strings ab and aсba can be obtained from string xacbac, and strings bx and aaa cannot be obtained from it. Sereja has two strings, w = [a, b] and q = [c, d]. He wants to find such maximum integer p (p > 0), that [q, p] can be obtained from string w. Input The first line contains two integers b, d (1 ≀ b, d ≀ 107). The second line contains string a. The third line contains string c. The given strings are not empty and consist of lowercase English letters. Their lengths do not exceed 100. Output In a single line print an integer β€” the largest number p. If the required value of p doesn't exist, print 0. Examples Input 10 3 abab bab Output 3 Submitted Solution: ``` b, p = map(int, input().split()) s1 = input() s2 = input() cnt = 0 pos = 0 flag = True while flag and cnt < b: for i in range(len(s1)): if i == 0: cnt += 1 if s1[i] == s2[pos]: pos += 1 if pos == len(s2): flag = False break if flag: ans = b // cnt // p else: ans = 0 print(ans) ``` No
105,564
[ 0.420654296875, -0.38671875, -0.1239013671875, 0.546875, -0.38134765625, -0.54736328125, -0.3134765625, 0.267822265625, 0.4453125, 0.7333984375, 0.73779296875, -0.07208251953125, -0.0836181640625, -1.0478515625, -0.576171875, -0.05377197265625, -0.4638671875, -0.63525390625, 0.10467529296875, -0.25732421875, -0.114990234375, -0.07342529296875, -1.4228515625, 0.049774169921875, -0.27001953125, 0.70556640625, 0.73876953125, -0.055328369140625, 0.64453125, 1.2958984375, -0.51708984375, -0.4697265625, 0.53173828125, -0.82080078125, -0.3212890625, -0.52978515625, 0.7646484375, -0.900390625, -0.425537109375, -0.414794921875, -0.02734375, -0.60546875, 0.58154296875, -0.720703125, -1.6279296875, -0.1256103515625, -0.2069091796875, -0.26708984375, -0.219482421875, -0.85107421875, -0.259521484375, -0.239990234375, 0.81103515625, 0.03607177734375, 0.0279998779296875, 0.250244140625, 0.26318359375, -0.375244140625, -0.7265625, 0.268798828125, 0.29931640625, 0.02178955078125, -0.03564453125, -0.71337890625, -0.544921875, 0.260498046875, -0.053192138671875, -0.33935546875, 0.2431640625, -0.82275390625, -0.3515625, 0.11895751953125, -0.80029296875, -0.2255859375, -0.2027587890625, 0.110107421875, 0.2225341796875, 0.04058837890625, -0.578125, 1.2939453125, 0.0254669189453125, 1.1357421875, 0.178955078125, 0.2998046875, -0.484130859375, -0.50634765625, 0.00527191162109375, 0.03643798828125, 0.132568359375, -0.08099365234375, -0.418701171875, 0.434814453125, -0.5966796875, 0.0897216796875, 0.60595703125, 0.35009765625, -0.39404296875, -0.0037555694580078125, 0.477783203125, 0.2198486328125, 0.49462890625, 0.68896484375, -0.5009765625, 1.0166015625, -0.433837890625, -0.0003466606140136719, 0.1993408203125, 0.10955810546875, 0.083251953125, -0.295654296875, -0.2156982421875, -0.25048828125, 0.72412109375, -0.30859375, -0.38818359375, 0.8623046875, 0.297119140625, 0.421142578125, -0.62353515625, 0.447509765625, 0.1845703125, 0.1436767578125, 0.89501953125, 0.09039306640625, 0.027618408203125, -0.499267578125, -0.52978515625, 0.9228515625, -0.6923828125, -0.135498046875, 0.291259765625, 0.1048583984375, -0.4189453125, 0.59814453125, -0.33349609375, 0.6943359375, -0.1722412109375, 0.453369140625, 0.374755859375, -0.60302734375, 0.76318359375, -0.487060546875, 0.303955078125, 1.6630859375, 0.47314453125, 0.123046875, 0.59912109375, 0.32373046875, -0.72021484375, 0.2178955078125, -1.2939453125, 0.52001953125, -0.043975830078125, 0.2061767578125, -0.3544921875, 0.440673828125, -0.1448974609375, 0.2049560546875, 0.499755859375, 0.17431640625, -0.25244140625, 0.333984375, -0.6748046875, 0.59326171875, -0.42138671875, 0.53564453125, -0.1497802734375, 0.12030029296875, -0.1571044921875, -0.439453125, 0.1732177734375, -0.1943359375, 0.1087646484375, 1.125, 0.62744140625, 1.2314453125, 0.86083984375, -0.0682373046875, 0.3408203125, 0.24609375, -0.440185546875, 0.28759765625, 0.0097198486328125, 0.8115234375, 0.25048828125, 0.76416015625, -0.101318359375, 0.00696563720703125, -0.2255859375, -0.814453125, 0.002346038818359375, 0.95458984375, -0.62939453125, 0.3232421875, -0.391357421875, 0.2890625, -0.927734375, -0.2587890625, -0.397216796875, -0.927734375, -0.483154296875, 0.3115234375, 0.16015625, 0.359130859375, -0.857421875, -0.81494140625, 0.7294921875, 1.0849609375, -0.29736328125, 0.055877685546875, 0.50537109375, 0.09466552734375, 0.006771087646484375, -0.04345703125, 0.3056640625, -0.2122802734375, -0.7080078125, 0.4619140625, -0.032958984375, -0.0186309814453125, -0.0970458984375, 0.892578125, 0.34326171875, 0.896484375, -0.12078857421875, -0.2998046875, 0.64990234375, 0.9697265625, -0.267333984375, 0.68115234375, 0.35205078125, 1.0546875, 0.6259765625, 0.74609375, 0.4462890625, 0.2412109375, 0.69921875, 0.6484375, -0.0653076171875, -0.0042572021484375, 0.04144287109375, 0.71484375, 0.12457275390625, 0.4892578125, 0.399169921875, 0.7373046875, -0.23046875, -0.07568359375, -0.240478515625, 0.204345703125, -0.32373046875, 0.7822265625, 0.1988525390625, 0.52490234375, -0.61962890625, -0.238037109375, 0.55615234375, 0.8740234375, -0.693359375, -0.79443359375, -0.140625, 0.037567138671875, -0.4375, 0.291748046875, 0.08868408203125, 0.316650390625, 0.292236328125, 0.32470703125, -0.496337890625, -0.5947265625, -0.7626953125, -0.69189453125, -0.955078125, -0.33642578125, -0.78369140625, -0.281005859375, 0.285888671875, -0.6337890625, -0.166748046875, -0.3642578125, -0.334716796875, 0.131591796875, -0.7099609375, 0.57373046875, -0.33447265625, 0.2034912109375, -0.5576171875, 0.40966796875, 0.5283203125, 1.00390625, -0.51220703125, 0.0262908935546875, -0.166259765625, -0.45166015625, 0.2279052734375, 0.08270263671875, 0.441650390625, 0.2548828125, -0.489990234375, -0.82080078125, -0.7294921875, 0.11370849609375, -0.407470703125, 0.2442626953125, -0.299560546875, 0.88623046875, 0.427490234375, -0.49609375, 0.55712890625, 1.0068359375, -0.85302734375, 0.441162109375, 0.3125, 0.301025390625, -0.671875, 1.32421875, 0.4248046875, 0.31103515625, -0.5673828125, -0.270263671875, -0.355712890625, 0.2322998046875, 0.1363525390625, -0.69482421875, -0.4833984375, 0.59326171875, -0.2113037109375, -0.69384765625, 0.7880859375, -0.90234375, -0.57568359375, -0.2027587890625, -0.71923828125, 0.810546875, 0.83837890625, 0.40576171875, -0.36572265625, -0.3115234375, -0.052337646484375, 0.32958984375, 0.57373046875, -0.697265625, -0.328369140625, 1.033203125, 0.026092529296875, -0.10833740234375, -0.01430511474609375, 0.07489013671875, -0.2607421875, 0.006114959716796875, 0.0784912109375, 0.9306640625, 0.2386474609375, 0.406494140625, 0.3203125, 0.63427734375, -1.0224609375, -0.2076416015625, -0.37353515625, 0.52783203125, 0.479736328125, 0.346435546875, 0.46435546875, -0.2076416015625, -0.5009765625, -0.88525390625, 0.403564453125, 0.362548828125, 0.98388671875, -0.495361328125, 0.82470703125, 0.31396484375, -0.6357421875, 0.8056640625, -0.7685546875, 0.102294921875, 1.2529296875, -0.0635986328125, 0.7236328125, -0.65185546875, 0.295166015625, 0.1278076171875, -0.16357421875, 0.46728515625, 0.144775390625, 0.5869140625, -0.458984375, -0.1422119140625, -0.611328125, -0.2237548828125, -0.04205322265625, -0.7099609375, 0.2470703125, -0.390380859375, -0.51513671875, -0.93994140625, 0.58984375, 0.59765625, 0.49853515625, 0.0063629150390625, 0.51904296875, 0.390380859375, 0.4306640625, 0.68115234375, -0.197021484375, -0.06787109375, -0.412109375, 1.05078125, 0.236572265625, -0.43701171875, -0.6015625, -0.30712890625, -0.128173828125, -0.0145416259765625, -0.3779296875, -0.11395263671875, -0.86279296875, 0.52978515625, -0.1536865234375, 0.53271484375, -0.59521484375, -0.05999755859375, -0.479736328125, 0.4755859375, 0.299560546875, -1.080078125, 0.285400390625, -0.84326171875, 0.4111328125, 0.183837890625, -0.1939697265625, -0.31884765625, -0.326904296875, -0.9521484375, -0.91552734375, -0.218017578125, 1.0732421875, -0.37646484375, 0.289794921875, -1.3349609375, 0.294921875, 0.533203125, -0.39453125, 0.33984375, -0.29443359375, 0.33154296875, 0.15625, 0.57861328125, -0.6875, -0.79296875, -0.088134765625, -1.265625, 0.5185546875, -0.56982421875, 0.466552734375, 0.51513671875, -0.195556640625, -0.3017578125, 0.2413330078125, -0.1622314453125, 0.055877685546875, -0.30322265625, 0.62353515625, -0.87255859375, -0.4609375, 0.412841796875, -0.325927734375, -0.68017578125, 0.99951171875, -0.072021484375, -0.2054443359375, 0.059326171875, 0.67236328125, -0.81689453125, 0.455810546875, -0.486083984375, 0.74169921875, -0.45263671875, -0.56787109375, -0.207275390625, -0.56640625, 0.9970703125, -0.015716552734375, -0.9736328125, 0.0086212158203125, -1.2431640625, -0.042816162109375, 0.07977294921875, -0.5771484375, 0.24267578125, 0.36376953125, -0.402099609375, 0.07666015625, -0.05096435546875, -0.3701171875, -0.5654296875, -0.371826171875, -0.144287109375, 0.300537109375, -0.14013671875, 0.875, 0.30517578125, -0.332763671875, 0.259033203125, -0.250244140625, -0.10662841796875, -0.52197265625, -0.1480712890625, -0.5107421875, -0.1761474609375, -0.2208251953125, 0.36376953125, -0.162841796875, 0.450927734375, 0.67578125, 0.08685302734375, 0.5732421875, 0.390380859375, -0.755859375, 1.2763671875, 0.09814453125, -1.0400390625, -0.322509765625, 0.83251953125, -0.0147857666015625, 0.6298828125, 0.2288818359375, -1.09375, -0.673828125, -0.81103515625, 0.513671875, -0.65380859375, -0.2069091796875, -1.2685546875, -0.38720703125, -0.3291015625, 0.45458984375, 0.0168609619140625, -0.2890625, 0.2548828125, -0.8017578125, 0.2181396484375, -1.1083984375, -0.362060546875, -1.0751953125, -0.2308349609375, -0.290771484375, 0.92578125, 0.055694580078125, 0.293701171875, -0.116455078125, -0.059539794921875, 0.48828125, -0.1336669921875, -0.548828125, -0.452392578125, 0.0697021484375, 0.232177734375, -0.058624267578125, -0.04083251953125, -0.275390625, 0.6806640625, -0.85498046875, 0.55419921875, -0.044281005859375, -0.296875, -0.1607666015625, -0.01525115966796875, 1.2138671875, -0.58935546875, 0.04718017578125, -0.342041015625, 0.28955078125, 0.671875, -0.350341796875, -0.6416015625, -0.459716796875, -0.58154296875, -1.0478515625, 0.56201171875, -0.2113037109375, -0.044281005859375, -0.841796875, 0.146484375, 1.0498046875, -0.8095703125, 0.55224609375, 1.2880859375, 0.2432861328125, 0.2066650390625, -0.62548828125, 0.6611328125, 0.720703125, -0.74462890625, 0.00746917724609375, -0.07525634765625, -0.87109375, 0.19140625, -0.65966796875, -1.267578125, -0.5478515625, 0.1937255859375, 1.1494140625, -0.30517578125, 0.9248046875, -0.123779296875, -1.341796875, -0.505859375, 0.763671875, 0.0469970703125, 0.2100830078125, 1.03125, -0.099853515625, -0.282470703125, -0.262451171875, -0.4150390625, -0.39453125, -0.368896484375, 1.046875, -0.64599609375, -0.235595703125, 0.953125, 0.9072265625, -1.0185546875, -1.095703125, -0.217529296875, -0.2470703125, -0.42822265625, -0.56298828125, 0.1890869140625, 0.80224609375, -0.62548828125, 0.09356689453125, 0.58447265625, -0.057342529296875, 0.459716796875, -0.30078125, 0.1611328125, -0.57470703125, 0.30810546875, 0.8173828125, -0.2183837890625, -0.58154296875, -0.90576171875, -0.01165771484375, -0.2049560546875, -0.0955810546875, 0.82861328125, -0.2218017578125, 0.34423828125, 0.411376953125, -0.0950927734375, 0.609375, -0.39990234375, -0.25634765625, 0.2919921875, -0.89013671875, -0.440673828125, 0.06854248046875, 0.53515625, -0.020477294921875, 0.61572265625, -0.499267578125, -0.160400390625, 0.434814453125, 0.33349609375, -0.2325439453125, -0.58447265625, -0.182861328125, -1.1767578125, -0.837890625, -0.80810546875, -0.54443359375, -0.07281494140625, 0.1324462890625, 0.1143798828125, -0.4892578125, 0.0051422119140625, 0.36279296875, -0.93701171875, 0.99365234375, -0.6845703125, 0.1915283203125, -0.443603515625, -0.50830078125, -0.75439453125, -0.127685546875, -0.454833984375, -0.32373046875, -0.447998046875, 0.446044921875, -0.399658203125, 0.297119140625, -0.334716796875, 0.62744140625, -0.2222900390625, -0.63134765625, 0.211181640625, 0.11273193359375, -0.13720703125, 1.091796875, 0.440185546875, -0.2117919921875, -0.01275634765625, -0.212890625, -0.18359375, -0.32275390625, 1.05078125, 0.48046875, 0.037933349609375, -0.1971435546875, 0.00876617431640625, -0.08538818359375, -0.9931640625, 0.226806640625, -0.29150390625, 0.414794921875, 0.18896484375, -0.0005626678466796875, 0.5419921875, 1.271484375, -0.751953125, 0.51953125, -0.0736083984375, 0.201171875, 0.64306640625, 0.46923828125, -0.38427734375, 0.422607421875, -0.1256103515625, -0.37353515625, 0.094482421875, 0.406494140625, 0.21142578125, 0.21337890625, -0.053680419921875, -0.8505859375, -0.873046875, -0.517578125, 0.1671142578125, 0.2227783203125, 0.311767578125, -0.404052734375, 0.0234832763671875, 0.1580810546875, -0.501953125, 0.10235595703125, -1.275390625, -0.919921875, 0.6318359375, 0.021148681640625, -1.0263671875, 0.196044921875, -0.1898193359375, 0.0011587142944335938, 0.169677734375, 0.25244140625, -0.416748046875, 0.414306640625, -0.1541748046875, 0.47119140625, -0.1585693359375, -0.399169921875, -0.01435089111328125, 0.3896484375, -0.81298828125, -0.76611328125, 0.1185302734375, 0.94189453125, 0.156982421875, -0.50048828125, -0.302978515625, 0.386962890625, -0.1016845703125, 0.2022705078125, -0.5732421875, 0.048675537109375, -0.323974609375, 0.255615234375, -0.72412109375, -0.05389404296875, -0.5576171875, 0.21044921875, 0.1510009765625, -0.389892578125, -0.6533203125, 0.806640625, 0.75537109375, -0.0245513916015625, 0.4384765625, 0.06549072265625, 0.77880859375, 0.5693359375, -0.318603515625, -0.2054443359375, 0.67236328125, 0.6279296875, 0.91162109375, -0.1822509765625, 0.401611328125, 0.86328125, -0.11181640625, -0.287109375, 0.33935546875, 0.1307373046875, -0.048614501953125, 0.360595703125, -0.00768280029296875, -0.3095703125, -0.08905029296875, -0.79833984375, 0.250244140625, -0.385986328125, -0.086669921875, 0.0927734375, -0.59375, 0.85009765625, -0.46728515625, -0.38134765625, 0.1923828125, -0.47021484375, 0.427978515625, 0.53271484375, -0.1009521484375, -0.275390625, 0.9697265625, 1.068359375, 0.88720703125, 0.70751953125, 0.3271484375, 0.385009765625, -0.55419921875, 0.068603515625, -0.06475830078125, 0.205078125, -0.2423095703125, -0.552734375, -1.064453125, 0.329833984375, 0.01213836669921875, -0.061767578125, 0.3974609375, -0.320068359375, 0.0273590087890625, -0.389892578125, 0.7060546875, -0.787109375, -0.07293701171875, 0.432373046875, -0.52880859375, -0.293212890625, 0.74609375, -0.09197998046875, 0.10430908203125, 0.157958984375, 1.1611328125, 0.004810333251953125, 1.6162109375, 0.77734375, -0.3134765625, 0.1146240234375, 0.69873046875, -0.3173828125, -0.5986328125, -0.462158203125, -0.40966796875, 0.12255859375, -0.59228515625, -0.533203125, -0.2044677734375, 0.81494140625, 0.474365234375, -0.884765625, -0.45166015625, 0.1668701171875, -0.759765625, 0.18212890625, 0.1627197265625, 0.366943359375, 0.08013916015625, -0.12493896484375, -0.3037109375, -0.6484375, 0.7900390625, -0.5869140625, 0.239501953125, -0.595703125, -0.393798828125, -0.33935546875, -0.47119140625, -0.1368408203125, -0.1883544921875, -0.32275390625, -0.69580078125, 0.497314453125, 0.466796875, 0.5185546875, 0.2027587890625, -0.2113037109375, 0.1290283203125, 1.150390625, 1.2685546875, 0.0246429443359375, 0.80078125, 0.2427978515625, -0.1552734375, 0.2008056640625, -0.55419921875, 0.5390625, 0.326416015625, 0.363525390625, -0.50830078125, 0.451171875, -1.0849609375, -1.12890625, -0.00885009765625, 0.6884765625, 0.314453125, -0.7783203125, -1.1533203125, -0.252197265625, -1.185546875, -0.241943359375, -0.38330078125, 0.77685546875, -0.47021484375, -0.1624755859375, -0.0994873046875, -1.2265625, 4.25390625, 0.5703125, 0.7939453125, 0.6552734375, 0.32421875, 0.8798828125, 0.5009765625, -0.443359375, -0.123291015625, -0.5859375, 0.75341796875, -0.29736328125, 0.019744873046875, 1.015625, 0.63330078125, 0.30615234375, -0.273193359375, -0.135498046875, 0.231201171875, -0.876953125, -0.72607421875, 0.54931640625, 0.13427734375, 0.87744140625, -0.163818359375, 0.298583984375, 0.65673828125, -0.79736328125, -0.5458984375, -0.55517578125, 0.343017578125, -0.337890625, 1.0751953125, 0.0265350341796875, -0.2030029296875, 0.8408203125, 0.1510009765625, -0.55322265625, -0.11334228515625, 0.329345703125, -0.0266265869140625, -0.153564453125, 0.60302734375, -0.9208984375, -0.407470703125, 0.440673828125, -0.93701171875, 0.71630859375, 0.07940673828125, -1.2333984375, 0.58056640625, -0.2027587890625, 0.037628173828125, -0.7587890625, -0.45751953125, 0.21826171875, -0.0579833984375, -0.11004638671875, -0.264404296875, 0.751953125, 0.515625, 0.521484375, 0.03094482421875, 0.75, -1.1318359375, 0.8203125, -0.183837890625, 0.7734375, -0.853515625, -0.05780029296875, -0.060577392578125, -0.66259765625, -0.266357421875, -0.53857421875, 0.38916015625, 0.405029296875, -0.1710205078125, 0.51123046875, 0.57421875, -0.67431640625, 0.12005615234375, 0.0740966796875, -0.4306640625, -0.60693359375, 0.50244140625, 1.1650390625, -0.97314453125, -0.2269287109375, -0.42578125, 0.576171875, 0.837890625, 0.69189453125, -0.06158447265625, -0.5341796875, -0.31396484375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Tags: combinatorics, greedy, implementation, math Correct Solution: ``` MOD = int(1e9)+7 def solve(): s = input() r=c=0 for i in range(len(s)-1, -1, -1): if s[i] == 'b': c+=1 else: r+=c c= (c*2)%MOD return r%MOD print(solve()) ```
105,788
[ 0.3525390625, -0.135986328125, 0.026947021484375, 0.08709716796875, -0.822265625, -0.65283203125, 0.039154052734375, -0.0982666015625, 0.259765625, 0.8134765625, 0.6572265625, -0.328125, -0.185791015625, -0.80712890625, -0.460205078125, -0.0007314682006835938, -0.448486328125, -0.7333984375, -0.3662109375, -0.335693359375, 0.09539794921875, -0.1473388671875, -1.189453125, -0.0194549560546875, -0.2200927734375, 1.0361328125, 0.7265625, -0.100341796875, 0.98681640625, 1.2939453125, -0.190673828125, -0.1290283203125, 0.498779296875, -0.99560546875, -0.356201171875, -0.4609375, 0.5888671875, -0.88720703125, -0.1761474609375, -0.32958984375, 0.2396240234375, -0.5869140625, 0.48193359375, -0.78515625, -1.5302734375, 0.05499267578125, -0.1368408203125, -0.477783203125, 0.01284027099609375, -0.61376953125, -0.12347412109375, -0.39306640625, 0.38818359375, 0.0285797119140625, 0.06195068359375, 0.1923828125, 0.28955078125, -0.35498046875, -0.865234375, 0.062347412109375, 0.430908203125, 0.0665283203125, 0.048980712890625, -0.802734375, -0.1307373046875, 0.156494140625, -0.30419921875, -0.0255279541015625, -0.1700439453125, -0.97509765625, -0.015899658203125, 0.275634765625, -0.295166015625, -0.5048828125, -0.1593017578125, 0.07867431640625, 0.3447265625, -0.260498046875, -0.640625, 1.1240234375, -0.2744140625, 0.76123046875, 0.16259765625, 0.2379150390625, -0.255615234375, -0.49267578125, 0.01837158203125, 0.308837890625, -0.060821533203125, -0.1683349609375, -0.374755859375, 0.75, -0.31982421875, 0.051025390625, 0.40087890625, 0.58984375, -0.370849609375, 0.166015625, 0.60498046875, 0.344970703125, 0.83349609375, 1.037109375, -0.59619140625, 0.8154296875, -0.5419921875, -0.058624267578125, -0.005733489990234375, -0.111572265625, -0.2880859375, 0.08880615234375, -0.25634765625, -0.28466796875, 0.58154296875, 0.31494140625, -0.50390625, 1.0693359375, 0.1612548828125, 0.344970703125, -0.61962890625, 0.63427734375, 0.42578125, 0.1551513671875, 0.73583984375, -0.2293701171875, -0.2490234375, -0.106689453125, -0.68896484375, 1.1640625, -0.759765625, -0.212646484375, 0.170166015625, 0.155029296875, 0.057464599609375, 0.324951171875, -0.2666015625, 0.70849609375, -0.08795166015625, 0.269775390625, 0.8115234375, -0.358642578125, 0.638671875, -0.3251953125, -0.12396240234375, 1.7236328125, 0.2080078125, -0.09765625, 0.857421875, 0.427490234375, -0.927734375, 0.2587890625, -1.0419921875, 0.779296875, 0.301025390625, 0.38037109375, -0.09912109375, 0.1512451171875, -0.314208984375, 0.45068359375, 0.1563720703125, -0.19873046875, -0.57373046875, 0.031280517578125, -0.3193359375, 1.015625, -0.429443359375, 0.8271484375, -0.269287109375, -0.1988525390625, -0.11163330078125, -0.445068359375, 0.2000732421875, -0.2149658203125, -0.269287109375, 0.95947265625, 0.335205078125, 1.04296875, 1.201171875, -0.265869140625, 0.51513671875, 0.27099609375, -0.4140625, 0.13134765625, 0.310791015625, 0.95947265625, 0.354736328125, 0.47265625, -0.3466796875, 0.0273284912109375, -0.71142578125, -0.438232421875, 0.3056640625, 0.62646484375, -0.86376953125, 0.4609375, -0.062164306640625, -0.054779052734375, -0.71435546875, -0.294189453125, -0.1768798828125, -0.94482421875, -0.2064208984375, 0.4833984375, -0.133544921875, 0.33349609375, -0.404541015625, -0.5673828125, 0.3408203125, 1.169921875, -0.488037109375, 0.06439208984375, 0.382568359375, -0.156494140625, -0.0743408203125, 0.4248046875, 0.07965087890625, -0.269287109375, -0.546875, 0.74462890625, -0.048919677734375, -0.11724853515625, -0.1649169921875, 0.6396484375, 0.425537109375, 0.7763671875, -0.1748046875, -0.5791015625, 0.56982421875, 0.92626953125, -0.10321044921875, 0.66748046875, 0.216552734375, 0.75537109375, 0.97412109375, 0.81787109375, 0.69921875, 0.207275390625, 0.365234375, 0.787109375, 0.134521484375, 0.282958984375, 0.5888671875, 0.63134765625, 0.2423095703125, 0.228271484375, 0.490966796875, 0.59619140625, 0.15771484375, -0.0997314453125, -0.038177490234375, -0.0092926025390625, -0.3955078125, 0.8232421875, 0.095703125, 0.64990234375, 0.0101165771484375, -0.28369140625, 0.1876220703125, 1.1025390625, -1.0419921875, -0.44287109375, -0.1202392578125, 0.036346435546875, -0.0009126663208007812, -0.01885986328125, 0.88916015625, 0.63232421875, 0.7646484375, 0.368896484375, -0.27685546875, -0.2490234375, -0.7685546875, -0.79296875, -0.83447265625, -0.2489013671875, -0.72802734375, -0.0950927734375, -0.1375732421875, -0.93359375, -0.01551055908203125, -0.212158203125, -0.153076171875, 0.30859375, -0.587890625, 0.833984375, 0.0018939971923828125, 0.34033203125, -0.6650390625, 0.572265625, 0.1060791015625, 1.08984375, -0.8837890625, 0.0128021240234375, -0.048370361328125, -0.732421875, 0.058135986328125, 0.375, 0.3408203125, -0.039093017578125, -0.74560546875, -0.84423828125, -0.5341796875, 0.291015625, -0.30908203125, 0.3173828125, -0.4404296875, 0.66259765625, 0.578125, -0.5966796875, 0.6630859375, 1.05078125, -0.92822265625, 0.6796875, 0.04913330078125, -0.4423828125, -0.82470703125, 1.115234375, 0.56103515625, 0.52880859375, -0.37744140625, -0.68603515625, -0.372802734375, 0.08038330078125, 0.19775390625, -0.76708984375, -0.1878662109375, 0.6611328125, -0.03497314453125, -0.8232421875, 0.5986328125, -0.9990234375, -0.60498046875, -0.6572265625, -0.423828125, 1.11328125, 0.84521484375, 0.138671875, 0.1168212890625, 0.1416015625, 0.0953369140625, 0.494384765625, 0.57421875, -0.66845703125, 0.270263671875, 0.9267578125, 0.042724609375, -0.033660888671875, 0.169189453125, -0.351806640625, -0.252685546875, 0.09130859375, 0.1441650390625, 0.642578125, -0.0012187957763671875, 0.423095703125, 0.34912109375, 0.494140625, -0.80908203125, -0.0011339187622070312, -0.2388916015625, 0.63623046875, 0.52197265625, 0.60595703125, -0.0654296875, -0.3720703125, -0.58251953125, -1.3818359375, 0.06756591796875, 0.308837890625, 0.70263671875, -0.537109375, 1.1435546875, 0.24755859375, -0.619140625, 0.308837890625, -0.68212890625, 0.331787109375, 0.9248046875, 0.2191162109375, 0.953125, -0.80419921875, 0.46728515625, 0.181884765625, 0.06353759765625, 0.43896484375, 0.62646484375, 0.2978515625, -0.63427734375, -0.74169921875, -0.5009765625, -0.06585693359375, -0.266845703125, -0.5185546875, 0.358154296875, -0.533203125, 0.0272979736328125, -1.0234375, 0.54541015625, 0.68701171875, 0.78173828125, 0.0190277099609375, 0.346435546875, 0.309326171875, 0.301513671875, 0.65234375, -0.130126953125, 0.198974609375, -0.5966796875, 0.72607421875, 0.2239990234375, -0.343994140625, -0.72509765625, -0.40478515625, 0.0487060546875, 0.1494140625, -0.440673828125, -0.1339111328125, -1.1083984375, 0.179443359375, -0.45703125, 0.69091796875, -0.6728515625, -0.229736328125, -0.1865234375, 0.287353515625, 0.188232421875, -1.044921875, 0.5380859375, -1.0341796875, 0.8115234375, 0.5673828125, 0.0780029296875, -0.123291015625, -0.36279296875, -0.7470703125, -0.43017578125, -0.131103515625, 0.7587890625, -0.189697265625, 0.435791015625, -1.373046875, 0.6025390625, 0.11273193359375, -0.433837890625, 0.2318115234375, -0.256103515625, 0.83544921875, -0.1807861328125, 0.84814453125, -0.50341796875, -0.6728515625, 0.10992431640625, -1.3291015625, 0.66259765625, -0.39892578125, 0.83349609375, 0.1513671875, -0.11859130859375, 0.29833984375, 0.2044677734375, -0.19873046875, 0.28173828125, -0.171630859375, 0.391845703125, -0.7685546875, -0.9462890625, 0.61328125, -0.18505859375, -0.27880859375, 0.74169921875, 0.0032062530517578125, -0.60546875, -0.05328369140625, 0.64453125, -0.564453125, 0.2398681640625, -0.1278076171875, 0.7578125, -0.434814453125, -0.71630859375, -0.1844482421875, -0.650390625, 0.705078125, -0.01248931884765625, -0.6015625, -0.1124267578125, -1.2783203125, -0.1531982421875, 0.1412353515625, -0.397705078125, 0.296875, 0.30810546875, -0.10040283203125, -0.280517578125, -0.126220703125, -0.439453125, -0.42333984375, -0.6474609375, -0.205810546875, 0.1256103515625, 0.76123046875, 0.98095703125, 0.01806640625, -0.303955078125, -0.02789306640625, 0.0955810546875, 0.2017822265625, -0.611328125, -0.154541015625, -0.25439453125, -0.149169921875, -0.3837890625, 0.2186279296875, 0.14013671875, 0.3828125, 0.8828125, -0.06573486328125, 0.2066650390625, 0.3349609375, -0.61083984375, 1.2783203125, 0.034210205078125, -1.01171875, -0.9833984375, 0.54443359375, -0.033111572265625, 0.5966796875, 0.481689453125, -1.0517578125, -0.56884765625, -0.9697265625, 0.17578125, -0.9677734375, -0.31396484375, -1.2216796875, -0.74072265625, -0.67138671875, 0.3388671875, 0.145263671875, -0.53125, 0.45361328125, -0.77490234375, 0.2254638671875, -0.8193359375, 0.1337890625, -0.62451171875, -0.71484375, 0.28955078125, 0.8564453125, 0.2802734375, 0.32470703125, -0.0016565322875976562, -0.44921875, 0.480712890625, -0.251953125, -0.7568359375, -0.2034912109375, -0.284912109375, 0.1802978515625, 0.0236053466796875, -0.1302490234375, -0.67724609375, 1.001953125, -0.67529296875, 0.4541015625, 0.1739501953125, -0.280517578125, -0.2447509765625, -0.331787109375, 0.91552734375, -0.2685546875, 0.032989501953125, -0.0670166015625, 0.36962890625, 0.78076171875, -0.469970703125, -0.54541015625, -0.7763671875, -0.64208984375, -0.966796875, 0.64453125, -0.2880859375, 0.1851806640625, -0.8134765625, -0.2362060546875, 1.3525390625, -0.480224609375, 0.431884765625, 1.041015625, 0.0223388671875, 0.18017578125, -0.2666015625, 0.64794921875, 0.45263671875, -0.2900390625, 0.19287109375, -0.06610107421875, -0.60107421875, -0.0516357421875, -0.161376953125, -0.8271484375, -0.7265625, 0.273681640625, 1.330078125, -0.4638671875, 0.62255859375, -0.306640625, -1.37109375, -0.7001953125, 0.498779296875, 0.3232421875, 0.27001953125, 0.6767578125, -0.077880859375, 0.06866455078125, -0.1160888671875, -0.35791015625, -0.44140625, -0.74755859375, 1.2705078125, -0.6416015625, -0.49609375, 0.9267578125, 1.0107421875, -1.193359375, -0.92431640625, 0.2470703125, -0.095703125, -0.418212890625, -0.468994140625, -0.044403076171875, 0.7412109375, -0.7021484375, 0.11773681640625, 0.348876953125, 0.004322052001953125, 0.2099609375, 0.013427734375, 0.6171875, -0.25634765625, 0.73681640625, 0.572265625, -0.5322265625, -0.40966796875, -0.98095703125, -0.27294921875, -0.286865234375, -0.031646728515625, 0.83203125, -0.07659912109375, 0.163818359375, 0.54638671875, 0.049774169921875, 0.73486328125, -0.469970703125, -0.389892578125, 0.14990234375, -0.68212890625, -0.568359375, 0.164794921875, 0.3994140625, -0.01200103759765625, 0.34423828125, -0.58251953125, -0.0340576171875, 0.240966796875, 0.529296875, -0.302978515625, -0.8095703125, -0.2252197265625, -1.4482421875, -0.50244140625, -0.76953125, -0.841796875, -0.1947021484375, 0.3935546875, 0.02484130859375, -0.66748046875, 0.01800537109375, 0.266845703125, -0.78857421875, 0.6103515625, -0.3359375, 0.29052734375, -0.362548828125, -0.6357421875, -0.95947265625, -0.1861572265625, -0.448974609375, -0.267822265625, -1.05859375, 0.7880859375, 0.10589599609375, 0.41357421875, -0.228759765625, 0.8779296875, -0.303955078125, -0.76171875, 0.33740234375, 0.1656494140625, -0.09906005859375, 1.2900390625, 0.42138671875, 0.1484375, 0.0631103515625, -0.121337890625, -0.221435546875, -0.52197265625, 0.56005859375, 0.372802734375, -0.5087890625, -0.134033203125, -0.08294677734375, 0.2296142578125, -0.92138671875, 0.3681640625, -0.273681640625, -0.005527496337890625, 0.12261962890625, -0.08642578125, 0.28466796875, 1.384765625, -0.2086181640625, 0.11138916015625, -0.005336761474609375, 0.1351318359375, 0.16455078125, 0.26953125, 0.005107879638671875, 0.51806640625, -0.188720703125, -0.3876953125, -0.328857421875, 0.486083984375, 0.0204315185546875, 0.045684814453125, -0.287841796875, -0.94580078125, -0.6376953125, -0.322265625, 0.0006775856018066406, 0.360107421875, 0.52880859375, -0.55322265625, -0.09600830078125, 0.0077972412109375, -0.60302734375, -0.01255035400390625, -1.109375, -0.9716796875, 0.5546875, -0.032745361328125, -0.6513671875, -0.1312255859375, -0.263427734375, -0.375, -0.0196990966796875, 0.62744140625, -0.50048828125, 0.513671875, -0.01194000244140625, 0.331787109375, -0.054595947265625, -0.2120361328125, 0.14208984375, 0.73974609375, -0.70458984375, -0.64013671875, 0.0723876953125, 0.884765625, 0.26025390625, -0.3603515625, -0.12164306640625, 0.452392578125, -0.192626953125, 0.28271484375, -0.61669921875, 0.018646240234375, 0.0413818359375, 0.9599609375, -0.8701171875, 0.10540771484375, -0.2064208984375, 0.196044921875, -0.0841064453125, -0.591796875, -0.537109375, 1.0546875, 0.61474609375, -0.1358642578125, 0.681640625, 0.080322265625, 0.277587890625, -0.041229248046875, -0.03619384765625, 0.222900390625, 0.56201171875, 0.74853515625, 0.58056640625, -0.18994140625, 0.282958984375, 0.92822265625, -0.197265625, -0.370849609375, 0.3525390625, -0.0033054351806640625, 0.032623291015625, -0.1805419921875, 0.0330810546875, -0.23974609375, -0.224853515625, -0.82421875, 0.810546875, -0.21337890625, 0.271240234375, -0.09075927734375, -0.80322265625, 0.86962890625, -0.3291015625, -0.297607421875, 0.2467041015625, -0.73095703125, 0.1768798828125, 0.5869140625, -0.351806640625, -0.32421875, 0.6572265625, 0.5830078125, 0.6845703125, 0.7412109375, 0.09930419921875, 0.447998046875, -0.475830078125, 0.1468505859375, -0.18310546875, -0.13330078125, -0.152099609375, -0.685546875, -1.1162109375, 0.455322265625, -0.64501953125, -0.5498046875, 0.759765625, -0.732421875, 0.1873779296875, -0.26611328125, 0.70458984375, -0.414306640625, 0.078125, 0.53662109375, -0.37109375, -0.8134765625, 0.8359375, -0.210693359375, 0.2374267578125, -0.252197265625, 1.203125, -0.163818359375, 1.4560546875, 0.59912109375, -0.281005859375, 0.115234375, 0.39990234375, -0.371826171875, -0.62744140625, -0.6328125, -0.5947265625, -0.133056640625, -0.6064453125, -0.49755859375, 0.199462890625, 0.3408203125, -0.061492919921875, -0.7900390625, -0.1746826171875, 0.341552734375, -0.7587890625, 0.389404296875, 0.250244140625, 0.07171630859375, 0.0968017578125, -0.075927734375, -0.11602783203125, -0.1611328125, 0.1422119140625, -0.818359375, 0.3974609375, -0.935546875, -0.25634765625, -0.65283203125, -0.65234375, -0.2305908203125, 0.08648681640625, -0.350341796875, -0.85693359375, 0.294677734375, 0.318603515625, 0.1761474609375, 0.418212890625, -0.1280517578125, 0.295166015625, 1.1064453125, 1.0810546875, 0.10076904296875, 0.86181640625, 0.31494140625, -0.142822265625, -0.01151275634765625, -0.31982421875, 0.3876953125, 0.002468109130859375, 0.55810546875, -0.415771484375, 0.1837158203125, -0.70263671875, -1.4736328125, 0.45263671875, 0.5439453125, 0.393310546875, -0.7177734375, -1.111328125, -0.10272216796875, -1.3125, -0.1766357421875, -0.73828125, 1.0400390625, -0.56005859375, -0.0034389495849609375, -0.133056640625, -1.2236328125, 4.26171875, 1.0634765625, 0.8369140625, 0.6796875, 0.1678466796875, 0.90380859375, 0.055755615234375, -0.458251953125, 0.0029582977294921875, -0.27880859375, 0.74072265625, -0.5078125, -0.044891357421875, 0.72314453125, 0.29833984375, 0.52001953125, -0.339111328125, 0.5634765625, -0.2435302734375, -0.9677734375, -0.97314453125, 0.473876953125, -0.13232421875, 0.42529296875, 0.05963134765625, 0.141845703125, 0.7958984375, -1.06640625, 0.1478271484375, -0.7578125, 0.1640625, -0.403564453125, 1.0791015625, 0.06097412109375, 0.08770751953125, 0.494140625, -0.08477783203125, -0.492919921875, 0.20654296875, 0.0124053955078125, -0.184326171875, -0.149169921875, 0.52587890625, -0.92578125, 0.043701171875, 0.493896484375, -0.6865234375, 0.374755859375, -0.189697265625, -1.0380859375, 0.86376953125, -0.206787109375, 0.38525390625, -0.89697265625, -0.26513671875, -0.1092529296875, 0.3955078125, -0.08685302734375, -0.46240234375, 0.40283203125, 0.5859375, 0.463134765625, 0.240966796875, 0.498046875, -0.96875, 0.19970703125, -0.162109375, 0.395751953125, -0.51123046875, 0.102294921875, -0.4658203125, -0.401123046875, -0.26123046875, -0.49755859375, 0.62890625, -0.08343505859375, -0.10723876953125, 0.4443359375, 0.4912109375, -0.61474609375, 0.1275634765625, -0.149169921875, -0.14111328125, -0.5615234375, 0.71533203125, 1.2099609375, -0.51123046875, -0.36669921875, -0.345947265625, 0.51123046875, 0.499267578125, 0.4814453125, -0.1279296875, -0.79345703125, -0.062042236328125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Tags: combinatorics, greedy, implementation, math Correct Solution: ``` MOD = 10**9 + 7 s = input() bcount, count = 0, 0 for c in reversed(s): if c == 'b': bcount += 1 else: count += bcount bcount *= 2 if bcount > 2**62: bcount %= MOD print(count % MOD) ```
105,789
[ 0.363037109375, -0.1741943359375, 0.03515625, 0.0992431640625, -0.78662109375, -0.693359375, -0.0017566680908203125, -0.10809326171875, 0.2041015625, 0.919921875, 0.6689453125, -0.2998046875, -0.1607666015625, -0.82373046875, -0.5107421875, -0.0001875162124633789, -0.499755859375, -0.7978515625, -0.41455078125, -0.306884765625, 0.0250701904296875, -0.1861572265625, -1.134765625, -0.041412353515625, -0.200927734375, 1.04296875, 0.71435546875, -0.06512451171875, 1.009765625, 1.2646484375, -0.1568603515625, -0.1610107421875, 0.5078125, -1.0869140625, -0.387939453125, -0.466796875, 0.619140625, -0.90234375, -0.139404296875, -0.3466796875, 0.2166748046875, -0.6650390625, 0.51708984375, -0.7900390625, -1.5341796875, 0.0838623046875, -0.186767578125, -0.51904296875, -0.05023193359375, -0.533203125, -0.1268310546875, -0.43212890625, 0.39306640625, 0.052398681640625, 0.022308349609375, 0.1436767578125, 0.259033203125, -0.389404296875, -0.779296875, 0.171630859375, 0.427734375, 0.0703125, 0.143798828125, -0.86572265625, -0.1185302734375, 0.194580078125, -0.32958984375, -0.0206451416015625, -0.1895751953125, -1.021484375, 0.0169677734375, 0.1904296875, -0.312255859375, -0.552734375, -0.1119384765625, 0.11163330078125, 0.419189453125, -0.2861328125, -0.6591796875, 1.150390625, -0.27490234375, 0.7431640625, 0.18896484375, 0.2161865234375, -0.283935546875, -0.453857421875, 0.08160400390625, 0.25537109375, -0.09136962890625, -0.1630859375, -0.33154296875, 0.74462890625, -0.346923828125, -0.035614013671875, 0.239501953125, 0.58544921875, -0.36328125, 0.1866455078125, 0.59033203125, 0.3359375, 0.8681640625, 1.01953125, -0.56298828125, 0.7939453125, -0.5634765625, -0.095458984375, 0.08221435546875, -0.07647705078125, -0.295166015625, -0.00484466552734375, -0.29541015625, -0.312744140625, 0.568359375, 0.37939453125, -0.494140625, 1.1259765625, 0.227783203125, 0.40625, -0.69970703125, 0.6787109375, 0.446533203125, 0.15625, 0.705078125, -0.240478515625, -0.2174072265625, -0.09344482421875, -0.60791015625, 1.171875, -0.865234375, -0.263916015625, 0.13720703125, 0.193603515625, 0.0919189453125, 0.375244140625, -0.250244140625, 0.673828125, -0.07373046875, 0.26123046875, 0.72412109375, -0.461181640625, 0.62451171875, -0.295166015625, -0.22314453125, 1.7685546875, 0.182861328125, -0.08917236328125, 0.81396484375, 0.4248046875, -0.90380859375, 0.29296875, -1.087890625, 0.7822265625, 0.308837890625, 0.395263671875, 0.003765106201171875, 0.1693115234375, -0.28857421875, 0.52490234375, 0.07611083984375, -0.226806640625, -0.6025390625, 0.0455322265625, -0.33544921875, 1.0615234375, -0.5341796875, 0.86669921875, -0.25927734375, -0.23193359375, -0.1353759765625, -0.5029296875, 0.2005615234375, -0.26416015625, -0.283447265625, 0.87548828125, 0.358154296875, 1.072265625, 1.21484375, -0.265380859375, 0.478271484375, 0.318603515625, -0.462890625, 0.20361328125, 0.34228515625, 0.91845703125, 0.29541015625, 0.39697265625, -0.342529296875, -0.0192413330078125, -0.74072265625, -0.447265625, 0.29052734375, 0.6962890625, -0.78466796875, 0.50341796875, -0.08892822265625, -0.07177734375, -0.70556640625, -0.259033203125, -0.145263671875, -0.9873046875, -0.2392578125, 0.5107421875, -0.0604248046875, 0.347900390625, -0.451171875, -0.54736328125, 0.394287109375, 1.12109375, -0.5146484375, 0.15380859375, 0.3857421875, -0.1395263671875, -0.07928466796875, 0.433349609375, 0.07281494140625, -0.279296875, -0.572265625, 0.73828125, -0.0191802978515625, -0.10479736328125, -0.183837890625, 0.62158203125, 0.483154296875, 0.7509765625, -0.1314697265625, -0.548828125, 0.58642578125, 0.99755859375, -0.08306884765625, 0.65185546875, 0.1817626953125, 0.81591796875, 0.9873046875, 0.8232421875, 0.6826171875, 0.2010498046875, 0.35595703125, 0.8056640625, 0.07342529296875, 0.266357421875, 0.5625, 0.73974609375, 0.21826171875, 0.253662109375, 0.495849609375, 0.60009765625, 0.2408447265625, -0.1136474609375, -0.0166015625, 0.011749267578125, -0.367919921875, 0.830078125, 0.0673828125, 0.650390625, 0.057647705078125, -0.2958984375, 0.175048828125, 1.0078125, -1.0791015625, -0.416748046875, -0.07080078125, -0.0006160736083984375, -0.041015625, -0.06732177734375, 0.919921875, 0.59619140625, 0.763671875, 0.43310546875, -0.2259521484375, -0.27099609375, -0.728515625, -0.83544921875, -0.80029296875, -0.256103515625, -0.77783203125, -0.08282470703125, -0.09490966796875, -0.93408203125, -0.061737060546875, -0.294677734375, -0.1417236328125, 0.3076171875, -0.55908203125, 0.8076171875, -0.0584716796875, 0.27294921875, -0.56689453125, 0.6123046875, 0.10943603515625, 1.109375, -0.82568359375, 0.032012939453125, -0.09771728515625, -0.6728515625, 0.010223388671875, 0.40625, 0.352783203125, -0.04736328125, -0.8427734375, -0.94140625, -0.52685546875, 0.281982421875, -0.36376953125, 0.32763671875, -0.40966796875, 0.72021484375, 0.60205078125, -0.6171875, 0.68115234375, 1.1318359375, -0.8916015625, 0.6337890625, 0.049102783203125, -0.422119140625, -0.810546875, 1.130859375, 0.5302734375, 0.54052734375, -0.386962890625, -0.63818359375, -0.371826171875, 0.0146636962890625, 0.2060546875, -0.806640625, -0.17724609375, 0.63720703125, 0.01435089111328125, -0.94775390625, 0.58349609375, -0.9619140625, -0.6533203125, -0.6845703125, -0.440185546875, 1.099609375, 0.90625, 0.051605224609375, 0.1578369140625, 0.0845947265625, 0.0982666015625, 0.474609375, 0.482421875, -0.5810546875, 0.185546875, 0.9580078125, -0.0116729736328125, 0.0165557861328125, 0.197509765625, -0.3740234375, -0.2451171875, 0.1815185546875, 0.19677734375, 0.6435546875, 0.0241546630859375, 0.465576171875, 0.287109375, 0.5224609375, -0.79541015625, 0.0789794921875, -0.21923828125, 0.69775390625, 0.52197265625, 0.59423828125, -0.124755859375, -0.3515625, -0.662109375, -1.37890625, 0.06866455078125, 0.30859375, 0.765625, -0.51416015625, 1.236328125, 0.172119140625, -0.51953125, 0.290771484375, -0.68505859375, 0.288330078125, 0.8662109375, 0.1461181640625, 0.958984375, -0.759765625, 0.50146484375, 0.16162109375, -0.0213623046875, 0.437744140625, 0.64501953125, 0.281494140625, -0.62255859375, -0.7626953125, -0.56591796875, -0.1085205078125, -0.25927734375, -0.5146484375, 0.342529296875, -0.54345703125, -0.125732421875, -0.984375, 0.480224609375, 0.6787109375, 0.7880859375, 0.03179931640625, 0.186279296875, 0.384765625, 0.26416015625, 0.66162109375, -0.1783447265625, 0.178466796875, -0.640625, 0.85546875, 0.1717529296875, -0.3623046875, -0.791015625, -0.381103515625, -0.023651123046875, 0.126708984375, -0.480712890625, -0.0953369140625, -1.1396484375, 0.1861572265625, -0.412841796875, 0.60888671875, -0.6416015625, -0.2626953125, -0.1796875, 0.341064453125, 0.255126953125, -1.0146484375, 0.56689453125, -1.0029296875, 0.82470703125, 0.65087890625, 0.07574462890625, -0.1932373046875, -0.35302734375, -0.81494140625, -0.464599609375, -0.1968994140625, 0.85107421875, -0.204833984375, 0.44091796875, -1.3125, 0.69140625, 0.024322509765625, -0.515625, 0.1341552734375, -0.253662109375, 0.8359375, -0.165283203125, 0.849609375, -0.50634765625, -0.71533203125, 0.09344482421875, -1.38671875, 0.72900390625, -0.4619140625, 0.900390625, 0.1458740234375, -0.11981201171875, 0.354248046875, 0.16845703125, -0.2425537109375, 0.31884765625, -0.216064453125, 0.475341796875, -0.80419921875, -0.8955078125, 0.6328125, -0.1614990234375, -0.344482421875, 0.74560546875, -0.0188446044921875, -0.51513671875, -0.09832763671875, 0.54345703125, -0.548828125, 0.1456298828125, -0.07586669921875, 0.740234375, -0.431884765625, -0.7333984375, -0.154541015625, -0.5048828125, 0.75, 0.064208984375, -0.56787109375, -0.098876953125, -1.3125, -0.2100830078125, 0.147705078125, -0.43359375, 0.266357421875, 0.35302734375, -0.045928955078125, -0.2269287109375, -0.087646484375, -0.43359375, -0.412353515625, -0.7490234375, -0.21484375, 0.12408447265625, 0.7470703125, 0.92138671875, -0.0166473388671875, -0.332763671875, -0.069091796875, 0.056396484375, 0.1754150390625, -0.55078125, -0.178955078125, -0.30517578125, -0.04150390625, -0.4365234375, 0.134765625, 0.15087890625, 0.361572265625, 0.919921875, -0.05072021484375, 0.1995849609375, 0.349853515625, -0.59033203125, 1.3349609375, 0.03265380859375, -0.92626953125, -0.95703125, 0.56494140625, -0.0303497314453125, 0.599609375, 0.487060546875, -1.021484375, -0.64697265625, -0.98291015625, 0.182861328125, -0.9609375, -0.390869140625, -1.140625, -0.77490234375, -0.65625, 0.397216796875, 0.12310791015625, -0.5615234375, 0.59521484375, -0.76220703125, 0.30859375, -0.76513671875, 0.11328125, -0.5546875, -0.75048828125, 0.25634765625, 0.8896484375, 0.322998046875, 0.37841796875, -0.006961822509765625, -0.40673828125, 0.46630859375, -0.2327880859375, -0.814453125, -0.156005859375, -0.275634765625, 0.292236328125, 0.060211181640625, -0.166259765625, -0.72021484375, 0.98095703125, -0.63720703125, 0.45458984375, 0.154296875, -0.27978515625, -0.340087890625, -0.3095703125, 0.857421875, -0.315185546875, 0.06597900390625, 0.0187225341796875, 0.369873046875, 0.6767578125, -0.4287109375, -0.4580078125, -0.794921875, -0.70751953125, -0.91943359375, 0.6943359375, -0.25439453125, 0.228759765625, -0.79833984375, -0.328857421875, 1.4091796875, -0.52197265625, 0.458740234375, 1.04296875, 0.0287628173828125, 0.1669921875, -0.328125, 0.6240234375, 0.409912109375, -0.303955078125, 0.1671142578125, -0.07177734375, -0.68505859375, -0.06134033203125, -0.137939453125, -0.81298828125, -0.74462890625, 0.317138671875, 1.31640625, -0.42578125, 0.58837890625, -0.40478515625, -1.33984375, -0.76025390625, 0.5068359375, 0.27734375, 0.359375, 0.734375, -0.10906982421875, 0.07666015625, -0.0167388916015625, -0.477783203125, -0.501953125, -0.78173828125, 1.2734375, -0.58984375, -0.537109375, 0.95849609375, 0.890625, -1.15234375, -0.9462890625, 0.201904296875, -0.1634521484375, -0.406494140625, -0.45947265625, -0.1114501953125, 0.83447265625, -0.57568359375, 0.11376953125, 0.30712890625, -0.1461181640625, 0.1390380859375, 0.0304412841796875, 0.59375, -0.268798828125, 0.6572265625, 0.57763671875, -0.51806640625, -0.5166015625, -0.97021484375, -0.2880859375, -0.288818359375, 0.033172607421875, 0.78857421875, -0.0226593017578125, 0.1866455078125, 0.51123046875, 0.0914306640625, 0.77587890625, -0.387451171875, -0.3193359375, 0.162353515625, -0.6708984375, -0.56005859375, 0.1265869140625, 0.344970703125, -0.070068359375, 0.34228515625, -0.6298828125, -0.11346435546875, 0.310791015625, 0.5166015625, -0.33056640625, -0.7822265625, -0.185302734375, -1.46484375, -0.53955078125, -0.7255859375, -0.8623046875, -0.1866455078125, 0.32958984375, 0.10467529296875, -0.66796875, 0.0726318359375, 0.25439453125, -0.68359375, 0.6162109375, -0.3232421875, 0.265625, -0.312744140625, -0.6171875, -1.0556640625, -0.10906982421875, -0.41357421875, -0.400146484375, -1.1162109375, 0.7060546875, 0.1636962890625, 0.373291015625, -0.24267578125, 0.841796875, -0.3466796875, -0.8154296875, 0.369873046875, 0.1514892578125, -0.022918701171875, 1.244140625, 0.443603515625, 0.12255859375, 0.09307861328125, -0.1517333984375, -0.308349609375, -0.412109375, 0.54931640625, 0.44091796875, -0.47802734375, -0.1683349609375, -0.071533203125, 0.35595703125, -0.87744140625, 0.380615234375, -0.22412109375, 0.0196380615234375, 0.09027099609375, -0.14404296875, 0.2548828125, 1.3994140625, -0.202880859375, 0.1490478515625, 0.0460205078125, 0.195556640625, 0.14599609375, 0.329833984375, -0.064208984375, 0.513671875, -0.2188720703125, -0.415771484375, -0.32666015625, 0.53173828125, 0.08209228515625, 0.0310821533203125, -0.336669921875, -0.88427734375, -0.607421875, -0.33203125, 0.0205841064453125, 0.403564453125, 0.5703125, -0.487548828125, -0.06536865234375, -0.017608642578125, -0.62744140625, -0.054595947265625, -1.125, -0.98291015625, 0.5263671875, 0.061370849609375, -0.68701171875, -0.1728515625, -0.2587890625, -0.37890625, -0.006542205810546875, 0.67626953125, -0.50537109375, 0.46484375, 0.05157470703125, 0.2861328125, -0.10400390625, -0.141357421875, 0.1502685546875, 0.763671875, -0.615234375, -0.68408203125, 0.0281982421875, 0.86279296875, 0.160888671875, -0.45849609375, -0.10260009765625, 0.396240234375, -0.18798828125, 0.302978515625, -0.58642578125, -0.04559326171875, 0.07843017578125, 1.0380859375, -0.7939453125, 0.0335693359375, -0.1851806640625, 0.1702880859375, -0.1090087890625, -0.6005859375, -0.491455078125, 1.1015625, 0.66455078125, -0.1651611328125, 0.71435546875, 0.0723876953125, 0.282958984375, -0.0253143310546875, -0.0537109375, 0.2421875, 0.568359375, 0.7548828125, 0.59423828125, -0.120849609375, 0.3779296875, 0.876953125, -0.2332763671875, -0.396484375, 0.41015625, -0.069580078125, 0.00382232666015625, -0.10400390625, 0.003662109375, -0.2359619140625, -0.2364501953125, -0.80908203125, 0.80517578125, -0.2156982421875, 0.295166015625, -0.0877685546875, -0.783203125, 0.9814453125, -0.3466796875, -0.41162109375, 0.28564453125, -0.72705078125, 0.1795654296875, 0.60986328125, -0.3701171875, -0.26318359375, 0.7431640625, 0.58740234375, 0.66650390625, 0.67724609375, 0.15185546875, 0.4345703125, -0.44677734375, 0.1240234375, -0.1578369140625, -0.252685546875, -0.2413330078125, -0.60205078125, -1.1220703125, 0.4072265625, -0.6474609375, -0.6240234375, 0.75927734375, -0.71044921875, 0.1982421875, -0.24853515625, 0.74853515625, -0.37060546875, 0.1456298828125, 0.60400390625, -0.2041015625, -0.83154296875, 0.85107421875, -0.2442626953125, 0.2489013671875, -0.218505859375, 1.224609375, -0.2047119140625, 1.3310546875, 0.60107421875, -0.277587890625, 0.188720703125, 0.37890625, -0.47216796875, -0.625, -0.578125, -0.5849609375, -0.1458740234375, -0.4775390625, -0.513671875, 0.186279296875, 0.347900390625, 0.04901123046875, -0.79833984375, -0.10552978515625, 0.305419921875, -0.7578125, 0.51123046875, 0.263671875, 0.004131317138671875, 0.0811767578125, -0.1064453125, -0.08880615234375, -0.10931396484375, 0.2337646484375, -0.7158203125, 0.43408203125, -0.96533203125, -0.2247314453125, -0.72412109375, -0.7880859375, -0.192138671875, 0.1478271484375, -0.266357421875, -0.93798828125, 0.272216796875, 0.2822265625, 0.2005615234375, 0.450927734375, -0.219482421875, 0.306884765625, 1.103515625, 1.025390625, 0.034454345703125, 0.79443359375, 0.33154296875, -0.1038818359375, 0.01273345947265625, -0.258056640625, 0.448486328125, 0.0261383056640625, 0.50634765625, -0.36181640625, 0.1689453125, -0.7763671875, -1.4951171875, 0.37744140625, 0.5556640625, 0.356689453125, -0.75439453125, -1.0810546875, -0.09521484375, -1.2822265625, -0.19921875, -0.77734375, 1.009765625, -0.58154296875, 0.0269775390625, -0.14404296875, -1.1669921875, 4.21875, 1.083984375, 0.8681640625, 0.60009765625, 0.1741943359375, 0.97216796875, 0.07501220703125, -0.408935546875, -0.044403076171875, -0.1875, 0.7841796875, -0.6484375, -0.1253662109375, 0.78173828125, 0.2958984375, 0.56494140625, -0.376953125, 0.5087890625, -0.092041015625, -1.013671875, -0.94140625, 0.46728515625, -0.099365234375, 0.51611328125, 0.06500244140625, 0.2008056640625, 0.84375, -1.1328125, 0.235107421875, -0.75146484375, 0.230712890625, -0.38623046875, 1.1328125, 0.056915283203125, 0.106201171875, 0.529296875, -0.09765625, -0.46630859375, 0.2457275390625, -0.00897216796875, -0.11090087890625, -0.059844970703125, 0.487548828125, -0.92236328125, -0.012237548828125, 0.478271484375, -0.6728515625, 0.400390625, -0.1795654296875, -1.064453125, 0.9150390625, -0.1561279296875, 0.39990234375, -0.9931640625, -0.285888671875, -0.2103271484375, 0.369384765625, -0.10595703125, -0.53466796875, 0.3974609375, 0.55517578125, 0.55615234375, 0.2744140625, 0.54443359375, -0.970703125, 0.175048828125, -0.1529541015625, 0.3662109375, -0.52099609375, 0.059661865234375, -0.396240234375, -0.42578125, -0.346923828125, -0.489990234375, 0.599609375, 0.0045166015625, -0.052520751953125, 0.410400390625, 0.51025390625, -0.65234375, 0.09417724609375, -0.0999755859375, -0.048614501953125, -0.626953125, 0.71240234375, 1.2197265625, -0.6044921875, -0.406494140625, -0.35693359375, 0.431396484375, 0.484375, 0.4580078125, -0.09588623046875, -0.783203125, -0.058990478515625 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Tags: combinatorics, greedy, implementation, math Correct Solution: ``` x = input() str0 = x x=x[::-1] # print(x) mod = 10**9 + 7 ans = 0 sum0 = 0 for i in x: if i == 'b': ans += 1 if i == 'a': sum0 += ans sum0 = sum0 % mod ans *=2 ans = ans % mod print(sum0) ```
105,790
[ 0.395751953125, -0.1475830078125, 0.061004638671875, 0.07562255859375, -0.7880859375, -0.6826171875, 0.04486083984375, -0.1361083984375, 0.246337890625, 0.84375, 0.662109375, -0.333984375, -0.1968994140625, -0.7919921875, -0.51904296875, 0.00777435302734375, -0.46875, -0.74658203125, -0.35888671875, -0.29443359375, 0.12939453125, -0.1611328125, -1.1396484375, -0.065673828125, -0.283203125, 1.0361328125, 0.6953125, -0.08331298828125, 1.02734375, 1.3173828125, -0.176513671875, -0.09991455078125, 0.45947265625, -1.0556640625, -0.414794921875, -0.50146484375, 0.638671875, -0.89013671875, -0.163330078125, -0.287353515625, 0.2890625, -0.62109375, 0.476318359375, -0.76171875, -1.45703125, 0.06756591796875, -0.1505126953125, -0.544921875, 0.03314208984375, -0.5830078125, -0.10284423828125, -0.399169921875, 0.400146484375, 0.0307159423828125, 0.040802001953125, 0.168701171875, 0.30517578125, -0.35009765625, -0.826171875, 0.08160400390625, 0.413818359375, 0.0509033203125, 0.098876953125, -0.91845703125, -0.0478515625, 0.1956787109375, -0.333984375, -0.0002636909484863281, -0.2039794921875, -0.97412109375, -0.07611083984375, 0.2049560546875, -0.378173828125, -0.4990234375, -0.13623046875, 0.076904296875, 0.364501953125, -0.2459716796875, -0.67529296875, 1.1484375, -0.25244140625, 0.6640625, 0.1895751953125, 0.289794921875, -0.260498046875, -0.443603515625, 0.035736083984375, 0.259521484375, -0.09454345703125, -0.13720703125, -0.369873046875, 0.681640625, -0.336181640625, 0.00262451171875, 0.35009765625, 0.60009765625, -0.348388671875, 0.2137451171875, 0.56494140625, 0.336669921875, 0.837890625, 1.029296875, -0.60205078125, 0.8173828125, -0.5146484375, -0.03179931640625, 0.0977783203125, -0.069580078125, -0.2861328125, 0.062744140625, -0.29150390625, -0.27587890625, 0.580078125, 0.36572265625, -0.525390625, 1.099609375, 0.15087890625, 0.371337890625, -0.63232421875, 0.611328125, 0.46875, 0.1707763671875, 0.68603515625, -0.1953125, -0.2110595703125, -0.08282470703125, -0.60595703125, 1.1171875, -0.77001953125, -0.2193603515625, 0.190185546875, 0.1982421875, -0.01087188720703125, 0.353515625, -0.2425537109375, 0.6708984375, -0.08526611328125, 0.238037109375, 0.7568359375, -0.416259765625, 0.6025390625, -0.372314453125, -0.17041015625, 1.7353515625, 0.220458984375, -0.09576416015625, 0.828125, 0.40625, -0.88232421875, 0.311767578125, -1.0439453125, 0.7353515625, 0.328125, 0.3447265625, -0.0653076171875, 0.10565185546875, -0.3515625, 0.5322265625, 0.103759765625, -0.2132568359375, -0.59912109375, -0.04791259765625, -0.35498046875, 1.056640625, -0.472900390625, 0.90087890625, -0.302734375, -0.2164306640625, -0.1551513671875, -0.415283203125, 0.180419921875, -0.2398681640625, -0.265380859375, 0.86669921875, 0.335693359375, 1.0390625, 1.193359375, -0.26513671875, 0.50048828125, 0.30126953125, -0.404052734375, 0.1815185546875, 0.283447265625, 1.025390625, 0.410888671875, 0.448486328125, -0.2958984375, 0.04339599609375, -0.68603515625, -0.496826171875, 0.310791015625, 0.65283203125, -0.85205078125, 0.48388671875, -0.042388916015625, -0.00470733642578125, -0.6748046875, -0.303955078125, -0.2119140625, -0.98681640625, -0.189453125, 0.43701171875, 0.00567626953125, 0.282958984375, -0.465087890625, -0.55078125, 0.359130859375, 1.1396484375, -0.54931640625, 0.11016845703125, 0.450439453125, -0.1387939453125, -0.04754638671875, 0.423828125, 0.0478515625, -0.2169189453125, -0.60595703125, 0.7158203125, 0.0022716522216796875, -0.10791015625, -0.194580078125, 0.63330078125, 0.491455078125, 0.7763671875, -0.15576171875, -0.5390625, 0.56591796875, 0.96337890625, -0.11004638671875, 0.63427734375, 0.2196044921875, 0.7451171875, 1.0107421875, 0.88427734375, 0.66552734375, 0.1793212890625, 0.40283203125, 0.78173828125, 0.09149169921875, 0.25732421875, 0.52734375, 0.68359375, 0.194091796875, 0.257568359375, 0.459228515625, 0.64111328125, 0.148681640625, -0.0933837890625, -0.04437255859375, -0.0132598876953125, -0.3935546875, 0.91357421875, 0.060089111328125, 0.68994140625, -0.0136566162109375, -0.391357421875, 0.151611328125, 1.1171875, -1.0146484375, -0.43798828125, -0.1885986328125, 0.0479736328125, -0.036407470703125, 0.0352783203125, 0.91748046875, 0.59912109375, 0.68701171875, 0.379150390625, -0.3486328125, -0.27392578125, -0.7685546875, -0.8095703125, -0.81640625, -0.27294921875, -0.703125, -0.1038818359375, -0.139404296875, -1.0205078125, 0.01505279541015625, -0.195068359375, -0.148681640625, 0.293701171875, -0.546875, 0.7744140625, 0.0165863037109375, 0.298095703125, -0.6201171875, 0.591796875, 0.114013671875, 1.0830078125, -0.85693359375, 0.0014209747314453125, -0.020721435546875, -0.66162109375, 0.09130859375, 0.387939453125, 0.27978515625, -0.05291748046875, -0.73583984375, -0.85546875, -0.53076171875, 0.230712890625, -0.330078125, 0.3330078125, -0.360595703125, 0.697265625, 0.66162109375, -0.59912109375, 0.61962890625, 1.0693359375, -0.90478515625, 0.62939453125, 0.0399169921875, -0.48828125, -0.76513671875, 1.08203125, 0.5703125, 0.55029296875, -0.353515625, -0.6142578125, -0.363525390625, -0.050628662109375, 0.1905517578125, -0.791015625, -0.1590576171875, 0.68310546875, -0.031494140625, -0.908203125, 0.60009765625, -0.9833984375, -0.67626953125, -0.693359375, -0.341552734375, 1.12109375, 0.84814453125, 0.1278076171875, 0.135009765625, 0.133544921875, 0.128662109375, 0.429443359375, 0.55615234375, -0.61083984375, 0.283447265625, 0.89990234375, 0.07537841796875, -0.020660400390625, 0.11383056640625, -0.373046875, -0.2308349609375, 0.12261962890625, 0.12548828125, 0.666015625, -0.002101898193359375, 0.51806640625, 0.3623046875, 0.52685546875, -0.74853515625, 0.061126708984375, -0.2471923828125, 0.66455078125, 0.525390625, 0.615234375, -0.12237548828125, -0.44677734375, -0.59033203125, -1.369140625, 0.026153564453125, 0.292236328125, 0.73779296875, -0.57861328125, 1.2265625, 0.2032470703125, -0.625, 0.250732421875, -0.66455078125, 0.3525390625, 0.9443359375, 0.142822265625, 0.95361328125, -0.75244140625, 0.428955078125, 0.214599609375, 0.040924072265625, 0.47998046875, 0.6484375, 0.324951171875, -0.56787109375, -0.662109375, -0.541015625, -0.060821533203125, -0.27490234375, -0.52587890625, 0.36181640625, -0.52490234375, -0.043487548828125, -1.0302734375, 0.5224609375, 0.67724609375, 0.76318359375, 0.0120849609375, 0.281982421875, 0.319091796875, 0.330322265625, 0.642578125, -0.12384033203125, 0.2177734375, -0.56689453125, 0.783203125, 0.220947265625, -0.34521484375, -0.77197265625, -0.371337890625, 0.0614013671875, 0.180908203125, -0.5068359375, -0.09808349609375, -1.119140625, 0.21484375, -0.41259765625, 0.6640625, -0.583984375, -0.2197265625, -0.1622314453125, 0.33349609375, 0.218017578125, -1.03515625, 0.52880859375, -1.0107421875, 0.75830078125, 0.6103515625, 0.1314697265625, -0.1812744140625, -0.3427734375, -0.76611328125, -0.465576171875, -0.054595947265625, 0.81396484375, -0.172119140625, 0.383544921875, -1.3251953125, 0.60693359375, 0.072265625, -0.460693359375, 0.243408203125, -0.2398681640625, 0.828125, -0.1993408203125, 0.7666015625, -0.45654296875, -0.740234375, 0.1337890625, -1.3857421875, 0.736328125, -0.426025390625, 0.87890625, 0.052490234375, -0.043670654296875, 0.2744140625, 0.175537109375, -0.26611328125, 0.322998046875, -0.12017822265625, 0.48291015625, -0.84521484375, -0.8740234375, 0.62841796875, -0.190673828125, -0.345458984375, 0.78271484375, 0.00031495094299316406, -0.53076171875, -0.0303192138671875, 0.556640625, -0.537109375, 0.2193603515625, -0.11297607421875, 0.7685546875, -0.408203125, -0.66259765625, -0.1639404296875, -0.5546875, 0.73291015625, 0.0282440185546875, -0.61279296875, -0.140869140625, -1.3037109375, -0.232421875, 0.1336669921875, -0.48681640625, 0.255615234375, 0.3818359375, -0.1265869140625, -0.299560546875, -0.1253662109375, -0.433349609375, -0.472900390625, -0.63916015625, -0.1888427734375, 0.11962890625, 0.75439453125, 0.98291015625, 0.036865234375, -0.263427734375, -0.0183258056640625, 0.0059051513671875, 0.14306640625, -0.5576171875, -0.1973876953125, -0.27392578125, -0.1009521484375, -0.424560546875, 0.1473388671875, 0.140625, 0.32421875, 0.90966796875, -0.033477783203125, 0.13623046875, 0.34130859375, -0.642578125, 1.3037109375, 0.066650390625, -0.96240234375, -1.009765625, 0.55810546875, -0.08380126953125, 0.568359375, 0.55078125, -1.0244140625, -0.62841796875, -0.9814453125, 0.17724609375, -0.94677734375, -0.29541015625, -1.2734375, -0.78564453125, -0.73583984375, 0.38330078125, 0.177490234375, -0.5791015625, 0.486572265625, -0.74560546875, 0.248291015625, -0.79345703125, 0.12359619140625, -0.60009765625, -0.7265625, 0.28369140625, 0.87353515625, 0.282958984375, 0.333740234375, -0.002288818359375, -0.407958984375, 0.4970703125, -0.2178955078125, -0.7705078125, -0.2061767578125, -0.298095703125, 0.21044921875, 0.0870361328125, -0.1629638671875, -0.69189453125, 1.0478515625, -0.6552734375, 0.455810546875, 0.1339111328125, -0.27880859375, -0.282958984375, -0.322998046875, 0.861328125, -0.263427734375, 0.0227813720703125, 0.00412750244140625, 0.3916015625, 0.65087890625, -0.45556640625, -0.505859375, -0.74462890625, -0.6845703125, -0.958984375, 0.61767578125, -0.310791015625, 0.21875, -0.8095703125, -0.332763671875, 1.4052734375, -0.50634765625, 0.423095703125, 1.0888671875, 0.07177734375, 0.1767578125, -0.245361328125, 0.6474609375, 0.398681640625, -0.299560546875, 0.1854248046875, -0.06976318359375, -0.71875, -0.0849609375, -0.1490478515625, -0.81689453125, -0.69140625, 0.33203125, 1.3369140625, -0.479736328125, 0.54833984375, -0.3486328125, -1.3603515625, -0.64990234375, 0.54345703125, 0.35595703125, 0.351318359375, 0.74853515625, -0.03936767578125, 0.08648681640625, -0.11834716796875, -0.48828125, -0.439697265625, -0.77978515625, 1.294921875, -0.6259765625, -0.44140625, 0.93505859375, 0.91552734375, -1.212890625, -0.8876953125, 0.239501953125, -0.09619140625, -0.41796875, -0.5068359375, -0.061920166015625, 0.755859375, -0.67236328125, 0.140380859375, 0.334228515625, -0.10003662109375, 0.11968994140625, 0.037139892578125, 0.56005859375, -0.2066650390625, 0.736328125, 0.5908203125, -0.544921875, -0.453857421875, -0.943359375, -0.236572265625, -0.272216796875, -0.07781982421875, 0.7958984375, -0.110595703125, 0.1600341796875, 0.46728515625, 0.04833984375, 0.7470703125, -0.4326171875, -0.373046875, 0.11614990234375, -0.673828125, -0.58056640625, 0.140625, 0.326171875, -0.01326751708984375, 0.3466796875, -0.62939453125, -0.016143798828125, 0.2489013671875, 0.45947265625, -0.2900390625, -0.84814453125, -0.12310791015625, -1.482421875, -0.53955078125, -0.775390625, -0.94189453125, -0.15283203125, 0.395751953125, 0.05322265625, -0.73828125, 0.04632568359375, 0.263427734375, -0.7646484375, 0.55810546875, -0.329833984375, 0.273681640625, -0.305419921875, -0.6630859375, -1.01953125, -0.1773681640625, -0.486083984375, -0.322021484375, -1.06640625, 0.78662109375, 0.10491943359375, 0.3251953125, -0.225830078125, 0.888671875, -0.34619140625, -0.84130859375, 0.26904296875, 0.16015625, -0.01105499267578125, 1.2783203125, 0.42919921875, 0.17041015625, 0.0655517578125, -0.1317138671875, -0.24560546875, -0.464599609375, 0.54150390625, 0.388916015625, -0.45654296875, -0.1805419921875, -0.08099365234375, 0.2744140625, -0.89208984375, 0.33154296875, -0.2353515625, 0.039215087890625, 0.14013671875, -0.1632080078125, 0.31396484375, 1.4072265625, -0.1834716796875, 0.1746826171875, 0.029632568359375, 0.2030029296875, 0.1444091796875, 0.40283203125, -0.04876708984375, 0.46826171875, -0.147216796875, -0.486328125, -0.274658203125, 0.43017578125, 0.12890625, 0.05718994140625, -0.313720703125, -0.9208984375, -0.69482421875, -0.319580078125, 0.039306640625, 0.40576171875, 0.56005859375, -0.47607421875, -0.1202392578125, -0.04913330078125, -0.58349609375, -0.032958984375, -1.1396484375, -0.9443359375, 0.52587890625, -0.05706787109375, -0.68359375, -0.1324462890625, -0.182861328125, -0.4189453125, -0.05633544921875, 0.60693359375, -0.46484375, 0.494384765625, 0.0165863037109375, 0.308837890625, -0.057037353515625, -0.1719970703125, 0.0955810546875, 0.73779296875, -0.6748046875, -0.68603515625, 0.06475830078125, 0.90771484375, 0.1854248046875, -0.422607421875, -0.1328125, 0.398193359375, -0.1900634765625, 0.313232421875, -0.6650390625, -0.04522705078125, -0.00640106201171875, 0.97998046875, -0.84375, 0.083740234375, -0.1981201171875, 0.200439453125, -0.07965087890625, -0.56787109375, -0.50439453125, 1.1103515625, 0.6240234375, -0.139404296875, 0.70751953125, 0.00860595703125, 0.30712890625, -0.007404327392578125, -0.11224365234375, 0.1954345703125, 0.5185546875, 0.76171875, 0.5966796875, -0.12939453125, 0.2244873046875, 0.90185546875, -0.16064453125, -0.407470703125, 0.37939453125, -0.03814697265625, -0.0024356842041015625, -0.10186767578125, 0.022125244140625, -0.25048828125, -0.278564453125, -0.7939453125, 0.8154296875, -0.24267578125, 0.3359375, -0.068359375, -0.763671875, 0.94091796875, -0.3837890625, -0.35498046875, 0.283447265625, -0.72265625, 0.216064453125, 0.59814453125, -0.345703125, -0.33935546875, 0.7001953125, 0.56982421875, 0.6708984375, 0.69873046875, 0.1431884765625, 0.42626953125, -0.5185546875, 0.1451416015625, -0.14990234375, -0.154541015625, -0.152099609375, -0.62939453125, -1.1513671875, 0.450927734375, -0.65283203125, -0.6015625, 0.70166015625, -0.67822265625, 0.19091796875, -0.284423828125, 0.7783203125, -0.393798828125, 0.10125732421875, 0.59814453125, -0.2783203125, -0.80126953125, 0.80224609375, -0.19384765625, 0.27587890625, -0.299560546875, 1.1865234375, -0.16064453125, 1.470703125, 0.55322265625, -0.254638671875, 0.2120361328125, 0.39453125, -0.394287109375, -0.626953125, -0.67578125, -0.58251953125, -0.09326171875, -0.491455078125, -0.443359375, 0.20654296875, 0.369384765625, 0.016143798828125, -0.74267578125, -0.1707763671875, 0.28466796875, -0.74609375, 0.414794921875, 0.30615234375, 0.006412506103515625, 0.0261993408203125, -0.07342529296875, -0.1231689453125, -0.14306640625, 0.1610107421875, -0.79296875, 0.381103515625, -0.947265625, -0.219970703125, -0.69677734375, -0.6650390625, -0.222900390625, 0.10693359375, -0.3466796875, -0.92724609375, 0.322021484375, 0.334716796875, 0.1807861328125, 0.421630859375, -0.1964111328125, 0.287353515625, 1.125, 1.0537109375, 0.07659912109375, 0.818359375, 0.281982421875, -0.08978271484375, 0.0247955322265625, -0.305908203125, 0.404541015625, -0.01038360595703125, 0.4619140625, -0.412109375, 0.2235107421875, -0.673828125, -1.525390625, 0.45068359375, 0.49658203125, 0.358154296875, -0.70361328125, -1.0908203125, -0.11077880859375, -1.23828125, -0.1805419921875, -0.73876953125, 1.0556640625, -0.5556640625, 0.048553466796875, -0.156494140625, -1.2373046875, 4.24609375, 1.05078125, 0.87353515625, 0.576171875, 0.225830078125, 1.0009765625, 0.05255126953125, -0.44775390625, -0.02789306640625, -0.20947265625, 0.8583984375, -0.537109375, -0.10498046875, 0.7314453125, 0.273193359375, 0.515625, -0.44091796875, 0.501953125, -0.2568359375, -0.9267578125, -0.8955078125, 0.53125, -0.12481689453125, 0.443115234375, 0.0740966796875, 0.141845703125, 0.81396484375, -1.0673828125, 0.1656494140625, -0.7373046875, 0.225341796875, -0.37548828125, 1.095703125, 0.057891845703125, 0.045135498046875, 0.556640625, -0.10418701171875, -0.5009765625, 0.206787109375, 0.051910400390625, -0.1844482421875, -0.136474609375, 0.47509765625, -0.912109375, -0.02001953125, 0.54833984375, -0.71142578125, 0.36376953125, -0.1693115234375, -1.11328125, 0.86083984375, -0.16162109375, 0.393798828125, -0.970703125, -0.294677734375, -0.1397705078125, 0.4130859375, -0.11590576171875, -0.483154296875, 0.385498046875, 0.5693359375, 0.466796875, 0.2744140625, 0.564453125, -0.96044921875, 0.2445068359375, -0.18896484375, 0.37890625, -0.55615234375, 0.1363525390625, -0.46484375, -0.402587890625, -0.284912109375, -0.50439453125, 0.58837890625, -0.0496826171875, -0.016082763671875, 0.44189453125, 0.5302734375, -0.63330078125, 0.0791015625, -0.12347412109375, -0.09527587890625, -0.54833984375, 0.66455078125, 1.2578125, -0.50341796875, -0.377685546875, -0.341064453125, 0.4912109375, 0.435302734375, 0.447021484375, -0.1629638671875, -0.79443359375, -0.045623779296875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Tags: combinatorics, greedy, implementation, math Correct Solution: ``` s = input() l = [x for x in range(len(s)) if s[x] == 'a'] # print(l) i, step = 0, 0 while l: step = (len(s) + 2*step - l.pop() - 1 - i) % (10 ** 9 + 7) i += 1 print(step) ```
105,791
[ 0.357177734375, -0.125, 0.06658935546875, 0.1075439453125, -0.79833984375, -0.67333984375, -0.01373291015625, -0.11029052734375, 0.317138671875, 0.8583984375, 0.6650390625, -0.344970703125, -0.22802734375, -0.8798828125, -0.51611328125, -0.0289154052734375, -0.50927734375, -0.75146484375, -0.343994140625, -0.309326171875, 0.095947265625, -0.2120361328125, -1.10546875, -0.09259033203125, -0.2060546875, 1.0498046875, 0.64306640625, -0.051422119140625, 0.9853515625, 1.3359375, -0.166748046875, -0.1580810546875, 0.485107421875, -1.0751953125, -0.380615234375, -0.52587890625, 0.55908203125, -0.8388671875, -0.1890869140625, -0.31201171875, 0.2208251953125, -0.62744140625, 0.5185546875, -0.7822265625, -1.5166015625, 0.0701904296875, -0.09393310546875, -0.467529296875, -0.01451873779296875, -0.60546875, -0.1219482421875, -0.375732421875, 0.437255859375, 0.0701904296875, 0.046234130859375, 0.10821533203125, 0.3154296875, -0.3505859375, -0.8125, 0.1641845703125, 0.40576171875, 0.076904296875, 0.09814453125, -0.91796875, -0.05328369140625, 0.219482421875, -0.33203125, 0.001094818115234375, -0.1761474609375, -1.0595703125, -0.09466552734375, 0.281982421875, -0.4443359375, -0.59716796875, -0.1461181640625, 0.160400390625, 0.337646484375, -0.2022705078125, -0.65673828125, 1.1103515625, -0.232666015625, 0.7080078125, 0.28125, 0.277587890625, -0.24169921875, -0.5439453125, 0.04840087890625, 0.32373046875, -0.06732177734375, -0.11163330078125, -0.366455078125, 0.740234375, -0.355712890625, -0.03692626953125, 0.287353515625, 0.6083984375, -0.390869140625, 0.1341552734375, 0.58349609375, 0.34521484375, 0.8251953125, 1.060546875, -0.56396484375, 0.76025390625, -0.5390625, -0.1002197265625, 0.10003662109375, -0.1553955078125, -0.37841796875, 0.0239410400390625, -0.383056640625, -0.276611328125, 0.62744140625, 0.30859375, -0.51611328125, 1.099609375, 0.2130126953125, 0.41259765625, -0.6142578125, 0.7060546875, 0.5126953125, 0.251953125, 0.77294921875, -0.20068359375, -0.2178955078125, -0.051483154296875, -0.607421875, 1.1630859375, -0.80322265625, -0.20751953125, 0.140869140625, 0.1671142578125, 0.03057861328125, 0.32763671875, -0.2568359375, 0.69580078125, -0.037445068359375, 0.2347412109375, 0.73583984375, -0.43603515625, 0.5966796875, -0.404052734375, -0.1456298828125, 1.7060546875, 0.247802734375, -0.11871337890625, 0.83251953125, 0.41455078125, -0.8837890625, 0.299072265625, -1.0986328125, 0.83740234375, 0.319580078125, 0.330810546875, 0.01442718505859375, 0.1781005859375, -0.336669921875, 0.50927734375, 0.09161376953125, -0.16455078125, -0.5751953125, -0.09979248046875, -0.36376953125, 1.0732421875, -0.4677734375, 0.89501953125, -0.338623046875, -0.160888671875, -0.1470947265625, -0.439208984375, 0.16845703125, -0.2388916015625, -0.1932373046875, 0.8896484375, 0.350341796875, 1.0908203125, 1.2421875, -0.2587890625, 0.50830078125, 0.2763671875, -0.419677734375, 0.185302734375, 0.282958984375, 0.9609375, 0.357421875, 0.41064453125, -0.310791015625, 0.03350830078125, -0.64501953125, -0.443115234375, 0.2744140625, 0.6708984375, -0.82568359375, 0.452880859375, -0.0740966796875, -0.0187225341796875, -0.63232421875, -0.282470703125, -0.25439453125, -1.0244140625, -0.2127685546875, 0.5029296875, 0.016815185546875, 0.302978515625, -0.466796875, -0.58740234375, 0.380859375, 1.15234375, -0.455810546875, 0.11334228515625, 0.40380859375, -0.0931396484375, -0.09539794921875, 0.4052734375, -0.039794921875, -0.26708984375, -0.5830078125, 0.72216796875, -0.0010671615600585938, -0.120849609375, -0.16357421875, 0.56396484375, 0.43017578125, 0.763671875, -0.0863037109375, -0.5400390625, 0.623046875, 0.923828125, -0.08319091796875, 0.58740234375, 0.200927734375, 0.77978515625, 1.0126953125, 0.91796875, 0.70703125, 0.250244140625, 0.32666015625, 0.8427734375, 0.093994140625, 0.2159423828125, 0.5224609375, 0.73486328125, 0.262939453125, 0.275390625, 0.45263671875, 0.6318359375, 0.1796875, -0.1011962890625, -0.0018987655639648438, -0.06927490234375, -0.419677734375, 0.95654296875, -0.007411956787109375, 0.708984375, 0.0245208740234375, -0.373779296875, 0.193603515625, 1.0458984375, -1.0185546875, -0.446533203125, -0.1546630859375, 0.06622314453125, 0.00890350341796875, 0.0560302734375, 0.87255859375, 0.625, 0.7490234375, 0.434326171875, -0.304931640625, -0.29833984375, -0.70751953125, -0.80615234375, -0.76416015625, -0.2491455078125, -0.68994140625, -0.07952880859375, -0.08544921875, -1.041015625, 0.00539398193359375, -0.280029296875, -0.1705322265625, 0.3017578125, -0.5576171875, 0.8017578125, -0.02215576171875, 0.262939453125, -0.6025390625, 0.55908203125, 0.1229248046875, 1.1328125, -0.84423828125, -0.041534423828125, -0.059814453125, -0.6689453125, 0.0280609130859375, 0.44287109375, 0.307861328125, 0.0004723072052001953, -0.720703125, -0.89404296875, -0.464599609375, 0.255859375, -0.39111328125, 0.343017578125, -0.443603515625, 0.72998046875, 0.6357421875, -0.60498046875, 0.63671875, 1.0712890625, -0.89013671875, 0.56494140625, 0.00579833984375, -0.458251953125, -0.81884765625, 1.1552734375, 0.5654296875, 0.51416015625, -0.392333984375, -0.69091796875, -0.35205078125, -0.06842041015625, 0.1890869140625, -0.7880859375, -0.184814453125, 0.6435546875, -0.0294189453125, -0.90185546875, 0.5986328125, -0.99267578125, -0.59765625, -0.67333984375, -0.36083984375, 1.1083984375, 0.8623046875, 0.1239013671875, 0.1546630859375, 0.154541015625, 0.1251220703125, 0.54541015625, 0.56689453125, -0.60546875, 0.1873779296875, 0.9130859375, -0.00019228458404541016, -0.0258026123046875, 0.107421875, -0.368896484375, -0.2420654296875, 0.145263671875, 0.1282958984375, 0.642578125, 0.07293701171875, 0.46435546875, 0.3662109375, 0.465087890625, -0.73291015625, 0.06744384765625, -0.1846923828125, 0.71728515625, 0.52880859375, 0.61962890625, -0.09722900390625, -0.372802734375, -0.5595703125, -1.3740234375, 0.0811767578125, 0.2020263671875, 0.73681640625, -0.64208984375, 1.2001953125, 0.204345703125, -0.63232421875, 0.239013671875, -0.7578125, 0.291748046875, 0.91796875, 0.145751953125, 0.97998046875, -0.75634765625, 0.42626953125, 0.10198974609375, 0.086669921875, 0.486328125, 0.654296875, 0.35693359375, -0.5302734375, -0.66552734375, -0.525390625, -0.1104736328125, -0.2861328125, -0.513671875, 0.35791015625, -0.52392578125, -0.07684326171875, -0.9580078125, 0.521484375, 0.79736328125, 0.82568359375, 0.023193359375, 0.1844482421875, 0.349853515625, 0.275146484375, 0.66796875, -0.1497802734375, 0.229736328125, -0.60791015625, 0.8046875, 0.2423095703125, -0.302490234375, -0.69873046875, -0.390869140625, 0.06524658203125, 0.1878662109375, -0.459716796875, -0.1588134765625, -1.1552734375, 0.1412353515625, -0.441650390625, 0.60791015625, -0.6630859375, -0.305419921875, -0.21240234375, 0.387939453125, 0.235595703125, -0.9970703125, 0.5234375, -1.041015625, 0.7822265625, 0.537109375, 0.06671142578125, -0.11944580078125, -0.393798828125, -0.77392578125, -0.464599609375, -0.151611328125, 0.82666015625, -0.2186279296875, 0.33984375, -1.3505859375, 0.564453125, 0.091064453125, -0.43212890625, 0.240234375, -0.261474609375, 0.84814453125, -0.2188720703125, 0.84521484375, -0.5341796875, -0.76953125, 0.10601806640625, -1.44140625, 0.75146484375, -0.4765625, 0.88037109375, 0.08148193359375, -0.19189453125, 0.2471923828125, 0.1297607421875, -0.1767578125, 0.3427734375, -0.15966796875, 0.439697265625, -0.8271484375, -0.9560546875, 0.650390625, -0.2347412109375, -0.339599609375, 0.73486328125, -0.0297088623046875, -0.5703125, -0.054107666015625, 0.5869140625, -0.57763671875, 0.2000732421875, -0.0987548828125, 0.693359375, -0.416015625, -0.7138671875, -0.110107421875, -0.5751953125, 0.73974609375, 0.033935546875, -0.6552734375, -0.22900390625, -1.3427734375, -0.1463623046875, 0.1619873046875, -0.349853515625, 0.244384765625, 0.39990234375, -0.1495361328125, -0.261962890625, -0.1363525390625, -0.4541015625, -0.50732421875, -0.61572265625, -0.2032470703125, 0.1517333984375, 0.716796875, 0.98779296875, 0.0198822021484375, -0.31591796875, 0.005939483642578125, 0.04815673828125, 0.2137451171875, -0.517578125, -0.18505859375, -0.27001953125, -0.01042938232421875, -0.428955078125, 0.188720703125, 0.1697998046875, 0.373779296875, 0.8837890625, 0.007015228271484375, 0.169921875, 0.41455078125, -0.625, 1.2822265625, 0.034210205078125, -0.9296875, -0.9951171875, 0.59228515625, -0.1806640625, 0.5732421875, 0.468017578125, -1.0322265625, -0.59130859375, -0.96240234375, 0.209716796875, -0.94140625, -0.280029296875, -1.255859375, -0.76123046875, -0.640625, 0.3505859375, 0.155517578125, -0.5546875, 0.458740234375, -0.74658203125, 0.340576171875, -0.80615234375, 0.13037109375, -0.56689453125, -0.75439453125, 0.2403564453125, 0.8515625, 0.300537109375, 0.35595703125, 0.0177001953125, -0.41552734375, 0.41455078125, -0.2099609375, -0.80810546875, -0.203125, -0.366455078125, 0.2381591796875, 0.039764404296875, -0.1981201171875, -0.6171875, 0.9384765625, -0.65283203125, 0.477294921875, 0.11138916015625, -0.276123046875, -0.29736328125, -0.2861328125, 0.88818359375, -0.255126953125, 0.077392578125, 0.008331298828125, 0.406005859375, 0.740234375, -0.418212890625, -0.525390625, -0.736328125, -0.6845703125, -0.978515625, 0.60986328125, -0.2254638671875, 0.1724853515625, -0.81396484375, -0.301513671875, 1.37890625, -0.55517578125, 0.439697265625, 1.0791015625, -0.01220703125, 0.2239990234375, -0.293701171875, 0.5673828125, 0.454833984375, -0.349365234375, 0.2178955078125, -0.0303192138671875, -0.75390625, -0.058624267578125, -0.1385498046875, -0.830078125, -0.74462890625, 0.36376953125, 1.3310546875, -0.444580078125, 0.57958984375, -0.326904296875, -1.3271484375, -0.66943359375, 0.59521484375, 0.372314453125, 0.3095703125, 0.70654296875, -0.0672607421875, 0.06256103515625, -0.1407470703125, -0.47119140625, -0.50927734375, -0.73046875, 1.2919921875, -0.62548828125, -0.51611328125, 0.97900390625, 0.94970703125, -1.1474609375, -0.927734375, 0.287109375, -0.07720947265625, -0.385009765625, -0.533203125, -0.044097900390625, 0.7744140625, -0.60107421875, 0.141357421875, 0.332275390625, -0.09271240234375, 0.15234375, 0.039276123046875, 0.56298828125, -0.2744140625, 0.751953125, 0.564453125, -0.5712890625, -0.467529296875, -0.99169921875, -0.322021484375, -0.27685546875, -0.08685302734375, 0.8046875, -0.0020809173583984375, 0.1273193359375, 0.490966796875, 0.0731201171875, 0.73974609375, -0.45458984375, -0.31103515625, 0.1495361328125, -0.65478515625, -0.55810546875, 0.169677734375, 0.429931640625, -0.035125732421875, 0.36962890625, -0.66064453125, -0.0283355712890625, 0.25244140625, 0.47412109375, -0.34521484375, -0.958984375, -0.176513671875, -1.4794921875, -0.54736328125, -0.7275390625, -0.91845703125, -0.17041015625, 0.340087890625, 0.0472412109375, -0.642578125, 0.01209259033203125, 0.22607421875, -0.76318359375, 0.587890625, -0.308349609375, 0.3232421875, -0.330078125, -0.6328125, -1.04296875, -0.060546875, -0.45166015625, -0.325927734375, -1.080078125, 0.7275390625, 0.095947265625, 0.3544921875, -0.252197265625, 0.935546875, -0.248046875, -0.826171875, 0.2587890625, 0.18408203125, -0.0328369140625, 1.3046875, 0.470703125, 0.12261962890625, 0.100830078125, -0.06903076171875, -0.206298828125, -0.50634765625, 0.59765625, 0.366943359375, -0.4560546875, -0.165771484375, -0.048431396484375, 0.289794921875, -0.8603515625, 0.33984375, -0.206787109375, 0.09039306640625, 0.08685302734375, -0.074462890625, 0.27490234375, 1.388671875, -0.20361328125, 0.1243896484375, 0.01514434814453125, 0.19873046875, 0.15869140625, 0.40380859375, -0.032958984375, 0.484375, -0.2484130859375, -0.505859375, -0.2705078125, 0.454345703125, 0.1328125, 0.0290679931640625, -0.341064453125, -0.94775390625, -0.67578125, -0.3486328125, 0.072998046875, 0.411865234375, 0.55419921875, -0.56103515625, -0.021881103515625, 0.008392333984375, -0.5927734375, 0.0010004043579101562, -1.109375, -1.001953125, 0.499267578125, 0.0352783203125, -0.7041015625, -0.18310546875, -0.1949462890625, -0.360107421875, -0.11029052734375, 0.6328125, -0.525390625, 0.43994140625, 0.052764892578125, 0.378662109375, -0.07904052734375, -0.207275390625, 0.10980224609375, 0.73388671875, -0.662109375, -0.70849609375, 0.042144775390625, 0.87353515625, 0.240234375, -0.37451171875, -0.09661865234375, 0.406494140625, -0.167724609375, 0.283203125, -0.642578125, 0.009429931640625, -0.01922607421875, 0.9384765625, -0.802734375, 0.06292724609375, -0.2088623046875, 0.26220703125, -0.067138671875, -0.59423828125, -0.4931640625, 1.140625, 0.62744140625, -0.131591796875, 0.63916015625, 0.05194091796875, 0.322021484375, 0.006244659423828125, 0.01236724853515625, 0.26806640625, 0.5869140625, 0.84423828125, 0.62744140625, -0.095703125, 0.300537109375, 0.9072265625, -0.238037109375, -0.357177734375, 0.411865234375, -0.027008056640625, 0.028167724609375, -0.18017578125, -0.0501708984375, -0.2705078125, -0.285888671875, -0.81103515625, 0.80712890625, -0.27734375, 0.285400390625, -0.10113525390625, -0.8095703125, 0.91796875, -0.334716796875, -0.313720703125, 0.25732421875, -0.7314453125, 0.1776123046875, 0.60009765625, -0.337158203125, -0.3330078125, 0.69677734375, 0.55712890625, 0.6337890625, 0.7705078125, 0.19921875, 0.459716796875, -0.5087890625, 0.195068359375, -0.2294921875, -0.08038330078125, -0.209228515625, -0.59423828125, -1.09765625, 0.460693359375, -0.60595703125, -0.56787109375, 0.75830078125, -0.6787109375, 0.1949462890625, -0.28173828125, 0.73974609375, -0.355224609375, 0.09332275390625, 0.61181640625, -0.326171875, -0.859375, 0.828125, -0.1552734375, 0.2413330078125, -0.30029296875, 1.2783203125, -0.2244873046875, 1.384765625, 0.59765625, -0.222900390625, 0.2259521484375, 0.390625, -0.407958984375, -0.7294921875, -0.63818359375, -0.60693359375, -0.08868408203125, -0.5224609375, -0.444091796875, 0.162109375, 0.4130859375, 0.0013628005981445312, -0.80615234375, -0.22705078125, 0.3203125, -0.7578125, 0.461669921875, 0.284423828125, 0.045440673828125, 0.045166015625, -0.1024169921875, -0.1500244140625, -0.1807861328125, 0.1932373046875, -0.74560546875, 0.45166015625, -0.96728515625, -0.2242431640625, -0.703125, -0.71630859375, -0.2154541015625, 0.1358642578125, -0.306640625, -0.82861328125, 0.273681640625, 0.280029296875, 0.23046875, 0.43505859375, -0.2364501953125, 0.287841796875, 1.0908203125, 1.0546875, 0.1099853515625, 0.78759765625, 0.30908203125, -0.10260009765625, 0.0017719268798828125, -0.315673828125, 0.458984375, -0.0029277801513671875, 0.50537109375, -0.33056640625, 0.2257080078125, -0.74462890625, -1.537109375, 0.470458984375, 0.436279296875, 0.35595703125, -0.75439453125, -1.0849609375, -0.129150390625, -1.3212890625, -0.1953125, -0.75048828125, 1.0537109375, -0.55615234375, 0.032379150390625, -0.1932373046875, -1.23046875, 4.20703125, 1.1123046875, 0.8828125, 0.67919921875, 0.2037353515625, 0.9697265625, 0.040252685546875, -0.48095703125, -0.054718017578125, -0.2081298828125, 0.830078125, -0.59375, -0.06280517578125, 0.736328125, 0.328369140625, 0.53662109375, -0.46142578125, 0.453125, -0.262939453125, -0.97021484375, -0.9248046875, 0.51171875, -0.10430908203125, 0.409912109375, 0.0077056884765625, 0.139404296875, 0.763671875, -1.087890625, 0.15380859375, -0.7509765625, 0.1650390625, -0.401123046875, 1.087890625, 0.12066650390625, 0.0743408203125, 0.52392578125, -0.07861328125, -0.388427734375, 0.1998291015625, 0.11578369140625, -0.1971435546875, -0.0771484375, 0.456787109375, -0.9306640625, -0.047271728515625, 0.49609375, -0.68408203125, 0.3818359375, -0.1864013671875, -1.1005859375, 0.9150390625, -0.221923828125, 0.372802734375, -0.92138671875, -0.40478515625, -0.19384765625, 0.4345703125, -0.08380126953125, -0.468505859375, 0.442626953125, 0.52880859375, 0.564453125, 0.251708984375, 0.5615234375, -1.0244140625, 0.2330322265625, -0.14111328125, 0.3310546875, -0.6240234375, 0.1234130859375, -0.47216796875, -0.43408203125, -0.28955078125, -0.4970703125, 0.53955078125, 0.0252685546875, -0.002895355224609375, 0.429931640625, 0.494140625, -0.67822265625, 0.08013916015625, -0.1175537109375, -0.1773681640625, -0.60107421875, 0.7353515625, 1.3173828125, -0.55908203125, -0.375, -0.401611328125, 0.427734375, 0.45166015625, 0.437744140625, -0.1383056640625, -0.71875, -0.01435089111328125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Tags: combinatorics, greedy, implementation, math Correct Solution: ``` def main(): s=input() r=0 c=0 m=(10**9)+7 for i in range(len(s)-1,-1,-1): if s[i]=='b': c=(c%m)+1 else: r=((r%m)+(c%m))%m c=(c*2)%m print(r) if __name__=='__main__': main() ```
105,792
[ 0.352783203125, -0.1361083984375, 0.104736328125, 0.0281219482421875, -0.76904296875, -0.61669921875, 0.01062774658203125, -0.1473388671875, 0.26708984375, 0.7646484375, 0.71044921875, -0.353515625, -0.2135009765625, -0.822265625, -0.5302734375, -0.04510498046875, -0.52685546875, -0.73486328125, -0.386474609375, -0.3759765625, 0.1187744140625, -0.1385498046875, -1.16796875, -0.06243896484375, -0.225341796875, 1.0693359375, 0.68310546875, -0.055145263671875, 0.9326171875, 1.2724609375, -0.2171630859375, -0.09686279296875, 0.51318359375, -1.0546875, -0.36962890625, -0.481201171875, 0.5751953125, -0.89892578125, -0.1990966796875, -0.356201171875, 0.2139892578125, -0.60595703125, 0.487548828125, -0.79443359375, -1.5048828125, 0.07110595703125, -0.1287841796875, -0.422607421875, 0.0223236083984375, -0.57080078125, -0.10675048828125, -0.354736328125, 0.3916015625, 0.06011962890625, -0.0218658447265625, 0.130615234375, 0.2763671875, -0.32666015625, -0.82177734375, 0.160888671875, 0.452392578125, 0.052398681640625, 0.045928955078125, -0.89013671875, -0.07244873046875, 0.1697998046875, -0.286376953125, -0.00901031494140625, -0.194580078125, -1.0458984375, -0.08135986328125, 0.325927734375, -0.41552734375, -0.58251953125, -0.187255859375, 0.107177734375, 0.327880859375, -0.34716796875, -0.65771484375, 1.11328125, -0.25537109375, 0.72412109375, 0.248779296875, 0.2568359375, -0.27001953125, -0.517578125, 0.045928955078125, 0.3154296875, -0.060791015625, -0.08782958984375, -0.333740234375, 0.70068359375, -0.33837890625, -0.043121337890625, 0.363525390625, 0.62060546875, -0.384521484375, 0.1505126953125, 0.55322265625, 0.318359375, 0.845703125, 1.0771484375, -0.58544921875, 0.78173828125, -0.54248046875, -0.043426513671875, 0.0826416015625, -0.09814453125, -0.317626953125, 0.090576171875, -0.260986328125, -0.2900390625, 0.61865234375, 0.265625, -0.513671875, 1.1005859375, 0.2158203125, 0.44921875, -0.66259765625, 0.62548828125, 0.452392578125, 0.255859375, 0.69921875, -0.2197265625, -0.22265625, -0.046966552734375, -0.59912109375, 1.173828125, -0.7490234375, -0.2255859375, 0.206787109375, 0.149658203125, 0.055023193359375, 0.351318359375, -0.2327880859375, 0.69873046875, -0.058349609375, 0.252685546875, 0.755859375, -0.4375, 0.62548828125, -0.386474609375, -0.10992431640625, 1.7216796875, 0.218505859375, -0.09747314453125, 0.84521484375, 0.40771484375, -0.876953125, 0.322998046875, -1.0009765625, 0.8349609375, 0.3779296875, 0.35546875, -0.038482666015625, 0.202392578125, -0.270751953125, 0.4443359375, 0.10308837890625, -0.2122802734375, -0.580078125, 0.006984710693359375, -0.353759765625, 1.0439453125, -0.44384765625, 0.8955078125, -0.27783203125, -0.17431640625, -0.177490234375, -0.43212890625, 0.1531982421875, -0.219482421875, -0.205810546875, 0.9013671875, 0.3369140625, 1.029296875, 1.189453125, -0.25732421875, 0.51318359375, 0.272705078125, -0.437255859375, 0.1549072265625, 0.29931640625, 0.92431640625, 0.277099609375, 0.4052734375, -0.259033203125, -0.02313232421875, -0.67919921875, -0.458984375, 0.2861328125, 0.65087890625, -0.77490234375, 0.44189453125, -0.0692138671875, -0.0186004638671875, -0.68310546875, -0.31982421875, -0.2275390625, -0.95263671875, -0.1873779296875, 0.48876953125, -0.04864501953125, 0.36279296875, -0.44677734375, -0.54541015625, 0.406982421875, 1.091796875, -0.49609375, 0.059722900390625, 0.414794921875, -0.10400390625, -0.09332275390625, 0.451416015625, -0.0048828125, -0.22021484375, -0.578125, 0.78271484375, -0.0255584716796875, -0.164306640625, -0.20654296875, 0.626953125, 0.424560546875, 0.7802734375, -0.055908203125, -0.53271484375, 0.5458984375, 0.88330078125, -0.060272216796875, 0.58349609375, 0.21826171875, 0.7587890625, 0.97412109375, 0.91064453125, 0.6533203125, 0.1962890625, 0.3291015625, 0.7998046875, 0.1260986328125, 0.2371826171875, 0.52734375, 0.650390625, 0.277587890625, 0.275390625, 0.421875, 0.5634765625, 0.2119140625, -0.08294677734375, 0.01229095458984375, -0.07525634765625, -0.36279296875, 0.87744140625, 0.0545654296875, 0.69189453125, -0.053253173828125, -0.324462890625, 0.1695556640625, 1.0654296875, -1.0244140625, -0.418212890625, -0.2083740234375, 0.060882568359375, 0.03790283203125, 0.036865234375, 0.89990234375, 0.60302734375, 0.67626953125, 0.425048828125, -0.35400390625, -0.323486328125, -0.72900390625, -0.78564453125, -0.7431640625, -0.251708984375, -0.73291015625, -0.11407470703125, -0.01148223876953125, -1.005859375, 0.0262298583984375, -0.225830078125, -0.1641845703125, 0.3740234375, -0.619140625, 0.810546875, -0.01300811767578125, 0.28076171875, -0.546875, 0.5458984375, 0.1318359375, 1.078125, -0.81982421875, 0.01180267333984375, -0.01232147216796875, -0.6962890625, 0.058990478515625, 0.4111328125, 0.274169921875, -0.0271759033203125, -0.7607421875, -0.87744140625, -0.51708984375, 0.268798828125, -0.325927734375, 0.316162109375, -0.5009765625, 0.70556640625, 0.56982421875, -0.59521484375, 0.63427734375, 1.076171875, -0.89453125, 0.59228515625, 0.031646728515625, -0.51611328125, -0.814453125, 1.1103515625, 0.5595703125, 0.5126953125, -0.407958984375, -0.69140625, -0.36279296875, -0.03790283203125, 0.2303466796875, -0.78662109375, -0.2261962890625, 0.62939453125, -0.03521728515625, -0.9130859375, 0.57568359375, -0.97021484375, -0.62109375, -0.64208984375, -0.3798828125, 1.0986328125, 0.84228515625, 0.07220458984375, 0.1766357421875, 0.1561279296875, 0.17919921875, 0.49609375, 0.546875, -0.61669921875, 0.327880859375, 0.8583984375, 0.0216827392578125, -0.05084228515625, 0.1617431640625, -0.34521484375, -0.206298828125, 0.1563720703125, 0.1693115234375, 0.63916015625, 0.007549285888671875, 0.448974609375, 0.3681640625, 0.476318359375, -0.72216796875, 0.02081298828125, -0.19384765625, 0.69970703125, 0.491455078125, 0.63330078125, -0.06878662109375, -0.42431640625, -0.58642578125, -1.3740234375, 0.04620361328125, 0.278564453125, 0.74169921875, -0.625, 1.2255859375, 0.1739501953125, -0.61865234375, 0.2783203125, -0.70751953125, 0.250244140625, 0.9501953125, 0.14306640625, 0.96240234375, -0.69970703125, 0.441650390625, 0.11334228515625, 0.089111328125, 0.452392578125, 0.62646484375, 0.328857421875, -0.5498046875, -0.70654296875, -0.51123046875, -0.0828857421875, -0.291259765625, -0.50830078125, 0.37255859375, -0.47021484375, -0.0157470703125, -0.97412109375, 0.53173828125, 0.71728515625, 0.8310546875, 0.045806884765625, 0.227294921875, 0.407958984375, 0.359375, 0.6142578125, -0.171630859375, 0.2344970703125, -0.62646484375, 0.74951171875, 0.1658935546875, -0.311279296875, -0.7373046875, -0.35693359375, 0.06396484375, 0.1759033203125, -0.4912109375, -0.1531982421875, -1.16015625, 0.1826171875, -0.4501953125, 0.6669921875, -0.61962890625, -0.289306640625, -0.1734619140625, 0.347900390625, 0.2266845703125, -0.9775390625, 0.5146484375, -1.044921875, 0.80859375, 0.560546875, 0.08428955078125, -0.150390625, -0.403564453125, -0.76611328125, -0.416015625, -0.17724609375, 0.82666015625, -0.224853515625, 0.4169921875, -1.33984375, 0.564453125, 0.1114501953125, -0.469482421875, 0.2435302734375, -0.287841796875, 0.83544921875, -0.206787109375, 0.85693359375, -0.51806640625, -0.716796875, 0.1533203125, -1.369140625, 0.70458984375, -0.3984375, 0.83447265625, 0.09197998046875, -0.1611328125, 0.28173828125, 0.2066650390625, -0.19921875, 0.30908203125, -0.1219482421875, 0.42578125, -0.80615234375, -0.9365234375, 0.65087890625, -0.2120361328125, -0.2408447265625, 0.716796875, -0.05255126953125, -0.55859375, 0.00012826919555664062, 0.61572265625, -0.54248046875, 0.2034912109375, -0.10650634765625, 0.732421875, -0.394287109375, -0.7216796875, -0.1575927734375, -0.54052734375, 0.677734375, 0.03167724609375, -0.58447265625, -0.2054443359375, -1.298828125, -0.16357421875, 0.11773681640625, -0.380126953125, 0.271728515625, 0.34130859375, -0.1170654296875, -0.33349609375, -0.1324462890625, -0.43603515625, -0.465087890625, -0.64794921875, -0.183349609375, 0.118896484375, 0.71630859375, 1.009765625, -0.055572509765625, -0.303955078125, -0.028656005859375, 0.07861328125, 0.185791015625, -0.5537109375, -0.190673828125, -0.3134765625, -0.055267333984375, -0.359619140625, 0.1676025390625, 0.143798828125, 0.370849609375, 0.865234375, -0.0218048095703125, 0.1322021484375, 0.36474609375, -0.64404296875, 1.2197265625, 0.09637451171875, -0.96240234375, -0.96044921875, 0.556640625, -0.08319091796875, 0.56787109375, 0.49951171875, -1.029296875, -0.630859375, -0.95849609375, 0.15380859375, -0.90087890625, -0.294921875, -1.25, -0.70654296875, -0.63037109375, 0.33447265625, 0.1566162109375, -0.54345703125, 0.407958984375, -0.7763671875, 0.2252197265625, -0.81982421875, 0.1539306640625, -0.62109375, -0.7236328125, 0.27734375, 0.84765625, 0.3037109375, 0.29736328125, -0.039520263671875, -0.373779296875, 0.473388671875, -0.2430419921875, -0.75830078125, -0.2376708984375, -0.270263671875, 0.2410888671875, 0.0166473388671875, -0.1968994140625, -0.68701171875, 0.93505859375, -0.6416015625, 0.427490234375, 0.11187744140625, -0.283203125, -0.25927734375, -0.296630859375, 0.873046875, -0.279296875, 0.022857666015625, -0.0035686492919921875, 0.427490234375, 0.72802734375, -0.4775390625, -0.5146484375, -0.76806640625, -0.6572265625, -0.95263671875, 0.56640625, -0.26220703125, 0.1370849609375, -0.86181640625, -0.301025390625, 1.3662109375, -0.5107421875, 0.41162109375, 1.078125, 0.0109100341796875, 0.17578125, -0.329345703125, 0.59521484375, 0.38037109375, -0.335693359375, 0.1478271484375, -0.03857421875, -0.69482421875, -0.0284271240234375, -0.09967041015625, -0.77783203125, -0.6826171875, 0.3193359375, 1.3330078125, -0.468505859375, 0.55615234375, -0.260009765625, -1.2763671875, -0.671875, 0.60595703125, 0.3544921875, 0.254638671875, 0.69873046875, -0.050537109375, 0.05413818359375, -0.12457275390625, -0.4169921875, -0.4326171875, -0.71044921875, 1.234375, -0.63330078125, -0.4560546875, 0.94921875, 0.9638671875, -1.150390625, -0.92578125, 0.2958984375, -0.07635498046875, -0.441650390625, -0.492919921875, -0.04083251953125, 0.78955078125, -0.66845703125, 0.1282958984375, 0.308837890625, -0.045166015625, 0.1202392578125, -0.0322265625, 0.5546875, -0.2247314453125, 0.7197265625, 0.58935546875, -0.5361328125, -0.399658203125, -0.9248046875, -0.25537109375, -0.320068359375, -0.06829833984375, 0.78662109375, -0.01200103759765625, 0.1510009765625, 0.52294921875, 0.06488037109375, 0.7666015625, -0.443603515625, -0.341796875, 0.158447265625, -0.591796875, -0.5537109375, 0.140380859375, 0.396240234375, -0.034759521484375, 0.302001953125, -0.64697265625, 0.01091766357421875, 0.24755859375, 0.50048828125, -0.271240234375, -0.86962890625, -0.173828125, -1.470703125, -0.52587890625, -0.69091796875, -0.9248046875, -0.213623046875, 0.3349609375, 0.024017333984375, -0.58984375, -0.045501708984375, 0.2449951171875, -0.7607421875, 0.68603515625, -0.2978515625, 0.277587890625, -0.332275390625, -0.6650390625, -0.986328125, -0.133544921875, -0.42041015625, -0.3203125, -1.0439453125, 0.70654296875, 0.1507568359375, 0.349365234375, -0.16943359375, 0.89208984375, -0.3154296875, -0.86083984375, 0.306884765625, 0.156494140625, 0.0236968994140625, 1.2509765625, 0.4404296875, 0.095458984375, 0.144775390625, -0.06329345703125, -0.2459716796875, -0.47705078125, 0.497314453125, 0.393798828125, -0.468017578125, -0.1290283203125, -0.0982666015625, 0.25830078125, -0.88427734375, 0.401611328125, -0.2275390625, 0.11993408203125, 0.080078125, -0.0628662109375, 0.2491455078125, 1.3388671875, -0.2237548828125, 0.1046142578125, 0.0020961761474609375, 0.1710205078125, 0.1478271484375, 0.33056640625, -0.0445556640625, 0.44873046875, -0.1395263671875, -0.383056640625, -0.2288818359375, 0.49267578125, 0.11993408203125, 0.036590576171875, -0.32080078125, -0.87890625, -0.70068359375, -0.36767578125, 0.1270751953125, 0.42578125, 0.53173828125, -0.55419921875, -0.037261962890625, -0.0035686492919921875, -0.5517578125, 0.025390625, -1.0830078125, -0.99072265625, 0.5078125, -0.057403564453125, -0.681640625, -0.1414794921875, -0.26513671875, -0.37548828125, -0.055450439453125, 0.60009765625, -0.429931640625, 0.47314453125, 0.050628662109375, 0.32958984375, -0.10064697265625, -0.167724609375, 0.12139892578125, 0.72216796875, -0.63427734375, -0.7001953125, 0.0909423828125, 0.81494140625, 0.1925048828125, -0.36474609375, -0.1251220703125, 0.46826171875, -0.1878662109375, 0.3466796875, -0.61181640625, 0.04962158203125, -0.05010986328125, 0.9814453125, -0.8134765625, 0.0989990234375, -0.19140625, 0.1746826171875, 0.005870819091796875, -0.5859375, -0.52978515625, 1.1435546875, 0.6494140625, -0.1661376953125, 0.65673828125, 0.08306884765625, 0.3203125, -0.0162506103515625, -0.0880126953125, 0.260986328125, 0.5615234375, 0.779296875, 0.59033203125, -0.11700439453125, 0.274658203125, 0.8720703125, -0.1964111328125, -0.415771484375, 0.35302734375, -0.0238037109375, -0.0062713623046875, -0.07269287109375, 0.062042236328125, -0.258544921875, -0.272705078125, -0.80029296875, 0.85791015625, -0.224853515625, 0.271484375, -0.1334228515625, -0.7890625, 0.8173828125, -0.2919921875, -0.343505859375, 0.277099609375, -0.71240234375, 0.15771484375, 0.58935546875, -0.317138671875, -0.33935546875, 0.63720703125, 0.5556640625, 0.66845703125, 0.71044921875, 0.1907958984375, 0.4423828125, -0.54736328125, 0.1629638671875, -0.18603515625, -0.131591796875, -0.191650390625, -0.64013671875, -1.11328125, 0.43359375, -0.5859375, -0.53564453125, 0.751953125, -0.68896484375, 0.19384765625, -0.264892578125, 0.72119140625, -0.37255859375, 0.1219482421875, 0.59326171875, -0.272216796875, -0.865234375, 0.814453125, -0.2261962890625, 0.25732421875, -0.248046875, 1.1708984375, -0.16943359375, 1.3603515625, 0.63818359375, -0.26806640625, 0.2061767578125, 0.33740234375, -0.413330078125, -0.701171875, -0.6103515625, -0.54248046875, -0.142578125, -0.492919921875, -0.41748046875, 0.2020263671875, 0.3857421875, -0.01194000244140625, -0.84033203125, -0.1859130859375, 0.311767578125, -0.73583984375, 0.458984375, 0.30712890625, 0.0599365234375, 0.041107177734375, -0.1016845703125, -0.1380615234375, -0.2197265625, 0.1856689453125, -0.8271484375, 0.414306640625, -0.8984375, -0.212158203125, -0.7197265625, -0.66015625, -0.190185546875, 0.095458984375, -0.348388671875, -0.8896484375, 0.2724609375, 0.29541015625, 0.2398681640625, 0.459228515625, -0.191162109375, 0.255615234375, 1.0908203125, 1.068359375, 0.0977783203125, 0.80517578125, 0.304443359375, -0.1112060546875, 0.060394287109375, -0.33984375, 0.40478515625, -0.023162841796875, 0.5126953125, -0.336669921875, 0.1995849609375, -0.68603515625, -1.513671875, 0.435302734375, 0.5439453125, 0.351318359375, -0.71337890625, -1.09765625, -0.116455078125, -1.2802734375, -0.2344970703125, -0.72998046875, 1.017578125, -0.53369140625, 0.0219573974609375, -0.1468505859375, -1.259765625, 4.296875, 1.0244140625, 0.88134765625, 0.6884765625, 0.1630859375, 0.9560546875, 0.053009033203125, -0.4296875, -0.0278472900390625, -0.2320556640625, 0.79248046875, -0.5439453125, -0.0960693359375, 0.75537109375, 0.2354736328125, 0.51171875, -0.38916015625, 0.4736328125, -0.23193359375, -0.98681640625, -0.91650390625, 0.456787109375, -0.12298583984375, 0.4609375, 0.036285400390625, 0.1038818359375, 0.7265625, -1.041015625, 0.146240234375, -0.7509765625, 0.2156982421875, -0.388916015625, 1.111328125, 0.130126953125, 0.09429931640625, 0.47509765625, -0.1563720703125, -0.495361328125, 0.179931640625, 0.040618896484375, -0.23046875, -0.09710693359375, 0.47314453125, -0.87548828125, -0.049468994140625, 0.486328125, -0.71728515625, 0.372314453125, -0.226806640625, -1.0693359375, 0.85986328125, -0.210693359375, 0.360595703125, -0.95361328125, -0.294677734375, -0.1317138671875, 0.41259765625, -0.12109375, -0.475341796875, 0.395751953125, 0.50244140625, 0.435546875, 0.2445068359375, 0.5126953125, -1.0537109375, 0.2471923828125, -0.130859375, 0.345458984375, -0.56005859375, 0.1011962890625, -0.4287109375, -0.43505859375, -0.219482421875, -0.471435546875, 0.55029296875, -0.025238037109375, 0.0081024169921875, 0.44873046875, 0.49365234375, -0.6181640625, 0.1153564453125, -0.12091064453125, -0.216064453125, -0.5556640625, 0.69482421875, 1.2373046875, -0.51953125, -0.34521484375, -0.361328125, 0.412109375, 0.49169921875, 0.372802734375, -0.1278076171875, -0.7666015625, -0.05419921875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Tags: combinatorics, greedy, implementation, math Correct Solution: ``` mod = 1000000007 qtdb = 0 jogadas = 0 s = input() for i in range(len(s)-1, -1, -1): if(s[i] == 'b'): qtdb = (qtdb + 1) % mod else: jogadas = (jogadas + qtdb) % mod qtdb = (2 * qtdb) % mod print(jogadas) ```
105,793
[ 0.342041015625, -0.11395263671875, 0.060272216796875, 0.0986328125, -0.83447265625, -0.5966796875, 0.0162353515625, -0.085693359375, 0.244140625, 0.87255859375, 0.6328125, -0.1783447265625, -0.2401123046875, -0.8564453125, -0.451416015625, 0.06732177734375, -0.490234375, -0.7041015625, -0.345458984375, -0.359375, 0.130859375, -0.0894775390625, -1.1474609375, -0.1060791015625, -0.2232666015625, 1.0009765625, 0.7158203125, -0.08984375, 0.94384765625, 1.2685546875, -0.146728515625, -0.1986083984375, 0.58642578125, -1.134765625, -0.393310546875, -0.28173828125, 0.68701171875, -0.9267578125, -0.12939453125, -0.337890625, 0.29541015625, -0.72412109375, 0.448974609375, -0.837890625, -1.4228515625, -0.0411376953125, -0.1480712890625, -0.458740234375, -0.0484619140625, -0.56494140625, -0.250732421875, -0.361328125, 0.422607421875, 0.04486083984375, -0.059051513671875, 0.1024169921875, 0.286865234375, -0.318359375, -0.89990234375, 0.1136474609375, 0.49462890625, 0.028778076171875, 0.1431884765625, -0.890625, -0.0304107666015625, 0.1728515625, -0.34765625, 0.0482177734375, -0.09857177734375, -1.0869140625, 0.02508544921875, 0.31640625, -0.344970703125, -0.64013671875, -0.1329345703125, 0.0260009765625, 0.45458984375, -0.486328125, -0.58447265625, 1.1455078125, -0.32470703125, 0.58056640625, 0.10443115234375, 0.298583984375, -0.349609375, -0.3291015625, 0.051361083984375, 0.31005859375, -0.0762939453125, -0.10504150390625, -0.401123046875, 0.7958984375, -0.334228515625, 0.004878997802734375, 0.4013671875, 0.59912109375, -0.305419921875, 0.1925048828125, 0.69970703125, 0.408447265625, 0.68359375, 1.1455078125, -0.640625, 0.8017578125, -0.454833984375, -0.0863037109375, 0.0799560546875, -0.1119384765625, -0.35693359375, 0.103515625, -0.2196044921875, -0.25634765625, 0.58056640625, 0.307373046875, -0.47119140625, 1.0615234375, 0.163818359375, 0.314208984375, -0.603515625, 0.53369140625, 0.310302734375, 0.2216796875, 0.736328125, -0.23193359375, -0.2242431640625, -0.1549072265625, -0.599609375, 1.150390625, -0.81591796875, -0.22802734375, 0.209716796875, 0.1568603515625, 0.1280517578125, 0.313720703125, -0.2384033203125, 0.70849609375, -0.0911865234375, 0.298828125, 0.6796875, -0.444091796875, 0.63720703125, -0.242919921875, -0.148193359375, 1.7578125, 0.213134765625, -0.04266357421875, 0.87451171875, 0.451171875, -0.96142578125, 0.3515625, -1.0087890625, 0.734375, 0.367431640625, 0.33642578125, -0.029083251953125, 0.14404296875, -0.275146484375, 0.63818359375, 0.2108154296875, -0.1697998046875, -0.46044921875, 0.044525146484375, -0.4248046875, 0.95947265625, -0.5625, 0.9609375, -0.1658935546875, -0.091064453125, -0.0531005859375, -0.51953125, 0.1494140625, -0.274169921875, -0.327880859375, 0.8603515625, 0.37890625, 1.064453125, 1.1162109375, -0.210693359375, 0.56396484375, 0.32373046875, -0.414306640625, 0.1951904296875, 0.409423828125, 1.021484375, 0.405029296875, 0.448486328125, -0.315185546875, -0.02117919921875, -0.58984375, -0.3828125, 0.3251953125, 0.68310546875, -0.7353515625, 0.42919921875, -0.08587646484375, -0.055145263671875, -0.65087890625, -0.2890625, -0.2127685546875, -0.9873046875, -0.133056640625, 0.48046875, -0.06817626953125, 0.325439453125, -0.443603515625, -0.52880859375, 0.308349609375, 1.0390625, -0.5087890625, 0.1636962890625, 0.419677734375, -0.162109375, 0.0352783203125, 0.41357421875, 0.004436492919921875, -0.29931640625, -0.61572265625, 0.8486328125, 0.040863037109375, -0.140380859375, -0.1541748046875, 0.74609375, 0.392822265625, 0.78076171875, -0.050567626953125, -0.45947265625, 0.5390625, 0.95751953125, 0.02447509765625, 0.626953125, 0.1881103515625, 0.74609375, 1.0029296875, 0.80078125, 0.7509765625, 0.0357666015625, 0.368896484375, 0.798828125, 0.11883544921875, 0.244873046875, 0.49560546875, 0.70751953125, 0.2496337890625, 0.2100830078125, 0.443115234375, 0.615234375, 0.15771484375, -0.142333984375, -0.01849365234375, -0.06304931640625, -0.478515625, 0.85546875, 0.06951904296875, 0.6552734375, 0.0369873046875, -0.419677734375, 0.32080078125, 1.060546875, -1.0595703125, -0.4560546875, -0.11187744140625, 0.05291748046875, 0.020172119140625, -0.0648193359375, 0.974609375, 0.6455078125, 0.75244140625, 0.4765625, -0.344482421875, -0.165283203125, -0.86962890625, -0.8095703125, -0.78466796875, -0.2496337890625, -0.78515625, -0.057403564453125, -0.07757568359375, -0.9482421875, 0.0235595703125, -0.21875, -0.1915283203125, 0.332275390625, -0.6826171875, 0.78369140625, -0.152587890625, 0.263427734375, -0.6455078125, 0.56689453125, 0.1297607421875, 1.0830078125, -0.79248046875, 0.1805419921875, -0.034515380859375, -0.74072265625, 0.042694091796875, 0.304443359375, 0.33740234375, 0.027923583984375, -0.76708984375, -0.84033203125, -0.4384765625, 0.24267578125, -0.27001953125, 0.360107421875, -0.490966796875, 0.7744140625, 0.60009765625, -0.54443359375, 0.65380859375, 1.048828125, -0.83447265625, 0.57080078125, -0.0266876220703125, -0.468505859375, -0.90625, 1.0478515625, 0.57080078125, 0.5888671875, -0.371337890625, -0.5849609375, -0.44775390625, 0.0023670196533203125, 0.267333984375, -0.68408203125, -0.131103515625, 0.6376953125, 0.000766754150390625, -0.86328125, 0.52197265625, -0.904296875, -0.51513671875, -0.65283203125, -0.460205078125, 1.1103515625, 0.7919921875, 0.06341552734375, 0.099609375, 0.1978759765625, 0.1529541015625, 0.3876953125, 0.53515625, -0.65185546875, 0.234375, 0.845703125, 0.03192138671875, 0.0256195068359375, 0.1331787109375, -0.319091796875, -0.1640625, 0.1439208984375, -0.1116943359375, 0.62841796875, 0.01202392578125, 0.410400390625, 0.408203125, 0.564453125, -0.75439453125, 0.0826416015625, -0.169189453125, 0.6748046875, 0.56005859375, 0.5703125, -0.06353759765625, -0.430908203125, -0.64794921875, -1.3896484375, 0.05438232421875, 0.350341796875, 0.7421875, -0.56298828125, 1.1396484375, 0.13037109375, -0.5927734375, 0.271484375, -0.78076171875, 0.380859375, 0.8857421875, 0.11309814453125, 0.96337890625, -0.76904296875, 0.422119140625, 0.2012939453125, -0.001712799072265625, 0.406494140625, 0.58251953125, 0.19189453125, -0.48828125, -0.64794921875, -0.50927734375, -0.103759765625, -0.27978515625, -0.43896484375, 0.33935546875, -0.6494140625, -0.0638427734375, -0.99169921875, 0.4921875, 0.68310546875, 0.78125, -0.053192138671875, 0.2196044921875, 0.498291015625, 0.272216796875, 0.59326171875, -0.1297607421875, 0.2646484375, -0.61865234375, 0.734375, 0.261474609375, -0.35498046875, -0.7392578125, -0.48388671875, 0.0498046875, 0.181640625, -0.436279296875, -0.085693359375, -1.140625, 0.2330322265625, -0.54833984375, 0.69580078125, -0.57666015625, -0.333740234375, -0.20556640625, 0.410400390625, 0.238525390625, -1.0595703125, 0.439697265625, -0.98876953125, 0.8837890625, 0.54052734375, 0.07513427734375, -0.1959228515625, -0.3525390625, -0.58154296875, -0.42529296875, -0.11993408203125, 0.8203125, -0.240234375, 0.434326171875, -1.28125, 0.58984375, 0.05810546875, -0.49853515625, 0.0933837890625, -0.299560546875, 0.8134765625, -0.22412109375, 0.9619140625, -0.5048828125, -0.75634765625, 0.2274169921875, -1.4326171875, 0.646484375, -0.4208984375, 0.7802734375, 0.0472412109375, -0.1396484375, 0.304443359375, 0.1175537109375, -0.26806640625, 0.2421875, -0.239990234375, 0.4501953125, -0.65087890625, -0.88134765625, 0.57958984375, -0.175048828125, -0.291015625, 0.72509765625, 0.047119140625, -0.494384765625, -0.030426025390625, 0.6845703125, -0.67138671875, 0.276123046875, -0.2183837890625, 0.7548828125, -0.420654296875, -0.6962890625, -0.273681640625, -0.65087890625, 0.71728515625, 0.13916015625, -0.56591796875, -0.1708984375, -1.2080078125, -0.250244140625, 0.059417724609375, -0.5185546875, 0.37646484375, 0.31591796875, -0.18408203125, -0.284423828125, 0.0200347900390625, -0.407958984375, -0.47509765625, -0.62744140625, -0.1546630859375, 0.1060791015625, 0.74365234375, 1.005859375, -0.1461181640625, -0.329833984375, -0.116943359375, 0.04888916015625, 0.2578125, -0.476318359375, -0.230712890625, -0.2587890625, -0.09783935546875, -0.36669921875, 0.07623291015625, 0.226806640625, 0.266845703125, 0.7685546875, -0.0149383544921875, 0.09228515625, 0.340087890625, -0.72509765625, 1.208984375, 0.1275634765625, -0.95751953125, -0.99462890625, 0.6728515625, -0.07025146484375, 0.609375, 0.473876953125, -0.99169921875, -0.65771484375, -0.98291015625, 0.1671142578125, -0.9306640625, -0.17529296875, -1.19921875, -0.77490234375, -0.677734375, 0.374267578125, 0.226318359375, -0.5986328125, 0.4482421875, -0.6884765625, 0.19970703125, -0.82958984375, 0.1781005859375, -0.6162109375, -0.6826171875, 0.1741943359375, 0.740234375, 0.253662109375, 0.34423828125, -0.0107879638671875, -0.396240234375, 0.478515625, -0.308349609375, -0.77294921875, -0.22802734375, -0.2578125, 0.2763671875, -0.00664520263671875, -0.2275390625, -0.7353515625, 0.96875, -0.70654296875, 0.49560546875, 0.130859375, -0.280029296875, -0.359130859375, -0.1827392578125, 0.84716796875, -0.241455078125, 0.07391357421875, 0.056182861328125, 0.384765625, 0.64501953125, -0.4228515625, -0.576171875, -0.75390625, -0.7421875, -0.9990234375, 0.595703125, -0.337646484375, 0.1796875, -0.69775390625, -0.188720703125, 1.3408203125, -0.418701171875, 0.476318359375, 1.0634765625, -0.0061492919921875, 0.203125, -0.347900390625, 0.6142578125, 0.38427734375, -0.365234375, 0.191650390625, -0.032562255859375, -0.63720703125, -0.05938720703125, -0.2476806640625, -0.828125, -0.6435546875, 0.335693359375, 1.376953125, -0.485107421875, 0.6162109375, -0.2210693359375, -1.265625, -0.76904296875, 0.448974609375, 0.2978515625, 0.26220703125, 0.69677734375, -0.1363525390625, 0.039642333984375, -0.0909423828125, -0.316650390625, -0.406005859375, -0.89501953125, 1.18359375, -0.63916015625, -0.43505859375, 0.955078125, 0.99462890625, -1.1650390625, -0.94189453125, 0.1793212890625, -0.041534423828125, -0.48828125, -0.343505859375, -0.0716552734375, 0.76220703125, -0.70556640625, 0.1468505859375, 0.259521484375, 0.0030612945556640625, 0.1739501953125, 0.056060791015625, 0.52490234375, -0.2069091796875, 0.6669921875, 0.61962890625, -0.56103515625, -0.45751953125, -1.0126953125, -0.30078125, -0.375, -0.060882568359375, 0.8291015625, -0.0071563720703125, 0.1285400390625, 0.450927734375, 0.12005615234375, 0.7294921875, -0.365966796875, -0.37255859375, 0.24462890625, -0.6328125, -0.6015625, 0.2130126953125, 0.30078125, -0.0670166015625, 0.361083984375, -0.65380859375, 0.08154296875, 0.25634765625, 0.465576171875, -0.3046875, -0.9521484375, -0.2166748046875, -1.4580078125, -0.472900390625, -0.7041015625, -0.7919921875, -0.301513671875, 0.583984375, 0.10308837890625, -0.66943359375, 0.0806884765625, 0.28271484375, -0.83154296875, 0.53125, -0.314453125, 0.2213134765625, -0.4013671875, -0.60986328125, -0.9755859375, -0.16552734375, -0.397705078125, -0.22802734375, -1.142578125, 0.71728515625, 0.0982666015625, 0.400634765625, -0.23876953125, 0.8505859375, -0.3076171875, -0.87939453125, 0.2205810546875, 0.10284423828125, -0.012847900390625, 1.1923828125, 0.465087890625, 0.2318115234375, -0.01465606689453125, -0.0670166015625, -0.2261962890625, -0.5, 0.50390625, 0.393310546875, -0.489013671875, -0.23095703125, -0.0650634765625, 0.2802734375, -0.87548828125, 0.3681640625, -0.1939697265625, 0.0576171875, 0.08642578125, -0.11541748046875, 0.1566162109375, 1.388671875, -0.1444091796875, 0.113525390625, -0.0159912109375, 0.22705078125, 0.202392578125, 0.28173828125, 0.0309295654296875, 0.449951171875, -0.1142578125, -0.4775390625, -0.388671875, 0.6142578125, 0.08935546875, 0.07647705078125, -0.443603515625, -0.74267578125, -0.677734375, -0.339599609375, 0.11871337890625, 0.355224609375, 0.5537109375, -0.4423828125, -0.10064697265625, -0.10992431640625, -0.470458984375, -0.004665374755859375, -1.2197265625, -1.0146484375, 0.55859375, 0.0036182403564453125, -0.62060546875, -0.12420654296875, -0.31005859375, -0.4541015625, 0.0250244140625, 0.625, -0.409423828125, 0.6103515625, 0.04840087890625, 0.358642578125, -0.11358642578125, -0.150634765625, 0.1263427734375, 0.6552734375, -0.7275390625, -0.685546875, 0.1510009765625, 0.84326171875, 0.276123046875, -0.345947265625, -0.1474609375, 0.5224609375, -0.22216796875, 0.35693359375, -0.63623046875, -0.0226898193359375, -0.05029296875, 0.99462890625, -0.76025390625, 0.1407470703125, -0.1900634765625, 0.1776123046875, 0.042144775390625, -0.48583984375, -0.580078125, 1.076171875, 0.75927734375, -0.161865234375, 0.67138671875, 0.10198974609375, 0.206787109375, -0.097412109375, -0.09930419921875, 0.18994140625, 0.6015625, 0.77734375, 0.54248046875, -0.2088623046875, 0.22802734375, 0.8798828125, -0.21240234375, -0.429443359375, 0.42333984375, 0.1004638671875, -0.1148681640625, -0.1368408203125, -0.11175537109375, -0.2308349609375, -0.308837890625, -0.810546875, 0.80078125, -0.1739501953125, 0.293701171875, -0.078125, -0.822265625, 0.8837890625, -0.28466796875, -0.35302734375, 0.17724609375, -0.6318359375, 0.1927490234375, 0.56982421875, -0.359619140625, -0.474365234375, 0.60400390625, 0.6044921875, 0.625, 0.65283203125, 0.08428955078125, 0.481689453125, -0.5712890625, 0.1944580078125, -0.1900634765625, -0.116943359375, -0.240478515625, -0.673828125, -1.1015625, 0.432861328125, -0.650390625, -0.541015625, 0.6845703125, -0.59912109375, 0.221923828125, -0.271240234375, 0.61376953125, -0.38720703125, 0.05352783203125, 0.5966796875, -0.25048828125, -0.8388671875, 0.75390625, -0.2568359375, 0.1431884765625, -0.2210693359375, 1.255859375, -0.197998046875, 1.3759765625, 0.61083984375, -0.3212890625, 0.282958984375, 0.349853515625, -0.355224609375, -0.62548828125, -0.73046875, -0.68603515625, -0.06695556640625, -0.53369140625, -0.39990234375, 0.157470703125, 0.375244140625, -0.0252838134765625, -0.849609375, -0.11346435546875, 0.324951171875, -0.7197265625, 0.431640625, 0.189697265625, -0.07513427734375, 0.099365234375, -0.08343505859375, -0.1622314453125, -0.2283935546875, 0.1827392578125, -0.869140625, 0.41015625, -0.9677734375, -0.367431640625, -0.62939453125, -0.61962890625, -0.1571044921875, 0.034912109375, -0.292236328125, -0.88330078125, 0.25634765625, 0.401123046875, 0.1070556640625, 0.487060546875, -0.178955078125, 0.264892578125, 1.125, 1.0673828125, 0.1405029296875, 0.671875, 0.356689453125, -0.016143798828125, 0.038665771484375, -0.28564453125, 0.486572265625, 0.06597900390625, 0.50439453125, -0.30126953125, 0.324951171875, -0.75244140625, -1.4296875, 0.3330078125, 0.6279296875, 0.368408203125, -0.77099609375, -1.076171875, -0.127197265625, -1.2421875, -0.24658203125, -0.6376953125, 1.0390625, -0.5791015625, -0.01422882080078125, -0.0899658203125, -1.2724609375, 4.26953125, 1.0068359375, 0.8935546875, 0.6318359375, 0.1463623046875, 0.9345703125, 0.135009765625, -0.4658203125, 0.0928955078125, -0.252197265625, 0.7744140625, -0.5087890625, -0.09942626953125, 0.75244140625, 0.22607421875, 0.48583984375, -0.35498046875, 0.50634765625, -0.1873779296875, -0.8603515625, -0.8623046875, 0.460693359375, -0.112060546875, 0.376708984375, 0.0272674560546875, 0.1671142578125, 0.705078125, -1.0234375, 0.176513671875, -0.69580078125, 0.269287109375, -0.38916015625, 1.1181640625, 0.06591796875, 0.12841796875, 0.47314453125, -0.12548828125, -0.409423828125, 0.2294921875, 0.06121826171875, -0.1861572265625, -0.050933837890625, 0.381103515625, -0.9990234375, -0.01397705078125, 0.48681640625, -0.7431640625, 0.38671875, -0.063720703125, -1.0361328125, 0.8603515625, -0.1737060546875, 0.34423828125, -1.021484375, -0.3486328125, -0.1612548828125, 0.438232421875, -0.203369140625, -0.55810546875, 0.396240234375, 0.53076171875, 0.38037109375, 0.35986328125, 0.560546875, -1.005859375, 0.2073974609375, -0.1754150390625, 0.3896484375, -0.5498046875, 0.2174072265625, -0.40087890625, -0.37744140625, -0.26416015625, -0.52001953125, 0.603515625, -0.07196044921875, -0.0828857421875, 0.464599609375, 0.544921875, -0.650390625, 0.17529296875, -0.156982421875, -0.19384765625, -0.5654296875, 0.74560546875, 1.2353515625, -0.5546875, -0.4560546875, -0.34228515625, 0.49169921875, 0.455810546875, 0.417724609375, -0.005779266357421875, -0.79736328125, -0.028411865234375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Tags: combinatorics, greedy, implementation, math Correct Solution: ``` s = input() ans, cnt = 0, 0 for i in range(1, len(s) + 1): if s[-i] == 'a': ans = (2 * ans + i - 1 - cnt) % (10 ** 9 + 7) cnt += 1 print(ans) ```
105,794
[ 0.3642578125, -0.126953125, 0.09039306640625, 0.061553955078125, -0.765625, -0.646484375, 0.06982421875, -0.157958984375, 0.276123046875, 0.87548828125, 0.6943359375, -0.327880859375, -0.2257080078125, -0.86572265625, -0.548828125, -0.047515869140625, -0.499755859375, -0.70751953125, -0.359375, -0.35693359375, 0.12310791015625, -0.2127685546875, -1.1669921875, -0.10467529296875, -0.2457275390625, 1.05078125, 0.6962890625, -0.08636474609375, 0.9814453125, 1.271484375, -0.211181640625, -0.1593017578125, 0.484130859375, -1.0634765625, -0.3828125, -0.509765625, 0.52978515625, -0.90673828125, -0.17236328125, -0.315185546875, 0.25732421875, -0.61328125, 0.48291015625, -0.78564453125, -1.455078125, 0.030303955078125, -0.109619140625, -0.43310546875, 0.0005826950073242188, -0.58935546875, -0.1075439453125, -0.367431640625, 0.4423828125, 0.043914794921875, -0.01366424560546875, 0.135009765625, 0.313720703125, -0.381591796875, -0.8408203125, 0.166015625, 0.4833984375, 0.0288848876953125, 0.05853271484375, -0.91748046875, -0.052734375, 0.1766357421875, -0.341796875, 0.035369873046875, -0.16943359375, -1.03515625, -0.046142578125, 0.28857421875, -0.40771484375, -0.5908203125, -0.1529541015625, 0.113037109375, 0.3681640625, -0.26513671875, -0.6572265625, 1.115234375, -0.24462890625, 0.6787109375, 0.216064453125, 0.27099609375, -0.251708984375, -0.5, 0.00274658203125, 0.3232421875, -0.059844970703125, -0.10748291015625, -0.36767578125, 0.70947265625, -0.360595703125, -0.05511474609375, 0.318359375, 0.56494140625, -0.401611328125, 0.1597900390625, 0.615234375, 0.306396484375, 0.8408203125, 1.1015625, -0.580078125, 0.78369140625, -0.5712890625, -0.047515869140625, 0.0701904296875, -0.12347412109375, -0.33447265625, 0.06390380859375, -0.304443359375, -0.2509765625, 0.63818359375, 0.3505859375, -0.5478515625, 1.126953125, 0.204833984375, 0.4013671875, -0.623046875, 0.63037109375, 0.411376953125, 0.19970703125, 0.7138671875, -0.2310791015625, -0.2215576171875, -0.068603515625, -0.60302734375, 1.140625, -0.79443359375, -0.1904296875, 0.1885986328125, 0.1513671875, 0.07373046875, 0.326171875, -0.2381591796875, 0.6875, -0.0640869140625, 0.2408447265625, 0.72607421875, -0.445068359375, 0.62646484375, -0.3544921875, -0.11871337890625, 1.75, 0.1927490234375, -0.091552734375, 0.8583984375, 0.394287109375, -0.84521484375, 0.302490234375, -1.095703125, 0.82177734375, 0.3388671875, 0.369873046875, -0.0531005859375, 0.1629638671875, -0.327392578125, 0.455810546875, 0.09539794921875, -0.1986083984375, -0.57373046875, -0.04193115234375, -0.373779296875, 1.0869140625, -0.47998046875, 0.92529296875, -0.294921875, -0.1829833984375, -0.1458740234375, -0.499755859375, 0.1658935546875, -0.2939453125, -0.20263671875, 0.9287109375, 0.342529296875, 1.056640625, 1.2060546875, -0.27392578125, 0.481689453125, 0.298828125, -0.405517578125, 0.149658203125, 0.3173828125, 0.9228515625, 0.334716796875, 0.433349609375, -0.313720703125, -0.0277862548828125, -0.6455078125, -0.427734375, 0.2744140625, 0.65087890625, -0.7958984375, 0.4677734375, -0.1673583984375, -0.052398681640625, -0.6923828125, -0.2626953125, -0.1669921875, -0.9677734375, -0.1796875, 0.497314453125, -0.073974609375, 0.29736328125, -0.5166015625, -0.5595703125, 0.396240234375, 1.12109375, -0.448974609375, 0.1268310546875, 0.387939453125, -0.10205078125, -0.07440185546875, 0.398681640625, 0.034271240234375, -0.2403564453125, -0.58837890625, 0.7529296875, 0.0186004638671875, -0.16064453125, -0.187255859375, 0.64697265625, 0.432373046875, 0.78515625, -0.033660888671875, -0.51611328125, 0.60595703125, 0.990234375, -0.022308349609375, 0.6064453125, 0.2032470703125, 0.7783203125, 0.97900390625, 0.88232421875, 0.7177734375, 0.2174072265625, 0.3564453125, 0.82275390625, 0.12109375, 0.247802734375, 0.5439453125, 0.677734375, 0.287841796875, 0.305908203125, 0.422607421875, 0.591796875, 0.2235107421875, -0.10272216796875, -0.0205078125, -0.055633544921875, -0.385009765625, 0.9228515625, 0.058563232421875, 0.6787109375, -0.004367828369140625, -0.330810546875, 0.1890869140625, 1.080078125, -1.0234375, -0.448486328125, -0.2054443359375, 0.0212860107421875, -0.0270843505859375, 0.00879669189453125, 0.89404296875, 0.65185546875, 0.74951171875, 0.432861328125, -0.32177734375, -0.27587890625, -0.75341796875, -0.79248046875, -0.81640625, -0.2413330078125, -0.728515625, -0.1326904296875, -0.08868408203125, -1.0234375, 0.0208587646484375, -0.249267578125, -0.2471923828125, 0.3310546875, -0.61767578125, 0.83935546875, -0.010833740234375, 0.291015625, -0.59765625, 0.56201171875, 0.057769775390625, 1.1103515625, -0.80859375, 0.0043487548828125, -0.017669677734375, -0.7451171875, 0.0186767578125, 0.41064453125, 0.302490234375, 0.0121002197265625, -0.77783203125, -0.88427734375, -0.498291015625, 0.315673828125, -0.348876953125, 0.399169921875, -0.450439453125, 0.67041015625, 0.546875, -0.556640625, 0.63671875, 1.0595703125, -0.90673828125, 0.58984375, 0.052398681640625, -0.4560546875, -0.830078125, 1.1015625, 0.5908203125, 0.546875, -0.3759765625, -0.6572265625, -0.376708984375, -0.0272369384765625, 0.2467041015625, -0.77783203125, -0.1951904296875, 0.64501953125, -0.002197265625, -0.92138671875, 0.56640625, -0.9892578125, -0.63037109375, -0.646484375, -0.363037109375, 1.1376953125, 0.86328125, 0.08251953125, 0.09283447265625, 0.158447265625, 0.09820556640625, 0.46923828125, 0.5546875, -0.62548828125, 0.2440185546875, 0.8837890625, 0.0614013671875, -0.027618408203125, 0.145751953125, -0.343505859375, -0.21630859375, 0.15966796875, 0.1334228515625, 0.66015625, 0.028167724609375, 0.4267578125, 0.36376953125, 0.49462890625, -0.72509765625, 0.0635986328125, -0.222900390625, 0.70703125, 0.54931640625, 0.64306640625, -0.0404052734375, -0.40771484375, -0.5810546875, -1.3671875, 0.0640869140625, 0.2095947265625, 0.7626953125, -0.58984375, 1.1806640625, 0.2158203125, -0.60400390625, 0.26513671875, -0.72021484375, 0.300048828125, 0.8779296875, 0.157958984375, 0.97998046875, -0.7568359375, 0.427490234375, 0.1329345703125, 0.075927734375, 0.48486328125, 0.673828125, 0.2919921875, -0.57177734375, -0.7431640625, -0.50048828125, -0.138671875, -0.27001953125, -0.55908203125, 0.299560546875, -0.464599609375, -0.052703857421875, -0.958984375, 0.50048828125, 0.74755859375, 0.8271484375, 0.0236358642578125, 0.2257080078125, 0.386962890625, 0.3583984375, 0.6640625, -0.1368408203125, 0.2252197265625, -0.61572265625, 0.7919921875, 0.23974609375, -0.323974609375, -0.7080078125, -0.353515625, 0.10577392578125, 0.165283203125, -0.51953125, -0.1363525390625, -1.1298828125, 0.2159423828125, -0.475830078125, 0.6318359375, -0.681640625, -0.302001953125, -0.2152099609375, 0.400634765625, 0.23046875, -1.056640625, 0.55908203125, -0.99560546875, 0.84716796875, 0.59228515625, 0.09893798828125, -0.0997314453125, -0.377197265625, -0.73681640625, -0.452880859375, -0.1484375, 0.8330078125, -0.2344970703125, 0.392333984375, -1.314453125, 0.5869140625, 0.07110595703125, -0.476806640625, 0.181640625, -0.27783203125, 0.87158203125, -0.251953125, 0.828125, -0.490478515625, -0.7490234375, 0.134521484375, -1.369140625, 0.70849609375, -0.44921875, 0.90380859375, 0.103271484375, -0.1441650390625, 0.263427734375, 0.1807861328125, -0.22314453125, 0.27587890625, -0.185302734375, 0.446533203125, -0.79443359375, -0.94140625, 0.6298828125, -0.201904296875, -0.295654296875, 0.759765625, -0.0255126953125, -0.53857421875, -0.051513671875, 0.60693359375, -0.56005859375, 0.20361328125, -0.08404541015625, 0.68310546875, -0.40673828125, -0.75341796875, -0.11492919921875, -0.56005859375, 0.7431640625, 0.00865936279296875, -0.6396484375, -0.2099609375, -1.3388671875, -0.2218017578125, 0.1241455078125, -0.3603515625, 0.298828125, 0.346923828125, -0.0958251953125, -0.287353515625, -0.077392578125, -0.454345703125, -0.463623046875, -0.70654296875, -0.1934814453125, 0.1285400390625, 0.712890625, 1.0107421875, -0.0426025390625, -0.31884765625, -0.039337158203125, 0.085693359375, 0.1705322265625, -0.52978515625, -0.201416015625, -0.261962890625, -0.069091796875, -0.373291015625, 0.182861328125, 0.1937255859375, 0.333984375, 0.90380859375, -0.01446533203125, 0.10467529296875, 0.378173828125, -0.65625, 1.2744140625, 0.08416748046875, -0.9189453125, -0.96484375, 0.5830078125, -0.10430908203125, 0.62255859375, 0.53955078125, -1.072265625, -0.61767578125, -0.94580078125, 0.2242431640625, -0.94482421875, -0.2822265625, -1.23046875, -0.7568359375, -0.67333984375, 0.3779296875, 0.1500244140625, -0.492431640625, 0.482666015625, -0.783203125, 0.273193359375, -0.8369140625, 0.108154296875, -0.59423828125, -0.763671875, 0.223388671875, 0.8798828125, 0.2398681640625, 0.329833984375, 0.0024929046630859375, -0.423828125, 0.48779296875, -0.2235107421875, -0.7646484375, -0.2337646484375, -0.301513671875, 0.242919921875, 0.0005812644958496094, -0.1898193359375, -0.6279296875, 0.9775390625, -0.64111328125, 0.443603515625, 0.0972900390625, -0.27783203125, -0.300048828125, -0.26904296875, 0.87353515625, -0.271728515625, 0.03802490234375, -0.0029430389404296875, 0.378662109375, 0.734375, -0.469482421875, -0.51611328125, -0.78857421875, -0.6904296875, -0.98583984375, 0.6220703125, -0.2352294921875, 0.2060546875, -0.82373046875, -0.30078125, 1.361328125, -0.52978515625, 0.442626953125, 0.99755859375, -0.017822265625, 0.2398681640625, -0.278564453125, 0.63623046875, 0.402587890625, -0.30224609375, 0.1824951171875, -0.0458984375, -0.68408203125, -0.04595947265625, -0.1280517578125, -0.8212890625, -0.70263671875, 0.370361328125, 1.3115234375, -0.4580078125, 0.5869140625, -0.324951171875, -1.326171875, -0.708984375, 0.58056640625, 0.331298828125, 0.278564453125, 0.69775390625, -0.06475830078125, 0.0767822265625, -0.103759765625, -0.444091796875, -0.483154296875, -0.7724609375, 1.30859375, -0.64794921875, -0.482666015625, 0.89794921875, 0.955078125, -1.1611328125, -0.958984375, 0.2401123046875, -0.0443115234375, -0.43896484375, -0.491455078125, -0.008758544921875, 0.79443359375, -0.60205078125, 0.146484375, 0.297119140625, -0.0775146484375, 0.1695556640625, 0.0469970703125, 0.59521484375, -0.23095703125, 0.734375, 0.60009765625, -0.51513671875, -0.41162109375, -0.9248046875, -0.3212890625, -0.317626953125, -0.07147216796875, 0.7919921875, -0.05181884765625, 0.1392822265625, 0.55224609375, 0.07232666015625, 0.75390625, -0.43798828125, -0.347412109375, 0.1866455078125, -0.58056640625, -0.537109375, 0.139892578125, 0.4169921875, -0.018951416015625, 0.350830078125, -0.66845703125, -0.061065673828125, 0.27001953125, 0.513671875, -0.30908203125, -0.89306640625, -0.1768798828125, -1.431640625, -0.5361328125, -0.71484375, -0.9296875, -0.16943359375, 0.360107421875, 0.033233642578125, -0.6181640625, 0.005764007568359375, 0.2685546875, -0.708984375, 0.61865234375, -0.324951171875, 0.251953125, -0.3349609375, -0.6376953125, -1.0322265625, -0.1483154296875, -0.442626953125, -0.30810546875, -1.0810546875, 0.74267578125, 0.154296875, 0.32177734375, -0.256591796875, 0.900390625, -0.325439453125, -0.87646484375, 0.266357421875, 0.1588134765625, -0.0231781005859375, 1.283203125, 0.46337890625, 0.1475830078125, 0.06719970703125, -0.095947265625, -0.18994140625, -0.48583984375, 0.5712890625, 0.392578125, -0.469970703125, -0.1640625, -0.0814208984375, 0.2861328125, -0.8505859375, 0.317626953125, -0.2210693359375, 0.0726318359375, 0.09210205078125, -0.0673828125, 0.269287109375, 1.36328125, -0.25, 0.1282958984375, -0.017608642578125, 0.1868896484375, 0.12298583984375, 0.3369140625, -0.006267547607421875, 0.48583984375, -0.155029296875, -0.456298828125, -0.298828125, 0.491455078125, 0.10198974609375, 0.0244598388671875, -0.323486328125, -0.87939453125, -0.685546875, -0.32958984375, 0.04327392578125, 0.402099609375, 0.61767578125, -0.51220703125, -0.048370361328125, 0.048187255859375, -0.63427734375, -0.010162353515625, -1.07421875, -0.98583984375, 0.5244140625, -0.00044155120849609375, -0.708984375, -0.1607666015625, -0.2467041015625, -0.343505859375, -0.112548828125, 0.62939453125, -0.44091796875, 0.494384765625, 0.027496337890625, 0.322998046875, -0.1031494140625, -0.21435546875, 0.09271240234375, 0.72705078125, -0.66162109375, -0.66455078125, 0.09716796875, 0.853515625, 0.2242431640625, -0.402587890625, -0.138916015625, 0.42822265625, -0.1610107421875, 0.333984375, -0.591796875, -0.016204833984375, -0.006015777587890625, 0.9775390625, -0.775390625, 0.09356689453125, -0.2135009765625, 0.1995849609375, -0.05755615234375, -0.62109375, -0.55078125, 1.0947265625, 0.640625, -0.1754150390625, 0.6943359375, 0.062469482421875, 0.2822265625, -0.01003265380859375, -0.01424407958984375, 0.279541015625, 0.52294921875, 0.779296875, 0.59765625, -0.10577392578125, 0.27880859375, 0.900390625, -0.290283203125, -0.42529296875, 0.3896484375, -0.029388427734375, 0.050994873046875, -0.1480712890625, 0.0017881393432617188, -0.2705078125, -0.250732421875, -0.83544921875, 0.84326171875, -0.239013671875, 0.268310546875, -0.0782470703125, -0.80859375, 0.912109375, -0.3505859375, -0.3203125, 0.267333984375, -0.69970703125, 0.2025146484375, 0.556640625, -0.345703125, -0.345947265625, 0.68505859375, 0.578125, 0.63525390625, 0.74658203125, 0.1824951171875, 0.476318359375, -0.5234375, 0.1519775390625, -0.201904296875, -0.1552734375, -0.187744140625, -0.6259765625, -1.130859375, 0.458740234375, -0.60400390625, -0.5908203125, 0.771484375, -0.64501953125, 0.25, -0.284423828125, 0.78857421875, -0.376220703125, 0.11993408203125, 0.5859375, -0.299072265625, -0.8515625, 0.81884765625, -0.21923828125, 0.26953125, -0.2451171875, 1.1953125, -0.18505859375, 1.4375, 0.63134765625, -0.244873046875, 0.2166748046875, 0.361572265625, -0.4150390625, -0.6728515625, -0.6201171875, -0.5703125, -0.1055908203125, -0.4990234375, -0.45654296875, 0.1881103515625, 0.39208984375, -0.0062103271484375, -0.7998046875, -0.2269287109375, 0.372314453125, -0.77001953125, 0.438232421875, 0.302734375, 0.027984619140625, 0.07843017578125, -0.1346435546875, -0.10626220703125, -0.201416015625, 0.1776123046875, -0.78271484375, 0.45166015625, -0.96728515625, -0.2401123046875, -0.75537109375, -0.69580078125, -0.201171875, 0.072998046875, -0.323974609375, -0.87548828125, 0.26416015625, 0.302734375, 0.177001953125, 0.46435546875, -0.2056884765625, 0.275146484375, 1.0556640625, 1.0458984375, 0.06329345703125, 0.7900390625, 0.298095703125, -0.0816650390625, 0.0025482177734375, -0.290771484375, 0.434326171875, -0.004955291748046875, 0.5458984375, -0.349853515625, 0.2437744140625, -0.7509765625, -1.4765625, 0.463623046875, 0.5234375, 0.377685546875, -0.76904296875, -1.0986328125, -0.1209716796875, -1.2880859375, -0.19580078125, -0.74755859375, 1.04296875, -0.5791015625, 0.00420379638671875, -0.16650390625, -1.25390625, 4.234375, 1.029296875, 0.87841796875, 0.658203125, 0.1806640625, 0.93359375, 0.0482177734375, -0.45166015625, -0.053375244140625, -0.1805419921875, 0.81298828125, -0.56884765625, -0.10760498046875, 0.77294921875, 0.2783203125, 0.5439453125, -0.439208984375, 0.45947265625, -0.21337890625, -0.98046875, -0.90478515625, 0.50048828125, -0.126708984375, 0.46533203125, 0.060821533203125, 0.10858154296875, 0.720703125, -1.0654296875, 0.1610107421875, -0.720703125, 0.185546875, -0.406005859375, 1.1171875, 0.10833740234375, 0.091064453125, 0.48388671875, -0.07647705078125, -0.454345703125, 0.190185546875, 0.056396484375, -0.1796875, -0.0872802734375, 0.470458984375, -0.904296875, -0.030731201171875, 0.46728515625, -0.705078125, 0.402587890625, -0.1795654296875, -1.09375, 0.89306640625, -0.208984375, 0.351318359375, -0.93310546875, -0.33154296875, -0.13623046875, 0.368408203125, -0.0904541015625, -0.41845703125, 0.42578125, 0.51904296875, 0.5048828125, 0.2900390625, 0.4951171875, -1.0341796875, 0.2017822265625, -0.1544189453125, 0.396240234375, -0.57177734375, 0.11614990234375, -0.426513671875, -0.48193359375, -0.271240234375, -0.51123046875, 0.58056640625, 0.0093231201171875, -0.0235443115234375, 0.448486328125, 0.454833984375, -0.681640625, 0.08050537109375, -0.134765625, -0.1307373046875, -0.6357421875, 0.7412109375, 1.3125, -0.55615234375, -0.335205078125, -0.3876953125, 0.3974609375, 0.473388671875, 0.45654296875, -0.1160888671875, -0.77294921875, -0.06976318359375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Tags: combinatorics, greedy, implementation, math Correct Solution: ``` s = input()[::-1] a, b = 0, 0 mod = 10 ** 9 + 7 for i in s: if i == 'b': b += 1 else: a += b a %= mod b <<= 1 b %= mod print(a) ```
105,795
[ 0.388427734375, -0.1572265625, 0.039215087890625, 0.0797119140625, -0.77392578125, -0.6650390625, 0.047821044921875, -0.14599609375, 0.264404296875, 0.875, 0.6494140625, -0.310302734375, -0.1531982421875, -0.81005859375, -0.4853515625, 0.004482269287109375, -0.451904296875, -0.7646484375, -0.35400390625, -0.33935546875, 0.0704345703125, -0.1781005859375, -1.15625, -0.05987548828125, -0.2418212890625, 1.037109375, 0.7216796875, -0.04638671875, 0.98583984375, 1.267578125, -0.1824951171875, -0.1285400390625, 0.45654296875, -1.0869140625, -0.36962890625, -0.46630859375, 0.5859375, -0.87890625, -0.166748046875, -0.35205078125, 0.260986328125, -0.6240234375, 0.55126953125, -0.7783203125, -1.462890625, 0.051788330078125, -0.128662109375, -0.50634765625, 0.00539398193359375, -0.57421875, -0.109619140625, -0.39501953125, 0.381103515625, 0.048248291015625, 0.0162353515625, 0.165771484375, 0.265869140625, -0.3515625, -0.8095703125, 0.12091064453125, 0.430908203125, 0.03533935546875, 0.07562255859375, -0.90625, -0.13330078125, 0.2020263671875, -0.29248046875, 0.0389404296875, -0.1910400390625, -1.033203125, -0.01222991943359375, 0.256103515625, -0.351806640625, -0.513671875, -0.1466064453125, 0.0980224609375, 0.36669921875, -0.26123046875, -0.6494140625, 1.140625, -0.2333984375, 0.71044921875, 0.22705078125, 0.258544921875, -0.264892578125, -0.465576171875, 0.0282745361328125, 0.312255859375, -0.04302978515625, -0.14501953125, -0.353271484375, 0.7490234375, -0.32763671875, -0.01267242431640625, 0.3232421875, 0.611328125, -0.35009765625, 0.20068359375, 0.56396484375, 0.3388671875, 0.84423828125, 1.0419921875, -0.56982421875, 0.794921875, -0.5517578125, -0.052093505859375, 0.06768798828125, -0.0859375, -0.31005859375, 0.047607421875, -0.3232421875, -0.286376953125, 0.60546875, 0.3642578125, -0.4990234375, 1.0859375, 0.181640625, 0.3935546875, -0.6376953125, 0.65185546875, 0.425537109375, 0.1756591796875, 0.6767578125, -0.212890625, -0.218994140625, -0.09771728515625, -0.59765625, 1.181640625, -0.75341796875, -0.234130859375, 0.179931640625, 0.153564453125, 0.07049560546875, 0.33935546875, -0.2261962890625, 0.7041015625, -0.07220458984375, 0.26171875, 0.7587890625, -0.419921875, 0.60009765625, -0.3525390625, -0.12213134765625, 1.73046875, 0.1865234375, -0.10003662109375, 0.876953125, 0.41650390625, -0.904296875, 0.291259765625, -1.0625, 0.771484375, 0.349609375, 0.375, -0.057952880859375, 0.1378173828125, -0.33154296875, 0.515625, 0.088134765625, -0.22216796875, -0.58056640625, -0.00563812255859375, -0.37744140625, 1.0615234375, -0.51611328125, 0.89404296875, -0.2418212890625, -0.26220703125, -0.1392822265625, -0.44775390625, 0.1651611328125, -0.2467041015625, -0.28125, 0.8798828125, 0.3505859375, 1.0146484375, 1.208984375, -0.265625, 0.48291015625, 0.272216796875, -0.41943359375, 0.1697998046875, 0.274658203125, 0.95361328125, 0.347900390625, 0.447021484375, -0.34326171875, 0.0132598876953125, -0.677734375, -0.455810546875, 0.309814453125, 0.6728515625, -0.81494140625, 0.461181640625, -0.07928466796875, -0.048126220703125, -0.6787109375, -0.26318359375, -0.1881103515625, -1.0078125, -0.2188720703125, 0.50634765625, -0.0628662109375, 0.299560546875, -0.44580078125, -0.572265625, 0.339599609375, 1.1171875, -0.5126953125, 0.07379150390625, 0.43603515625, -0.1490478515625, -0.033416748046875, 0.406494140625, 0.061431884765625, -0.251220703125, -0.5927734375, 0.7451171875, -0.0523681640625, -0.11981201171875, -0.2059326171875, 0.62353515625, 0.48974609375, 0.74755859375, -0.127685546875, -0.53515625, 0.55712890625, 0.97998046875, -0.07391357421875, 0.5849609375, 0.2108154296875, 0.76806640625, 0.99365234375, 0.8759765625, 0.69677734375, 0.200439453125, 0.36865234375, 0.76513671875, 0.1094970703125, 0.259033203125, 0.5400390625, 0.67626953125, 0.213623046875, 0.250732421875, 0.451416015625, 0.58447265625, 0.184326171875, -0.10064697265625, 0.01149749755859375, -0.0022945404052734375, -0.396484375, 0.8642578125, 0.0860595703125, 0.68896484375, 0.025787353515625, -0.360595703125, 0.118408203125, 1.087890625, -1.04296875, -0.4150390625, -0.1348876953125, 0.03875732421875, -0.0265045166015625, -0.004673004150390625, 0.93017578125, 0.61328125, 0.74462890625, 0.36865234375, -0.2802734375, -0.268798828125, -0.7646484375, -0.802734375, -0.84228515625, -0.2353515625, -0.71826171875, -0.103515625, -0.10614013671875, -0.98828125, -0.01280975341796875, -0.2322998046875, -0.1165771484375, 0.34228515625, -0.576171875, 0.7890625, -0.024993896484375, 0.2705078125, -0.576171875, 0.630859375, 0.1173095703125, 1.0791015625, -0.8583984375, 0.01406097412109375, -0.055389404296875, -0.6826171875, 0.0523681640625, 0.37060546875, 0.302734375, -0.0041656494140625, -0.78173828125, -0.87451171875, -0.513671875, 0.277587890625, -0.330810546875, 0.331787109375, -0.44189453125, 0.68994140625, 0.6064453125, -0.60986328125, 0.66162109375, 1.1015625, -0.92529296875, 0.634765625, 0.026123046875, -0.478515625, -0.81494140625, 1.123046875, 0.5810546875, 0.53857421875, -0.373779296875, -0.654296875, -0.37255859375, -0.00865936279296875, 0.2086181640625, -0.7626953125, -0.1898193359375, 0.65673828125, -0.0214080810546875, -0.89794921875, 0.59765625, -0.97998046875, -0.60888671875, -0.69970703125, -0.393798828125, 1.1142578125, 0.8671875, 0.113525390625, 0.08123779296875, 0.089599609375, 0.1328125, 0.4609375, 0.51025390625, -0.6474609375, 0.25390625, 0.88623046875, 0.0167999267578125, -0.0166168212890625, 0.1629638671875, -0.360595703125, -0.2125244140625, 0.144287109375, 0.1806640625, 0.69873046875, 0.018463134765625, 0.433349609375, 0.3134765625, 0.54833984375, -0.765625, 0.05181884765625, -0.2198486328125, 0.64013671875, 0.5146484375, 0.6005859375, -0.0904541015625, -0.3828125, -0.63525390625, -1.41015625, 0.0809326171875, 0.2607421875, 0.7666015625, -0.5712890625, 1.2099609375, 0.197265625, -0.60205078125, 0.26171875, -0.689453125, 0.312255859375, 0.9013671875, 0.1539306640625, 0.9443359375, -0.77099609375, 0.452880859375, 0.1832275390625, 0.02142333984375, 0.46728515625, 0.625, 0.321533203125, -0.59228515625, -0.72705078125, -0.52783203125, -0.09844970703125, -0.269287109375, -0.53173828125, 0.3193359375, -0.492919921875, -0.03375244140625, -1.009765625, 0.498779296875, 0.72509765625, 0.78955078125, 0.0188751220703125, 0.255615234375, 0.37744140625, 0.28857421875, 0.6162109375, -0.1461181640625, 0.21533203125, -0.5986328125, 0.78662109375, 0.2108154296875, -0.33349609375, -0.73828125, -0.366943359375, 0.04278564453125, 0.1507568359375, -0.4931640625, -0.1044921875, -1.1435546875, 0.2227783203125, -0.435546875, 0.66259765625, -0.6181640625, -0.27490234375, -0.1934814453125, 0.353515625, 0.2069091796875, -1.0595703125, 0.53564453125, -1.0126953125, 0.80712890625, 0.63916015625, 0.07403564453125, -0.181640625, -0.364501953125, -0.74951171875, -0.451904296875, -0.11614990234375, 0.84228515625, -0.2178955078125, 0.39208984375, -1.3173828125, 0.6298828125, 0.068603515625, -0.49365234375, 0.2393798828125, -0.2763671875, 0.8603515625, -0.208740234375, 0.8603515625, -0.487548828125, -0.77685546875, 0.10296630859375, -1.359375, 0.681640625, -0.449951171875, 0.86767578125, 0.0836181640625, -0.101806640625, 0.304931640625, 0.173583984375, -0.2034912109375, 0.307373046875, -0.1251220703125, 0.477783203125, -0.8134765625, -0.93212890625, 0.64208984375, -0.189208984375, -0.334228515625, 0.74951171875, -0.0186309814453125, -0.529296875, -0.0330810546875, 0.58837890625, -0.556640625, 0.1763916015625, -0.088623046875, 0.71630859375, -0.41455078125, -0.68505859375, -0.1851806640625, -0.56591796875, 0.73779296875, 0.048095703125, -0.61767578125, -0.1513671875, -1.3330078125, -0.2139892578125, 0.1065673828125, -0.402587890625, 0.27392578125, 0.36181640625, -0.0638427734375, -0.280029296875, -0.1220703125, -0.428466796875, -0.457763671875, -0.65869140625, -0.177734375, 0.1312255859375, 0.7646484375, 0.97314453125, -0.010498046875, -0.3154296875, -0.042816162109375, 0.07666015625, 0.171142578125, -0.54638671875, -0.1951904296875, -0.2548828125, -0.0819091796875, -0.3857421875, 0.15087890625, 0.1483154296875, 0.359130859375, 0.88037109375, -0.07794189453125, 0.2147216796875, 0.315673828125, -0.65673828125, 1.275390625, 0.08111572265625, -0.99072265625, -0.9658203125, 0.55859375, -0.06402587890625, 0.60302734375, 0.544921875, -1.0166015625, -0.62451171875, -1.013671875, 0.1676025390625, -0.94970703125, -0.302978515625, -1.2421875, -0.71923828125, -0.693359375, 0.39453125, 0.128173828125, -0.556640625, 0.47802734375, -0.7685546875, 0.271484375, -0.80126953125, 0.1392822265625, -0.5927734375, -0.7451171875, 0.251953125, 0.8515625, 0.301025390625, 0.336181640625, 0.0171356201171875, -0.42333984375, 0.454833984375, -0.23779296875, -0.76171875, -0.1971435546875, -0.330322265625, 0.2493896484375, 0.0302276611328125, -0.18115234375, -0.69189453125, 1.0087890625, -0.69384765625, 0.47216796875, 0.09991455078125, -0.275390625, -0.312255859375, -0.3125, 0.84765625, -0.24462890625, 0.058074951171875, -0.0080108642578125, 0.385986328125, 0.6875, -0.446533203125, -0.5400390625, -0.74755859375, -0.67724609375, -0.93603515625, 0.6552734375, -0.29833984375, 0.1939697265625, -0.822265625, -0.2744140625, 1.3896484375, -0.47802734375, 0.440673828125, 1.064453125, 0.01224517822265625, 0.1541748046875, -0.32177734375, 0.6259765625, 0.40625, -0.274169921875, 0.2037353515625, -0.048095703125, -0.6650390625, -0.07427978515625, -0.1295166015625, -0.78076171875, -0.72705078125, 0.3310546875, 1.33203125, -0.4501953125, 0.5927734375, -0.330322265625, -1.337890625, -0.67919921875, 0.53857421875, 0.372802734375, 0.30419921875, 0.7490234375, -0.081787109375, 0.06695556640625, -0.115966796875, -0.458984375, -0.473388671875, -0.76513671875, 1.31640625, -0.5927734375, -0.48779296875, 0.92919921875, 0.92626953125, -1.19140625, -0.92236328125, 0.253173828125, -0.07720947265625, -0.4345703125, -0.46875, -0.059783935546875, 0.7744140625, -0.65380859375, 0.1488037109375, 0.3115234375, -0.0384521484375, 0.14111328125, 0.016357421875, 0.580078125, -0.232666015625, 0.7236328125, 0.58984375, -0.5576171875, -0.447265625, -0.96533203125, -0.294921875, -0.287353515625, -0.0288543701171875, 0.80078125, -0.061614990234375, 0.1566162109375, 0.51416015625, 0.0615234375, 0.75732421875, -0.45263671875, -0.3447265625, 0.1558837890625, -0.66015625, -0.57568359375, 0.1368408203125, 0.348876953125, -0.01403045654296875, 0.3291015625, -0.67333984375, -0.05706787109375, 0.27685546875, 0.458740234375, -0.302978515625, -0.84130859375, -0.1763916015625, -1.458984375, -0.5146484375, -0.7548828125, -0.875, -0.1580810546875, 0.3701171875, 0.051788330078125, -0.6845703125, 0.024566650390625, 0.257568359375, -0.72509765625, 0.59326171875, -0.3271484375, 0.28125, -0.33349609375, -0.64111328125, -0.99658203125, -0.1568603515625, -0.44287109375, -0.34326171875, -1.119140625, 0.74560546875, 0.1436767578125, 0.384033203125, -0.2020263671875, 0.87548828125, -0.325927734375, -0.83837890625, 0.325927734375, 0.1556396484375, -0.03466796875, 1.2431640625, 0.42041015625, 0.1707763671875, 0.0909423828125, -0.117431640625, -0.2362060546875, -0.4716796875, 0.517578125, 0.40625, -0.446044921875, -0.182861328125, -0.09521484375, 0.33642578125, -0.8720703125, 0.343505859375, -0.265625, 0.016387939453125, 0.1531982421875, -0.107666015625, 0.253173828125, 1.4189453125, -0.1478271484375, 0.1484375, 0.039398193359375, 0.191162109375, 0.17626953125, 0.369384765625, -0.0291290283203125, 0.487548828125, -0.209716796875, -0.43017578125, -0.296630859375, 0.46337890625, 0.0760498046875, 0.031463623046875, -0.323486328125, -0.90478515625, -0.67041015625, -0.3447265625, 0.077880859375, 0.39501953125, 0.53564453125, -0.487060546875, -0.0885009765625, -0.0155792236328125, -0.56396484375, -0.016204833984375, -1.146484375, -0.9755859375, 0.55322265625, 0.007770538330078125, -0.7138671875, -0.1287841796875, -0.232177734375, -0.39404296875, -0.05023193359375, 0.640625, -0.477294921875, 0.48095703125, -0.01537322998046875, 0.34375, -0.084716796875, -0.1387939453125, 0.10455322265625, 0.755859375, -0.66943359375, -0.65673828125, 0.060394287109375, 0.8564453125, 0.19873046875, -0.3857421875, -0.10394287109375, 0.43212890625, -0.2064208984375, 0.324462890625, -0.66259765625, -0.01337432861328125, 0.021148681640625, 0.9921875, -0.77490234375, 0.06744384765625, -0.20458984375, 0.21533203125, -0.05657958984375, -0.59765625, -0.46728515625, 1.1259765625, 0.66064453125, -0.15234375, 0.71240234375, 0.0435791015625, 0.334716796875, -0.02398681640625, -0.07281494140625, 0.244384765625, 0.5693359375, 0.755859375, 0.5859375, -0.1439208984375, 0.2705078125, 0.91845703125, -0.2301025390625, -0.38916015625, 0.385986328125, -0.0631103515625, -0.01326751708984375, -0.136474609375, -0.00885009765625, -0.2060546875, -0.244873046875, -0.82958984375, 0.853515625, -0.2056884765625, 0.274169921875, -0.1156005859375, -0.78271484375, 0.95263671875, -0.3544921875, -0.343505859375, 0.276123046875, -0.708984375, 0.1956787109375, 0.62451171875, -0.3310546875, -0.298095703125, 0.7001953125, 0.5703125, 0.6396484375, 0.72119140625, 0.11907958984375, 0.443603515625, -0.488037109375, 0.1878662109375, -0.1732177734375, -0.1712646484375, -0.2066650390625, -0.67041015625, -1.10546875, 0.452880859375, -0.6240234375, -0.57568359375, 0.75244140625, -0.71728515625, 0.2496337890625, -0.258056640625, 0.75732421875, -0.39599609375, 0.10540771484375, 0.5888671875, -0.275634765625, -0.8076171875, 0.80078125, -0.1905517578125, 0.27783203125, -0.28564453125, 1.1962890625, -0.224365234375, 1.3779296875, 0.59375, -0.290283203125, 0.2037353515625, 0.38720703125, -0.39208984375, -0.6484375, -0.62548828125, -0.58349609375, -0.12152099609375, -0.5009765625, -0.49609375, 0.1966552734375, 0.380126953125, 0.00632476806640625, -0.7451171875, -0.1658935546875, 0.32373046875, -0.791015625, 0.416259765625, 0.2744140625, 0.0240936279296875, 0.056243896484375, -0.08258056640625, -0.1319580078125, -0.1395263671875, 0.155517578125, -0.775390625, 0.41357421875, -0.9619140625, -0.2452392578125, -0.716796875, -0.6767578125, -0.1907958984375, 0.10235595703125, -0.30908203125, -0.8876953125, 0.277587890625, 0.322998046875, 0.1981201171875, 0.402587890625, -0.189697265625, 0.2802734375, 1.0751953125, 1.044921875, 0.10791015625, 0.81396484375, 0.32763671875, -0.10772705078125, 0.0228118896484375, -0.32958984375, 0.423095703125, -0.03680419921875, 0.53564453125, -0.39208984375, 0.2210693359375, -0.72314453125, -1.4970703125, 0.4521484375, 0.5166015625, 0.400390625, -0.732421875, -1.12890625, -0.11163330078125, -1.2568359375, -0.2015380859375, -0.77783203125, 1.0546875, -0.52734375, 0.0049285888671875, -0.1353759765625, -1.2294921875, 4.24609375, 1.0556640625, 0.87353515625, 0.61767578125, 0.1920166015625, 0.9931640625, 0.051239013671875, -0.43408203125, -0.0303802490234375, -0.2293701171875, 0.82763671875, -0.54833984375, -0.1134033203125, 0.72900390625, 0.282470703125, 0.533203125, -0.38818359375, 0.494873046875, -0.2568359375, -0.96728515625, -0.90771484375, 0.49365234375, -0.10089111328125, 0.45458984375, 0.03277587890625, 0.1328125, 0.8056640625, -1.0771484375, 0.19140625, -0.7568359375, 0.20458984375, -0.395263671875, 1.0849609375, 0.061798095703125, 0.06146240234375, 0.498046875, -0.145751953125, -0.461181640625, 0.1934814453125, 0.05633544921875, -0.1732177734375, -0.11151123046875, 0.485595703125, -0.9326171875, -0.036651611328125, 0.5068359375, -0.7119140625, 0.345703125, -0.1563720703125, -1.064453125, 0.90283203125, -0.216552734375, 0.364990234375, -0.97607421875, -0.31103515625, -0.1588134765625, 0.39697265625, -0.1129150390625, -0.45458984375, 0.37939453125, 0.552734375, 0.50048828125, 0.264404296875, 0.52294921875, -0.99267578125, 0.21435546875, -0.177001953125, 0.3671875, -0.51171875, 0.1279296875, -0.449462890625, -0.39794921875, -0.2822265625, -0.51953125, 0.58837890625, -0.0307769775390625, -0.051544189453125, 0.436767578125, 0.4892578125, -0.65625, 0.059051513671875, -0.11590576171875, -0.0977783203125, -0.5947265625, 0.67919921875, 1.2548828125, -0.541015625, -0.388916015625, -0.340576171875, 0.4677734375, 0.45263671875, 0.45361328125, -0.1162109375, -0.78125, -0.0556640625 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Submitted Solution: ``` inp = input() cnt_b = 0 ans = 0 mod = 1000000000 + 7 for i in inp[::-1]: if i == 'b': cnt_b += 1 else: ans = (ans + cnt_b) % mod cnt_b = (cnt_b * 2) % mod print(ans) ``` Yes
105,796
[ 0.52001953125, -0.171630859375, -0.057037353515625, 0.021270751953125, -0.83740234375, -0.44091796875, -0.0537109375, -0.1513671875, 0.1712646484375, 0.8974609375, 0.50634765625, -0.3564453125, -0.1700439453125, -1.0068359375, -0.447998046875, -0.0310821533203125, -0.448486328125, -0.6962890625, -0.307861328125, -0.379638671875, -0.0079803466796875, -0.30419921875, -1.19140625, 0.06744384765625, -0.1751708984375, 0.91455078125, 0.591796875, -0.088134765625, 1.0576171875, 1.1279296875, -0.2120361328125, -0.28076171875, 0.58203125, -0.78173828125, -0.277587890625, -0.5810546875, 0.58447265625, -0.8056640625, -0.25634765625, -0.392578125, 0.2347412109375, -0.48193359375, 0.5458984375, -0.5625, -1.7314453125, -0.080810546875, -0.0026531219482421875, -0.42822265625, -0.037994384765625, -0.472900390625, -0.19091796875, -0.279296875, 0.349365234375, -0.143310546875, 0.179443359375, 0.319580078125, 0.2314453125, -0.2880859375, -1.0126953125, 0.003932952880859375, 0.457275390625, 0.1180419921875, 0.1343994140625, -0.87109375, -0.08795166015625, 0.294677734375, -0.2724609375, 0.10260009765625, -0.132080078125, -0.5849609375, -0.053314208984375, 0.087158203125, -0.361083984375, -0.4990234375, -0.30517578125, 0.10003662109375, 0.430419921875, 0.017852783203125, -0.84716796875, 1.125, -0.404541015625, 0.849609375, 0.26171875, 0.177490234375, -0.411865234375, -0.58251953125, 0.208740234375, 0.2388916015625, 0.049072265625, -0.1077880859375, -0.394775390625, 0.5400390625, -0.327392578125, -0.1614990234375, 0.44189453125, 0.493408203125, -0.478515625, 0.03997802734375, 0.5302734375, 0.376708984375, 1.0166015625, 0.884765625, -0.50830078125, 0.9208984375, -0.36669921875, -0.0775146484375, 0.036407470703125, -0.23779296875, -0.312255859375, -0.1170654296875, -0.1502685546875, -0.2210693359375, 0.452880859375, 0.348876953125, -0.57177734375, 0.92529296875, 0.32568359375, 0.5634765625, -0.53955078125, 0.53515625, 0.36376953125, 0.0267791748046875, 0.796875, -0.232177734375, -0.090087890625, -0.10833740234375, -0.833984375, 1.1630859375, -0.65869140625, -0.31787109375, 0.3369140625, 0.1177978515625, -0.07794189453125, 0.360595703125, -0.48974609375, 0.654296875, 0.01837158203125, 0.2203369140625, 0.75341796875, -0.44873046875, 0.71826171875, -0.20263671875, -0.10687255859375, 1.80078125, 0.1524658203125, -0.186279296875, 0.603515625, 0.406982421875, -0.9287109375, 0.278076171875, -1.0869140625, 0.76513671875, 0.2491455078125, 0.1478271484375, -0.2607421875, 0.11456298828125, -0.350341796875, 0.40771484375, 0.1715087890625, -0.26708984375, -0.45068359375, 0.17138671875, -0.473876953125, 0.857421875, -0.368408203125, 0.580078125, -0.12890625, -0.164306640625, -0.0061187744140625, -0.390869140625, 0.07470703125, -0.211669921875, -0.0138702392578125, 0.9404296875, 0.51806640625, 1.009765625, 1.13671875, -0.1895751953125, 0.459716796875, 0.34619140625, -0.4453125, 0.364013671875, 0.245849609375, 0.92236328125, 0.4140625, 0.53857421875, -0.338623046875, 0.0029735565185546875, -0.3603515625, -0.4052734375, 0.3955078125, 0.5966796875, -0.8134765625, 0.461181640625, -0.1915283203125, -0.1458740234375, -0.7666015625, -0.283203125, 0.06854248046875, -1.05859375, -0.33056640625, 0.45263671875, 0.01296234130859375, 0.420654296875, -0.5107421875, -0.5458984375, 0.24462890625, 1.279296875, -0.30615234375, 0.2335205078125, 0.424560546875, -0.0950927734375, -0.05938720703125, 0.361328125, 0.148193359375, -0.316162109375, -0.60107421875, 0.54638671875, -0.0784912109375, -0.1124267578125, -0.175048828125, 0.59326171875, 0.3330078125, 0.6796875, -0.300048828125, -0.6591796875, 0.474853515625, 1.1630859375, -0.1361083984375, 0.6328125, 0.291015625, 0.78466796875, 0.93798828125, 0.92822265625, 0.6455078125, 0.267333984375, 0.623046875, 0.88525390625, -0.12408447265625, 0.306640625, 0.2471923828125, 0.5830078125, 0.27294921875, 0.45458984375, 0.49951171875, 0.463134765625, 0.12042236328125, -0.276611328125, -0.077880859375, -0.034423828125, -0.5107421875, 0.728515625, 0.0280609130859375, 0.5634765625, 0.09820556640625, -0.125732421875, 0.4501953125, 1.005859375, -1.3115234375, -0.6494140625, 0.0186004638671875, 0.045074462890625, 0.11309814453125, 0.043792724609375, 0.7568359375, 0.494140625, 0.82080078125, 0.57666015625, -0.2264404296875, -0.2498779296875, -0.52783203125, -0.81640625, -1.0244140625, -0.268310546875, -0.935546875, -0.232177734375, -0.154296875, -0.97509765625, 0.10546875, -0.54638671875, -0.08123779296875, 0.11859130859375, -0.445068359375, 0.93896484375, -0.0833740234375, 0.1397705078125, -0.59619140625, 0.56494140625, 0.078857421875, 1.0712890625, -0.8193359375, 0.112060546875, -0.38671875, -0.6787109375, -0.06201171875, 0.2425537109375, 0.43359375, 0.13720703125, -0.68359375, -0.70556640625, -0.5029296875, 0.13720703125, -0.2978515625, 0.1568603515625, -0.6328125, 0.65185546875, 0.410888671875, -0.71533203125, 0.53369140625, 1.0771484375, -0.9697265625, 0.671875, 0.29833984375, -0.2037353515625, -0.7431640625, 1.2333984375, 0.587890625, 0.65478515625, -0.37744140625, -0.75439453125, -0.42236328125, 0.08135986328125, 0.11712646484375, -0.72265625, -0.4287109375, 0.66162109375, 0.062286376953125, -0.970703125, 0.51611328125, -1.1025390625, -0.491455078125, -0.5869140625, -0.61767578125, 1.0771484375, 0.87109375, 0.232666015625, 0.1171875, -0.0152587890625, -0.125732421875, 0.591796875, 0.59521484375, -0.84228515625, 0.2098388671875, 1.017578125, -0.1107177734375, 0.27880859375, 0.2303466796875, -0.51904296875, -0.260009765625, 0.0421142578125, -0.048004150390625, 0.67431640625, -0.040496826171875, 0.4931640625, 0.3134765625, 0.6337890625, -0.89013671875, 0.08056640625, -0.2064208984375, 0.83349609375, 0.4072265625, 0.7119140625, 0.310546875, -0.0604248046875, -0.65673828125, -1.0673828125, 0.0250244140625, 0.1534423828125, 0.58447265625, -0.382080078125, 0.99072265625, 0.1473388671875, -0.7216796875, 0.515625, -0.65478515625, 0.458251953125, 1.087890625, 0.3232421875, 0.8408203125, -0.8564453125, 0.41943359375, 0.07415771484375, -0.20751953125, 0.488525390625, 0.63232421875, 0.346923828125, -0.50244140625, -0.7421875, -0.380615234375, 0.005207061767578125, -0.186767578125, -0.395263671875, 0.1302490234375, -0.50048828125, -0.2396240234375, -0.953125, 0.630859375, 0.619140625, 0.76025390625, 0.197265625, 0.285888671875, 0.156982421875, 0.1798095703125, 0.62841796875, 0.07080078125, 0.2440185546875, -0.5947265625, 0.923828125, 0.297607421875, -0.3046875, -0.464599609375, -0.39697265625, -0.1260986328125, 0.10882568359375, -0.491943359375, -0.087158203125, -1.1533203125, 0.1900634765625, -0.200927734375, 0.6357421875, -0.876953125, -0.0726318359375, -0.35888671875, 0.1923828125, 0.2103271484375, -1.0810546875, 0.6494140625, -0.9931640625, 0.67236328125, 0.58203125, -0.1209716796875, -0.1285400390625, -0.25390625, -0.87646484375, -0.69287109375, -0.1812744140625, 0.73779296875, -0.1199951171875, 0.42919921875, -1.3984375, 0.6103515625, 0.342041015625, -0.63330078125, 0.310302734375, -0.411865234375, 0.63671875, -0.1898193359375, 0.67236328125, -0.427734375, -0.63623046875, 0.07257080078125, -1.3837890625, 0.58154296875, -0.47998046875, 0.78173828125, 0.2484130859375, -0.1798095703125, 0.25146484375, 0.2120361328125, -0.15478515625, 0.2049560546875, -0.2174072265625, 0.50537109375, -0.98974609375, -1.0654296875, 0.58544921875, -0.1336669921875, -0.4345703125, 0.7001953125, -0.04522705078125, -0.60498046875, -0.1859130859375, 0.4931640625, -0.444091796875, 0.397216796875, -0.1712646484375, 0.654296875, -0.335205078125, -0.73681640625, -0.31982421875, -0.68896484375, 0.7900390625, -0.302734375, -0.62060546875, -0.1357421875, -1.3037109375, -0.306884765625, 0.0238494873046875, -0.361328125, 0.1893310546875, 0.43505859375, 0.0012159347534179688, -0.19384765625, -0.1439208984375, -0.5341796875, -0.426025390625, -0.7109375, -0.321533203125, 0.0802001953125, 0.52783203125, 0.9951171875, -0.0213165283203125, -0.29736328125, -0.091064453125, -0.049652099609375, 0.01145172119140625, -0.57373046875, -0.27294921875, -0.0831298828125, -0.461181640625, -0.282958984375, 0.412841796875, 0.0560302734375, 0.54541015625, 0.8427734375, -0.076416015625, 0.374755859375, 0.33154296875, -0.64892578125, 1.439453125, 0.01271820068359375, -1.251953125, -0.71435546875, 0.6376953125, 0.1588134765625, 0.75927734375, 0.33349609375, -1.001953125, -0.7158203125, -1.087890625, 0.417724609375, -0.94482421875, -0.353271484375, -1.1572265625, -0.69921875, -0.64306640625, 0.30810546875, 0.125, -0.498046875, 0.5107421875, -0.884765625, 0.289794921875, -0.94482421875, 0.06671142578125, -0.63427734375, -0.537109375, -0.021240234375, 0.96484375, 0.10003662109375, 0.2822265625, 0.0041656494140625, -0.376220703125, 0.38330078125, -0.1259765625, -0.7666015625, -0.323486328125, -0.1678466796875, 0.3076171875, -0.250244140625, -0.15576171875, -0.693359375, 0.98828125, -0.55322265625, 0.59423828125, 0.2186279296875, -0.4599609375, -0.148681640625, -0.3271484375, 0.94677734375, -0.44384765625, 0.1986083984375, -0.0230712890625, 0.300537109375, 0.59326171875, -0.55810546875, -0.379638671875, -0.59716796875, -0.6044921875, -0.99462890625, 0.515625, -0.346923828125, 0.2052001953125, -0.75146484375, -0.06781005859375, 1.107421875, -0.61474609375, 0.44482421875, 1.0166015625, 0.065185546875, 0.2626953125, -0.31640625, 0.77197265625, 0.533203125, -0.2171630859375, 0.0236053466796875, -0.08624267578125, -0.51416015625, -0.0175018310546875, -0.431396484375, -0.88037109375, -0.736328125, 0.2196044921875, 1.3876953125, -0.314453125, 0.7421875, -0.18994140625, -1.1953125, -0.45703125, 0.57958984375, 0.112548828125, 0.1287841796875, 0.67138671875, -0.08319091796875, -0.081787109375, 0.07086181640625, -0.45751953125, -0.6533203125, -0.71630859375, 1.3017578125, -0.75537109375, -0.6103515625, 1.044921875, 0.92724609375, -1.19140625, -1.0029296875, 0.10577392578125, 0.03955078125, -0.205322265625, -0.63720703125, 0.006725311279296875, 0.66796875, -0.59716796875, 0.045196533203125, 0.1953125, -0.016143798828125, 0.2529296875, -0.04205322265625, 0.56201171875, -0.385498046875, 0.46728515625, 0.6494140625, -0.55224609375, -0.333251953125, -0.98388671875, -0.2174072265625, -0.26220703125, 0.1822509765625, 0.7783203125, -0.0160980224609375, 0.364013671875, 0.72021484375, -0.06390380859375, 0.6943359375, -0.50830078125, -0.251708984375, 0.26171875, -0.484619140625, -0.423095703125, 0.07666015625, 0.3388671875, -0.0264892578125, 0.55126953125, -0.58447265625, -0.04791259765625, 0.2890625, 0.61572265625, -0.2445068359375, -0.603515625, -0.2607421875, -1.4658203125, -0.5283203125, -0.59033203125, -0.91015625, -0.1917724609375, 0.568359375, 0.1741943359375, -0.60693359375, 0.045196533203125, 0.43603515625, -0.68115234375, 0.53076171875, -0.390625, 0.2237548828125, -0.323974609375, -0.51708984375, -0.9775390625, -0.228759765625, -0.6669921875, -0.521484375, -0.646484375, 0.701171875, 0.0202484130859375, 0.22265625, -0.314453125, 0.8798828125, -0.08892822265625, -0.5859375, 0.435302734375, 0.111328125, -0.1590576171875, 1.3642578125, 0.317138671875, 0.2130126953125, 0.09039306640625, -0.3525390625, -0.12493896484375, -0.3154296875, 0.82421875, 0.36279296875, -0.357177734375, -0.1627197265625, -0.061248779296875, 0.236083984375, -0.79296875, 0.330810546875, -0.35595703125, 0.12481689453125, -0.053131103515625, -0.06536865234375, 0.26708984375, 1.2998046875, -0.314453125, 0.110595703125, 0.142578125, 0.1571044921875, 0.3212890625, 0.275146484375, 0.07965087890625, 0.6669921875, -0.2242431640625, -0.42724609375, -0.1832275390625, 0.434814453125, 0.0225372314453125, 0.2120361328125, -0.41650390625, -0.9599609375, -0.69384765625, -0.21240234375, -0.07879638671875, 0.453369140625, 0.44970703125, -0.463134765625, -0.0168914794921875, 0.08648681640625, -0.60693359375, 0.054962158203125, -1.1572265625, -1.0712890625, 0.56494140625, -0.1683349609375, -0.63037109375, 0.0191650390625, -0.383544921875, -0.084228515625, 0.0153961181640625, 0.5654296875, -0.4833984375, 0.270751953125, 0.074462890625, 0.51318359375, -0.051605224609375, -0.3017578125, 0.2025146484375, 0.64208984375, -0.8759765625, -0.64404296875, 0.0251922607421875, 0.921875, 0.134033203125, -0.51318359375, -0.177978515625, 0.375, -0.1527099609375, 0.1834716796875, -0.58544921875, 0.093505859375, 0.1630859375, 0.9287109375, -0.7939453125, 0.018646240234375, -0.165771484375, 0.174072265625, -0.11212158203125, -0.72314453125, -0.599609375, 1.02734375, 0.58544921875, -0.1380615234375, 0.64306640625, -0.0113067626953125, 0.4228515625, 0.01129150390625, 0.040740966796875, 0.10479736328125, 0.5673828125, 0.86181640625, 0.7119140625, -0.1728515625, 0.450439453125, 0.83056640625, -0.309326171875, -0.2078857421875, 0.44091796875, 0.2003173828125, -0.08514404296875, -0.1253662109375, -0.326904296875, -0.378173828125, -0.213623046875, -0.64453125, 0.70947265625, -0.188232421875, 0.290771484375, -0.192138671875, -0.7392578125, 0.82421875, -0.37255859375, -0.15576171875, 0.269775390625, -0.7470703125, 0.45166015625, 0.5927734375, -0.344970703125, -0.3828125, 0.63330078125, 0.76416015625, 0.6142578125, 0.732421875, 0.2039794921875, 0.264892578125, -0.59619140625, 0.09381103515625, -0.041595458984375, -0.1427001953125, -0.130859375, -0.7255859375, -1.2294921875, 0.66845703125, -0.5322265625, -0.30419921875, 0.60107421875, -0.71435546875, 0.263671875, -0.19970703125, 0.998046875, -0.55126953125, 0.2060546875, 0.560546875, -0.353759765625, -0.853515625, 0.97802734375, -0.09161376953125, 0.1749267578125, -0.00958251953125, 1.291015625, -0.1077880859375, 1.46875, 0.64892578125, -0.322265625, 0.255615234375, 0.548828125, -0.335205078125, -0.45263671875, -0.37353515625, -0.625, -0.3447265625, -0.6728515625, -0.5888671875, 0.10968017578125, 0.4384765625, 0.061737060546875, -0.70166015625, -0.3046875, 0.204345703125, -0.68505859375, 0.61767578125, 0.1502685546875, 0.342041015625, 0.301513671875, -0.1153564453125, -0.039306640625, -0.26513671875, 0.274169921875, -0.4306640625, 0.52001953125, -1.025390625, -0.276611328125, -0.71484375, -0.72119140625, -0.1929931640625, 0.017822265625, -0.33056640625, -0.83935546875, 0.24560546875, 0.50390625, 0.1856689453125, 0.316650390625, -0.265869140625, 0.2176513671875, 0.98046875, 1.0517578125, -0.00603485107421875, 0.8427734375, 0.4033203125, 0.00745391845703125, -0.19580078125, -0.2144775390625, 0.4306640625, 0.0159912109375, 0.475830078125, -0.431396484375, 0.337890625, -0.64453125, -1.2861328125, 0.256103515625, 0.415283203125, 0.048858642578125, -0.8330078125, -1.24609375, -0.52685546875, -1.16796875, -0.1822509765625, -0.9375, 1.0751953125, -0.479736328125, -0.035369873046875, -0.0213165283203125, -1.1513671875, 4.234375, 0.9912109375, 0.677734375, 0.54345703125, 0.266845703125, 0.76416015625, 0.060455322265625, -0.611328125, 0.0211181640625, -0.493896484375, 0.74072265625, -0.48779296875, -0.09930419921875, 0.9609375, 0.40185546875, 0.53125, -0.475341796875, 0.09320068359375, 0.0214080810546875, -1.04296875, -0.91796875, 0.359375, 0.0111236572265625, 0.36669921875, 0.145263671875, 0.1888427734375, 0.93701171875, -0.90478515625, 0.12493896484375, -0.703125, 0.27685546875, -0.351318359375, 1.11328125, 0.1663818359375, 0.069091796875, 0.42529296875, -0.039093017578125, -0.360107421875, 0.016693115234375, 0.11474609375, -0.287353515625, -0.20263671875, 0.513671875, -0.79541015625, -0.1583251953125, 0.63671875, -0.69580078125, 0.57275390625, 0.0174560546875, -1.1181640625, 0.9765625, -0.1639404296875, 0.33544921875, -0.7138671875, -0.2548828125, 0.132080078125, 0.380126953125, -0.197265625, -0.2548828125, 0.5712890625, 0.3798828125, 0.474609375, 0.046112060546875, 0.68408203125, -1.0791015625, 0.08349609375, -0.03253173828125, 0.436767578125, -0.443115234375, -0.035400390625, -0.5556640625, -0.456298828125, -0.306884765625, -0.6142578125, 0.56884765625, -0.00011080503463745117, -0.0335693359375, 0.37939453125, 0.560546875, -0.646484375, 0.1910400390625, -0.1475830078125, -0.0249176025390625, -0.73876953125, 0.83935546875, 1.255859375, -0.5439453125, -0.40380859375, -0.3369140625, 0.474853515625, 0.6171875, 0.67236328125, -0.059661865234375, -0.8173828125, -0.261962890625 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Submitted Solution: ``` s = input() a = 0 m = 10 ** 9 + 7 t = 0 for i in range(len(s)): if s[~i] == 'a': a = (a + t) % m t = (t * 2) % m else: t += 1 print(a) ``` Yes
105,797
[ 0.4921875, -0.1483154296875, -0.026214599609375, 0.051422119140625, -0.88525390625, -0.381591796875, -0.07379150390625, -0.147705078125, 0.175048828125, 0.8515625, 0.50146484375, -0.357177734375, -0.1865234375, -0.98974609375, -0.458984375, -0.0706787109375, -0.4873046875, -0.66015625, -0.326416015625, -0.373779296875, 0.0072174072265625, -0.264404296875, -1.09375, 0.1376953125, -0.1490478515625, 0.9560546875, 0.578125, -0.05596923828125, 1.0087890625, 1.185546875, -0.218017578125, -0.2161865234375, 0.60498046875, -0.81201171875, -0.223876953125, -0.669921875, 0.56787109375, -0.833984375, -0.3564453125, -0.463134765625, 0.21728515625, -0.43115234375, 0.564453125, -0.52392578125, -1.744140625, -0.10723876953125, -0.0011739730834960938, -0.450439453125, -0.040252685546875, -0.44140625, -0.159912109375, -0.365234375, 0.3623046875, -0.1387939453125, 0.17626953125, 0.278076171875, 0.222900390625, -0.30810546875, -0.99755859375, 0.08587646484375, 0.454833984375, 0.1761474609375, 0.060211181640625, -0.830078125, -0.11773681640625, 0.273681640625, -0.2142333984375, 0.104248046875, -0.170654296875, -0.5712890625, -0.062225341796875, 0.1502685546875, -0.367919921875, -0.483642578125, -0.331298828125, 0.08935546875, 0.34619140625, -0.050994873046875, -0.84814453125, 1.111328125, -0.37841796875, 0.88232421875, 0.3603515625, 0.274169921875, -0.394775390625, -0.58642578125, 0.2083740234375, 0.339599609375, 0.100830078125, -0.08160400390625, -0.371337890625, 0.5576171875, -0.3466796875, -0.18359375, 0.480224609375, 0.5390625, -0.437744140625, 0.0130157470703125, 0.479248046875, 0.398193359375, 0.970703125, 0.8046875, -0.49462890625, 0.978515625, -0.373779296875, -0.1138916015625, 0.0662841796875, -0.26025390625, -0.324951171875, -0.138427734375, -0.22021484375, -0.25244140625, 0.488525390625, 0.35205078125, -0.611328125, 0.95556640625, 0.351318359375, 0.56103515625, -0.5576171875, 0.5126953125, 0.441162109375, 0.12457275390625, 0.83154296875, -0.2587890625, -0.1387939453125, -0.07763671875, -0.85400390625, 1.1728515625, -0.658203125, -0.3046875, 0.316650390625, 0.093017578125, -0.053863525390625, 0.327392578125, -0.4716796875, 0.654296875, 0.0121917724609375, 0.2265625, 0.73388671875, -0.42578125, 0.73583984375, -0.228759765625, -0.1575927734375, 1.8115234375, 0.1778564453125, -0.2052001953125, 0.62451171875, 0.4677734375, -0.931640625, 0.27685546875, -1.10546875, 0.77685546875, 0.219970703125, 0.09698486328125, -0.26708984375, 0.0823974609375, -0.2783203125, 0.32763671875, 0.1572265625, -0.2685546875, -0.52099609375, 0.1429443359375, -0.479248046875, 0.8193359375, -0.3583984375, 0.5947265625, -0.153076171875, -0.178466796875, -0.047698974609375, -0.3681640625, 0.0924072265625, -0.1630859375, -0.0165557861328125, 1.005859375, 0.5126953125, 0.98583984375, 1.1943359375, -0.242431640625, 0.400146484375, 0.3603515625, -0.466796875, 0.3330078125, 0.239013671875, 0.943359375, 0.4189453125, 0.5224609375, -0.328857421875, -0.0048370361328125, -0.406494140625, -0.451171875, 0.363525390625, 0.61181640625, -0.7626953125, 0.48193359375, -0.220703125, -0.10186767578125, -0.73974609375, -0.304443359375, -0.0273590087890625, -1.0703125, -0.36572265625, 0.4775390625, 0.012115478515625, 0.472900390625, -0.408447265625, -0.6142578125, 0.305908203125, 1.310546875, -0.21435546875, 0.2296142578125, 0.41162109375, -0.0709228515625, -0.13525390625, 0.3359375, 0.1119384765625, -0.37939453125, -0.498779296875, 0.59228515625, -0.114990234375, -0.057708740234375, -0.271484375, 0.5673828125, 0.278564453125, 0.74755859375, -0.2890625, -0.630859375, 0.501953125, 1.087890625, -0.21044921875, 0.57080078125, 0.337158203125, 0.763671875, 0.9453125, 0.95751953125, 0.63818359375, 0.294921875, 0.5908203125, 0.8349609375, -0.046173095703125, 0.2421875, 0.30859375, 0.564453125, 0.2919921875, 0.53564453125, 0.447509765625, 0.46630859375, 0.1290283203125, -0.2415771484375, -0.045867919921875, -0.08807373046875, -0.484619140625, 0.72509765625, 0.0219268798828125, 0.68505859375, 0.140625, -0.1876220703125, 0.344482421875, 0.95947265625, -1.2939453125, -0.61279296875, -0.016845703125, 0.07379150390625, 0.15869140625, 0.06927490234375, 0.7177734375, 0.43359375, 0.76025390625, 0.51220703125, -0.22705078125, -0.343505859375, -0.53759765625, -0.8759765625, -1.009765625, -0.262939453125, -0.9091796875, -0.1982421875, -0.1356201171875, -1.0537109375, 0.056304931640625, -0.5498046875, -0.07977294921875, 0.169921875, -0.452880859375, 0.99267578125, -0.15625, 0.1602783203125, -0.5302734375, 0.5166015625, 0.1502685546875, 1.0869140625, -0.85009765625, 0.1334228515625, -0.37109375, -0.62255859375, -0.0657958984375, 0.283935546875, 0.403076171875, 0.1605224609375, -0.65478515625, -0.77734375, -0.51171875, 0.1495361328125, -0.392333984375, 0.08245849609375, -0.666015625, 0.6962890625, 0.43212890625, -0.77783203125, 0.591796875, 1.099609375, -0.97509765625, 0.69091796875, 0.302001953125, -0.3154296875, -0.7177734375, 1.232421875, 0.576171875, 0.59228515625, -0.357421875, -0.759765625, -0.39697265625, 0.05047607421875, 0.154296875, -0.7373046875, -0.364013671875, 0.62646484375, -0.0020465850830078125, -0.93212890625, 0.51123046875, -1.11328125, -0.50830078125, -0.6298828125, -0.552734375, 1.037109375, 0.88623046875, 0.234130859375, 0.2171630859375, -0.0189208984375, 0.0211181640625, 0.72802734375, 0.61181640625, -0.8759765625, 0.25439453125, 0.99072265625, -0.08056640625, 0.251953125, 0.260986328125, -0.488037109375, -0.28759765625, 0.0270538330078125, 0.0247802734375, 0.6796875, -0.053466796875, 0.5341796875, 0.258544921875, 0.59130859375, -0.876953125, 0.10284423828125, -0.1903076171875, 0.88427734375, 0.3798828125, 0.7158203125, 0.239990234375, -0.06512451171875, -0.6171875, -1.1220703125, 0.035552978515625, 0.140625, 0.57470703125, -0.412841796875, 1.05859375, 0.09326171875, -0.74072265625, 0.55078125, -0.68408203125, 0.490478515625, 1.1455078125, 0.27978515625, 0.869140625, -0.80859375, 0.400634765625, 0.08087158203125, -0.1790771484375, 0.40283203125, 0.62109375, 0.384521484375, -0.426025390625, -0.7109375, -0.4248046875, 0.01220703125, -0.2347412109375, -0.422607421875, 0.1917724609375, -0.49658203125, -0.2427978515625, -0.9248046875, 0.60107421875, 0.66162109375, 0.80517578125, 0.2239990234375, 0.21337890625, 0.12481689453125, 0.2138671875, 0.61865234375, 0.005218505859375, 0.2154541015625, -0.62744140625, 0.85791015625, 0.30224609375, -0.29296875, -0.477783203125, -0.42578125, -0.1278076171875, 0.09954833984375, -0.477294921875, -0.050262451171875, -1.2353515625, 0.17822265625, -0.231689453125, 0.59423828125, -0.84375, -0.12030029296875, -0.33154296875, 0.0787353515625, 0.199951171875, -1.044921875, 0.6123046875, -0.99560546875, 0.62451171875, 0.54443359375, -0.12548828125, -0.1087646484375, -0.312255859375, -0.9248046875, -0.69775390625, -0.18994140625, 0.7373046875, -0.077880859375, 0.408447265625, -1.4443359375, 0.60693359375, 0.421875, -0.6376953125, 0.28515625, -0.5048828125, 0.603515625, -0.201171875, 0.73974609375, -0.50537109375, -0.66796875, 0.06365966796875, -1.42578125, 0.60693359375, -0.491455078125, 0.8310546875, 0.1834716796875, -0.1917724609375, 0.28173828125, 0.2457275390625, -0.15869140625, 0.238037109375, -0.213623046875, 0.44775390625, -0.94775390625, -1.0732421875, 0.60693359375, -0.1981201171875, -0.38134765625, 0.6845703125, -0.0723876953125, -0.62060546875, -0.1729736328125, 0.48779296875, -0.4609375, 0.38671875, -0.19580078125, 0.57421875, -0.36572265625, -0.7607421875, -0.25830078125, -0.6640625, 0.78125, -0.336669921875, -0.63671875, -0.1876220703125, -1.3232421875, -0.225341796875, 0.021881103515625, -0.344482421875, 0.237548828125, 0.4296875, 0.0295867919921875, -0.234375, -0.194580078125, -0.56884765625, -0.404296875, -0.64453125, -0.32275390625, 0.0328369140625, 0.587890625, 0.96337890625, -0.0053863525390625, -0.2763671875, -0.1636962890625, -0.0771484375, 0.091796875, -0.537109375, -0.3447265625, -0.06610107421875, -0.434814453125, -0.2373046875, 0.4423828125, 0.0015001296997070312, 0.6171875, 0.79443359375, -0.136474609375, 0.413330078125, 0.36328125, -0.68798828125, 1.4296875, 0.022369384765625, -1.1953125, -0.73193359375, 0.56103515625, 0.11517333984375, 0.7099609375, 0.31298828125, -1.0205078125, -0.65283203125, -1.08984375, 0.423583984375, -0.91015625, -0.40869140625, -1.2451171875, -0.6494140625, -0.63232421875, 0.23291015625, 0.1632080078125, -0.47802734375, 0.5205078125, -0.88525390625, 0.2264404296875, -0.94140625, 0.057830810546875, -0.58837890625, -0.5166015625, 0.050567626953125, 0.94384765625, 0.0916748046875, 0.327880859375, 0.006099700927734375, -0.41943359375, 0.37890625, -0.1478271484375, -0.74658203125, -0.37060546875, -0.2357177734375, 0.27001953125, -0.2325439453125, -0.1884765625, -0.6884765625, 0.9775390625, -0.6015625, 0.58349609375, 0.2294921875, -0.406494140625, -0.12017822265625, -0.3408203125, 0.90478515625, -0.438720703125, 0.133056640625, -0.058258056640625, 0.3447265625, 0.6474609375, -0.5654296875, -0.369384765625, -0.5986328125, -0.5224609375, -0.984375, 0.441650390625, -0.34130859375, 0.180419921875, -0.8564453125, -0.1361083984375, 1.2119140625, -0.6123046875, 0.4150390625, 1.0439453125, 0.052947998046875, 0.259765625, -0.36328125, 0.71484375, 0.5302734375, -0.2744140625, 0.0257110595703125, -0.06488037109375, -0.5302734375, 0.0295562744140625, -0.361083984375, -0.849609375, -0.7333984375, 0.292724609375, 1.359375, -0.32080078125, 0.7744140625, -0.159423828125, -1.1865234375, -0.4267578125, 0.642578125, 0.2060546875, 0.1290283203125, 0.60693359375, -0.1708984375, -0.07025146484375, 0.06817626953125, -0.46533203125, -0.5869140625, -0.61474609375, 1.28515625, -0.73193359375, -0.64892578125, 1.185546875, 0.92919921875, -1.2275390625, -0.978515625, 0.1446533203125, 0.01058197021484375, -0.2249755859375, -0.6298828125, 0.0017652511596679688, 0.68994140625, -0.6416015625, 0.12139892578125, 0.18115234375, -0.0762939453125, 0.27685546875, -0.0595703125, 0.611328125, -0.379150390625, 0.4853515625, 0.68505859375, -0.6181640625, -0.292236328125, -0.953125, -0.1761474609375, -0.287109375, 0.152587890625, 0.75341796875, 0.01352691650390625, 0.3193359375, 0.751953125, -0.098388671875, 0.740234375, -0.5361328125, -0.238037109375, 0.2410888671875, -0.51416015625, -0.486083984375, 0.056304931640625, 0.357177734375, -0.034332275390625, 0.496826171875, -0.63525390625, -0.0950927734375, 0.328369140625, 0.63330078125, -0.1767578125, -0.64599609375, -0.2430419921875, -1.4072265625, -0.464599609375, -0.58154296875, -0.8671875, -0.240966796875, 0.59521484375, 0.173583984375, -0.5830078125, 0.04400634765625, 0.51416015625, -0.673828125, 0.599609375, -0.44921875, 0.2091064453125, -0.28369140625, -0.47705078125, -1.0322265625, -0.12139892578125, -0.64013671875, -0.4755859375, -0.64599609375, 0.6953125, 0.013275146484375, 0.2218017578125, -0.244873046875, 0.94677734375, -0.062286376953125, -0.591796875, 0.498779296875, 0.08221435546875, -0.18896484375, 1.36328125, 0.26904296875, 0.1490478515625, 0.1414794921875, -0.381591796875, -0.1751708984375, -0.312255859375, 0.77783203125, 0.37255859375, -0.395263671875, -0.1868896484375, -0.042724609375, 0.2200927734375, -0.755859375, 0.33447265625, -0.313232421875, 0.1224365234375, -0.055389404296875, -0.022247314453125, 0.27294921875, 1.224609375, -0.274169921875, 0.11285400390625, 0.0771484375, 0.1396484375, 0.260986328125, 0.31591796875, 0.09393310546875, 0.60595703125, -0.265625, -0.422607421875, -0.1502685546875, 0.382568359375, 0.07989501953125, 0.19287109375, -0.4541015625, -1.0107421875, -0.65966796875, -0.1949462890625, -0.039306640625, 0.466796875, 0.40185546875, -0.485595703125, 0.04119873046875, 0.10357666015625, -0.55517578125, 0.10638427734375, -1.1337890625, -1.091796875, 0.564453125, -0.0933837890625, -0.64453125, -0.0091552734375, -0.36279296875, -0.051483154296875, 0.053924560546875, 0.54248046875, -0.54345703125, 0.277587890625, 0.10809326171875, 0.5146484375, 0.02862548828125, -0.250732421875, 0.2197265625, 0.7197265625, -0.8515625, -0.67431640625, 0.087158203125, 0.88818359375, 0.09173583984375, -0.51025390625, -0.142333984375, 0.431884765625, -0.1732177734375, 0.2037353515625, -0.468505859375, 0.166748046875, 0.0777587890625, 0.95703125, -0.87158203125, 0.0684814453125, -0.1923828125, 0.2308349609375, -0.1741943359375, -0.7236328125, -0.5556640625, 1.099609375, 0.61083984375, -0.0782470703125, 0.5791015625, 0.00995635986328125, 0.46484375, 0.0083160400390625, -0.00400543212890625, 0.129638671875, 0.6279296875, 0.89111328125, 0.724609375, -0.2017822265625, 0.54736328125, 0.8515625, -0.248046875, -0.11700439453125, 0.468017578125, 0.1864013671875, -0.07269287109375, -0.09283447265625, -0.30859375, -0.38134765625, -0.1639404296875, -0.68408203125, 0.81201171875, -0.19921875, 0.30908203125, -0.22265625, -0.7265625, 0.826171875, -0.319580078125, -0.1739501953125, 0.222412109375, -0.748046875, 0.419677734375, 0.5888671875, -0.342041015625, -0.337646484375, 0.61962890625, 0.74560546875, 0.56982421875, 0.71435546875, 0.248046875, 0.2376708984375, -0.69970703125, 0.11761474609375, 0.0177001953125, -0.09210205078125, -0.2191162109375, -0.75244140625, -1.2421875, 0.6650390625, -0.51416015625, -0.275146484375, 0.62890625, -0.77685546875, 0.2418212890625, -0.19580078125, 0.9833984375, -0.51904296875, 0.1868896484375, 0.50927734375, -0.427490234375, -0.85791015625, 1.0146484375, -0.03717041015625, 0.222900390625, -0.1005859375, 1.3388671875, -0.1121826171875, 1.390625, 0.7099609375, -0.331298828125, 0.259765625, 0.55712890625, -0.341552734375, -0.5654296875, -0.4169921875, -0.5556640625, -0.369384765625, -0.66357421875, -0.54833984375, 0.0226287841796875, 0.418701171875, 0.00872802734375, -0.73486328125, -0.35791015625, 0.194091796875, -0.72509765625, 0.68017578125, 0.1497802734375, 0.3330078125, 0.294189453125, -0.1285400390625, -0.040771484375, -0.26806640625, 0.274658203125, -0.44287109375, 0.482421875, -0.9521484375, -0.264892578125, -0.72314453125, -0.6171875, -0.1781005859375, 0.09930419921875, -0.314208984375, -0.796875, 0.219482421875, 0.439453125, 0.1951904296875, 0.302734375, -0.285400390625, 0.269287109375, 1.0224609375, 1.083984375, -0.0179290771484375, 0.86962890625, 0.3427734375, -0.0791015625, -0.11944580078125, -0.282470703125, 0.417236328125, 0.04119873046875, 0.4599609375, -0.410888671875, 0.304443359375, -0.65283203125, -1.3046875, 0.260986328125, 0.37548828125, -0.03802490234375, -0.7568359375, -1.2666015625, -0.477783203125, -1.177734375, -0.140869140625, -1.0009765625, 1.078125, -0.3740234375, -0.048309326171875, 0.0160675048828125, -1.1376953125, 4.20703125, 0.98876953125, 0.73876953125, 0.52685546875, 0.2298583984375, 0.7880859375, 0.03314208984375, -0.6533203125, -0.00167083740234375, -0.452392578125, 0.7216796875, -0.53466796875, -0.072265625, 0.9716796875, 0.40380859375, 0.489013671875, -0.48876953125, 0.0711669921875, 0.0010271072387695312, -1.08984375, -0.92919921875, 0.359130859375, 0.08428955078125, 0.374755859375, 0.1331787109375, 0.170166015625, 0.92041015625, -0.92919921875, 0.1412353515625, -0.7431640625, 0.2783203125, -0.3828125, 1.046875, 0.2095947265625, 0.11279296875, 0.4560546875, -0.09454345703125, -0.3583984375, -0.0299530029296875, 0.10687255859375, -0.335693359375, -0.2330322265625, 0.498046875, -0.7666015625, -0.1717529296875, 0.5888671875, -0.74609375, 0.513671875, -0.0169830322265625, -1.203125, 0.96923828125, -0.220947265625, 0.31982421875, -0.74658203125, -0.2376708984375, 0.0789794921875, 0.496826171875, -0.1124267578125, -0.289306640625, 0.52099609375, 0.405517578125, 0.552734375, -0.0343017578125, 0.7333984375, -1.150390625, 0.061767578125, 0.0019140243530273438, 0.405517578125, -0.444580078125, 0.0020046234130859375, -0.59814453125, -0.418212890625, -0.2464599609375, -0.59130859375, 0.5361328125, -0.0196380615234375, -0.0501708984375, 0.3359375, 0.5966796875, -0.62841796875, 0.19482421875, -0.09930419921875, -0.07476806640625, -0.6943359375, 0.888671875, 1.3232421875, -0.5537109375, -0.41943359375, -0.345458984375, 0.50146484375, 0.69482421875, 0.68896484375, -0.032501220703125, -0.77880859375, -0.304931640625 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Submitted Solution: ``` s = input().rstrip() mod = 10 ** 9 + 7 a_count = 0 rs = 0 cur_mod = (2 ** a_count) % mod for c in s: if c == 'a': a_count += 1 cur_mod = (cur_mod * 2) % mod elif c == 'b': rs = (rs + cur_mod - 1) % mod print(rs) ``` Yes
105,798
[ 0.493896484375, -0.192138671875, -0.00438690185546875, 0.0684814453125, -0.8935546875, -0.37548828125, -0.07684326171875, -0.166748046875, 0.13427734375, 0.91455078125, 0.5615234375, -0.3984375, -0.1619873046875, -0.96044921875, -0.3603515625, 0.006317138671875, -0.446044921875, -0.73681640625, -0.346435546875, -0.33837890625, -0.0732421875, -0.300048828125, -1.0478515625, 0.118408203125, -0.12744140625, 0.87646484375, 0.6962890625, -0.01007843017578125, 1.0771484375, 1.2470703125, -0.1934814453125, -0.298583984375, 0.578125, -0.73193359375, -0.1417236328125, -0.58154296875, 0.609375, -0.7763671875, -0.382080078125, -0.37451171875, 0.1815185546875, -0.41357421875, 0.646484375, -0.5498046875, -1.650390625, -0.04364013671875, -0.035552978515625, -0.55517578125, -0.0220947265625, -0.58056640625, -0.179443359375, -0.24658203125, 0.3330078125, -0.1505126953125, 0.29345703125, 0.357666015625, 0.18994140625, -0.302001953125, -1.0556640625, -0.020843505859375, 0.388427734375, 0.2271728515625, 0.1456298828125, -0.779296875, -0.0679931640625, 0.30078125, -0.204833984375, 0.02349853515625, -0.125732421875, -0.6328125, 0.06439208984375, 0.1409912109375, -0.354736328125, -0.488037109375, -0.315673828125, 0.07122802734375, 0.377197265625, -0.1138916015625, -0.8427734375, 1.162109375, -0.34814453125, 0.87353515625, 0.364501953125, 0.31103515625, -0.355712890625, -0.51025390625, 0.315673828125, 0.28125, 0.03558349609375, -0.09759521484375, -0.28564453125, 0.52783203125, -0.303955078125, -0.286376953125, 0.453857421875, 0.45849609375, -0.441162109375, 0.0897216796875, 0.556640625, 0.41064453125, 1.0478515625, 0.75634765625, -0.54638671875, 0.9658203125, -0.3017578125, -0.1539306640625, 0.0022754669189453125, -0.215576171875, -0.343017578125, -0.1070556640625, -0.236083984375, -0.262451171875, 0.459716796875, 0.35498046875, -0.5751953125, 0.9404296875, 0.341552734375, 0.53076171875, -0.480712890625, 0.57080078125, 0.421875, 0.0013265609741210938, 0.8544921875, -0.26025390625, -0.08489990234375, -0.10015869140625, -0.89794921875, 1.154296875, -0.66455078125, -0.3427734375, 0.2496337890625, 0.1298828125, -0.07373046875, 0.3857421875, -0.404052734375, 0.56640625, -0.1756591796875, 0.273681640625, 0.84130859375, -0.4736328125, 0.6357421875, -0.09967041015625, -0.1727294921875, 1.8115234375, 0.133544921875, -0.1756591796875, 0.7109375, 0.46923828125, -0.9892578125, 0.2393798828125, -1.03125, 0.736328125, 0.2257080078125, 0.1392822265625, -0.2724609375, 0.0872802734375, -0.308837890625, 0.396484375, 0.07012939453125, -0.155029296875, -0.48486328125, 0.2149658203125, -0.466552734375, 0.88525390625, -0.440185546875, 0.58837890625, -0.2056884765625, -0.26953125, -0.01049041748046875, -0.34521484375, 0.1961669921875, -0.18896484375, -0.08258056640625, 0.9296875, 0.446044921875, 0.95166015625, 1.18359375, -0.1351318359375, 0.472412109375, 0.370849609375, -0.471435546875, 0.332275390625, 0.2489013671875, 0.93505859375, 0.33203125, 0.591796875, -0.3388671875, 0.017730712890625, -0.3857421875, -0.3505859375, 0.34716796875, 0.634765625, -0.77685546875, 0.45263671875, -0.117431640625, -0.107666015625, -0.7705078125, -0.337890625, -0.0255279541015625, -0.96728515625, -0.40673828125, 0.459716796875, 0.00691986083984375, 0.50244140625, -0.347412109375, -0.5947265625, 0.276123046875, 1.2744140625, -0.34033203125, 0.20166015625, 0.432861328125, -0.023712158203125, -0.08843994140625, 0.3330078125, 0.104248046875, -0.34765625, -0.471923828125, 0.450927734375, -0.1380615234375, -0.1492919921875, -0.230224609375, 0.53564453125, 0.38330078125, 0.58154296875, -0.378173828125, -0.59765625, 0.420654296875, 1.201171875, -0.2266845703125, 0.658203125, 0.279541015625, 0.7724609375, 0.93408203125, 0.95166015625, 0.66650390625, 0.285400390625, 0.55419921875, 0.78466796875, -0.0714111328125, 0.193603515625, 0.338623046875, 0.564453125, 0.218017578125, 0.361083984375, 0.42431640625, 0.485595703125, 0.036163330078125, -0.296875, 0.01361846923828125, -0.005794525146484375, -0.4990234375, 0.67138671875, 0.0421142578125, 0.6357421875, 0.0889892578125, -0.229248046875, 0.378662109375, 0.94580078125, -1.29296875, -0.62451171875, 0.052947998046875, 0.1395263671875, 0.108642578125, 0.0012359619140625, 0.78759765625, 0.51904296875, 0.712890625, 0.60693359375, -0.21240234375, -0.273681640625, -0.6455078125, -0.9140625, -1.0625, -0.259765625, -0.85302734375, -0.128173828125, -0.10137939453125, -0.97021484375, 0.04840087890625, -0.5791015625, 0.049713134765625, 0.07623291015625, -0.295654296875, 0.94921875, -0.11297607421875, 0.2081298828125, -0.572265625, 0.5712890625, 0.1124267578125, 1.109375, -0.83251953125, 0.13330078125, -0.435302734375, -0.576171875, -0.11907958984375, 0.276123046875, 0.479248046875, 0.12841796875, -0.5576171875, -0.68603515625, -0.54833984375, 0.1239013671875, -0.4208984375, 0.0491943359375, -0.5478515625, 0.5830078125, 0.43505859375, -0.80615234375, 0.64697265625, 1.0869140625, -1.0361328125, 0.666015625, 0.359130859375, -0.333984375, -0.67529296875, 1.1923828125, 0.426513671875, 0.6494140625, -0.382080078125, -0.77294921875, -0.517578125, 0.11553955078125, 0.1519775390625, -0.74169921875, -0.337158203125, 0.6748046875, -0.01062774658203125, -0.86083984375, 0.56396484375, -0.98583984375, -0.463134765625, -0.6767578125, -0.63232421875, 0.955078125, 0.904296875, 0.2318115234375, 0.1693115234375, -0.002048492431640625, -0.09014892578125, 0.62646484375, 0.5068359375, -0.81982421875, 0.1964111328125, 0.9501953125, -0.0552978515625, 0.187255859375, 0.262451171875, -0.54833984375, -0.2235107421875, 0.02349853515625, -0.0164794921875, 0.650390625, 0.0094757080078125, 0.45947265625, 0.2353515625, 0.71728515625, -0.86669921875, 0.0810546875, -0.220703125, 0.74609375, 0.38037109375, 0.7744140625, 0.18408203125, -0.033782958984375, -0.60400390625, -1.0703125, 0.02520751953125, 0.14013671875, 0.49853515625, -0.421875, 0.998046875, 0.1280517578125, -0.6474609375, 0.57763671875, -0.63232421875, 0.380126953125, 1.1962890625, 0.2783203125, 0.8994140625, -0.80126953125, 0.4091796875, 0.01824951171875, -0.161376953125, 0.479248046875, 0.52783203125, 0.35498046875, -0.57275390625, -0.7568359375, -0.431640625, -0.02374267578125, -0.1839599609375, -0.387451171875, 0.17724609375, -0.4658203125, -0.306396484375, -0.80224609375, 0.69970703125, 0.54931640625, 0.740234375, 0.197509765625, 0.2147216796875, 0.161865234375, 0.229248046875, 0.60009765625, -0.019989013671875, 0.265625, -0.65576171875, 0.962890625, 0.244873046875, -0.3525390625, -0.63330078125, -0.456787109375, -0.1162109375, 0.15478515625, -0.30859375, -0.08349609375, -1.2763671875, 0.172119140625, -0.314453125, 0.6005859375, -0.775390625, -0.101806640625, -0.260009765625, 0.134765625, 0.1593017578125, -1.1162109375, 0.66259765625, -1.046875, 0.64306640625, 0.63427734375, -0.0994873046875, -0.248779296875, -0.227294921875, -0.89453125, -0.7451171875, -0.1497802734375, 0.8056640625, 0.06964111328125, 0.44873046875, -1.3876953125, 0.5546875, 0.394287109375, -0.587890625, 0.331298828125, -0.432373046875, 0.69287109375, -0.09576416015625, 0.62548828125, -0.5263671875, -0.71240234375, 0.04974365234375, -1.40625, 0.54150390625, -0.50439453125, 0.7890625, 0.10888671875, -0.1363525390625, 0.373046875, 0.117431640625, -0.166259765625, 0.25, -0.1986083984375, 0.55126953125, -0.96923828125, -0.9814453125, 0.62158203125, -0.1883544921875, -0.50048828125, 0.689453125, -0.0307159423828125, -0.673828125, -0.1546630859375, 0.487060546875, -0.39111328125, 0.383056640625, -0.2113037109375, 0.73193359375, -0.30322265625, -0.74365234375, -0.436767578125, -0.7314453125, 0.7578125, -0.348388671875, -0.5244140625, -0.07781982421875, -1.310546875, -0.28369140625, 0.046173095703125, -0.446044921875, 0.286376953125, 0.40087890625, -0.01506805419921875, -0.186279296875, -0.2100830078125, -0.5263671875, -0.401611328125, -0.7431640625, -0.244873046875, -0.058868408203125, 0.62744140625, 0.9091796875, -0.06597900390625, -0.283203125, -0.1544189453125, -0.11016845703125, 0.096923828125, -0.57177734375, -0.2177734375, -0.0312042236328125, -0.4033203125, -0.3046875, 0.485107421875, 0.040191650390625, 0.52490234375, 0.78271484375, -0.199951171875, 0.46923828125, 0.331787109375, -0.68212890625, 1.3193359375, -0.01158905029296875, -1.2626953125, -0.603515625, 0.556640625, 0.09368896484375, 0.6552734375, 0.322265625, -0.97705078125, -0.587890625, -1.060546875, 0.4111328125, -0.95166015625, -0.332763671875, -1.2822265625, -0.63916015625, -0.6357421875, 0.294677734375, 0.1805419921875, -0.4990234375, 0.52880859375, -0.8681640625, 0.319580078125, -0.94287109375, 0.10833740234375, -0.58349609375, -0.5302734375, 0.0823974609375, 0.904296875, 0.15673828125, 0.33642578125, 0.044769287109375, -0.414306640625, 0.43115234375, -0.2073974609375, -0.7197265625, -0.32763671875, -0.322998046875, 0.25341796875, -0.22412109375, -0.2081298828125, -0.64697265625, 1.0107421875, -0.5712890625, 0.61181640625, 0.126953125, -0.422607421875, -0.139892578125, -0.22509765625, 1.033203125, -0.401611328125, 0.140380859375, -0.00807952880859375, 0.3662109375, 0.5712890625, -0.521484375, -0.385986328125, -0.52685546875, -0.54248046875, -0.87451171875, 0.5107421875, -0.349609375, 0.21484375, -0.73486328125, -0.163330078125, 1.2353515625, -0.422119140625, 0.44580078125, 1.0546875, 0.1014404296875, 0.2802734375, -0.427490234375, 0.71337890625, 0.51123046875, -0.275390625, -0.000667572021484375, -0.1763916015625, -0.50048828125, 0.0017385482788085938, -0.365234375, -0.86181640625, -0.71435546875, 0.220703125, 1.3525390625, -0.230224609375, 0.783203125, -0.221923828125, -1.2109375, -0.459228515625, 0.5830078125, 0.1983642578125, 0.203857421875, 0.5791015625, -0.1922607421875, -0.01526641845703125, 0.0107269287109375, -0.425048828125, -0.587890625, -0.69140625, 1.353515625, -0.7412109375, -0.6572265625, 1.044921875, 0.8642578125, -1.171875, -0.95751953125, 0.0217132568359375, -0.080078125, -0.1827392578125, -0.56494140625, -0.022918701171875, 0.6103515625, -0.6044921875, 0.0119476318359375, 0.2081298828125, -0.12255859375, 0.2135009765625, -0.03692626953125, 0.494873046875, -0.34423828125, 0.525390625, 0.62060546875, -0.603515625, -0.371826171875, -0.97314453125, -0.1385498046875, -0.337158203125, 0.263427734375, 0.728515625, -0.0716552734375, 0.340576171875, 0.64404296875, -0.060821533203125, 0.69873046875, -0.5751953125, -0.1712646484375, 0.2027587890625, -0.54833984375, -0.476806640625, 0.058624267578125, 0.29150390625, -0.1134033203125, 0.443359375, -0.56787109375, -0.10894775390625, 0.325927734375, 0.58837890625, -0.1815185546875, -0.6884765625, -0.2193603515625, -1.396484375, -0.455078125, -0.54833984375, -0.8154296875, -0.1104736328125, 0.5341796875, 0.0943603515625, -0.62646484375, 0.07904052734375, 0.61865234375, -0.6103515625, 0.5771484375, -0.41943359375, 0.2470703125, -0.330078125, -0.478759765625, -0.984375, -0.1505126953125, -0.595703125, -0.40478515625, -0.62255859375, 0.73486328125, 0.038177490234375, 0.294189453125, -0.23193359375, 0.8359375, -0.149658203125, -0.463134765625, 0.417724609375, 0.08551025390625, -0.1533203125, 1.2705078125, 0.2462158203125, 0.08294677734375, 0.275146484375, -0.35009765625, -0.194580078125, -0.39208984375, 0.7841796875, 0.334716796875, -0.411376953125, -0.259765625, -0.044342041015625, 0.1669921875, -0.78857421875, 0.312255859375, -0.33544921875, 0.09722900390625, -0.00838470458984375, -0.09173583984375, 0.247314453125, 1.2158203125, -0.1917724609375, 0.1185302734375, 0.171142578125, 0.19970703125, 0.24755859375, 0.321533203125, 0.1243896484375, 0.59326171875, -0.32275390625, -0.346923828125, -0.205322265625, 0.424560546875, 0.040679931640625, 0.2132568359375, -0.5107421875, -0.94091796875, -0.63916015625, -0.125732421875, -0.06463623046875, 0.48974609375, 0.376220703125, -0.434814453125, 0.058349609375, -0.036956787109375, -0.477783203125, 0.1199951171875, -1.1328125, -1.0859375, 0.55517578125, -0.0875244140625, -0.55029296875, -0.05059814453125, -0.353271484375, -0.147216796875, 0.10760498046875, 0.5634765625, -0.57177734375, 0.30126953125, 0.04412841796875, 0.5537109375, 0.0209808349609375, -0.237548828125, 0.23876953125, 0.66796875, -0.84619140625, -0.6640625, -0.013641357421875, 0.958984375, 0.054962158203125, -0.5166015625, -0.1591796875, 0.42919921875, -0.240966796875, 0.1458740234375, -0.467529296875, 0.08343505859375, 0.2091064453125, 0.9296875, -0.9453125, -0.00930023193359375, -0.17431640625, 0.2178955078125, -0.1282958984375, -0.72314453125, -0.51123046875, 1.126953125, 0.5673828125, 0.00035190582275390625, 0.58447265625, 0.06500244140625, 0.53466796875, -0.0908203125, 0.04461669921875, 0.11834716796875, 0.62841796875, 0.8193359375, 0.62255859375, -0.30712890625, 0.427490234375, 0.77587890625, -0.25341796875, -0.3369140625, 0.41943359375, 0.190185546875, -0.194580078125, -0.0295562744140625, -0.277587890625, -0.343017578125, -0.1573486328125, -0.6982421875, 0.71044921875, -0.1202392578125, 0.33251953125, -0.2783203125, -0.60595703125, 0.86962890625, -0.368408203125, -0.185791015625, 0.2071533203125, -0.6748046875, 0.365234375, 0.6376953125, -0.263916015625, -0.352783203125, 0.650390625, 0.7412109375, 0.66650390625, 0.7275390625, 0.26171875, 0.150146484375, -0.6376953125, 0.060638427734375, 0.017578125, -0.1265869140625, -0.2376708984375, -0.693359375, -1.2958984375, 0.66943359375, -0.564453125, -0.409423828125, 0.63330078125, -0.83056640625, 0.2330322265625, -0.13525390625, 1.0126953125, -0.51953125, 0.2021484375, 0.52783203125, -0.307861328125, -0.7978515625, 0.96875, -0.088623046875, 0.1444091796875, -0.1754150390625, 1.365234375, -0.05914306640625, 1.2958984375, 0.6044921875, -0.346923828125, 0.2313232421875, 0.50439453125, -0.36767578125, -0.5400390625, -0.404296875, -0.5107421875, -0.2900390625, -0.69140625, -0.5322265625, 0.09332275390625, 0.3525390625, -0.0008606910705566406, -0.6533203125, -0.2413330078125, 0.099609375, -0.84716796875, 0.7470703125, 0.1199951171875, 0.28955078125, 0.252685546875, -0.016876220703125, -0.067138671875, -0.2108154296875, 0.1959228515625, -0.432373046875, 0.466796875, -0.9384765625, -0.269287109375, -0.66748046875, -0.7001953125, -0.2208251953125, 0.040771484375, -0.332763671875, -0.74853515625, 0.25537109375, 0.43896484375, 0.1273193359375, 0.26220703125, -0.213134765625, 0.2900390625, 0.95068359375, 1.0849609375, -0.0283050537109375, 0.80224609375, 0.4267578125, -0.04833984375, -0.1383056640625, -0.265869140625, 0.452392578125, -0.01369476318359375, 0.383056640625, -0.406982421875, 0.309326171875, -0.70166015625, -1.3466796875, 0.1839599609375, 0.385009765625, 0.0184173583984375, -0.78271484375, -1.2451171875, -0.4638671875, -1.2021484375, -0.2000732421875, -0.97900390625, 1.0478515625, -0.334716796875, -0.00983428955078125, -0.09613037109375, -1.1103515625, 4.2734375, 0.99853515625, 0.7353515625, 0.389404296875, 0.197509765625, 0.80029296875, -0.006198883056640625, -0.64306640625, -0.004184722900390625, -0.44921875, 0.69677734375, -0.55029296875, -0.061004638671875, 0.94384765625, 0.4130859375, 0.4912109375, -0.5380859375, 0.1856689453125, 0.0189361572265625, -1.00390625, -0.9765625, 0.2288818359375, 0.040069580078125, 0.45751953125, 0.131591796875, 0.2384033203125, 0.97900390625, -0.7919921875, 0.32470703125, -0.72509765625, 0.32373046875, -0.433349609375, 1.044921875, 0.1185302734375, 0.09814453125, 0.4248046875, -0.06304931640625, -0.357177734375, 0.04150390625, 0.024566650390625, -0.28662109375, -0.1827392578125, 0.5498046875, -0.71923828125, -0.1376953125, 0.63623046875, -0.71875, 0.52978515625, 0.060821533203125, -1.19921875, 0.919921875, -0.1885986328125, 0.3984375, -0.7744140625, -0.136962890625, 0.00799560546875, 0.412841796875, -0.189697265625, -0.281494140625, 0.470703125, 0.47021484375, 0.5322265625, -0.076171875, 0.669921875, -1.123046875, 0.0030117034912109375, -0.045013427734375, 0.263916015625, -0.4013671875, -0.0136566162109375, -0.52685546875, -0.341064453125, -0.35498046875, -0.6318359375, 0.55712890625, -0.01050567626953125, -0.1522216796875, 0.3408203125, 0.5908203125, -0.62109375, 0.219970703125, -0.1595458984375, -0.002361297607421875, -0.60009765625, 0.8779296875, 1.310546875, -0.60595703125, -0.435302734375, -0.328125, 0.58056640625, 0.65087890625, 0.66748046875, -0.0005326271057128906, -0.703125, -0.27880859375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Submitted Solution: ``` MOD = 1e9 + 7 s = input() ans = 0 b = 0 for c in s[::-1]: if c == 'a': ans = (ans + b) % MOD b = (2 * b) % MOD else: b = (b + 1) % MOD print(int(ans)) ``` Yes
105,799
[ 0.50390625, -0.14501953125, -0.0394287109375, 0.033660888671875, -0.90087890625, -0.423583984375, -0.0860595703125, -0.129150390625, 0.1475830078125, 0.89111328125, 0.50244140625, -0.349365234375, -0.139892578125, -0.97802734375, -0.41796875, -0.043853759765625, -0.44189453125, -0.693359375, -0.320556640625, -0.38623046875, -0.029266357421875, -0.278564453125, -1.1376953125, 0.147216796875, -0.150634765625, 0.91162109375, 0.65234375, -0.057525634765625, 1.0361328125, 1.197265625, -0.214111328125, -0.2445068359375, 0.60302734375, -0.80810546875, -0.2393798828125, -0.60693359375, 0.62744140625, -0.8154296875, -0.301513671875, -0.421875, 0.227294921875, -0.456787109375, 0.615234375, -0.56689453125, -1.7236328125, -0.09375, -0.0404052734375, -0.484375, -0.0218505859375, -0.463623046875, -0.19677734375, -0.365234375, 0.321044921875, -0.1480712890625, 0.23876953125, 0.30712890625, 0.24072265625, -0.3115234375, -1.02734375, 0.048828125, 0.41357421875, 0.1778564453125, 0.10406494140625, -0.8095703125, -0.1610107421875, 0.251220703125, -0.230712890625, 0.0914306640625, -0.1776123046875, -0.60302734375, -0.0194549560546875, 0.1082763671875, -0.315185546875, -0.46240234375, -0.283203125, 0.05950927734375, 0.39306640625, -0.07940673828125, -0.80859375, 1.162109375, -0.379638671875, 0.875, 0.328857421875, 0.273681640625, -0.359375, -0.53271484375, 0.2147216796875, 0.3232421875, 0.024383544921875, -0.127685546875, -0.3642578125, 0.59228515625, -0.31103515625, -0.1756591796875, 0.45654296875, 0.50732421875, -0.41796875, 0.04400634765625, 0.5078125, 0.379150390625, 0.95654296875, 0.77099609375, -0.51708984375, 0.9501953125, -0.335693359375, -0.12176513671875, 0.04052734375, -0.223388671875, -0.3251953125, -0.1365966796875, -0.2108154296875, -0.265869140625, 0.46044921875, 0.3701171875, -0.5693359375, 0.95166015625, 0.335693359375, 0.5556640625, -0.55712890625, 0.54931640625, 0.427001953125, 0.1202392578125, 0.82080078125, -0.261962890625, -0.1453857421875, -0.10186767578125, -0.8408203125, 1.16796875, -0.6767578125, -0.328125, 0.3095703125, 0.1043701171875, -0.046295166015625, 0.38232421875, -0.49169921875, 0.66845703125, -0.01177215576171875, 0.25390625, 0.8046875, -0.432373046875, 0.72900390625, -0.16943359375, -0.1468505859375, 1.82421875, 0.1488037109375, -0.1812744140625, 0.6162109375, 0.461669921875, -0.970703125, 0.2027587890625, -1.109375, 0.72119140625, 0.257568359375, 0.1396484375, -0.2783203125, 0.08880615234375, -0.329833984375, 0.388671875, 0.1429443359375, -0.24560546875, -0.46923828125, 0.1888427734375, -0.4765625, 0.84228515625, -0.375, 0.54296875, -0.140869140625, -0.207763671875, -0.049072265625, -0.35107421875, 0.1024169921875, -0.1273193359375, -0.13134765625, 0.97265625, 0.51513671875, 0.986328125, 1.173828125, -0.225830078125, 0.420654296875, 0.368896484375, -0.47509765625, 0.358642578125, 0.208740234375, 0.95263671875, 0.408447265625, 0.53857421875, -0.3759765625, 0.006763458251953125, -0.43115234375, -0.4404296875, 0.40478515625, 0.63330078125, -0.74755859375, 0.4619140625, -0.177978515625, -0.1375732421875, -0.76611328125, -0.28857421875, -0.023468017578125, -1.0634765625, -0.375732421875, 0.45849609375, -0.02630615234375, 0.452392578125, -0.3828125, -0.58349609375, 0.27978515625, 1.306640625, -0.2861328125, 0.192138671875, 0.396484375, -0.09765625, -0.09051513671875, 0.404052734375, 0.1229248046875, -0.36865234375, -0.50732421875, 0.53173828125, -0.154541015625, -0.08782958984375, -0.2318115234375, 0.5849609375, 0.318603515625, 0.7138671875, -0.362548828125, -0.62548828125, 0.498779296875, 1.150390625, -0.2025146484375, 0.6328125, 0.3251953125, 0.79248046875, 0.98974609375, 0.92919921875, 0.634765625, 0.273193359375, 0.611328125, 0.84033203125, -0.061981201171875, 0.276611328125, 0.324462890625, 0.55224609375, 0.25732421875, 0.4599609375, 0.50537109375, 0.440673828125, 0.12359619140625, -0.2435302734375, -0.0011920928955078125, -0.051513671875, -0.497802734375, 0.6533203125, 0.0478515625, 0.64794921875, 0.1221923828125, -0.1771240234375, 0.36865234375, 0.9990234375, -1.3134765625, -0.59375, 0.07208251953125, 0.082763671875, 0.1268310546875, 0.034027099609375, 0.7275390625, 0.449951171875, 0.802734375, 0.5302734375, -0.206787109375, -0.30322265625, -0.55126953125, -0.85400390625, -1.0419921875, -0.2496337890625, -0.91259765625, -0.1624755859375, -0.171630859375, -0.99755859375, 0.0090789794921875, -0.53564453125, 0.01556396484375, 0.1282958984375, -0.47900390625, 0.97216796875, -0.1102294921875, 0.1402587890625, -0.55126953125, 0.568359375, 0.129638671875, 1.0869140625, -0.89501953125, 0.1746826171875, -0.423828125, -0.62109375, -0.0758056640625, 0.2445068359375, 0.43408203125, 0.09368896484375, -0.63671875, -0.7373046875, -0.54443359375, 0.12255859375, -0.361083984375, 0.109619140625, -0.611328125, 0.64111328125, 0.4697265625, -0.791015625, 0.591796875, 1.1005859375, -0.97314453125, 0.7265625, 0.266357421875, -0.317138671875, -0.748046875, 1.2021484375, 0.51953125, 0.6416015625, -0.3876953125, -0.74365234375, -0.444091796875, 0.0902099609375, 0.1077880859375, -0.75537109375, -0.3623046875, 0.6533203125, 0.01312255859375, -0.9013671875, 0.5498046875, -1.0771484375, -0.50732421875, -0.6767578125, -0.56591796875, 1.0517578125, 0.890625, 0.2587890625, 0.172119140625, -0.0207061767578125, -0.02655029296875, 0.66845703125, 0.5859375, -0.9111328125, 0.240478515625, 0.974609375, -0.0972900390625, 0.2452392578125, 0.271484375, -0.521484375, -0.300048828125, -0.02032470703125, 0.055328369140625, 0.70947265625, -0.060760498046875, 0.53173828125, 0.2418212890625, 0.69580078125, -0.9072265625, 0.056854248046875, -0.2001953125, 0.8193359375, 0.381591796875, 0.6826171875, 0.220458984375, -0.07354736328125, -0.61572265625, -1.140625, 0.0248565673828125, 0.19677734375, 0.55712890625, -0.36962890625, 1.0341796875, 0.10223388671875, -0.708984375, 0.5322265625, -0.640625, 0.521484375, 1.1171875, 0.3232421875, 0.830078125, -0.84912109375, 0.447509765625, 0.10235595703125, -0.2298583984375, 0.433349609375, 0.59716796875, 0.36767578125, -0.50341796875, -0.76806640625, -0.458740234375, 0.01727294921875, -0.205078125, -0.422607421875, 0.178466796875, -0.53076171875, -0.19873046875, -0.94775390625, 0.61376953125, 0.6201171875, 0.7724609375, 0.255126953125, 0.2294921875, 0.15380859375, 0.17236328125, 0.59228515625, -0.0158843994140625, 0.2288818359375, -0.60986328125, 0.876953125, 0.2890625, -0.321044921875, -0.51513671875, -0.418701171875, -0.1253662109375, 0.10675048828125, -0.4296875, -0.050628662109375, -1.2177734375, 0.1832275390625, -0.2261962890625, 0.6015625, -0.81640625, -0.11492919921875, -0.310546875, 0.0782470703125, 0.2027587890625, -1.0478515625, 0.607421875, -1.0263671875, 0.65966796875, 0.5927734375, -0.13720703125, -0.17041015625, -0.250244140625, -0.88037109375, -0.70068359375, -0.1939697265625, 0.7294921875, -0.041259765625, 0.436767578125, -1.4091796875, 0.64208984375, 0.36181640625, -0.67431640625, 0.300048828125, -0.426025390625, 0.630859375, -0.1519775390625, 0.69677734375, -0.51953125, -0.677734375, 0.07379150390625, -1.37890625, 0.57177734375, -0.48291015625, 0.80126953125, 0.2403564453125, -0.1502685546875, 0.3173828125, 0.2230224609375, -0.180419921875, 0.2130126953125, -0.212158203125, 0.48486328125, -0.97216796875, -1.0712890625, 0.59912109375, -0.1600341796875, -0.41748046875, 0.72265625, -0.06597900390625, -0.595703125, -0.175537109375, 0.50439453125, -0.452392578125, 0.37646484375, -0.22216796875, 0.63427734375, -0.38623046875, -0.70751953125, -0.347412109375, -0.736328125, 0.80078125, -0.34228515625, -0.6123046875, -0.1182861328125, -1.2998046875, -0.25390625, 0.01392364501953125, -0.381103515625, 0.2181396484375, 0.39306640625, 0.04107666015625, -0.1947021484375, -0.211669921875, -0.5263671875, -0.40966796875, -0.6796875, -0.27099609375, 0.0462646484375, 0.658203125, 0.95703125, 0.0060272216796875, -0.2890625, -0.1434326171875, -0.084716796875, 0.0826416015625, -0.5390625, -0.302490234375, -0.06787109375, -0.4453125, -0.272705078125, 0.43359375, 0.03851318359375, 0.6005859375, 0.78173828125, -0.1533203125, 0.4423828125, 0.288330078125, -0.68017578125, 1.44921875, 0.0131988525390625, -1.2451171875, -0.70458984375, 0.57470703125, 0.1280517578125, 0.71533203125, 0.3291015625, -1.03515625, -0.6435546875, -1.087890625, 0.40283203125, -0.93212890625, -0.392822265625, -1.2392578125, -0.66015625, -0.693359375, 0.269287109375, 0.1524658203125, -0.537109375, 0.525390625, -0.8623046875, 0.2230224609375, -0.9736328125, 0.07269287109375, -0.5830078125, -0.497314453125, 0.08172607421875, 0.93115234375, 0.11505126953125, 0.359619140625, -0.009796142578125, -0.43798828125, 0.40966796875, -0.1815185546875, -0.73291015625, -0.28955078125, -0.22119140625, 0.29638671875, -0.24951171875, -0.11688232421875, -0.71826171875, 1.0400390625, -0.603515625, 0.5810546875, 0.251708984375, -0.414306640625, -0.12310791015625, -0.333740234375, 0.927734375, -0.457763671875, 0.135498046875, -0.0250396728515625, 0.361083984375, 0.61376953125, -0.541015625, -0.39013671875, -0.57421875, -0.55224609375, -0.95654296875, 0.478271484375, -0.365966796875, 0.18408203125, -0.810546875, -0.09307861328125, 1.2060546875, -0.56494140625, 0.400634765625, 1.041015625, 0.09423828125, 0.2113037109375, -0.35498046875, 0.72119140625, 0.5693359375, -0.23876953125, 0.0220184326171875, -0.0916748046875, -0.5009765625, 0.01000213623046875, -0.401611328125, -0.8525390625, -0.765625, 0.2154541015625, 1.3798828125, -0.281982421875, 0.78466796875, -0.1793212890625, -1.2001953125, -0.45263671875, 0.57958984375, 0.1749267578125, 0.19482421875, 0.6455078125, -0.1458740234375, -0.056610107421875, 0.0767822265625, -0.4443359375, -0.615234375, -0.6787109375, 1.2958984375, -0.7158203125, -0.60205078125, 1.0810546875, 0.9296875, -1.2578125, -0.978515625, 0.10272216796875, -0.03692626953125, -0.2435302734375, -0.61865234375, -0.0173797607421875, 0.64990234375, -0.65087890625, 0.10284423828125, 0.2174072265625, -0.05059814453125, 0.302978515625, -0.0791015625, 0.58154296875, -0.412109375, 0.5390625, 0.6669921875, -0.61572265625, -0.30224609375, -1.025390625, -0.1790771484375, -0.2452392578125, 0.2020263671875, 0.70751953125, 0.037200927734375, 0.338134765625, 0.74755859375, -0.09539794921875, 0.697265625, -0.51123046875, -0.2337646484375, 0.237060546875, -0.517578125, -0.488037109375, 0.07763671875, 0.306884765625, -0.032867431640625, 0.5009765625, -0.64501953125, -0.06695556640625, 0.306396484375, 0.62548828125, -0.21435546875, -0.5576171875, -0.275146484375, -1.4365234375, -0.469970703125, -0.640625, -0.83056640625, -0.248291015625, 0.58203125, 0.16748046875, -0.62841796875, 0.032562255859375, 0.51806640625, -0.7021484375, 0.537109375, -0.440185546875, 0.253662109375, -0.302734375, -0.51123046875, -1.029296875, -0.1851806640625, -0.65380859375, -0.47412109375, -0.65625, 0.73291015625, 0.01019287109375, 0.24951171875, -0.26513671875, 0.92138671875, -0.07781982421875, -0.55517578125, 0.5146484375, 0.10595703125, -0.1673583984375, 1.3466796875, 0.275146484375, 0.2025146484375, 0.15625, -0.383544921875, -0.16845703125, -0.322998046875, 0.7822265625, 0.38525390625, -0.403076171875, -0.1868896484375, -0.033843994140625, 0.2108154296875, -0.791015625, 0.342041015625, -0.372314453125, 0.0809326171875, -0.0006284713745117188, -0.056060791015625, 0.24365234375, 1.291015625, -0.2193603515625, 0.10601806640625, 0.1297607421875, 0.1392822265625, 0.279296875, 0.3251953125, 0.10540771484375, 0.658203125, -0.265869140625, -0.37060546875, -0.188720703125, 0.384765625, 0.0269317626953125, 0.2117919921875, -0.46142578125, -1.0048828125, -0.623046875, -0.211669921875, -0.09320068359375, 0.449951171875, 0.370361328125, -0.473876953125, 0.031402587890625, 0.073486328125, -0.5244140625, 0.08660888671875, -1.1591796875, -1.103515625, 0.56591796875, -0.10980224609375, -0.59228515625, -0.004791259765625, -0.341796875, -0.1400146484375, 0.07501220703125, 0.576171875, -0.51904296875, 0.33740234375, 0.069580078125, 0.529296875, 0.058349609375, -0.2376708984375, 0.2442626953125, 0.701171875, -0.865234375, -0.701171875, 0.08331298828125, 0.8935546875, 0.0987548828125, -0.50439453125, -0.1424560546875, 0.420166015625, -0.227294921875, 0.2056884765625, -0.5078125, 0.1409912109375, 0.1417236328125, 0.98046875, -0.87060546875, 0.0213623046875, -0.192626953125, 0.169921875, -0.147216796875, -0.70849609375, -0.5576171875, 1.0888671875, 0.607421875, -0.08697509765625, 0.62744140625, 0.0136871337890625, 0.4833984375, -0.014068603515625, 0.007904052734375, 0.0906982421875, 0.60595703125, 0.8466796875, 0.68212890625, -0.207275390625, 0.4912109375, 0.84619140625, -0.2177734375, -0.1353759765625, 0.460205078125, 0.1883544921875, -0.113525390625, -0.111083984375, -0.2998046875, -0.356689453125, -0.1717529296875, -0.7001953125, 0.75634765625, -0.141845703125, 0.36865234375, -0.2210693359375, -0.7158203125, 0.841796875, -0.35595703125, -0.1539306640625, 0.246337890625, -0.724609375, 0.410888671875, 0.6630859375, -0.32470703125, -0.335693359375, 0.6142578125, 0.7783203125, 0.54638671875, 0.73486328125, 0.191162109375, 0.2255859375, -0.650390625, 0.1663818359375, 0.00983428955078125, -0.10760498046875, -0.2203369140625, -0.7939453125, -1.2255859375, 0.677734375, -0.59765625, -0.338623046875, 0.61474609375, -0.79296875, 0.269775390625, -0.1729736328125, 0.95263671875, -0.5205078125, 0.18408203125, 0.54541015625, -0.375732421875, -0.8349609375, 1.01953125, -0.039215087890625, 0.2071533203125, -0.11798095703125, 1.326171875, -0.1295166015625, 1.3935546875, 0.68798828125, -0.377685546875, 0.256103515625, 0.5517578125, -0.3359375, -0.485107421875, -0.43505859375, -0.58740234375, -0.328369140625, -0.66650390625, -0.5615234375, 0.09002685546875, 0.406982421875, 0.00811004638671875, -0.70068359375, -0.26611328125, 0.17333984375, -0.77001953125, 0.6640625, 0.10833740234375, 0.341064453125, 0.3076171875, -0.050567626953125, 0.0036468505859375, -0.24755859375, 0.259033203125, -0.46142578125, 0.484619140625, -0.99169921875, -0.255126953125, -0.70849609375, -0.66796875, -0.1785888671875, 0.08282470703125, -0.293701171875, -0.81787109375, 0.2392578125, 0.47509765625, 0.1710205078125, 0.289794921875, -0.2744140625, 0.3115234375, 1.029296875, 1.0703125, -0.001979827880859375, 0.87646484375, 0.38818359375, -0.07452392578125, -0.1473388671875, -0.255615234375, 0.41064453125, -0.02325439453125, 0.48779296875, -0.40625, 0.30029296875, -0.6298828125, -1.3388671875, 0.254638671875, 0.410888671875, 0.009307861328125, -0.77001953125, -1.263671875, -0.466552734375, -1.1943359375, -0.136474609375, -0.984375, 1.0791015625, -0.421630859375, -0.07611083984375, -0.039794921875, -1.1279296875, 4.19921875, 1.0283203125, 0.72802734375, 0.483154296875, 0.26318359375, 0.7802734375, 0.002559661865234375, -0.61962890625, 0.028961181640625, -0.484130859375, 0.72998046875, -0.50390625, -0.0662841796875, 0.951171875, 0.41455078125, 0.50830078125, -0.48291015625, 0.127685546875, -0.025115966796875, -1.052734375, -0.9677734375, 0.3603515625, 0.06365966796875, 0.398681640625, 0.08050537109375, 0.1717529296875, 0.9677734375, -0.91455078125, 0.1519775390625, -0.77197265625, 0.267822265625, -0.3994140625, 1.0615234375, 0.14990234375, 0.11163330078125, 0.41015625, -0.08221435546875, -0.364501953125, 0.01039886474609375, 0.061553955078125, -0.29345703125, -0.227294921875, 0.494140625, -0.8017578125, -0.1591796875, 0.634765625, -0.78369140625, 0.546875, -0.01031494140625, -1.1953125, 0.97314453125, -0.23193359375, 0.348876953125, -0.74755859375, -0.2105712890625, 0.094970703125, 0.4658203125, -0.15087890625, -0.306640625, 0.4921875, 0.39013671875, 0.501953125, -0.029083251953125, 0.72314453125, -1.107421875, 0.0302886962890625, -0.03485107421875, 0.39892578125, -0.413330078125, 0.0236968994140625, -0.59521484375, -0.384765625, -0.274169921875, -0.580078125, 0.54296875, -0.00774383544921875, -0.0809326171875, 0.34228515625, 0.57275390625, -0.61865234375, 0.1697998046875, -0.1334228515625, -0.04736328125, -0.67822265625, 0.8671875, 1.2666015625, -0.572265625, -0.421630859375, -0.3056640625, 0.54736328125, 0.66748046875, 0.67041015625, -0.00971221923828125, -0.794921875, -0.295654296875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Submitted Solution: ``` n=input() i=0 while "ab" in n: n=n.replace("ab","bba") i+=1 print(i%(10**6+7)) ``` No
105,800
[ 0.4892578125, -0.146240234375, -0.03466796875, 0.05078125, -0.859375, -0.433837890625, -0.11346435546875, -0.146484375, 0.2171630859375, 0.85009765625, 0.5068359375, -0.3359375, -0.1800537109375, -0.99658203125, -0.44189453125, -0.056854248046875, -0.450927734375, -0.75927734375, -0.30712890625, -0.3583984375, -0.032440185546875, -0.2109375, -1.0693359375, 0.0970458984375, -0.154296875, 0.93603515625, 0.576171875, -0.032684326171875, 0.990234375, 1.185546875, -0.235107421875, -0.21484375, 0.59375, -0.81591796875, -0.2342529296875, -0.62939453125, 0.56591796875, -0.8203125, -0.373779296875, -0.40771484375, 0.2294921875, -0.49853515625, 0.58740234375, -0.489501953125, -1.7099609375, -0.048370361328125, -0.000522613525390625, -0.46533203125, -0.0202789306640625, -0.424072265625, -0.1551513671875, -0.370361328125, 0.33349609375, -0.1375732421875, 0.2230224609375, 0.277099609375, 0.2147216796875, -0.2890625, -0.96044921875, 0.1229248046875, 0.5087890625, 0.221435546875, 0.06634521484375, -0.81494140625, -0.1385498046875, 0.29443359375, -0.279052734375, 0.1632080078125, -0.163818359375, -0.5791015625, -0.0157623291015625, 0.1551513671875, -0.362060546875, -0.4658203125, -0.332275390625, 0.07379150390625, 0.36572265625, -0.0775146484375, -0.8662109375, 1.1064453125, -0.38671875, 0.888671875, 0.365234375, 0.18212890625, -0.399658203125, -0.58935546875, 0.1954345703125, 0.339599609375, 0.079345703125, -0.06634521484375, -0.428955078125, 0.56787109375, -0.369384765625, -0.18505859375, 0.413330078125, 0.57080078125, -0.4775390625, 0.046661376953125, 0.455078125, 0.41259765625, 1.0107421875, 0.7890625, -0.48681640625, 0.96923828125, -0.35693359375, -0.1363525390625, 0.083984375, -0.27197265625, -0.303955078125, -0.12091064453125, -0.2271728515625, -0.288818359375, 0.414794921875, 0.364501953125, -0.6015625, 0.97119140625, 0.34326171875, 0.587890625, -0.50390625, 0.57763671875, 0.464599609375, 0.1031494140625, 0.798828125, -0.24462890625, -0.12420654296875, -0.11236572265625, -0.89306640625, 1.1533203125, -0.6669921875, -0.32421875, 0.303955078125, 0.1226806640625, -0.0518798828125, 0.326416015625, -0.48828125, 0.6396484375, 0.041595458984375, 0.2257080078125, 0.70361328125, -0.404052734375, 0.73681640625, -0.222900390625, -0.191162109375, 1.8212890625, 0.1875, -0.173828125, 0.65283203125, 0.42529296875, -0.94140625, 0.30810546875, -1.078125, 0.75390625, 0.2685546875, 0.120361328125, -0.32275390625, 0.08416748046875, -0.285400390625, 0.353271484375, 0.1661376953125, -0.262451171875, -0.4990234375, 0.152099609375, -0.51025390625, 0.86279296875, -0.359375, 0.6181640625, -0.185302734375, -0.188232421875, -0.0548095703125, -0.3349609375, 0.10400390625, -0.1937255859375, 0.0015697479248046875, 1.0029296875, 0.459228515625, 1.0166015625, 1.134765625, -0.210693359375, 0.448486328125, 0.375244140625, -0.4482421875, 0.32568359375, 0.284912109375, 0.93798828125, 0.411865234375, 0.487060546875, -0.34912109375, 0.024444580078125, -0.37841796875, -0.4501953125, 0.44287109375, 0.638671875, -0.77685546875, 0.4091796875, -0.1973876953125, -0.11102294921875, -0.76904296875, -0.325927734375, 0.033477783203125, -1.029296875, -0.371826171875, 0.463623046875, -0.007167816162109375, 0.47216796875, -0.362060546875, -0.56201171875, 0.281005859375, 1.291015625, -0.2396240234375, 0.28173828125, 0.453125, -0.07861328125, -0.1583251953125, 0.282470703125, 0.09527587890625, -0.36669921875, -0.459228515625, 0.5712890625, -0.1309814453125, -0.0958251953125, -0.2366943359375, 0.5732421875, 0.31298828125, 0.6865234375, -0.285888671875, -0.63671875, 0.464599609375, 1.1103515625, -0.2498779296875, 0.6015625, 0.30224609375, 0.71337890625, 0.9560546875, 0.919921875, 0.58984375, 0.331787109375, 0.60791015625, 0.83349609375, -0.0596923828125, 0.262939453125, 0.3212890625, 0.59619140625, 0.292724609375, 0.5009765625, 0.479736328125, 0.453125, 0.07733154296875, -0.2054443359375, -0.047393798828125, -0.07537841796875, -0.44921875, 0.6982421875, 0.015594482421875, 0.72509765625, 0.1259765625, -0.1649169921875, 0.4013671875, 0.9716796875, -1.3017578125, -0.6220703125, -0.059417724609375, 0.05877685546875, 0.183349609375, 0.07025146484375, 0.70654296875, 0.417236328125, 0.734375, 0.58251953125, -0.187744140625, -0.261474609375, -0.5068359375, -0.94091796875, -0.97802734375, -0.287841796875, -0.9365234375, -0.2320556640625, -0.1541748046875, -1.0390625, 0.1187744140625, -0.51220703125, -0.0858154296875, 0.1412353515625, -0.405029296875, 1.0078125, -0.1387939453125, 0.21923828125, -0.5498046875, 0.5458984375, 0.131591796875, 1.056640625, -0.837890625, 0.1572265625, -0.3134765625, -0.59814453125, -0.08258056640625, 0.32080078125, 0.408447265625, 0.161865234375, -0.63720703125, -0.78466796875, -0.525390625, 0.14501953125, -0.38671875, 0.06671142578125, -0.65771484375, 0.70458984375, 0.426025390625, -0.7607421875, 0.60693359375, 1.0986328125, -0.96875, 0.67822265625, 0.2978515625, -0.263916015625, -0.7314453125, 1.22265625, 0.572265625, 0.62353515625, -0.378173828125, -0.79052734375, -0.411376953125, 0.09112548828125, 0.1273193359375, -0.77685546875, -0.341552734375, 0.62451171875, 0.0307464599609375, -0.9375, 0.490234375, -1.111328125, -0.55419921875, -0.662109375, -0.6025390625, 1.08984375, 0.8955078125, 0.2130126953125, 0.1890869140625, -0.052276611328125, -0.018707275390625, 0.7177734375, 0.65087890625, -0.86376953125, 0.278564453125, 1.0205078125, -0.07598876953125, 0.255126953125, 0.31884765625, -0.51416015625, -0.286376953125, 0.080810546875, 0.01471710205078125, 0.69482421875, -0.0172119140625, 0.56396484375, 0.24365234375, 0.578125, -0.88037109375, 0.1285400390625, -0.13818359375, 0.869140625, 0.40283203125, 0.71826171875, 0.204345703125, -0.08648681640625, -0.6220703125, -1.111328125, 0.04632568359375, 0.1771240234375, 0.56591796875, -0.4169921875, 1.0634765625, 0.0941162109375, -0.76513671875, 0.6015625, -0.66748046875, 0.438720703125, 1.10546875, 0.271728515625, 0.8408203125, -0.82275390625, 0.414306640625, 0.06939697265625, -0.1480712890625, 0.40625, 0.623046875, 0.401123046875, -0.460693359375, -0.70556640625, -0.4287109375, 0.029205322265625, -0.1982421875, -0.42724609375, 0.2073974609375, -0.537109375, -0.2489013671875, -0.93701171875, 0.60888671875, 0.62646484375, 0.79296875, 0.22021484375, 0.2489013671875, 0.135009765625, 0.1868896484375, 0.64306640625, -0.0091705322265625, 0.282470703125, -0.6689453125, 0.876953125, 0.327880859375, -0.29345703125, -0.494140625, -0.4140625, -0.1322021484375, 0.12286376953125, -0.450439453125, -0.047088623046875, -1.23046875, 0.159423828125, -0.1954345703125, 0.61669921875, -0.88916015625, -0.08367919921875, -0.332275390625, 0.1302490234375, 0.2137451171875, -1.0693359375, 0.62939453125, -1.0302734375, 0.5830078125, 0.56591796875, -0.07861328125, -0.12261962890625, -0.278564453125, -0.8896484375, -0.66357421875, -0.1783447265625, 0.6748046875, -0.11102294921875, 0.38427734375, -1.453125, 0.60888671875, 0.412353515625, -0.654296875, 0.349609375, -0.461669921875, 0.64111328125, -0.2042236328125, 0.73046875, -0.46337890625, -0.6943359375, 0.0863037109375, -1.3896484375, 0.6396484375, -0.50244140625, 0.84130859375, 0.17626953125, -0.1729736328125, 0.332275390625, 0.196044921875, -0.12115478515625, 0.254638671875, -0.24462890625, 0.43359375, -0.94580078125, -1.099609375, 0.6435546875, -0.201416015625, -0.405517578125, 0.71142578125, -0.10577392578125, -0.60888671875, -0.197509765625, 0.446533203125, -0.419677734375, 0.34423828125, -0.194580078125, 0.60400390625, -0.3232421875, -0.7216796875, -0.251953125, -0.638671875, 0.76123046875, -0.347900390625, -0.62109375, -0.1478271484375, -1.396484375, -0.261962890625, 0.06439208984375, -0.38623046875, 0.1749267578125, 0.4677734375, -0.01324462890625, -0.1944580078125, -0.20947265625, -0.55029296875, -0.428466796875, -0.68017578125, -0.30419921875, 0.060821533203125, 0.54638671875, 1.005859375, -0.0038280487060546875, -0.313232421875, -0.150390625, -0.11346435546875, 0.060028076171875, -0.58642578125, -0.336669921875, -0.05535888671875, -0.43408203125, -0.2646484375, 0.458251953125, 0.0433349609375, 0.62890625, 0.8408203125, -0.1536865234375, 0.414306640625, 0.326904296875, -0.6708984375, 1.3857421875, -0.0077362060546875, -1.2529296875, -0.72119140625, 0.5546875, 0.119873046875, 0.744140625, 0.294921875, -0.98193359375, -0.67431640625, -1.0908203125, 0.43603515625, -0.9443359375, -0.41552734375, -1.1591796875, -0.66796875, -0.6240234375, 0.271240234375, 0.1651611328125, -0.5283203125, 0.53564453125, -0.87255859375, 0.2490234375, -0.8974609375, 0.0628662109375, -0.58203125, -0.51318359375, 0.07708740234375, 1.00390625, 0.1590576171875, 0.274658203125, 0.056793212890625, -0.4296875, 0.3740234375, -0.15087890625, -0.7890625, -0.340087890625, -0.21337890625, 0.2822265625, -0.18603515625, -0.2265625, -0.68212890625, 0.97314453125, -0.59765625, 0.583984375, 0.240234375, -0.437744140625, -0.1334228515625, -0.36572265625, 0.900390625, -0.47705078125, 0.1068115234375, -0.119873046875, 0.34326171875, 0.6572265625, -0.51123046875, -0.338134765625, -0.57080078125, -0.58056640625, -1.0029296875, 0.45849609375, -0.38134765625, 0.1761474609375, -0.84033203125, -0.11181640625, 1.1806640625, -0.63232421875, 0.385009765625, 1.0654296875, 0.062225341796875, 0.239501953125, -0.37939453125, 0.72900390625, 0.487548828125, -0.28125, 0.04034423828125, -0.039093017578125, -0.5244140625, 0.0017824172973632812, -0.36328125, -0.87060546875, -0.7509765625, 0.257080078125, 1.41015625, -0.3359375, 0.80419921875, -0.116943359375, -1.173828125, -0.43994140625, 0.6005859375, 0.2322998046875, 0.1541748046875, 0.5927734375, -0.1756591796875, -0.0682373046875, 0.057952880859375, -0.46142578125, -0.6005859375, -0.58056640625, 1.345703125, -0.72216796875, -0.6220703125, 1.134765625, 0.92919921875, -1.21875, -0.9755859375, 0.1263427734375, 0.06915283203125, -0.275634765625, -0.63671875, 0.01447296142578125, 0.69921875, -0.68115234375, 0.07476806640625, 0.133056640625, -0.07867431640625, 0.260009765625, -0.017730712890625, 0.55517578125, -0.345703125, 0.498291015625, 0.65966796875, -0.63427734375, -0.297607421875, -0.9326171875, -0.1805419921875, -0.2900390625, 0.1436767578125, 0.75634765625, -0.029815673828125, 0.3212890625, 0.705078125, -0.1484375, 0.78515625, -0.52685546875, -0.253173828125, 0.171875, -0.50927734375, -0.446044921875, 0.046142578125, 0.33056640625, -0.12841796875, 0.47216796875, -0.64306640625, -0.07720947265625, 0.351318359375, 0.625, -0.151123046875, -0.61376953125, -0.24072265625, -1.4521484375, -0.481689453125, -0.5986328125, -0.9033203125, -0.267333984375, 0.5947265625, 0.202392578125, -0.5244140625, 0.051666259765625, 0.46044921875, -0.677734375, 0.5859375, -0.4375, 0.2548828125, -0.24609375, -0.4765625, -1.0126953125, -0.146240234375, -0.67138671875, -0.51611328125, -0.6484375, 0.72802734375, 0.00983428955078125, 0.2159423828125, -0.2210693359375, 0.94140625, -0.05224609375, -0.58203125, 0.468505859375, 0.0582275390625, -0.1820068359375, 1.33203125, 0.30810546875, 0.1641845703125, 0.108154296875, -0.411865234375, -0.2010498046875, -0.33837890625, 0.74951171875, 0.37548828125, -0.376220703125, -0.2264404296875, -0.042266845703125, 0.2425537109375, -0.79541015625, 0.36572265625, -0.31005859375, 0.08917236328125, -0.08807373046875, -0.01483917236328125, 0.28076171875, 1.234375, -0.234375, 0.099365234375, 0.075927734375, 0.1986083984375, 0.28955078125, 0.28515625, 0.1239013671875, 0.59814453125, -0.30322265625, -0.374755859375, -0.1705322265625, 0.39599609375, 0.08746337890625, 0.192138671875, -0.483154296875, -0.95556640625, -0.64501953125, -0.2132568359375, -0.064208984375, 0.469970703125, 0.357666015625, -0.5244140625, 0.01910400390625, 0.09130859375, -0.57470703125, 0.1199951171875, -1.1396484375, -1.0634765625, 0.55322265625, -0.135009765625, -0.59912109375, -0.0287628173828125, -0.382080078125, -0.0723876953125, 0.041717529296875, 0.53125, -0.55859375, 0.2587890625, 0.11663818359375, 0.5341796875, 0.0259246826171875, -0.2205810546875, 0.21728515625, 0.70947265625, -0.88525390625, -0.65966796875, 0.037628173828125, 0.884765625, 0.08026123046875, -0.47509765625, -0.20166015625, 0.44287109375, -0.1959228515625, 0.2259521484375, -0.495361328125, 0.1240234375, 0.069580078125, 0.9375, -0.8427734375, 0.0201873779296875, -0.254638671875, 0.236572265625, -0.188720703125, -0.7177734375, -0.51318359375, 1.1396484375, 0.568359375, -0.111572265625, 0.5537109375, 0.037384033203125, 0.452880859375, 0.021484375, -0.030364990234375, 0.09539794921875, 0.580078125, 0.88916015625, 0.6826171875, -0.244384765625, 0.4931640625, 0.8291015625, -0.2037353515625, -0.11090087890625, 0.458251953125, 0.163330078125, -0.046478271484375, -0.1241455078125, -0.323974609375, -0.447265625, -0.1807861328125, -0.6767578125, 0.7587890625, -0.1956787109375, 0.298095703125, -0.1907958984375, -0.74365234375, 0.826171875, -0.3251953125, -0.184326171875, 0.209228515625, -0.73193359375, 0.387939453125, 0.6552734375, -0.30419921875, -0.34130859375, 0.56494140625, 0.74169921875, 0.5927734375, 0.71337890625, 0.234619140625, 0.25146484375, -0.68115234375, 0.08123779296875, 0.021087646484375, -0.0806884765625, -0.194091796875, -0.73291015625, -1.240234375, 0.6728515625, -0.54541015625, -0.263916015625, 0.62060546875, -0.7734375, 0.1624755859375, -0.2235107421875, 0.986328125, -0.54443359375, 0.2171630859375, 0.52978515625, -0.45654296875, -0.8505859375, 1.0361328125, -0.0736083984375, 0.1846923828125, -0.11236572265625, 1.328125, -0.0830078125, 1.384765625, 0.70361328125, -0.313232421875, 0.263427734375, 0.5791015625, -0.306884765625, -0.55224609375, -0.36474609375, -0.525390625, -0.35693359375, -0.6689453125, -0.55126953125, 0.07177734375, 0.44091796875, 0.01497650146484375, -0.7353515625, -0.35400390625, 0.1802978515625, -0.71630859375, 0.6552734375, 0.1458740234375, 0.322998046875, 0.316162109375, -0.1151123046875, -0.0267181396484375, -0.280517578125, 0.2188720703125, -0.439697265625, 0.50830078125, -0.923828125, -0.283447265625, -0.728515625, -0.62060546875, -0.181640625, 0.05419921875, -0.3330078125, -0.7900390625, 0.206787109375, 0.4951171875, 0.1947021484375, 0.31640625, -0.281494140625, 0.271728515625, 1.0009765625, 1.0810546875, -0.042266845703125, 0.85693359375, 0.347900390625, -0.045684814453125, -0.124267578125, -0.221923828125, 0.40185546875, 0.0224151611328125, 0.421630859375, -0.422607421875, 0.3203125, -0.65087890625, -1.3154296875, 0.288818359375, 0.40380859375, 0.0001443624496459961, -0.775390625, -1.2509765625, -0.490966796875, -1.1767578125, -0.145263671875, -1.0107421875, 1.0703125, -0.3701171875, -0.051727294921875, 0.00865936279296875, -1.1416015625, 4.2109375, 1.0029296875, 0.72900390625, 0.52294921875, 0.265625, 0.79052734375, 0.020965576171875, -0.63916015625, -0.0032100677490234375, -0.46728515625, 0.6943359375, -0.5185546875, -0.03607177734375, 0.921875, 0.40771484375, 0.482666015625, -0.494873046875, 0.143310546875, -0.0190887451171875, -1.0576171875, -0.94580078125, 0.3447265625, 0.0310516357421875, 0.35693359375, 0.1466064453125, 0.1934814453125, 0.89013671875, -0.89599609375, 0.12225341796875, -0.6923828125, 0.32763671875, -0.37109375, 1.0712890625, 0.213134765625, 0.0887451171875, 0.42919921875, -0.11083984375, -0.36669921875, 0.00736236572265625, 0.068359375, -0.32568359375, -0.2001953125, 0.52294921875, -0.8212890625, -0.152099609375, 0.6025390625, -0.72998046875, 0.52392578125, -0.012420654296875, -1.1630859375, 0.96533203125, -0.20947265625, 0.304931640625, -0.7900390625, -0.19287109375, 0.0648193359375, 0.50732421875, -0.12646484375, -0.271484375, 0.498779296875, 0.389404296875, 0.5478515625, -0.01485443115234375, 0.7041015625, -1.166015625, 0.049163818359375, 0.0290069580078125, 0.417236328125, -0.404052734375, -0.02734375, -0.56103515625, -0.41015625, -0.2294921875, -0.583984375, 0.61572265625, -0.0404052734375, -0.036865234375, 0.285888671875, 0.61279296875, -0.64013671875, 0.18505859375, -0.121826171875, -0.1241455078125, -0.73876953125, 0.83984375, 1.28515625, -0.517578125, -0.442626953125, -0.345947265625, 0.499267578125, 0.66259765625, 0.71728515625, -0.01010894775390625, -0.74169921875, -0.2939453125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Submitted Solution: ``` n = input() r = 0 c = 0 t = [] for i in range(len(n)): if n[i]=="a": c+=1 else: t.append(c) c = 0 for i in t: if i==1: r+=1 elif i>1: r+=i+1 print(r%(10**9+7)) ``` No
105,801
[ 0.453125, -0.1556396484375, 0.00811767578125, 0.044830322265625, -0.876953125, -0.4189453125, -0.08624267578125, -0.1409912109375, 0.1929931640625, 0.86083984375, 0.52978515625, -0.377197265625, -0.192626953125, -0.998046875, -0.47216796875, -0.048065185546875, -0.513671875, -0.6796875, -0.346923828125, -0.36328125, -0.007396697998046875, -0.27490234375, -1.1142578125, 0.12432861328125, -0.13134765625, 0.9677734375, 0.59521484375, -0.053192138671875, 1.021484375, 1.1884765625, -0.2159423828125, -0.253173828125, 0.61669921875, -0.80126953125, -0.2410888671875, -0.615234375, 0.576171875, -0.83056640625, -0.363525390625, -0.465087890625, 0.1954345703125, -0.468505859375, 0.556640625, -0.5185546875, -1.7353515625, -0.07568359375, 0.030853271484375, -0.45263671875, -0.016754150390625, -0.46875, -0.1728515625, -0.346923828125, 0.35986328125, -0.1690673828125, 0.1356201171875, 0.233642578125, 0.248046875, -0.31396484375, -0.994140625, 0.11865234375, 0.482421875, 0.218505859375, 0.08697509765625, -0.81201171875, -0.109619140625, 0.26904296875, -0.256591796875, 0.098876953125, -0.1610107421875, -0.5625, -0.086669921875, 0.14208984375, -0.32861328125, -0.51904296875, -0.317138671875, 0.1038818359375, 0.3408203125, -0.0960693359375, -0.8291015625, 1.0947265625, -0.37451171875, 0.896484375, 0.368408203125, 0.263671875, -0.364013671875, -0.5849609375, 0.2205810546875, 0.356201171875, 0.086181640625, -0.0863037109375, -0.411376953125, 0.52978515625, -0.38671875, -0.234130859375, 0.46142578125, 0.546875, -0.4541015625, 0.040191650390625, 0.50732421875, 0.41064453125, 0.94140625, 0.81201171875, -0.483642578125, 0.951171875, -0.34814453125, -0.082275390625, 0.0645751953125, -0.2578125, -0.345947265625, -0.11334228515625, -0.2371826171875, -0.251953125, 0.52880859375, 0.34814453125, -0.58837890625, 0.97119140625, 0.341064453125, 0.57275390625, -0.57421875, 0.56396484375, 0.420654296875, 0.161865234375, 0.8134765625, -0.28955078125, -0.12274169921875, -0.06280517578125, -0.8408203125, 1.203125, -0.68115234375, -0.3076171875, 0.320068359375, 0.119140625, -0.002910614013671875, 0.352294921875, -0.478759765625, 0.64111328125, 0.02435302734375, 0.2156982421875, 0.74658203125, -0.406982421875, 0.71923828125, -0.204833984375, -0.19775390625, 1.810546875, 0.210693359375, -0.1658935546875, 0.6484375, 0.40625, -0.953125, 0.27734375, -1.123046875, 0.76611328125, 0.2509765625, 0.0833740234375, -0.264892578125, 0.10333251953125, -0.28076171875, 0.321044921875, 0.147216796875, -0.2379150390625, -0.5224609375, 0.1322021484375, -0.47216796875, 0.8408203125, -0.37353515625, 0.5966796875, -0.165283203125, -0.2066650390625, -0.050750732421875, -0.390869140625, 0.052703857421875, -0.153076171875, -0.010498046875, 0.99755859375, 0.493408203125, 0.99365234375, 1.1904296875, -0.2139892578125, 0.464111328125, 0.345458984375, -0.4423828125, 0.343994140625, 0.23779296875, 0.9267578125, 0.416259765625, 0.529296875, -0.33740234375, -0.0222625732421875, -0.375732421875, -0.45361328125, 0.36572265625, 0.61279296875, -0.759765625, 0.46875, -0.2044677734375, -0.1160888671875, -0.7626953125, -0.276611328125, -0.044281005859375, -1.0576171875, -0.38671875, 0.46826171875, -0.0245819091796875, 0.466552734375, -0.396240234375, -0.59033203125, 0.305908203125, 1.30859375, -0.21240234375, 0.25341796875, 0.400390625, -0.0601806640625, -0.1224365234375, 0.35546875, 0.0648193359375, -0.37939453125, -0.51171875, 0.5517578125, -0.1224365234375, -0.06646728515625, -0.273681640625, 0.56201171875, 0.274169921875, 0.72802734375, -0.277587890625, -0.62744140625, 0.485107421875, 1.0927734375, -0.2197265625, 0.60693359375, 0.314453125, 0.76611328125, 0.95458984375, 0.9619140625, 0.662109375, 0.32470703125, 0.5810546875, 0.85595703125, -0.023895263671875, 0.2275390625, 0.302734375, 0.607421875, 0.28076171875, 0.52294921875, 0.412353515625, 0.488037109375, 0.14990234375, -0.2607421875, -0.0535888671875, -0.11468505859375, -0.4912109375, 0.728515625, -0.0004305839538574219, 0.671875, 0.1463623046875, -0.1883544921875, 0.37060546875, 0.9365234375, -1.2744140625, -0.63232421875, -0.03057861328125, 0.07421875, 0.1336669921875, 0.0638427734375, 0.73095703125, 0.47509765625, 0.771484375, 0.53955078125, -0.2293701171875, -0.291015625, -0.57763671875, -0.87841796875, -0.99169921875, -0.235107421875, -0.908203125, -0.1954345703125, -0.0985107421875, -1.0546875, 0.033721923828125, -0.5791015625, -0.07373046875, 0.16162109375, -0.4873046875, 0.94775390625, -0.1370849609375, 0.18505859375, -0.4951171875, 0.517578125, 0.13525390625, 1.1142578125, -0.8466796875, 0.09173583984375, -0.380126953125, -0.61865234375, -0.059844970703125, 0.280029296875, 0.42138671875, 0.122314453125, -0.68017578125, -0.7744140625, -0.5009765625, 0.1461181640625, -0.376953125, 0.10064697265625, -0.66796875, 0.68408203125, 0.47265625, -0.73779296875, 0.609375, 1.0693359375, -0.97265625, 0.66552734375, 0.306396484375, -0.331298828125, -0.7109375, 1.2099609375, 0.552734375, 0.6025390625, -0.364990234375, -0.7822265625, -0.405517578125, 0.049835205078125, 0.140380859375, -0.7109375, -0.3115234375, 0.62353515625, -0.00714874267578125, -0.91650390625, 0.5224609375, -1.1044921875, -0.51025390625, -0.65087890625, -0.51611328125, 1.04296875, 0.87744140625, 0.2340087890625, 0.226806640625, -0.0168609619140625, -0.0252838134765625, 0.7265625, 0.63427734375, -0.8759765625, 0.2578125, 0.9931640625, -0.06915283203125, 0.243896484375, 0.254150390625, -0.490966796875, -0.264892578125, 0.0126953125, 0.033905029296875, 0.693359375, -0.0322265625, 0.5107421875, 0.2978515625, 0.60791015625, -0.861328125, 0.1043701171875, -0.16796875, 0.89501953125, 0.349365234375, 0.6904296875, 0.2333984375, -0.07061767578125, -0.57275390625, -1.166015625, 0.04522705078125, 0.146728515625, 0.5849609375, -0.421630859375, 1.05859375, 0.07073974609375, -0.7021484375, 0.5283203125, -0.67236328125, 0.46142578125, 1.1328125, 0.272705078125, 0.86572265625, -0.79443359375, 0.345458984375, 0.10723876953125, -0.16357421875, 0.419189453125, 0.6484375, 0.3974609375, -0.443359375, -0.71728515625, -0.444091796875, 0.007266998291015625, -0.2197265625, -0.4013671875, 0.21875, -0.52294921875, -0.2449951171875, -0.90087890625, 0.59619140625, 0.6826171875, 0.8115234375, 0.226806640625, 0.2142333984375, 0.1446533203125, 0.2193603515625, 0.60546875, -0.0173797607421875, 0.233154296875, -0.6298828125, 0.88037109375, 0.30126953125, -0.317626953125, -0.48828125, -0.41259765625, -0.1497802734375, 0.09521484375, -0.48291015625, -0.04022216796875, -1.2333984375, 0.209716796875, -0.271728515625, 0.58056640625, -0.84912109375, -0.13525390625, -0.33447265625, 0.11517333984375, 0.1922607421875, -1.052734375, 0.6201171875, -1.0029296875, 0.66455078125, 0.5439453125, -0.12744140625, -0.129638671875, -0.29150390625, -0.92626953125, -0.66650390625, -0.181396484375, 0.77783203125, -0.07513427734375, 0.408203125, -1.4208984375, 0.603515625, 0.376953125, -0.64697265625, 0.252197265625, -0.49755859375, 0.603515625, -0.1876220703125, 0.71923828125, -0.50341796875, -0.6630859375, 0.048370361328125, -1.41015625, 0.61474609375, -0.4921875, 0.8251953125, 0.16259765625, -0.2203369140625, 0.331787109375, 0.218994140625, -0.174560546875, 0.2314453125, -0.2384033203125, 0.452880859375, -0.9677734375, -1.0888671875, 0.58544921875, -0.2059326171875, -0.447021484375, 0.71630859375, -0.0654296875, -0.63623046875, -0.2076416015625, 0.5107421875, -0.433349609375, 0.366455078125, -0.19873046875, 0.5908203125, -0.36083984375, -0.7763671875, -0.266845703125, -0.654296875, 0.771484375, -0.35107421875, -0.634765625, -0.179931640625, -1.3427734375, -0.271484375, 0.01287841796875, -0.358642578125, 0.23779296875, 0.4384765625, -0.0003266334533691406, -0.236572265625, -0.2235107421875, -0.54931640625, -0.415771484375, -0.6630859375, -0.344482421875, 0.034942626953125, 0.57568359375, 0.998046875, 0.0222015380859375, -0.299560546875, -0.1903076171875, -0.0814208984375, 0.11737060546875, -0.53564453125, -0.3251953125, -0.0517578125, -0.42236328125, -0.252685546875, 0.42138671875, 0.006465911865234375, 0.58935546875, 0.765625, -0.12310791015625, 0.3857421875, 0.402587890625, -0.69580078125, 1.427734375, 0.00054168701171875, -1.16796875, -0.72607421875, 0.58544921875, 0.08441162109375, 0.69970703125, 0.34521484375, -1.017578125, -0.6650390625, -1.0849609375, 0.429931640625, -0.9208984375, -0.424560546875, -1.2294921875, -0.61083984375, -0.61669921875, 0.27392578125, 0.19189453125, -0.460205078125, 0.52685546875, -0.90087890625, 0.236083984375, -0.95166015625, 0.0501708984375, -0.5986328125, -0.49072265625, 0.049713134765625, 0.931640625, 0.1268310546875, 0.35009765625, 0.028472900390625, -0.37451171875, 0.390869140625, -0.172119140625, -0.74560546875, -0.37744140625, -0.25634765625, 0.301513671875, -0.177978515625, -0.1962890625, -0.7001953125, 0.9482421875, -0.56298828125, 0.572265625, 0.218505859375, -0.38623046875, -0.12005615234375, -0.332763671875, 0.91357421875, -0.4501953125, 0.123291015625, -0.039825439453125, 0.357177734375, 0.654296875, -0.56201171875, -0.3564453125, -0.57421875, -0.533203125, -0.99951171875, 0.463134765625, -0.345703125, 0.1573486328125, -0.87109375, -0.156982421875, 1.19921875, -0.59228515625, 0.38916015625, 1.033203125, 0.0496826171875, 0.2333984375, -0.33349609375, 0.72216796875, 0.52587890625, -0.287109375, -0.00035691261291503906, -0.06268310546875, -0.57470703125, 0.07391357421875, -0.342529296875, -0.84130859375, -0.7158203125, 0.283203125, 1.3564453125, -0.33447265625, 0.79931640625, -0.159423828125, -1.1845703125, -0.44384765625, 0.62451171875, 0.230224609375, 0.1495361328125, 0.59326171875, -0.189697265625, -0.0648193359375, 0.0653076171875, -0.484375, -0.60009765625, -0.6201171875, 1.291015625, -0.75634765625, -0.6708984375, 1.1376953125, 0.9130859375, -1.2177734375, -0.97607421875, 0.118408203125, 0.032928466796875, -0.235595703125, -0.630859375, 0.0228271484375, 0.66357421875, -0.6474609375, 0.0926513671875, 0.1741943359375, -0.0877685546875, 0.29248046875, -0.045989990234375, 0.5693359375, -0.384521484375, 0.491455078125, 0.634765625, -0.59521484375, -0.303955078125, -0.943359375, -0.129638671875, -0.27685546875, 0.188720703125, 0.755859375, 0.05499267578125, 0.35400390625, 0.7587890625, -0.09857177734375, 0.7587890625, -0.52294921875, -0.2491455078125, 0.2327880859375, -0.50341796875, -0.47412109375, 0.05133056640625, 0.368408203125, -0.0677490234375, 0.501953125, -0.64453125, -0.0775146484375, 0.3466796875, 0.62060546875, -0.1617431640625, -0.625, -0.2430419921875, -1.42578125, -0.5009765625, -0.58935546875, -0.8671875, -0.2490234375, 0.53125, 0.171875, -0.5537109375, 0.046142578125, 0.54833984375, -0.65771484375, 0.6396484375, -0.45751953125, 0.2286376953125, -0.302734375, -0.473388671875, -1.056640625, -0.11151123046875, -0.62939453125, -0.468505859375, -0.66064453125, 0.712890625, -0.0036563873291015625, 0.229248046875, -0.256103515625, 0.9287109375, -0.0672607421875, -0.58203125, 0.47119140625, 0.119384765625, -0.1761474609375, 1.330078125, 0.304931640625, 0.1346435546875, 0.16015625, -0.36962890625, -0.20556640625, -0.372802734375, 0.7861328125, 0.38720703125, -0.405517578125, -0.1693115234375, -0.054229736328125, 0.213623046875, -0.75927734375, 0.33642578125, -0.3232421875, 0.1265869140625, -0.10455322265625, -0.0091552734375, 0.27099609375, 1.2666015625, -0.28515625, 0.09088134765625, 0.0999755859375, 0.1614990234375, 0.2568359375, 0.34326171875, 0.10662841796875, 0.63427734375, -0.265869140625, -0.369873046875, -0.152587890625, 0.3857421875, 0.09039306640625, 0.20849609375, -0.482666015625, -0.97998046875, -0.6630859375, -0.177978515625, -0.0087432861328125, 0.47216796875, 0.406982421875, -0.50341796875, 0.0577392578125, 0.08355712890625, -0.56982421875, 0.109130859375, -1.095703125, -1.09765625, 0.49853515625, -0.074462890625, -0.62060546875, 0.00016748905181884766, -0.3359375, -0.0438232421875, 0.0595703125, 0.568359375, -0.541015625, 0.270751953125, 0.10247802734375, 0.53955078125, 0.0208282470703125, -0.1947021484375, 0.267822265625, 0.69775390625, -0.8486328125, -0.6708984375, 0.05792236328125, 0.869140625, 0.15576171875, -0.4853515625, -0.14013671875, 0.41845703125, -0.19873046875, 0.1922607421875, -0.4814453125, 0.1292724609375, 0.0767822265625, 0.978515625, -0.87255859375, 0.04119873046875, -0.18115234375, 0.2491455078125, -0.161865234375, -0.72119140625, -0.5771484375, 1.0927734375, 0.63623046875, -0.082763671875, 0.57080078125, 0.016571044921875, 0.4697265625, 0.02618408203125, -0.015167236328125, 0.1246337890625, 0.61083984375, 0.86865234375, 0.69677734375, -0.21337890625, 0.54541015625, 0.8310546875, -0.2449951171875, -0.1553955078125, 0.455322265625, 0.176513671875, -0.052459716796875, -0.10028076171875, -0.327880859375, -0.36181640625, -0.1805419921875, -0.6474609375, 0.7705078125, -0.199462890625, 0.30712890625, -0.1798095703125, -0.71533203125, 0.82275390625, -0.3583984375, -0.1650390625, 0.207763671875, -0.728515625, 0.4169921875, 0.58837890625, -0.32763671875, -0.33984375, 0.62939453125, 0.72607421875, 0.5751953125, 0.7490234375, 0.254638671875, 0.2413330078125, -0.7275390625, 0.0987548828125, -0.0017175674438476562, -0.09576416015625, -0.197998046875, -0.73291015625, -1.2470703125, 0.65673828125, -0.53271484375, -0.3232421875, 0.650390625, -0.7734375, 0.26318359375, -0.199462890625, 0.9853515625, -0.51904296875, 0.2230224609375, 0.53759765625, -0.384765625, -0.85302734375, 1.0322265625, -0.07452392578125, 0.1910400390625, -0.089599609375, 1.314453125, -0.07769775390625, 1.392578125, 0.65185546875, -0.33447265625, 0.282958984375, 0.57373046875, -0.344482421875, -0.60107421875, -0.4033203125, -0.5224609375, -0.395263671875, -0.666015625, -0.53564453125, 0.0046844482421875, 0.376953125, 0.003856658935546875, -0.71044921875, -0.32958984375, 0.17041015625, -0.75146484375, 0.681640625, 0.1446533203125, 0.337158203125, 0.269775390625, -0.142333984375, -0.0300140380859375, -0.2626953125, 0.306884765625, -0.453125, 0.50634765625, -0.9765625, -0.279296875, -0.72412109375, -0.65283203125, -0.156982421875, 0.08172607421875, -0.329833984375, -0.7890625, 0.213134765625, 0.4619140625, 0.1624755859375, 0.289794921875, -0.31005859375, 0.265380859375, 0.9931640625, 1.05859375, -0.0228271484375, 0.83984375, 0.34765625, -0.047576904296875, -0.10870361328125, -0.2490234375, 0.385009765625, 0.02105712890625, 0.450439453125, -0.394287109375, 0.34130859375, -0.65087890625, -1.3544921875, 0.235595703125, 0.388671875, -0.00659942626953125, -0.75390625, -1.259765625, -0.462646484375, -1.201171875, -0.16162109375, -0.9677734375, 1.0546875, -0.399169921875, -0.07208251953125, 0.037841796875, -1.123046875, 4.2109375, 1.001953125, 0.72314453125, 0.52099609375, 0.2490234375, 0.8095703125, 0.0231170654296875, -0.650390625, -0.01113128662109375, -0.4228515625, 0.720703125, -0.53271484375, -0.10235595703125, 0.96923828125, 0.399169921875, 0.513671875, -0.494140625, 0.080078125, -0.028594970703125, -1.083984375, -0.951171875, 0.3408203125, 0.0966796875, 0.3798828125, 0.1337890625, 0.18359375, 0.92431640625, -0.90625, 0.132080078125, -0.74462890625, 0.26171875, -0.42822265625, 1.0400390625, 0.22314453125, 0.09527587890625, 0.44873046875, -0.0797119140625, -0.373291015625, -0.0175628662109375, 0.043670654296875, -0.328857421875, -0.21826171875, 0.5205078125, -0.78076171875, -0.1688232421875, 0.57275390625, -0.71923828125, 0.5625, -0.0299072265625, -1.1826171875, 0.91748046875, -0.2310791015625, 0.3125, -0.73779296875, -0.24169921875, 0.06103515625, 0.475830078125, -0.130126953125, -0.285888671875, 0.55078125, 0.378662109375, 0.52392578125, 0.00940704345703125, 0.72265625, -1.15625, 0.0625, 0.03887939453125, 0.4072265625, -0.446533203125, 0.00832366943359375, -0.580078125, -0.43505859375, -0.2783203125, -0.56005859375, 0.52685546875, 0.02252197265625, -0.036651611328125, 0.320068359375, 0.58251953125, -0.62548828125, 0.1888427734375, -0.10931396484375, -0.057464599609375, -0.68359375, 0.8779296875, 1.318359375, -0.56884765625, -0.445068359375, -0.33544921875, 0.52685546875, 0.68896484375, 0.681640625, -0.030670166015625, -0.75341796875, -0.323486328125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Submitted Solution: ``` s=input() ans=0 j=0 for i in range(0,len(s)): if i>=j: cnt1=0 while i<len(s) and s[i]=='a': cnt1=cnt1+1 i=i+1 cnt2=0 while i<len(s) and s[i]=='b': cnt2=cnt2+1 i=i+1 j=i; if cnt1>0 and cnt2>0: ans=ans + cnt2 bb= cnt2*2 cnt1=cnt1-1 ans = ans + bb*(pow(2,cnt1,1000000007)-1) #print(ans) print(ans%1000000007) ``` No
105,802
[ 0.47998046875, -0.1317138671875, -0.010833740234375, 0.07525634765625, -0.77099609375, -0.35302734375, -0.06573486328125, -0.1522216796875, 0.2095947265625, 0.91064453125, 0.5693359375, -0.33984375, -0.3173828125, -1.10546875, -0.43017578125, -0.08056640625, -0.53564453125, -0.70654296875, -0.3388671875, -0.361328125, 0.06787109375, -0.36572265625, -1.2158203125, -0.0277099609375, -0.200927734375, 0.8916015625, 0.6279296875, -0.043365478515625, 0.966796875, 1.1337890625, -0.25927734375, -0.31005859375, 0.501953125, -0.7998046875, -0.262939453125, -0.60205078125, 0.5087890625, -0.875, -0.204833984375, -0.364013671875, 0.1590576171875, -0.489990234375, 0.439697265625, -0.56591796875, -1.642578125, -0.148193359375, 0.042205810546875, -0.3828125, 0.07708740234375, -0.470947265625, -0.200927734375, -0.30517578125, 0.404052734375, -0.17333984375, 0.167236328125, 0.354736328125, 0.32275390625, -0.305419921875, -1.0146484375, 0.10809326171875, 0.4833984375, 0.1239013671875, 0.07525634765625, -0.888671875, -0.05670166015625, 0.2744140625, -0.301513671875, 0.08489990234375, -0.10455322265625, -0.6015625, -0.08843994140625, 0.10626220703125, -0.470947265625, -0.5673828125, -0.287353515625, 0.1942138671875, 0.436767578125, -0.06304931640625, -0.90234375, 1.080078125, -0.403076171875, 0.83935546875, 0.2529296875, 0.276611328125, -0.38916015625, -0.71337890625, 0.195556640625, 0.222900390625, 0.0181732177734375, -0.0699462890625, -0.35986328125, 0.473388671875, -0.432373046875, -0.263671875, 0.480712890625, 0.52294921875, -0.5341796875, 0.08685302734375, 0.51123046875, 0.33349609375, 0.953125, 0.94384765625, -0.501953125, 0.94873046875, -0.422119140625, 0.002552032470703125, 0.03521728515625, -0.26416015625, -0.385498046875, -0.1634521484375, -0.0982666015625, -0.115966796875, 0.485107421875, 0.36181640625, -0.62060546875, 0.96826171875, 0.375, 0.54248046875, -0.4970703125, 0.55615234375, 0.336669921875, -0.0018415451049804688, 0.8115234375, -0.2041015625, -0.095458984375, -0.071044921875, -0.80712890625, 1.1455078125, -0.71826171875, -0.314453125, 0.3818359375, 0.1456298828125, -0.13037109375, 0.290771484375, -0.5947265625, 0.603515625, -0.0167236328125, 0.2032470703125, 0.7548828125, -0.5302734375, 0.72412109375, -0.1802978515625, -0.006198883056640625, 1.8486328125, 0.16552734375, -0.167236328125, 0.56982421875, 0.4013671875, -0.771484375, 0.322998046875, -1.123046875, 0.82080078125, 0.19140625, 0.1259765625, -0.31787109375, 0.08282470703125, -0.301513671875, 0.3271484375, 0.1343994140625, -0.2568359375, -0.398681640625, 0.11370849609375, -0.5029296875, 0.91064453125, -0.45263671875, 0.57861328125, -0.224365234375, -0.06878662109375, 0.01265716552734375, -0.409423828125, 0.0848388671875, -0.29931640625, 0.01763916015625, 1.0126953125, 0.46728515625, 1.029296875, 1.0986328125, -0.2034912109375, 0.50439453125, 0.380615234375, -0.326416015625, 0.2061767578125, 0.2724609375, 0.93701171875, 0.4267578125, 0.560546875, -0.3330078125, -0.05548095703125, -0.334716796875, -0.374755859375, 0.341796875, 0.568359375, -0.8232421875, 0.468994140625, -0.2880859375, -0.11419677734375, -0.84912109375, -0.306640625, 0.061798095703125, -1.0244140625, -0.232666015625, 0.552734375, 0.015167236328125, 0.431396484375, -0.62109375, -0.491943359375, 0.42236328125, 1.2294921875, -0.2484130859375, 0.338134765625, 0.450927734375, -0.08038330078125, -0.06817626953125, 0.314453125, 0.1126708984375, -0.2890625, -0.5703125, 0.556640625, 0.03643798828125, -0.150634765625, -0.231201171875, 0.62646484375, 0.29541015625, 0.7373046875, -0.19189453125, -0.6669921875, 0.53759765625, 1.162109375, -0.18212890625, 0.65234375, 0.346435546875, 0.8642578125, 0.93017578125, 1.0048828125, 0.7421875, 0.303955078125, 0.6552734375, 0.8818359375, -0.10894775390625, 0.2666015625, 0.26904296875, 0.482421875, 0.385986328125, 0.5380859375, 0.5302734375, 0.434326171875, 0.14013671875, -0.284423828125, -0.133544921875, -0.0498046875, -0.5029296875, 0.8125, 0.0248260498046875, 0.6201171875, 0.050201416015625, -0.1712646484375, 0.52783203125, 1.009765625, -1.248046875, -0.73095703125, -0.06402587890625, 0.0130157470703125, 0.053375244140625, 0.0185394287109375, 0.6865234375, 0.5263671875, 0.74462890625, 0.6337890625, -0.230712890625, -0.25537109375, -0.55322265625, -0.8251953125, -1.0302734375, -0.32763671875, -0.9208984375, -0.2091064453125, -0.08795166015625, -1.0185546875, 0.10955810546875, -0.5654296875, -0.1859130859375, 0.110107421875, -0.451171875, 1.0205078125, -0.0736083984375, 0.189208984375, -0.6572265625, 0.50390625, -0.027557373046875, 1.1435546875, -0.779296875, 0.077880859375, -0.251953125, -0.73681640625, -0.0701904296875, 0.2073974609375, 0.46826171875, 0.1492919921875, -0.64404296875, -0.67919921875, -0.50537109375, 0.205810546875, -0.3349609375, 0.259765625, -0.61083984375, 0.71484375, 0.27197265625, -0.65087890625, 0.52783203125, 1.0634765625, -0.98974609375, 0.62841796875, 0.322998046875, -0.1536865234375, -0.740234375, 1.125, 0.63232421875, 0.63720703125, -0.3994140625, -0.78125, -0.431640625, -0.01036834716796875, 0.1622314453125, -0.74267578125, -0.41259765625, 0.69580078125, 0.0021076202392578125, -0.97802734375, 0.4658203125, -1.0595703125, -0.43896484375, -0.5634765625, -0.58447265625, 1.01953125, 0.83056640625, 0.239990234375, 0.145751953125, 0.0389404296875, -0.099609375, 0.64794921875, 0.61474609375, -0.85205078125, 0.352294921875, 1.0458984375, 0.021759033203125, 0.168212890625, 0.22509765625, -0.45751953125, -0.29296875, 0.1458740234375, -0.08465576171875, 0.69287109375, 0.006679534912109375, 0.449951171875, 0.40966796875, 0.58642578125, -0.865234375, 0.09075927734375, -0.324462890625, 0.86279296875, 0.427001953125, 0.72412109375, 0.382568359375, -0.08551025390625, -0.65771484375, -1.06640625, 0.03271484375, 0.03265380859375, 0.6025390625, -0.414794921875, 0.9931640625, 0.144775390625, -0.67919921875, 0.50390625, -0.69580078125, 0.41357421875, 1.078125, 0.3232421875, 0.84521484375, -0.87646484375, 0.365966796875, 0.1212158203125, -0.0030517578125, 0.56640625, 0.6435546875, 0.40087890625, -0.580078125, -0.6962890625, -0.35791015625, -0.044586181640625, -0.1849365234375, -0.398681640625, 0.163818359375, -0.343505859375, -0.2135009765625, -0.90576171875, 0.6669921875, 0.66357421875, 0.7724609375, 0.20458984375, 0.257080078125, 0.21533203125, 0.2301025390625, 0.65966796875, 0.0295867919921875, 0.2010498046875, -0.59033203125, 0.95263671875, 0.3828125, -0.335693359375, -0.486083984375, -0.397216796875, -0.0306243896484375, 0.10845947265625, -0.544921875, -0.02093505859375, -1.080078125, 0.245849609375, -0.3623046875, 0.64208984375, -0.9208984375, -0.1260986328125, -0.369873046875, 0.319091796875, 0.252197265625, -1.060546875, 0.5703125, -1.0029296875, 0.705078125, 0.58154296875, -0.139892578125, -0.08367919921875, -0.303955078125, -0.8994140625, -0.7412109375, -0.2039794921875, 0.65234375, -0.0733642578125, 0.462646484375, -1.3134765625, 0.5849609375, 0.365478515625, -0.62841796875, 0.1837158203125, -0.3623046875, 0.611328125, -0.1619873046875, 0.5888671875, -0.41015625, -0.66162109375, 0.162109375, -1.39453125, 0.60205078125, -0.489013671875, 0.79296875, 0.286865234375, -0.2232666015625, 0.277099609375, 0.1751708984375, -0.1358642578125, 0.099609375, -0.291748046875, 0.521484375, -0.98193359375, -0.966796875, 0.5546875, -0.145263671875, -0.3330078125, 0.732421875, -0.02850341796875, -0.54833984375, -0.158203125, 0.492919921875, -0.5126953125, 0.386962890625, -0.2376708984375, 0.6123046875, -0.353759765625, -0.7744140625, -0.264404296875, -0.66455078125, 0.8779296875, -0.4248046875, -0.6572265625, -0.1370849609375, -1.353515625, -0.31787109375, -0.0027027130126953125, -0.341064453125, 0.306396484375, 0.42919921875, -0.08038330078125, -0.259033203125, -0.0908203125, -0.53466796875, -0.424072265625, -0.77392578125, -0.260009765625, 0.05914306640625, 0.480712890625, 1.103515625, -0.1043701171875, -0.28857421875, -0.03485107421875, -0.060455322265625, 0.053863525390625, -0.56103515625, -0.285400390625, -0.1531982421875, -0.427978515625, -0.302734375, 0.3759765625, 0.0031299591064453125, 0.5078125, 0.76953125, -0.018402099609375, 0.234130859375, 0.406005859375, -0.72119140625, 1.521484375, 0.0689697265625, -1.02734375, -0.72412109375, 0.6640625, 0.1524658203125, 0.72021484375, 0.2978515625, -1.0703125, -0.66162109375, -0.9462890625, 0.41796875, -0.88525390625, -0.42236328125, -1.12890625, -0.76513671875, -0.658203125, 0.29931640625, 0.1649169921875, -0.5244140625, 0.52197265625, -0.8671875, 0.2802734375, -1.0087890625, 0.0648193359375, -0.69140625, -0.63525390625, -0.08746337890625, 0.97021484375, 0.010223388671875, 0.28173828125, 0.053192138671875, -0.34423828125, 0.3984375, -0.1324462890625, -0.73828125, -0.286376953125, -0.1619873046875, 0.306884765625, -0.292236328125, -0.1676025390625, -0.5478515625, 0.90380859375, -0.55908203125, 0.466064453125, 0.20947265625, -0.33203125, -0.12078857421875, -0.273681640625, 0.99853515625, -0.48193359375, 0.179443359375, -0.01271820068359375, 0.27734375, 0.6826171875, -0.62451171875, -0.48876953125, -0.62890625, -0.6044921875, -1.0810546875, 0.51708984375, -0.2337646484375, 0.12109375, -0.79736328125, -0.1539306640625, 1.1064453125, -0.7470703125, 0.432861328125, 0.91650390625, 0.01239013671875, 0.286376953125, -0.37353515625, 0.78759765625, 0.483642578125, -0.302734375, -0.005573272705078125, -0.10650634765625, -0.5185546875, -0.0157318115234375, -0.458251953125, -0.94580078125, -0.6640625, 0.291748046875, 1.2939453125, -0.251953125, 0.7548828125, -0.1455078125, -1.1962890625, -0.505859375, 0.61572265625, 0.06964111328125, 0.1329345703125, 0.67236328125, -0.040802001953125, -0.04705810546875, 0.0110626220703125, -0.439453125, -0.66796875, -0.7314453125, 1.310546875, -0.73388671875, -0.60205078125, 0.97998046875, 0.89013671875, -1.1494140625, -0.9970703125, 0.129150390625, 0.07794189453125, -0.22216796875, -0.64599609375, 0.0733642578125, 0.60205078125, -0.5751953125, 0.06805419921875, 0.1663818359375, -0.0157928466796875, 0.253173828125, -0.052520751953125, 0.56103515625, -0.39599609375, 0.46826171875, 0.7177734375, -0.465576171875, -0.344970703125, -0.93115234375, -0.1796875, -0.3125, 0.0706787109375, 0.80419921875, -0.0216522216796875, 0.340576171875, 0.7578125, -0.0985107421875, 0.798828125, -0.490478515625, -0.174560546875, 0.341796875, -0.391357421875, -0.4365234375, 0.08563232421875, 0.358642578125, -0.045318603515625, 0.488037109375, -0.5869140625, -0.046630859375, 0.288330078125, 0.66845703125, -0.28173828125, -0.65869140625, -0.31298828125, -1.3349609375, -0.578125, -0.53564453125, -0.9208984375, -0.184326171875, 0.62744140625, 0.07586669921875, -0.4609375, -0.0433349609375, 0.48095703125, -0.66845703125, 0.5634765625, -0.429443359375, 0.254638671875, -0.4228515625, -0.54150390625, -0.96044921875, -0.2095947265625, -0.66357421875, -0.54833984375, -0.57421875, 0.703125, 0.07867431640625, 0.239501953125, -0.391845703125, 0.86474609375, -0.1597900390625, -0.6826171875, 0.366943359375, 0.123291015625, -0.110107421875, 1.3916015625, 0.302490234375, 0.25439453125, 0.0199432373046875, -0.33740234375, -0.15576171875, -0.322265625, 0.908203125, 0.3330078125, -0.403076171875, -0.2042236328125, -0.004245758056640625, 0.2178955078125, -0.7314453125, 0.2900390625, -0.277099609375, 0.2010498046875, -0.08929443359375, -0.056243896484375, 0.270263671875, 1.240234375, -0.433837890625, 0.0914306640625, 0.0760498046875, 0.233642578125, 0.30322265625, 0.322509765625, 0.05621337890625, 0.5595703125, -0.15576171875, -0.486083984375, -0.1751708984375, 0.4521484375, 0.017974853515625, 0.2154541015625, -0.486572265625, -0.95263671875, -0.6884765625, -0.268798828125, -0.07281494140625, 0.477294921875, 0.58935546875, -0.53466796875, 0.041534423828125, 0.238525390625, -0.70458984375, 0.09716796875, -1.125, -1.0771484375, 0.552734375, -0.1575927734375, -0.6259765625, -0.033782958984375, -0.3515625, -0.11505126953125, -0.06134033203125, 0.5205078125, -0.47265625, 0.22998046875, 0.1722412109375, 0.59619140625, -0.1187744140625, -0.3037109375, 0.12548828125, 0.58447265625, -0.8291015625, -0.7109375, 0.055023193359375, 0.93310546875, 0.1456298828125, -0.5576171875, -0.236572265625, 0.353759765625, -0.0711669921875, 0.1881103515625, -0.541015625, 0.02471923828125, 0.06842041015625, 0.94482421875, -0.8046875, -0.0066680908203125, -0.19775390625, 0.2100830078125, -0.0755615234375, -0.71728515625, -0.72412109375, 1.0810546875, 0.650390625, -0.2376708984375, 0.6044921875, 0.045867919921875, 0.42578125, 0.06976318359375, 0.084228515625, 0.1829833984375, 0.50390625, 0.85107421875, 0.70849609375, -0.0863037109375, 0.39013671875, 0.9052734375, -0.300048828125, -0.291748046875, 0.447021484375, 0.2354736328125, -0.0220947265625, -0.07305908203125, -0.274658203125, -0.4501953125, -0.166015625, -0.6875, 0.70263671875, -0.269287109375, 0.294677734375, -0.1636962890625, -0.6953125, 0.85888671875, -0.378173828125, -0.1923828125, 0.29833984375, -0.763671875, 0.48388671875, 0.484130859375, -0.30859375, -0.378662109375, 0.6376953125, 0.74462890625, 0.72607421875, 0.79638671875, 0.23291015625, 0.34228515625, -0.60302734375, 0.10693359375, -0.035247802734375, -0.09619140625, -0.1328125, -0.67041015625, -1.3349609375, 0.64453125, -0.57421875, -0.39404296875, 0.64697265625, -0.70849609375, 0.305908203125, -0.274169921875, 0.935546875, -0.53662109375, 0.2041015625, 0.5, -0.384765625, -0.90087890625, 1.064453125, -0.16552734375, 0.2413330078125, -0.08819580078125, 1.2646484375, -0.0181121826171875, 1.51953125, 0.654296875, -0.2459716796875, 0.271728515625, 0.461181640625, -0.37255859375, -0.49951171875, -0.357177734375, -0.51171875, -0.304931640625, -0.61865234375, -0.5986328125, 0.0880126953125, 0.44189453125, 0.0129241943359375, -0.703125, -0.272705078125, 0.2073974609375, -0.67724609375, 0.62158203125, 0.1866455078125, 0.319580078125, 0.271728515625, -0.1817626953125, -0.0931396484375, -0.284912109375, 0.2333984375, -0.396728515625, 0.5, -1.0048828125, -0.297607421875, -0.7685546875, -0.6884765625, -0.2548828125, -0.03692626953125, -0.369384765625, -0.83203125, 0.2327880859375, 0.472412109375, 0.148681640625, 0.45361328125, -0.40771484375, 0.1439208984375, 1.017578125, 1.0537109375, -0.03729248046875, 0.86572265625, 0.4267578125, 0.0648193359375, -0.1724853515625, -0.205078125, 0.475341796875, -0.0081329345703125, 0.505859375, -0.382568359375, 0.32373046875, -0.6328125, -1.3271484375, 0.2734375, 0.430908203125, 0.07025146484375, -0.8583984375, -1.2763671875, -0.5546875, -1.1416015625, -0.11285400390625, -0.89794921875, 1.0830078125, -0.454833984375, -0.12213134765625, -0.08831787109375, -1.16796875, 4.19921875, 0.8994140625, 0.65869140625, 0.58740234375, 0.316650390625, 0.79443359375, 0.041290283203125, -0.60498046875, -0.0138702392578125, -0.373291015625, 0.67138671875, -0.5, -0.108642578125, 0.92333984375, 0.325439453125, 0.54638671875, -0.491455078125, 0.039642333984375, 0.03717041015625, -1.0478515625, -0.93798828125, 0.351806640625, 0.011962890625, 0.44921875, 0.12347412109375, 0.21044921875, 0.8271484375, -0.97314453125, 0.14794921875, -0.5908203125, 0.2191162109375, -0.387451171875, 1.126953125, 0.29443359375, 0.1148681640625, 0.44775390625, 0.0133209228515625, -0.322509765625, 0.00922393798828125, 0.1588134765625, -0.332275390625, -0.17724609375, 0.478759765625, -0.81640625, -0.1771240234375, 0.70068359375, -0.69677734375, 0.68212890625, 0.05133056640625, -1.1533203125, 0.9794921875, -0.176513671875, 0.325927734375, -0.6806640625, -0.2423095703125, 0.0859375, 0.341552734375, -0.1324462890625, -0.158935546875, 0.568359375, 0.366455078125, 0.50830078125, 0.032623291015625, 0.61474609375, -1.1396484375, 0.055908203125, -0.007595062255859375, 0.4892578125, -0.46728515625, -0.01094818115234375, -0.5673828125, -0.50732421875, -0.327880859375, -0.6015625, 0.65771484375, 0.161865234375, -0.07464599609375, 0.359619140625, 0.5048828125, -0.66357421875, 0.1541748046875, -0.239990234375, -0.1593017578125, -0.7685546875, 0.95166015625, 1.330078125, -0.497314453125, -0.359375, -0.379150390625, 0.501953125, 0.6767578125, 0.7109375, -0.0665283203125, -0.83984375, -0.24755859375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7. The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. Input The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. Output Print the minimum number of steps modulo 109 + 7. Examples Input ab Output 1 Input aab Output 3 Note The first example: "ab" β†’ "bba". The second example: "aab" β†’ "abba" β†’ "bbaba" β†’ "bbbbaa". Submitted Solution: ``` s = input() r = 0 na = 0 for i in range(len(s)): if s[i] == 'a': na += 1 else: r += (2**na - 1)%1000000007 print(r) ``` No
105,803
[ 0.433349609375, -0.1109619140625, 0.014556884765625, 0.07476806640625, -0.880859375, -0.392333984375, -0.082275390625, -0.1026611328125, 0.1075439453125, 0.8515625, 0.5634765625, -0.308349609375, -0.18017578125, -1.015625, -0.490478515625, -0.035980224609375, -0.484619140625, -0.63671875, -0.28125, -0.385986328125, -0.0156707763671875, -0.2452392578125, -1.154296875, 0.147705078125, -0.2020263671875, 0.95849609375, 0.5654296875, -0.03680419921875, 0.97216796875, 1.1748046875, -0.2255859375, -0.31494140625, 0.60205078125, -0.779296875, -0.2008056640625, -0.591796875, 0.61767578125, -0.83544921875, -0.367431640625, -0.450927734375, 0.1905517578125, -0.379638671875, 0.5263671875, -0.5908203125, -1.6904296875, -0.087646484375, -0.058807373046875, -0.459716796875, -0.013427734375, -0.431884765625, -0.17333984375, -0.37890625, 0.368408203125, -0.15283203125, 0.2291259765625, 0.2408447265625, 0.2391357421875, -0.30126953125, -1.0302734375, 0.08551025390625, 0.4521484375, 0.11700439453125, 0.05560302734375, -0.81787109375, -0.09326171875, 0.294189453125, -0.261962890625, 0.1336669921875, -0.1685791015625, -0.5107421875, -0.006786346435546875, 0.1571044921875, -0.3662109375, -0.494873046875, -0.326416015625, 0.0736083984375, 0.35546875, -0.0252838134765625, -0.8232421875, 1.103515625, -0.372314453125, 0.9033203125, 0.334716796875, 0.1796875, -0.322998046875, -0.6005859375, 0.20703125, 0.365478515625, 0.049835205078125, -0.09521484375, -0.399169921875, 0.5419921875, -0.385986328125, -0.21923828125, 0.44287109375, 0.5244140625, -0.42138671875, 0.038604736328125, 0.52783203125, 0.385986328125, 0.998046875, 0.80615234375, -0.45654296875, 0.93359375, -0.368896484375, -0.123046875, 0.07757568359375, -0.23388671875, -0.325927734375, -0.12054443359375, -0.16162109375, -0.2568359375, 0.45849609375, 0.32275390625, -0.6435546875, 0.94921875, 0.32080078125, 0.55224609375, -0.51953125, 0.529296875, 0.3720703125, 0.10882568359375, 0.78466796875, -0.235595703125, -0.073486328125, -0.1170654296875, -0.81298828125, 1.1982421875, -0.64208984375, -0.3349609375, 0.290283203125, 0.06243896484375, -0.0362548828125, 0.286865234375, -0.487060546875, 0.6767578125, 0.01251983642578125, 0.220947265625, 0.76123046875, -0.44287109375, 0.74072265625, -0.250244140625, -0.1488037109375, 1.8037109375, 0.198486328125, -0.1619873046875, 0.654296875, 0.408447265625, -0.9189453125, 0.27490234375, -1.1474609375, 0.8017578125, 0.256103515625, 0.07659912109375, -0.291259765625, 0.056671142578125, -0.256103515625, 0.330810546875, 0.1334228515625, -0.24755859375, -0.434326171875, 0.187255859375, -0.5390625, 0.87255859375, -0.388916015625, 0.6064453125, -0.1468505859375, -0.1845703125, -0.048187255859375, -0.45849609375, 0.12841796875, -0.133056640625, -0.0108489990234375, 1.017578125, 0.460693359375, 0.99755859375, 1.2275390625, -0.2220458984375, 0.388427734375, 0.374267578125, -0.430908203125, 0.34033203125, 0.32666015625, 0.9736328125, 0.45703125, 0.51708984375, -0.306640625, -0.036773681640625, -0.40869140625, -0.461669921875, 0.346923828125, 0.61083984375, -0.71240234375, 0.49853515625, -0.18994140625, -0.1495361328125, -0.79541015625, -0.28857421875, 0.0350341796875, -1.0634765625, -0.336669921875, 0.463134765625, 0.01442718505859375, 0.496826171875, -0.43408203125, -0.587890625, 0.322265625, 1.296875, -0.1844482421875, 0.252685546875, 0.408447265625, -0.050689697265625, -0.1353759765625, 0.309814453125, 0.06402587890625, -0.366455078125, -0.58740234375, 0.58642578125, -0.12322998046875, -0.0986328125, -0.2744140625, 0.59912109375, 0.31298828125, 0.712890625, -0.326904296875, -0.681640625, 0.5458984375, 1.1083984375, -0.1923828125, 0.59130859375, 0.343505859375, 0.76123046875, 0.87890625, 0.95166015625, 0.69482421875, 0.235595703125, 0.6826171875, 0.82470703125, -0.0721435546875, 0.26123046875, 0.3330078125, 0.53271484375, 0.2841796875, 0.546875, 0.44970703125, 0.48486328125, 0.147216796875, -0.241943359375, -0.050018310546875, -0.0992431640625, -0.4443359375, 0.68505859375, 0.040313720703125, 0.7138671875, 0.1026611328125, -0.2286376953125, 0.399169921875, 0.939453125, -1.28125, -0.6376953125, -0.0784912109375, 0.043731689453125, 0.161865234375, 0.071533203125, 0.7041015625, 0.434814453125, 0.74560546875, 0.5576171875, -0.2900390625, -0.33251953125, -0.59619140625, -0.87255859375, -1.0419921875, -0.2421875, -0.8564453125, -0.1983642578125, -0.1488037109375, -1.041015625, 0.08013916015625, -0.5400390625, -0.0750732421875, 0.12200927734375, -0.44970703125, 0.96044921875, -0.174560546875, 0.2188720703125, -0.52490234375, 0.5517578125, 0.171875, 1.0869140625, -0.80029296875, 0.097412109375, -0.331298828125, -0.6572265625, -0.0750732421875, 0.271240234375, 0.413330078125, 0.138671875, -0.6875, -0.80859375, -0.496826171875, 0.14990234375, -0.409423828125, 0.07666015625, -0.63232421875, 0.68505859375, 0.383056640625, -0.7412109375, 0.6025390625, 1.0947265625, -1.0029296875, 0.732421875, 0.276611328125, -0.261962890625, -0.7490234375, 1.259765625, 0.5888671875, 0.5830078125, -0.367431640625, -0.7822265625, -0.4384765625, 0.09576416015625, 0.1436767578125, -0.7763671875, -0.360595703125, 0.64697265625, 0.0400390625, -0.93896484375, 0.501953125, -1.1669921875, -0.537109375, -0.546875, -0.5546875, 1.080078125, 0.896484375, 0.2110595703125, 0.2276611328125, -0.0208282470703125, -0.0221710205078125, 0.69140625, 0.607421875, -0.9208984375, 0.22705078125, 1.0087890625, -0.061187744140625, 0.220947265625, 0.281005859375, -0.411865234375, -0.1851806640625, 0.0858154296875, -0.005016326904296875, 0.728515625, -0.07080078125, 0.55615234375, 0.301513671875, 0.5673828125, -0.884765625, 0.142578125, -0.166259765625, 0.849609375, 0.316162109375, 0.6884765625, 0.235107421875, -0.08612060546875, -0.67333984375, -1.10546875, 0.041351318359375, 0.12744140625, 0.58251953125, -0.406982421875, 1.0673828125, 0.0482177734375, -0.6982421875, 0.55224609375, -0.68212890625, 0.501953125, 1.1474609375, 0.286865234375, 0.82275390625, -0.88623046875, 0.45947265625, 0.08392333984375, -0.1533203125, 0.4208984375, 0.517578125, 0.401123046875, -0.450927734375, -0.71435546875, -0.489990234375, 0.047943115234375, -0.17236328125, -0.453857421875, 0.1116943359375, -0.544921875, -0.2705078125, -0.9541015625, 0.6142578125, 0.6416015625, 0.8076171875, 0.2081298828125, 0.2435302734375, 0.1080322265625, 0.243408203125, 0.59375, 0.046661376953125, 0.227294921875, -0.6669921875, 0.85205078125, 0.28076171875, -0.3232421875, -0.444091796875, -0.42333984375, -0.1119384765625, 0.10443115234375, -0.470703125, -0.08941650390625, -1.2314453125, 0.1676025390625, -0.300048828125, 0.60986328125, -0.80908203125, -0.10382080078125, -0.335205078125, 0.1678466796875, 0.2171630859375, -1.068359375, 0.6171875, -0.962890625, 0.6865234375, 0.56494140625, -0.131591796875, -0.11444091796875, -0.287841796875, -0.94873046875, -0.6650390625, -0.234130859375, 0.75146484375, -0.047088623046875, 0.484130859375, -1.4609375, 0.60107421875, 0.4111328125, -0.66015625, 0.2802734375, -0.52490234375, 0.61083984375, -0.1844482421875, 0.7099609375, -0.451904296875, -0.66064453125, 0.07421875, -1.37109375, 0.58251953125, -0.5283203125, 0.8671875, 0.1929931640625, -0.14794921875, 0.261474609375, 0.258544921875, -0.1429443359375, 0.264404296875, -0.2003173828125, 0.51123046875, -0.95361328125, -1.0732421875, 0.6064453125, -0.24609375, -0.4033203125, 0.69921875, -0.06390380859375, -0.638671875, -0.1685791015625, 0.53173828125, -0.44970703125, 0.42529296875, -0.1727294921875, 0.603515625, -0.348388671875, -0.69189453125, -0.2841796875, -0.650390625, 0.7841796875, -0.275390625, -0.68115234375, -0.184814453125, -1.3447265625, -0.2442626953125, 0.04193115234375, -0.327392578125, 0.27490234375, 0.437744140625, -0.002887725830078125, -0.244384765625, -0.2017822265625, -0.53076171875, -0.33984375, -0.66162109375, -0.302490234375, 0.03564453125, 0.53564453125, 0.953125, -0.03240966796875, -0.276611328125, -0.227294921875, -0.0977783203125, 0.10546875, -0.52783203125, -0.28515625, -0.07415771484375, -0.462158203125, -0.272705078125, 0.447021484375, 0.0311126708984375, 0.599609375, 0.76611328125, -0.11431884765625, 0.42333984375, 0.414306640625, -0.67333984375, 1.41015625, 0.03759765625, -1.19921875, -0.69677734375, 0.578125, 0.13232421875, 0.73583984375, 0.26025390625, -1.01171875, -0.6474609375, -1.0791015625, 0.45068359375, -0.87939453125, -0.448486328125, -1.248046875, -0.7099609375, -0.55419921875, 0.282958984375, 0.1514892578125, -0.451904296875, 0.50341796875, -0.90771484375, 0.2005615234375, -0.93212890625, 0.0223236083984375, -0.5576171875, -0.52734375, 0.0148468017578125, 0.98046875, 0.038055419921875, 0.279541015625, 0.04266357421875, -0.418212890625, 0.4052734375, -0.1671142578125, -0.77099609375, -0.376953125, -0.230224609375, 0.27099609375, -0.25146484375, -0.1641845703125, -0.69970703125, 0.9443359375, -0.61669921875, 0.55029296875, 0.207275390625, -0.37158203125, -0.119384765625, -0.387451171875, 0.88037109375, -0.451416015625, 0.153564453125, -0.07830810546875, 0.364501953125, 0.62353515625, -0.47705078125, -0.384765625, -0.66015625, -0.5009765625, -0.98876953125, 0.4638671875, -0.357177734375, 0.1939697265625, -0.88330078125, -0.1842041015625, 1.13671875, -0.6552734375, 0.45654296875, 0.9970703125, 0.057647705078125, 0.2861328125, -0.38671875, 0.74365234375, 0.53759765625, -0.2939453125, -0.023468017578125, -0.0433349609375, -0.56591796875, 0.053802490234375, -0.34375, -0.87939453125, -0.728515625, 0.3232421875, 1.37109375, -0.265869140625, 0.8447265625, -0.1329345703125, -1.197265625, -0.45166015625, 0.708984375, 0.1898193359375, 0.1373291015625, 0.64013671875, -0.1434326171875, -0.0975341796875, 0.10809326171875, -0.43505859375, -0.56787109375, -0.6083984375, 1.37109375, -0.75439453125, -0.6689453125, 1.1357421875, 0.92626953125, -1.2626953125, -0.99609375, 0.14892578125, 0.00884246826171875, -0.230712890625, -0.6201171875, -0.00806427001953125, 0.63671875, -0.6552734375, 0.0469970703125, 0.11590576171875, -0.0290679931640625, 0.3056640625, -0.036834716796875, 0.63330078125, -0.367431640625, 0.49560546875, 0.74462890625, -0.61962890625, -0.26611328125, -0.89111328125, -0.1568603515625, -0.342529296875, 0.18408203125, 0.76904296875, 0.0055999755859375, 0.34033203125, 0.78076171875, -0.05133056640625, 0.7548828125, -0.58642578125, -0.2242431640625, 0.28564453125, -0.501953125, -0.47509765625, 0.080810546875, 0.330078125, -0.06964111328125, 0.56103515625, -0.623046875, -0.084716796875, 0.33203125, 0.62744140625, -0.1422119140625, -0.64208984375, -0.2200927734375, -1.3544921875, -0.489501953125, -0.59033203125, -0.9384765625, -0.2264404296875, 0.630859375, 0.1614990234375, -0.576171875, 0.04376220703125, 0.5390625, -0.681640625, 0.6298828125, -0.4169921875, 0.242431640625, -0.37060546875, -0.46728515625, -1.0126953125, -0.1484375, -0.69775390625, -0.458740234375, -0.6630859375, 0.73193359375, 0.0175323486328125, 0.1732177734375, -0.2471923828125, 0.91552734375, -0.053802490234375, -0.556640625, 0.5205078125, 0.09814453125, -0.2071533203125, 1.3232421875, 0.280517578125, 0.1597900390625, 0.126953125, -0.361328125, -0.2159423828125, -0.405517578125, 0.74755859375, 0.42529296875, -0.3759765625, -0.1895751953125, -0.0379638671875, 0.207275390625, -0.7578125, 0.29150390625, -0.261962890625, 0.1004638671875, -0.040191650390625, -0.10272216796875, 0.2410888671875, 1.2724609375, -0.264404296875, 0.07177734375, 0.0531005859375, 0.12225341796875, 0.241943359375, 0.265380859375, 0.08868408203125, 0.6123046875, -0.27294921875, -0.4052734375, -0.1566162109375, 0.4833984375, 0.1326904296875, 0.187255859375, -0.52685546875, -0.95654296875, -0.7119140625, -0.1690673828125, -0.06939697265625, 0.44921875, 0.421142578125, -0.513671875, 0.045867919921875, 0.035491943359375, -0.5673828125, 0.11810302734375, -1.1904296875, -1.0888671875, 0.52685546875, -0.08990478515625, -0.677734375, -0.053802490234375, -0.380615234375, -0.028106689453125, 0.05303955078125, 0.5029296875, -0.54833984375, 0.255126953125, 0.08392333984375, 0.53759765625, 0.037567138671875, -0.21630859375, 0.2047119140625, 0.68701171875, -0.88232421875, -0.67822265625, 0.070068359375, 0.9296875, 0.09173583984375, -0.470947265625, -0.18359375, 0.434326171875, -0.1422119140625, 0.1651611328125, -0.517578125, 0.203857421875, 0.0897216796875, 0.9638671875, -0.80078125, 0.0921630859375, -0.1629638671875, 0.2333984375, -0.185546875, -0.7587890625, -0.6162109375, 1.1123046875, 0.6572265625, -0.1065673828125, 0.58154296875, 0.04486083984375, 0.48291015625, 0.00753021240234375, -0.0193328857421875, 0.1661376953125, 0.6572265625, 0.82470703125, 0.701171875, -0.27880859375, 0.55322265625, 0.79931640625, -0.32177734375, -0.1407470703125, 0.421630859375, 0.2100830078125, -0.0682373046875, -0.1346435546875, -0.272216796875, -0.3857421875, -0.1484375, -0.712890625, 0.740234375, -0.180908203125, 0.30224609375, -0.2127685546875, -0.7333984375, 0.87548828125, -0.28369140625, -0.1953125, 0.2447509765625, -0.71240234375, 0.40966796875, 0.6181640625, -0.288330078125, -0.369140625, 0.60986328125, 0.74365234375, 0.57275390625, 0.740234375, 0.269287109375, 0.28125, -0.7138671875, 0.11798095703125, 0.0012903213500976562, -0.06524658203125, -0.2186279296875, -0.73486328125, -1.2294921875, 0.69873046875, -0.489013671875, -0.280517578125, 0.66650390625, -0.72314453125, 0.242919921875, -0.2091064453125, 0.95361328125, -0.52783203125, 0.12353515625, 0.52099609375, -0.443603515625, -0.85302734375, 1.0087890625, -0.051025390625, 0.15478515625, -0.0755615234375, 1.3525390625, -0.08538818359375, 1.43359375, 0.671875, -0.342041015625, 0.28759765625, 0.50341796875, -0.3349609375, -0.607421875, -0.431396484375, -0.5703125, -0.291748046875, -0.67138671875, -0.5849609375, 0.033721923828125, 0.42919921875, 0.008880615234375, -0.7119140625, -0.27734375, 0.21240234375, -0.75390625, 0.6884765625, 0.05487060546875, 0.333984375, 0.330322265625, -0.10089111328125, -0.06866455078125, -0.299072265625, 0.3125, -0.410400390625, 0.529296875, -0.935546875, -0.25048828125, -0.775390625, -0.64306640625, -0.166259765625, 0.0888671875, -0.327880859375, -0.78662109375, 0.1962890625, 0.48828125, 0.137451171875, 0.264892578125, -0.3095703125, 0.2548828125, 1.0048828125, 1.123046875, -0.1180419921875, 0.8837890625, 0.354736328125, -0.0273895263671875, -0.12457275390625, -0.27392578125, 0.4365234375, -0.016326904296875, 0.431884765625, -0.420654296875, 0.3681640625, -0.6806640625, -1.2880859375, 0.28662109375, 0.347900390625, -0.0085601806640625, -0.72900390625, -1.2509765625, -0.482666015625, -1.2060546875, -0.17333984375, -0.98828125, 1.0244140625, -0.4091796875, -0.0802001953125, -0.0262298583984375, -1.1396484375, 4.19140625, 0.97607421875, 0.7548828125, 0.5146484375, 0.2486572265625, 0.775390625, 0.053985595703125, -0.67578125, 0.0186920166015625, -0.4462890625, 0.7353515625, -0.58642578125, -0.08734130859375, 0.94677734375, 0.388671875, 0.5380859375, -0.489013671875, 0.11468505859375, 0.0230255126953125, -1.1376953125, -0.89453125, 0.330078125, -0.0077667236328125, 0.3203125, 0.1568603515625, 0.1868896484375, 0.89453125, -0.8916015625, 0.1248779296875, -0.671875, 0.3271484375, -0.419921875, 1.064453125, 0.1868896484375, 0.099853515625, 0.422119140625, -0.12261962890625, -0.406494140625, -0.0225982666015625, 0.11199951171875, -0.37060546875, -0.22021484375, 0.52001953125, -0.76611328125, -0.1947021484375, 0.61962890625, -0.71923828125, 0.467041015625, -0.03985595703125, -1.20703125, 0.96044921875, -0.255615234375, 0.339111328125, -0.6943359375, -0.278076171875, 0.0711669921875, 0.50048828125, -0.0965576171875, -0.262451171875, 0.55419921875, 0.376220703125, 0.5322265625, 0.033203125, 0.74609375, -1.103515625, 0.08966064453125, 0.029022216796875, 0.372314453125, -0.447265625, 0.0007805824279785156, -0.5693359375, -0.452880859375, -0.260986328125, -0.52734375, 0.55322265625, 0.00894927978515625, -0.060211181640625, 0.335205078125, 0.57373046875, -0.6123046875, 0.1925048828125, -0.12939453125, -0.0811767578125, -0.7529296875, 0.89599609375, 1.3720703125, -0.53076171875, -0.430419921875, -0.33203125, 0.53955078125, 0.69140625, 0.71533203125, -0.037261962890625, -0.76416015625, -0.296875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are going to take the entrance examination of Kyoto University tomorrow and have decided to memorize a set of strings S that is expected to appear in the examination. Since it is really tough to memorize S as it is, you have decided to memorize a single string T that efficiently contains all the strings in S. You have already confirmed the following conditions for S and T are satisfied. * Every string in S is a consecutive subsequence(1) in T . * For every pair of strings x, y (x \neq y) in S , x is not a subsequence(2) of y. Note that (1) is ''consecutive subsequence'', while (2) is ''subsequence''. The next day, you opened the problem booklet at the examination and found that you can get a full score only if you remember S. However, You have forgot how to reconstruct S from T . Since all you remember is that T satisfies the above conditions, first you have decided to find the maximum possible number of elements in S . Constraints * 1 \leq |T| \leq 10^5 * T consists of only lowercase letters. Partial points * 30 points will be awarded for passing the test set satisfying the condition: 1 \leq |T| \leq 50 . * Another 30 points will be awarded for passing the test set satisfying the condition: 1 \leq |T| \leq 10^3. Input The input is given from Standard Input in the following format: T The input only consists of T on one line. Output Print the maximum number of elements inS . Examples Input abcabc Output 3 Input abracadabra Output 7 Input abcbabbcabbc Output 8 Input bbcacbcbcabbabacccbbcacbaaababbacabaaccbccabcaabba Output 44 Submitted Solution: ``` from collections import Counter T = input() M = 0 for i in range(1, 1001): c = Counter(T[j:j+i] for j in range(0, len(T)-i+1)) M = max(len(c), M) print(M) ``` No
106,007
[ 0.189208984375, 0.1671142578125, 0.2626953125, 0.29150390625, -0.59521484375, -0.13232421875, -0.2276611328125, 0.06488037109375, 0.347900390625, 0.93115234375, 0.423095703125, -0.07830810546875, 0.08343505859375, -0.98291015625, -0.5009765625, -0.291015625, -0.89501953125, -0.49267578125, -0.60302734375, -0.26025390625, 0.0731201171875, 0.00417327880859375, -1.15625, -0.1033935546875, -0.085205078125, 0.83056640625, 0.367919921875, 0.75927734375, 0.8935546875, 0.984375, -0.1063232421875, -0.361083984375, 0.2191162109375, -1.0078125, -0.384765625, -0.430908203125, 0.75244140625, -0.47607421875, -0.1600341796875, -0.6884765625, 0.10113525390625, -0.447021484375, 0.75634765625, -0.54296875, -1.3642578125, -0.427978515625, -0.23095703125, -0.439697265625, -0.5439453125, -0.59716796875, 0.197509765625, -0.12432861328125, 0.407470703125, -0.1036376953125, 0.076416015625, 0.4375, -0.23779296875, -0.1905517578125, -0.765625, 0.124267578125, 0.28759765625, 0.39794921875, 0.0689697265625, -0.53857421875, -0.439453125, 0.29833984375, 0.0050811767578125, -0.2376708984375, 0.3046875, -0.494140625, -0.5927734375, -0.383544921875, -0.325439453125, -0.2218017578125, -0.51513671875, 0.268798828125, 0.1328125, 0.1719970703125, -0.517578125, 0.7587890625, 0.144775390625, 1.009765625, 0.40869140625, 0.108154296875, -0.91162109375, -0.6337890625, 0.2496337890625, 0.157470703125, 0.49609375, -0.09771728515625, -0.6640625, 0.54443359375, -0.478759765625, -0.053680419921875, 0.487548828125, 0.46630859375, -0.453125, 0.1925048828125, 0.6845703125, 0.241455078125, 0.6513671875, 0.67822265625, -0.3212890625, 1.3193359375, -0.343017578125, -0.10382080078125, 0.099609375, 0.015655517578125, -0.08990478515625, -0.48583984375, -0.20361328125, -0.34765625, 0.546875, 0.254150390625, -0.5224609375, 0.97119140625, 0.07891845703125, 0.751953125, -0.81103515625, 0.1075439453125, 0.44873046875, 0.1424560546875, 0.454345703125, -0.31103515625, 0.09771728515625, -0.34423828125, -0.5224609375, 0.83251953125, -0.70458984375, 0.1422119140625, 0.30810546875, -0.036224365234375, -0.276611328125, 0.58154296875, -0.454833984375, 0.437744140625, -0.413330078125, 0.446533203125, 0.53759765625, -0.44482421875, 1.0576171875, 0.037139892578125, -0.0709228515625, 1.671875, 0.353515625, -0.01210784912109375, 0.6005859375, 0.369140625, -0.45751953125, 0.407958984375, -0.91552734375, 0.40380859375, -0.10302734375, 0.268310546875, -0.1373291015625, -0.0266265869140625, -0.269287109375, 0.21240234375, 0.387939453125, -0.1439208984375, -0.42822265625, 0.310791015625, -0.251708984375, 0.69140625, -0.444580078125, 0.78564453125, -0.16748046875, -0.46240234375, -0.07513427734375, -0.53125, 0.1878662109375, -0.18798828125, 0.210205078125, 0.86083984375, 0.63720703125, 0.9892578125, 1.126953125, -0.233642578125, 0.217529296875, 0.345947265625, -0.362548828125, -0.0740966796875, 0.66943359375, 0.499267578125, 0.58935546875, 0.4580078125, -0.1251220703125, 0.148193359375, -0.395751953125, -0.68505859375, -0.0013856887817382812, 1.0556640625, -0.418212890625, 0.3125, -0.1937255859375, 0.050201416015625, -0.986328125, -0.172119140625, -0.06573486328125, -0.70556640625, -0.475830078125, 0.74658203125, 0.08245849609375, 0.328369140625, -0.424560546875, -0.64404296875, 0.43115234375, 1.2939453125, -0.38671875, 0.11114501953125, 0.42431640625, 0.237060546875, -0.11981201171875, 0.1385498046875, 0.27978515625, -0.458251953125, -0.66259765625, 0.44189453125, 0.066650390625, 0.0693359375, -0.1585693359375, 0.88916015625, 0.361572265625, 0.31298828125, -0.042572021484375, -0.032989501953125, 0.289794921875, 1.44140625, -0.1639404296875, 0.497802734375, 0.428955078125, 0.7880859375, 0.56689453125, 0.814453125, 0.1956787109375, 0.291015625, 0.44384765625, 0.83349609375, 0.18701171875, 0.42919921875, 0.24560546875, 0.47509765625, 0.88623046875, 0.931640625, -0.11572265625, 0.216796875, -0.42919921875, -0.085693359375, -0.75634765625, 0.3818359375, -0.1451416015625, 0.78857421875, -0.05975341796875, 0.60888671875, -0.3056640625, -0.278564453125, 0.267578125, 1.0751953125, -0.93212890625, -0.9794921875, 0.293701171875, 0.1734619140625, 0.19580078125, 0.08270263671875, 0.0251617431640625, 0.1639404296875, 0.7958984375, 0.363037109375, -0.1378173828125, -0.27392578125, -0.440185546875, -0.86474609375, -1.0537109375, -0.240966796875, -0.439453125, -0.285400390625, 0.228759765625, -0.8974609375, 0.07916259765625, -0.5634765625, 0.021575927734375, 0.1390380859375, -0.308837890625, 0.76220703125, -0.298583984375, 0.391357421875, -0.76220703125, 0.6962890625, 0.254150390625, 0.9775390625, -0.410888671875, -0.373779296875, -0.01189422607421875, -0.83349609375, 0.444580078125, -0.2449951171875, 0.1837158203125, 0.130126953125, -0.3798828125, -0.62158203125, -0.29833984375, 0.08587646484375, -0.2197265625, 0.1328125, -0.56982421875, 1.1298828125, 0.37255859375, -0.6123046875, 0.49755859375, 0.8916015625, -0.68701171875, 0.383544921875, 0.313720703125, 0.046875, -0.52685546875, 1.2841796875, 0.61962890625, 0.450439453125, -0.50048828125, -0.43701171875, -0.6953125, -0.1904296875, 0.293212890625, -0.79736328125, 0.017486572265625, 0.796875, -0.27978515625, -0.94580078125, 0.69921875, -1.5166015625, -0.6025390625, -0.040130615234375, -0.2135009765625, 0.814453125, 1.1884765625, 0.354248046875, -0.489013671875, -0.378173828125, 0.1610107421875, 0.71630859375, 0.615234375, -0.70458984375, 0.03985595703125, 0.59228515625, 0.057647705078125, 0.073974609375, 0.463623046875, -0.40673828125, -0.260009765625, 0.1885986328125, -0.135009765625, 0.8505859375, -0.0204010009765625, 0.55419921875, 0.226806640625, 0.49560546875, -0.77978515625, -0.214599609375, -0.29736328125, 0.95751953125, 0.42431640625, 0.5224609375, 0.33642578125, 0.1314697265625, -0.6015625, -0.7978515625, 0.1722412109375, 0.2325439453125, 0.728515625, -0.88818359375, 0.78857421875, 0.23583984375, -0.330322265625, 0.5966796875, -0.71337890625, -0.0994873046875, 0.9638671875, -0.037017822265625, 0.317138671875, -0.57421875, 0.09417724609375, -0.180419921875, -0.0704345703125, 0.260986328125, 0.77587890625, 0.5732421875, -0.0260467529296875, -0.312255859375, -0.420654296875, 0.05804443359375, -0.06414794921875, -0.3759765625, 0.271484375, -0.5185546875, -0.307861328125, -0.6787109375, 0.324462890625, 0.76416015625, 0.607421875, -0.1314697265625, 0.142333984375, 0.1259765625, 0.578125, 0.6826171875, -0.367919921875, -0.10467529296875, -0.73828125, 0.9716796875, 0.13525390625, -0.0726318359375, -0.451171875, -0.32861328125, -0.262939453125, 0.17529296875, 0.1036376953125, -0.31396484375, -1.0732421875, 0.11456298828125, -0.22216796875, 0.332763671875, -0.72705078125, -0.1248779296875, -0.441650390625, 0.646484375, 0.0859375, -1.0673828125, 0.161865234375, -1.1083984375, 0.2066650390625, 0.287841796875, -0.253173828125, -0.75927734375, -0.0966796875, -0.62744140625, -1.1533203125, 0.05145263671875, 1.00390625, -0.0640869140625, 0.06072998046875, -1.4306640625, 0.3779296875, 0.49755859375, -0.495849609375, 0.375732421875, -0.036773681640625, 0.6123046875, 0.142822265625, 0.8662109375, -0.48681640625, -0.52734375, 0.07769775390625, -1.15625, 0.63037109375, -0.48583984375, 0.35888671875, -0.044891357421875, -0.0909423828125, 0.046051025390625, 0.55908203125, -0.2607421875, -0.05364990234375, -0.34521484375, -0.0020427703857421875, -0.62255859375, -0.80029296875, 0.9365234375, 0.095947265625, -0.53466796875, 0.986328125, -0.305419921875, -0.25732421875, 0.438232421875, 0.7490234375, -0.361328125, 0.324951171875, -0.3720703125, 0.55517578125, -0.2099609375, -0.677734375, -0.258544921875, -0.356689453125, 0.9462890625, -0.153076171875, -1.0732421875, -0.0301666259765625, -1.0283203125, -0.24658203125, -0.1175537109375, -0.6435546875, 0.10064697265625, 0.282470703125, -0.10223388671875, -0.169189453125, 0.033416748046875, -0.5634765625, -0.365234375, -0.207275390625, -0.2486572265625, 0.2259521484375, 0.34375, 0.8818359375, 0.08465576171875, -0.374755859375, 0.0916748046875, 0.1693115234375, -0.0799560546875, -0.58056640625, -0.7490234375, -0.30517578125, -0.5146484375, -0.51416015625, 0.264404296875, 0.02789306640625, 0.48095703125, 0.765625, 0.369140625, 0.215576171875, 0.21923828125, -0.79150390625, 0.9326171875, 0.287353515625, -1.126953125, -0.251220703125, 0.293212890625, -0.172119140625, 0.658203125, 0.08636474609375, -0.63232421875, -0.61962890625, -1.1865234375, 0.27392578125, -0.422119140625, -0.11431884765625, -1.0595703125, -0.449951171875, -0.1614990234375, 0.5517578125, -0.166748046875, -0.5634765625, 0.055419921875, -1.2900390625, 0.352783203125, -0.8671875, -0.0771484375, -1.2646484375, -0.7197265625, -0.0672607421875, 0.6484375, 0.12139892578125, 0.642578125, 0.2412109375, -0.02783203125, 0.0227508544921875, -0.1976318359375, -0.890625, -0.47900390625, 0.194580078125, -0.10107421875, -0.300537109375, 0.01166534423828125, -0.54931640625, 0.77783203125, -0.82080078125, 0.385986328125, -0.10540771484375, -0.32421875, -0.2352294921875, 0.03570556640625, 1.201171875, -0.525390625, -0.1953125, -0.4130859375, 0.395263671875, 0.74072265625, 0.008270263671875, -0.300048828125, -0.413818359375, -0.286376953125, -1.2216796875, 0.69677734375, -0.7138671875, 0.281982421875, -0.74609375, -0.319580078125, 1.0693359375, -0.47216796875, 0.317626953125, 1.3447265625, 0.172119140625, 0.42724609375, -0.400146484375, 0.61279296875, 0.497314453125, -0.89013671875, -0.6015625, -0.1795654296875, -0.955078125, 0.2462158203125, -0.6220703125, -1.1728515625, -0.452392578125, 0.3173828125, 1.29296875, -0.326171875, 0.65283203125, -0.0242919921875, -1.1435546875, -0.487060546875, 0.8427734375, -0.0079803466796875, 0.4150390625, 0.75390625, -0.10491943359375, -0.3828125, -0.44287109375, -0.1568603515625, -0.2392578125, -0.3544921875, 0.91455078125, -0.53662109375, -0.6875, 0.84228515625, 0.78515625, -1.318359375, -0.9638671875, 0.0225982666015625, 0.062225341796875, -0.09375, -0.7265625, 0.22705078125, 0.7294921875, -0.5927734375, 0.02606201171875, 0.72900390625, -0.27880859375, 0.06768798828125, 0.07073974609375, 0.10986328125, -0.8232421875, 0.62353515625, 0.6162109375, -0.38037109375, -0.61962890625, -1.1376953125, -0.08306884765625, -0.10382080078125, -0.040130615234375, 1.0126953125, -0.5322265625, 0.2431640625, 0.41064453125, -0.2298583984375, 0.90966796875, -0.84130859375, -0.225830078125, 0.316162109375, -0.654296875, -0.7109375, -0.1502685546875, 0.496337890625, 0.2012939453125, 0.496826171875, -0.52001953125, 0.07122802734375, 0.78076171875, 0.42626953125, -0.447265625, -1.2900390625, -0.417236328125, -1.0068359375, -0.29833984375, -0.67236328125, -0.76416015625, -0.152099609375, 0.587890625, 0.209716796875, -0.5419921875, 0.02630615234375, 0.900390625, -0.62890625, 1.0263671875, -0.5029296875, 0.27978515625, -0.448974609375, -0.06640625, -0.7822265625, -0.241943359375, -0.62890625, 0.245361328125, -0.439208984375, 0.382080078125, -0.2322998046875, 0.4052734375, -0.19921875, 0.7431640625, -0.139404296875, -0.41064453125, 0.08514404296875, 0.156982421875, -0.41748046875, 1.05859375, 0.5634765625, 0.10845947265625, 0.00785064697265625, -0.2196044921875, -0.1680908203125, -0.2587890625, 0.94775390625, 0.54443359375, -0.027008056640625, -0.05316162109375, -0.264404296875, -0.1856689453125, -0.83251953125, 0.1671142578125, -0.1500244140625, 0.213623046875, 0.26806640625, -0.1922607421875, 0.64892578125, 1.1845703125, -0.48193359375, 0.429443359375, 0.29736328125, 0.16064453125, 0.70849609375, 0.58056640625, -0.2479248046875, 0.71923828125, 0.099609375, -0.1827392578125, -0.2181396484375, 0.291015625, 0.04986572265625, 0.57421875, -0.241455078125, -0.53564453125, -0.92138671875, -0.2325439453125, 0.27685546875, 0.415283203125, 0.1060791015625, -0.52783203125, -0.11578369140625, -0.1900634765625, -0.76220703125, 0.0506591796875, -1.068359375, -1.306640625, 0.348388671875, -0.14208984375, -1.2275390625, -0.0750732421875, -0.284912109375, 0.25634765625, 0.32861328125, 0.272705078125, -0.64599609375, 0.54931640625, -0.0941162109375, 0.52685546875, -0.24853515625, -0.22216796875, -0.0273895263671875, 0.3271484375, -0.7216796875, -0.249755859375, 0.302734375, 1.08203125, 0.362548828125, -0.085693359375, -0.447265625, 0.34716796875, 0.07763671875, -0.100830078125, -0.457763671875, 0.287841796875, -0.306396484375, 0.32470703125, -0.7783203125, -0.183349609375, -0.06304931640625, 0.325927734375, 0.035675048828125, -0.452392578125, -0.8134765625, 0.292236328125, 0.5205078125, -0.165771484375, 0.3310546875, -0.03692626953125, 0.58349609375, -0.13427734375, -0.28076171875, -0.115234375, 0.8427734375, 0.69873046875, 0.9697265625, -0.0684814453125, 0.79931640625, 0.7255859375, 0.0789794921875, 0.2132568359375, 0.6357421875, 0.07904052734375, -0.08233642578125, -0.11456298828125, -0.426025390625, -0.03826904296875, 0.2626953125, -0.5947265625, 0.60546875, -0.62109375, -0.057037353515625, -0.226318359375, -0.83935546875, 0.89892578125, -0.337158203125, -0.089599609375, 0.07037353515625, -0.68701171875, 0.383544921875, 0.5751953125, 0.286865234375, -0.57470703125, 1.2421875, 0.89501953125, 0.75048828125, 0.68505859375, 0.408447265625, 0.2548828125, -0.39208984375, -0.07269287109375, 0.2216796875, -0.027587890625, -0.443359375, -0.5830078125, -1.060546875, 0.21240234375, -0.318359375, -0.259033203125, 0.6220703125, -1.109375, -0.2225341796875, -0.501953125, 0.7744140625, -0.57373046875, 0.052703857421875, 0.30224609375, -0.180908203125, -1.0068359375, 1.1376953125, 0.17236328125, 0.1395263671875, 0.2783203125, 0.712890625, -0.0687255859375, 1.2236328125, 0.62109375, -0.088623046875, -0.059814453125, 0.51025390625, -0.423583984375, -0.33740234375, -0.35546875, -0.060821533203125, -0.162109375, -0.896484375, -0.25, -0.2230224609375, 0.5478515625, -0.1878662109375, -1.181640625, -0.32666015625, 0.03668212890625, -0.7216796875, 0.65380859375, 0.413818359375, 0.349609375, -0.2193603515625, -0.1654052734375, -0.345703125, -0.587890625, 0.31298828125, -0.6484375, 0.268798828125, -0.48095703125, -0.4873046875, -0.6728515625, -0.266845703125, 0.0199127197265625, -0.2724609375, -0.28466796875, -0.89111328125, 0.59033203125, 0.340576171875, 0.30126953125, 0.04534912109375, -0.81298828125, 0.10626220703125, 1.0048828125, 0.75439453125, -0.11151123046875, 0.90380859375, 0.2099609375, 0.021453857421875, 0.1363525390625, -0.23046875, 0.61669921875, 0.0726318359375, 0.33203125, -0.28955078125, 0.2421875, -0.8984375, -0.892578125, -0.264404296875, 0.228759765625, -0.228515625, -0.7509765625, -1.1142578125, -0.4228515625, -0.93994140625, -0.1563720703125, -0.73291015625, 0.6611328125, -0.41015625, -0.024993896484375, -0.607421875, -1.33984375, 4.2734375, 1.0302734375, 0.88037109375, 0.298583984375, 0.371826171875, 1.044921875, 0.364501953125, -0.67041015625, 0.075927734375, -0.331298828125, 0.358642578125, -0.346923828125, -0.053070068359375, 0.38427734375, 0.1197509765625, 0.32861328125, -0.5341796875, 0.1868896484375, 0.161376953125, -1.03125, -1.1796875, 0.55029296875, 0.1593017578125, 0.352783203125, 0.1395263671875, 0.1456298828125, 0.63671875, -0.796875, -0.18408203125, -0.646484375, 0.174072265625, -0.362548828125, 1.2138671875, 0.1065673828125, 0.344970703125, 0.6220703125, -0.038238525390625, -0.2462158203125, -0.3173828125, 0.128662109375, -0.260498046875, 0.1805419921875, 0.8046875, -0.958984375, -0.0200958251953125, 0.396240234375, -0.537109375, 0.57861328125, 0.2061767578125, -1.16015625, 0.61083984375, -0.439208984375, 0.404052734375, -0.5068359375, -0.67529296875, -0.15771484375, 0.1541748046875, -0.08648681640625, -0.31494140625, 0.1971435546875, 0.279296875, 0.60107421875, 0.033233642578125, 0.74609375, -1.35546875, 0.74609375, 0.30419921875, 0.402099609375, -0.251708984375, 0.05908203125, -0.10235595703125, -0.302490234375, -0.2431640625, -0.30224609375, 0.33740234375, 0.50634765625, -0.339111328125, 0.83154296875, 0.7587890625, -0.447021484375, 0.1668701171875, -0.2939453125, -0.411865234375, -0.74609375, 0.61767578125, 1.3857421875, -0.62060546875, -0.3564453125, -0.341552734375, 0.771484375, 0.81982421875, 0.6904296875, 0.1268310546875, -0.79248046875, -0.35546875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Tags: games Correct Solution: ``` import sys input = sys.stdin.readline t = int(input()) for _ in range(t): a,b = map(int,input().split()) s = input() n = len(s) ls = [] if s[0] == ".": cnt = 1 else: cnt = 0 for i in range(1,n+1): if i < n and s[i] == ".": cnt += 1 else: if cnt >= b: ls.append(cnt) cnt = 0 if not ls: print("NO") continue ls.sort() if a >= 2*b: if len(ls) >= 2 or ls[0] > a+(b-1)*2 or ls[0] < a: print("NO") else: print("YES") else: if ls[0] < a:# or ls[-1] > a+(2*b-1)*2: print("NO") elif len(ls) >= 2 and ls[-2] >= 2*b: print("NO") else: l = len(ls)-1 t = ls[-1] for i in range(t): if i+a <= t: p,q = i,t-(i+a) if not (b<=p<a or b<=q<a or p>=2*b or q>=2*b): x = l+(a<=p<2*b)+(a<=q<2*b) if x%2 == 0: print("YES") break else: print("NO") ```
106,221
[ 0.2432861328125, 0.25244140625, -0.0284423828125, 0.39697265625, -0.60546875, -0.57177734375, -0.124267578125, 0.179931640625, 0.296142578125, 0.88623046875, 0.82666015625, 0.1943359375, 0.1842041015625, -0.60791015625, -0.51904296875, 0.12939453125, -0.77734375, -0.923828125, -0.388427734375, -0.1505126953125, 0.11309814453125, 0.0036067962646484375, -1.3173828125, -0.00513458251953125, -0.197509765625, 0.83642578125, 0.1290283203125, -0.01087188720703125, 0.9296875, 1.130859375, 0.0889892578125, -0.53564453125, 0.461669921875, -0.8095703125, -0.443603515625, -0.263916015625, 0.83251953125, -0.599609375, -0.06732177734375, -0.439697265625, 0.323486328125, -0.53369140625, 0.347412109375, -0.61376953125, -1.2734375, 0.005489349365234375, -0.2998046875, -0.50732421875, -0.1939697265625, -0.52685546875, -0.04132080078125, -0.385498046875, 0.44482421875, -0.242919921875, 0.1131591796875, 0.09869384765625, 0.2291259765625, 0.1610107421875, -0.6962890625, 0.26171875, 0.245849609375, -0.350830078125, 0.04052734375, -0.79638671875, 0.232421875, 0.018157958984375, 0.199462890625, -0.441650390625, 0.342529296875, -0.74267578125, -0.2227783203125, -0.06903076171875, -0.64306640625, -0.5068359375, -0.055572509765625, 0.435302734375, 0.35791015625, -0.14404296875, -0.84326171875, 0.71630859375, -0.2421875, 0.84423828125, 0.64453125, -0.05474853515625, -0.3134765625, -0.58251953125, 0.43212890625, 0.2276611328125, 0.364013671875, -0.2197265625, -0.12384033203125, 0.49853515625, -0.29541015625, -0.267578125, 0.17578125, 0.86376953125, -0.177001953125, 0.158203125, 0.7451171875, -0.09759521484375, 0.568359375, 0.73681640625, -0.61083984375, 1.0849609375, -0.436279296875, 0.074951171875, 0.427001953125, 0.0109405517578125, -0.1859130859375, -0.5419921875, -0.2724609375, -0.4228515625, 0.60498046875, 0.48046875, -0.5146484375, 0.90576171875, 0.0615234375, 0.58544921875, -0.63525390625, 0.10992431640625, 0.708984375, 0.028839111328125, 0.65087890625, -0.1412353515625, 0.01461029052734375, -0.28173828125, -0.60888671875, 1.0390625, -0.66015625, -0.1875, 0.59375, -0.04638671875, -0.2254638671875, 0.418701171875, -0.31689453125, 0.720703125, -0.150634765625, 0.33544921875, 0.7255859375, -0.5068359375, 0.98486328125, -0.0112762451171875, 0.0811767578125, 1.3583984375, 0.3388671875, -0.1407470703125, 0.416259765625, 0.576171875, -0.83251953125, 0.265869140625, -1.0712890625, 0.498046875, -0.0316162109375, 0.2147216796875, -0.1856689453125, -0.2286376953125, -0.501953125, 0.57421875, 0.36669921875, 0.0225067138671875, -0.1441650390625, 0.4677734375, -0.475341796875, 0.76513671875, -0.339599609375, 0.763671875, -0.439208984375, -0.1793212890625, 0.06060791015625, -0.30419921875, 0.0274200439453125, -0.404052734375, 0.057220458984375, 0.69384765625, 0.419677734375, 1.3134765625, 1.23046875, -0.349609375, 0.48681640625, 0.449462890625, -0.4794921875, 0.44482421875, 0.404541015625, 1.0244140625, 0.4287109375, 0.462890625, -0.07708740234375, 0.0635986328125, -0.78466796875, -0.317626953125, 0.1864013671875, 0.5908203125, -0.399658203125, 0.288818359375, 0.31689453125, 0.0997314453125, -1.0654296875, -0.1409912109375, -0.0579833984375, -0.75341796875, -0.55517578125, 0.416015625, 0.04644775390625, 0.3828125, -0.51123046875, -0.556640625, 0.26513671875, 1.2080078125, -0.3828125, -0.095458984375, 0.51318359375, 0.1256103515625, 0.0880126953125, -0.1456298828125, -0.0869140625, -0.100341796875, -0.6083984375, 1.0771484375, 0.08349609375, -0.15234375, 0.004337310791015625, 0.7216796875, 0.24658203125, 0.84375, -0.66552734375, -0.3193359375, 0.517578125, 1.0771484375, 0.11627197265625, 0.83642578125, 0.58544921875, 1.1611328125, 0.29150390625, 0.728515625, 0.30224609375, 0.283935546875, 0.6591796875, 1.044921875, -0.07086181640625, -0.06689453125, 0.250244140625, 0.38916015625, 0.1929931640625, 0.6025390625, 0.27294921875, 0.53662109375, -0.188720703125, 0.057769775390625, -0.8125, 0.1368408203125, -0.303466796875, 0.53759765625, 0.263427734375, 0.5634765625, -0.428466796875, -0.1690673828125, 0.25341796875, 0.9833984375, -1.060546875, -0.62109375, 0.0430908203125, -0.1282958984375, -0.0501708984375, -0.038116455078125, 0.52880859375, 0.12939453125, 0.55224609375, 0.4462890625, -0.28515625, -0.4560546875, -0.8701171875, -0.7216796875, -0.79248046875, -0.4208984375, -0.56103515625, -0.1527099609375, 0.2415771484375, -1.0810546875, -0.00861358642578125, -0.390625, -0.059173583984375, 0.2420654296875, -0.759765625, 1.0244140625, -0.666015625, 0.36669921875, -0.73193359375, 0.393798828125, 0.2666015625, 1.0947265625, -0.35107421875, -0.0738525390625, -0.06805419921875, -0.355224609375, 0.160400390625, -0.168212890625, 0.34228515625, -0.12152099609375, -0.353759765625, -0.74072265625, -0.433837890625, -0.335693359375, -0.59814453125, 0.324951171875, -0.5791015625, 0.77685546875, 0.66552734375, -0.495849609375, 0.7744140625, 1.0205078125, -0.58349609375, 0.4580078125, 0.075927734375, 0.0177459716796875, -0.71533203125, 1.2958984375, 0.716796875, 0.35791015625, -0.384521484375, -0.5693359375, -0.3935546875, -0.384521484375, 0.352294921875, -0.50537109375, -0.59228515625, 0.70068359375, -0.05267333984375, -1.0576171875, 0.160400390625, -0.98828125, -0.640625, -0.33251953125, -0.3798828125, 0.810546875, 0.79443359375, 0.16357421875, -0.1533203125, -0.321533203125, 0.1978759765625, 0.49365234375, 0.31494140625, -0.7724609375, 0.285400390625, 0.6962890625, 0.11297607421875, 0.370849609375, 0.292236328125, -0.282470703125, -0.10418701171875, 0.0341796875, -0.185791015625, 0.65283203125, 0.1177978515625, 0.214599609375, 0.4931640625, 0.419921875, -0.73779296875, -0.059173583984375, -0.2392578125, 0.51708984375, 0.4521484375, 0.46630859375, 0.248291015625, -0.357666015625, -0.650390625, -1.1513671875, 0.378662109375, 0.07000732421875, 0.7939453125, -0.763671875, 0.927734375, -0.01424407958984375, -0.2347412109375, 0.347412109375, -0.66357421875, 0.1539306640625, 1.1240234375, -0.431640625, 0.367919921875, -0.63427734375, 0.489013671875, 0.25537109375, 0.270751953125, 0.486328125, 0.278564453125, 0.70068359375, -0.2349853515625, -0.56982421875, -0.591796875, -0.1993408203125, -0.053375244140625, -0.75341796875, 0.2666015625, -0.6484375, -0.308349609375, -0.64697265625, 0.3857421875, 0.97021484375, 1.0126953125, -0.022369384765625, 0.65234375, 0.04449462890625, 0.28125, 0.47314453125, -0.57568359375, 0.0972900390625, -0.53173828125, 0.81103515625, 0.490234375, 0.3349609375, -0.70361328125, 0.021331787109375, -0.2099609375, -0.261474609375, 0.152099609375, -0.281005859375, -1.1494140625, 0.0467529296875, -0.192626953125, 0.5390625, -0.487548828125, -0.29052734375, -0.1641845703125, 0.44384765625, 0.48583984375, -0.70556640625, 0.11822509765625, -1.07421875, 0.779296875, 0.25390625, -0.262451171875, -0.39697265625, -0.56396484375, -0.61865234375, -1.0869140625, -0.07196044921875, 0.97412109375, 0.1558837890625, 0.494873046875, -0.93896484375, 0.4384765625, -0.07281494140625, -0.4580078125, 0.08062744140625, -0.291015625, 0.414306640625, -0.12237548828125, 0.70703125, -0.681640625, -0.52685546875, -0.04833984375, -0.92333984375, 0.6650390625, -0.486572265625, 0.330322265625, -0.026702880859375, -0.254150390625, -0.2362060546875, 0.27001953125, -0.2032470703125, 0.392333984375, -0.452880859375, 0.28466796875, -0.7958984375, -0.382080078125, 0.728515625, -0.35546875, -0.10601806640625, 0.71435546875, -0.10003662109375, -0.462890625, 0.09808349609375, 0.52392578125, -0.404296875, 0.429443359375, -0.496826171875, 0.40966796875, -0.2215576171875, -0.43115234375, -0.25, -0.70947265625, 0.86865234375, 0.29345703125, -0.5224609375, -0.445556640625, -1.0068359375, -0.267333984375, 0.026702880859375, -0.1964111328125, 0.560546875, 0.033905029296875, 0.059051513671875, 0.08074951171875, -0.1968994140625, -0.5517578125, -0.08392333984375, -0.29345703125, -0.00732421875, -0.02569580078125, 0.51953125, 0.482177734375, -0.179931640625, -0.5361328125, -0.454833984375, -0.294189453125, 0.09356689453125, -0.498291015625, -0.4560546875, -0.28515625, -0.288818359375, -0.69384765625, 0.1002197265625, -0.08123779296875, 0.46142578125, 0.953125, 0.0721435546875, 0.623046875, 0.320556640625, -0.84375, 1.1298828125, 0.37451171875, -1.091796875, -0.73095703125, 0.359619140625, -0.1285400390625, 0.5322265625, 0.176025390625, -0.515625, -0.826171875, -0.89599609375, 0.168701171875, -0.94189453125, -0.158935546875, -1.1455078125, -0.468994140625, -0.4716796875, 0.35888671875, -0.0592041015625, -0.7060546875, 0.27294921875, -0.9169921875, 0.332275390625, -0.7958984375, 0.10467529296875, -0.6123046875, -0.61767578125, -0.1968994140625, 1.1044921875, 0.12939453125, 0.5986328125, 0.09564208984375, -0.3583984375, 0.25439453125, 0.200439453125, -0.6005859375, -0.353759765625, 0.2322998046875, 0.0212249755859375, -0.1309814453125, -0.3447265625, -0.5478515625, 0.56787109375, -0.81396484375, 0.410888671875, -0.04638671875, -0.26953125, -0.1529541015625, -0.3349609375, 1.09375, -0.37890625, 0.2021484375, -0.35302734375, 0.28759765625, 0.509765625, -0.0271148681640625, -0.2568359375, -0.37841796875, -0.58544921875, -1.2841796875, 0.55712890625, -0.2073974609375, 0.041229248046875, -0.6953125, -0.30517578125, 1.2958984375, -0.455078125, 0.2412109375, 1.47265625, 0.177001953125, 0.21435546875, -0.4521484375, 0.61181640625, 0.6044921875, -0.43505859375, -0.07476806640625, 0.2271728515625, -0.62158203125, -0.038848876953125, -0.474365234375, -1.2001953125, -0.71875, 0.447021484375, 1.2177734375, -0.444580078125, 0.77197265625, -0.251708984375, -1.0654296875, -0.56884765625, 0.84521484375, -0.060882568359375, 0.256591796875, 0.888671875, 0.1416015625, -0.220947265625, 0.264404296875, -0.154541015625, -0.337890625, -0.6904296875, 0.9970703125, -0.3916015625, -0.08599853515625, 1.2236328125, 0.9052734375, -1.1552734375, -0.81494140625, -0.465087890625, -0.057525634765625, 0.17919921875, -0.91064453125, -0.0112457275390625, 0.5595703125, -0.60888671875, -0.0207366943359375, 0.61572265625, -0.3603515625, 0.3837890625, 0.0994873046875, 0.1588134765625, -0.2374267578125, 0.36669921875, 0.60546875, -0.2452392578125, -0.34033203125, -0.904296875, -0.3857421875, -0.2197265625, 0.007320404052734375, 1.0625, -0.1510009765625, 0.3935546875, 0.1929931640625, -0.0814208984375, 0.7529296875, -0.44091796875, -0.3251953125, 0.2158203125, -0.64013671875, -0.295166015625, -0.20556640625, 0.400146484375, 0.1787109375, 0.78369140625, -0.626953125, -0.00919342041015625, 0.218505859375, 0.43798828125, -0.469482421875, -1.103515625, -0.1787109375, -1.1591796875, -0.42626953125, -0.61962890625, -0.767578125, 0.0220947265625, 0.716796875, 0.057281494140625, -0.64111328125, -0.09588623046875, 0.1610107421875, -0.426513671875, 0.61328125, -0.5830078125, 0.2117919921875, -0.5009765625, -0.266845703125, -0.68701171875, 0.09002685546875, -0.80859375, -0.138671875, -0.50537109375, 0.413818359375, -0.56884765625, 0.33984375, -0.48486328125, 0.408935546875, -0.2744140625, -0.70361328125, -0.35693359375, 0.08843994140625, -0.56640625, 0.9501953125, 0.75341796875, 0.279541015625, 0.36328125, -0.46044921875, -0.328369140625, -0.474365234375, 0.424560546875, 0.07135009765625, 0.02484130859375, -0.34033203125, -0.244384765625, 0.16455078125, -1.0205078125, 0.1898193359375, -0.154052734375, 0.103759765625, 0.097412109375, -0.26123046875, 0.5400390625, 1.361328125, -0.1944580078125, 0.349365234375, -0.055694580078125, 0.42822265625, 0.371826171875, 0.2271728515625, -0.12481689453125, 0.82080078125, -0.278564453125, -0.6064453125, 0.1619873046875, 0.07098388671875, 0.2239990234375, 0.032440185546875, -0.401611328125, -0.72998046875, -0.8359375, -0.30078125, -0.00490570068359375, 0.52392578125, 0.58642578125, -0.15234375, 0.028076171875, -0.517578125, -0.3798828125, -0.5439453125, -1.255859375, -0.87109375, 0.5166015625, -0.190673828125, -0.8056640625, -0.0565185546875, -0.17431640625, -0.1336669921875, 0.0828857421875, 0.29541015625, -0.317138671875, 0.57568359375, -0.407958984375, 0.51318359375, -0.12164306640625, -0.033172607421875, 0.08575439453125, 0.484130859375, -0.58154296875, -0.6630859375, 0.392578125, 0.91748046875, 0.1627197265625, -0.3037109375, -0.720703125, 0.41796875, -0.1314697265625, -0.12457275390625, -0.53173828125, 0.3818359375, -0.08203125, 0.457275390625, -0.79443359375, -0.1103515625, -0.53173828125, 0.62744140625, 0.223388671875, -0.56103515625, -0.64404296875, 0.91552734375, 0.467529296875, -0.28125, 0.283935546875, -0.04327392578125, 0.27685546875, -0.14208984375, 0.1534423828125, -0.32275390625, 0.80029296875, 0.87255859375, 0.9091796875, -0.1287841796875, 0.258544921875, 0.56396484375, 0.438232421875, -0.1573486328125, 0.49267578125, 0.09405517578125, 0.09857177734375, 0.076904296875, -0.1295166015625, -0.2142333984375, -0.369873046875, -0.6328125, 0.325927734375, -0.34716796875, 0.245361328125, 0.0673828125, -0.63134765625, 0.955078125, -0.36572265625, -0.135498046875, 0.0916748046875, -0.66552734375, 0.185546875, 0.57568359375, -0.12841796875, -0.4765625, 0.681640625, 0.65576171875, 0.404296875, 0.44189453125, 0.2222900390625, 0.5947265625, -0.5966796875, 0.1895751953125, 0.27197265625, 0.034210205078125, -0.45947265625, -0.5654296875, -1.021484375, 0.406982421875, -0.77685546875, -0.3740234375, 0.439208984375, -0.80810546875, 0.06964111328125, -0.12298583984375, 0.80517578125, -0.275146484375, 0.157470703125, 0.46923828125, -0.11871337890625, -0.564453125, 0.90283203125, -0.1419677734375, 0.25537109375, -0.23876953125, 1.259765625, -0.006412506103515625, 1.4482421875, 0.80859375, 0.1181640625, 0.01335906982421875, 0.302734375, -0.42626953125, -0.66552734375, -0.304443359375, -0.29345703125, 0.008148193359375, -0.64453125, -0.48486328125, -0.232421875, 0.91357421875, -0.09100341796875, -0.7470703125, -0.262939453125, 0.31396484375, -0.85693359375, 0.493896484375, 0.414306640625, 0.3916015625, -0.0021076202392578125, -0.230224609375, -0.482666015625, -0.603515625, 0.61962890625, -0.63671875, 0.320556640625, -0.6396484375, -0.244384765625, -0.459716796875, -0.673828125, -0.39892578125, -0.1478271484375, -0.1920166015625, -0.98828125, 0.56884765625, 0.2047119140625, 0.4775390625, 0.33740234375, -0.71484375, 0.2578125, 0.75439453125, 1.095703125, 0.0182952880859375, 0.60498046875, 0.462890625, -0.203369140625, 0.12213134765625, -0.2423095703125, 0.4345703125, 0.1707763671875, 0.482421875, -0.26806640625, 0.06396484375, -0.71923828125, -1.13671875, 0.185791015625, 0.4541015625, 0.1781005859375, -0.61328125, -1.1064453125, -0.473388671875, -0.8916015625, -0.10845947265625, -0.84423828125, 0.517578125, -0.316650390625, 0.30322265625, -0.056854248046875, -1.0087890625, 4.39453125, 1.0048828125, 1.064453125, 0.005756378173828125, 0.433349609375, 1.1171875, 0.212646484375, -0.7734375, -0.00690460205078125, -0.400146484375, 1, -0.253662109375, 0.0831298828125, 0.66748046875, 0.25537109375, 0.6484375, -0.8798828125, 0.15185546875, -0.05828857421875, -1.251953125, -0.47216796875, 0.2392578125, -0.12420654296875, 0.77099609375, -0.10614013671875, 0.205810546875, 0.8125, -1.15625, -0.261962890625, -0.81884765625, 0.293701171875, -0.160400390625, 0.5068359375, 0.29248046875, 0.04779052734375, 0.8349609375, -0.309814453125, -0.3037109375, -0.2100830078125, -0.0213623046875, -0.0941162109375, -0.236083984375, 0.258056640625, -0.619140625, -0.373046875, 0.14013671875, -0.483154296875, 0.59716796875, 0.1412353515625, -0.93408203125, 0.50244140625, 0.074951171875, 0.76953125, -0.8671875, -0.5986328125, 0.0000445246696472168, 0.463134765625, -0.251953125, -0.06951904296875, 0.6767578125, 0.395751953125, 0.884765625, -0.3173828125, 0.69384765625, -0.80322265625, 0.93408203125, -0.30908203125, 0.273681640625, -0.72412109375, 0.377685546875, -0.1566162109375, -0.6591796875, -0.423583984375, -0.58544921875, 0.591796875, 0.11773681640625, -0.29443359375, 0.64990234375, 0.86376953125, -0.347900390625, -0.0310211181640625, -0.52099609375, -0.427490234375, -0.295166015625, 0.36767578125, 1.3271484375, -0.42626953125, -0.27294921875, -0.1180419921875, 0.52978515625, 0.330322265625, 0.58251953125, 0.027496337890625, -0.54833984375, -0.431396484375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Tags: games Correct Solution: ``` import sys from itertools import groupby readline = sys.stdin.readline t = int(input()) for _ in range(t): a, b = map(int, readline().split()) dots = [len(list(v)) for k, v in groupby(readline().rstrip()) if k == '.'] lose = 0 med = 0 long = 0 longest = 0 for x in dots: if x < b: continue if b <= x < a: lose = 1 elif 2*b <= x: long += 1 if longest < x: longest = x elif a <= x < 2*b: med += 1 if lose or long > 1: print("NO") continue if long: for left, right in zip(range(longest), range(longest-a, -1, -1)): if (left < b or a <= left < 2*b) and (right < b or a <= right < 2*b): if (((med + (1 if a <= left else 0) + (1 if a <= right else 0)) & 1) == 0): print("YES") break else: print("NO") else: print("YES" if med & 1 else "NO") ```
106,222
[ 0.2432861328125, 0.25244140625, -0.0284423828125, 0.39697265625, -0.60546875, -0.57177734375, -0.124267578125, 0.179931640625, 0.296142578125, 0.88623046875, 0.82666015625, 0.1943359375, 0.1842041015625, -0.60791015625, -0.51904296875, 0.12939453125, -0.77734375, -0.923828125, -0.388427734375, -0.1505126953125, 0.11309814453125, 0.0036067962646484375, -1.3173828125, -0.00513458251953125, -0.197509765625, 0.83642578125, 0.1290283203125, -0.01087188720703125, 0.9296875, 1.130859375, 0.0889892578125, -0.53564453125, 0.461669921875, -0.8095703125, -0.443603515625, -0.263916015625, 0.83251953125, -0.599609375, -0.06732177734375, -0.439697265625, 0.323486328125, -0.53369140625, 0.347412109375, -0.61376953125, -1.2734375, 0.005489349365234375, -0.2998046875, -0.50732421875, -0.1939697265625, -0.52685546875, -0.04132080078125, -0.385498046875, 0.44482421875, -0.242919921875, 0.1131591796875, 0.09869384765625, 0.2291259765625, 0.1610107421875, -0.6962890625, 0.26171875, 0.245849609375, -0.350830078125, 0.04052734375, -0.79638671875, 0.232421875, 0.018157958984375, 0.199462890625, -0.441650390625, 0.342529296875, -0.74267578125, -0.2227783203125, -0.06903076171875, -0.64306640625, -0.5068359375, -0.055572509765625, 0.435302734375, 0.35791015625, -0.14404296875, -0.84326171875, 0.71630859375, -0.2421875, 0.84423828125, 0.64453125, -0.05474853515625, -0.3134765625, -0.58251953125, 0.43212890625, 0.2276611328125, 0.364013671875, -0.2197265625, -0.12384033203125, 0.49853515625, -0.29541015625, -0.267578125, 0.17578125, 0.86376953125, -0.177001953125, 0.158203125, 0.7451171875, -0.09759521484375, 0.568359375, 0.73681640625, -0.61083984375, 1.0849609375, -0.436279296875, 0.074951171875, 0.427001953125, 0.0109405517578125, -0.1859130859375, -0.5419921875, -0.2724609375, -0.4228515625, 0.60498046875, 0.48046875, -0.5146484375, 0.90576171875, 0.0615234375, 0.58544921875, -0.63525390625, 0.10992431640625, 0.708984375, 0.028839111328125, 0.65087890625, -0.1412353515625, 0.01461029052734375, -0.28173828125, -0.60888671875, 1.0390625, -0.66015625, -0.1875, 0.59375, -0.04638671875, -0.2254638671875, 0.418701171875, -0.31689453125, 0.720703125, -0.150634765625, 0.33544921875, 0.7255859375, -0.5068359375, 0.98486328125, -0.0112762451171875, 0.0811767578125, 1.3583984375, 0.3388671875, -0.1407470703125, 0.416259765625, 0.576171875, -0.83251953125, 0.265869140625, -1.0712890625, 0.498046875, -0.0316162109375, 0.2147216796875, -0.1856689453125, -0.2286376953125, -0.501953125, 0.57421875, 0.36669921875, 0.0225067138671875, -0.1441650390625, 0.4677734375, -0.475341796875, 0.76513671875, -0.339599609375, 0.763671875, -0.439208984375, -0.1793212890625, 0.06060791015625, -0.30419921875, 0.0274200439453125, -0.404052734375, 0.057220458984375, 0.69384765625, 0.419677734375, 1.3134765625, 1.23046875, -0.349609375, 0.48681640625, 0.449462890625, -0.4794921875, 0.44482421875, 0.404541015625, 1.0244140625, 0.4287109375, 0.462890625, -0.07708740234375, 0.0635986328125, -0.78466796875, -0.317626953125, 0.1864013671875, 0.5908203125, -0.399658203125, 0.288818359375, 0.31689453125, 0.0997314453125, -1.0654296875, -0.1409912109375, -0.0579833984375, -0.75341796875, -0.55517578125, 0.416015625, 0.04644775390625, 0.3828125, -0.51123046875, -0.556640625, 0.26513671875, 1.2080078125, -0.3828125, -0.095458984375, 0.51318359375, 0.1256103515625, 0.0880126953125, -0.1456298828125, -0.0869140625, -0.100341796875, -0.6083984375, 1.0771484375, 0.08349609375, -0.15234375, 0.004337310791015625, 0.7216796875, 0.24658203125, 0.84375, -0.66552734375, -0.3193359375, 0.517578125, 1.0771484375, 0.11627197265625, 0.83642578125, 0.58544921875, 1.1611328125, 0.29150390625, 0.728515625, 0.30224609375, 0.283935546875, 0.6591796875, 1.044921875, -0.07086181640625, -0.06689453125, 0.250244140625, 0.38916015625, 0.1929931640625, 0.6025390625, 0.27294921875, 0.53662109375, -0.188720703125, 0.057769775390625, -0.8125, 0.1368408203125, -0.303466796875, 0.53759765625, 0.263427734375, 0.5634765625, -0.428466796875, -0.1690673828125, 0.25341796875, 0.9833984375, -1.060546875, -0.62109375, 0.0430908203125, -0.1282958984375, -0.0501708984375, -0.038116455078125, 0.52880859375, 0.12939453125, 0.55224609375, 0.4462890625, -0.28515625, -0.4560546875, -0.8701171875, -0.7216796875, -0.79248046875, -0.4208984375, -0.56103515625, -0.1527099609375, 0.2415771484375, -1.0810546875, -0.00861358642578125, -0.390625, -0.059173583984375, 0.2420654296875, -0.759765625, 1.0244140625, -0.666015625, 0.36669921875, -0.73193359375, 0.393798828125, 0.2666015625, 1.0947265625, -0.35107421875, -0.0738525390625, -0.06805419921875, -0.355224609375, 0.160400390625, -0.168212890625, 0.34228515625, -0.12152099609375, -0.353759765625, -0.74072265625, -0.433837890625, -0.335693359375, -0.59814453125, 0.324951171875, -0.5791015625, 0.77685546875, 0.66552734375, -0.495849609375, 0.7744140625, 1.0205078125, -0.58349609375, 0.4580078125, 0.075927734375, 0.0177459716796875, -0.71533203125, 1.2958984375, 0.716796875, 0.35791015625, -0.384521484375, -0.5693359375, -0.3935546875, -0.384521484375, 0.352294921875, -0.50537109375, -0.59228515625, 0.70068359375, -0.05267333984375, -1.0576171875, 0.160400390625, -0.98828125, -0.640625, -0.33251953125, -0.3798828125, 0.810546875, 0.79443359375, 0.16357421875, -0.1533203125, -0.321533203125, 0.1978759765625, 0.49365234375, 0.31494140625, -0.7724609375, 0.285400390625, 0.6962890625, 0.11297607421875, 0.370849609375, 0.292236328125, -0.282470703125, -0.10418701171875, 0.0341796875, -0.185791015625, 0.65283203125, 0.1177978515625, 0.214599609375, 0.4931640625, 0.419921875, -0.73779296875, -0.059173583984375, -0.2392578125, 0.51708984375, 0.4521484375, 0.46630859375, 0.248291015625, -0.357666015625, -0.650390625, -1.1513671875, 0.378662109375, 0.07000732421875, 0.7939453125, -0.763671875, 0.927734375, -0.01424407958984375, -0.2347412109375, 0.347412109375, -0.66357421875, 0.1539306640625, 1.1240234375, -0.431640625, 0.367919921875, -0.63427734375, 0.489013671875, 0.25537109375, 0.270751953125, 0.486328125, 0.278564453125, 0.70068359375, -0.2349853515625, -0.56982421875, -0.591796875, -0.1993408203125, -0.053375244140625, -0.75341796875, 0.2666015625, -0.6484375, -0.308349609375, -0.64697265625, 0.3857421875, 0.97021484375, 1.0126953125, -0.022369384765625, 0.65234375, 0.04449462890625, 0.28125, 0.47314453125, -0.57568359375, 0.0972900390625, -0.53173828125, 0.81103515625, 0.490234375, 0.3349609375, -0.70361328125, 0.021331787109375, -0.2099609375, -0.261474609375, 0.152099609375, -0.281005859375, -1.1494140625, 0.0467529296875, -0.192626953125, 0.5390625, -0.487548828125, -0.29052734375, -0.1641845703125, 0.44384765625, 0.48583984375, -0.70556640625, 0.11822509765625, -1.07421875, 0.779296875, 0.25390625, -0.262451171875, -0.39697265625, -0.56396484375, -0.61865234375, -1.0869140625, -0.07196044921875, 0.97412109375, 0.1558837890625, 0.494873046875, -0.93896484375, 0.4384765625, -0.07281494140625, -0.4580078125, 0.08062744140625, -0.291015625, 0.414306640625, -0.12237548828125, 0.70703125, -0.681640625, -0.52685546875, -0.04833984375, -0.92333984375, 0.6650390625, -0.486572265625, 0.330322265625, -0.026702880859375, -0.254150390625, -0.2362060546875, 0.27001953125, -0.2032470703125, 0.392333984375, -0.452880859375, 0.28466796875, -0.7958984375, -0.382080078125, 0.728515625, -0.35546875, -0.10601806640625, 0.71435546875, -0.10003662109375, -0.462890625, 0.09808349609375, 0.52392578125, -0.404296875, 0.429443359375, -0.496826171875, 0.40966796875, -0.2215576171875, -0.43115234375, -0.25, -0.70947265625, 0.86865234375, 0.29345703125, -0.5224609375, -0.445556640625, -1.0068359375, -0.267333984375, 0.026702880859375, -0.1964111328125, 0.560546875, 0.033905029296875, 0.059051513671875, 0.08074951171875, -0.1968994140625, -0.5517578125, -0.08392333984375, -0.29345703125, -0.00732421875, -0.02569580078125, 0.51953125, 0.482177734375, -0.179931640625, -0.5361328125, -0.454833984375, -0.294189453125, 0.09356689453125, -0.498291015625, -0.4560546875, -0.28515625, -0.288818359375, -0.69384765625, 0.1002197265625, -0.08123779296875, 0.46142578125, 0.953125, 0.0721435546875, 0.623046875, 0.320556640625, -0.84375, 1.1298828125, 0.37451171875, -1.091796875, -0.73095703125, 0.359619140625, -0.1285400390625, 0.5322265625, 0.176025390625, -0.515625, -0.826171875, -0.89599609375, 0.168701171875, -0.94189453125, -0.158935546875, -1.1455078125, -0.468994140625, -0.4716796875, 0.35888671875, -0.0592041015625, -0.7060546875, 0.27294921875, -0.9169921875, 0.332275390625, -0.7958984375, 0.10467529296875, -0.6123046875, -0.61767578125, -0.1968994140625, 1.1044921875, 0.12939453125, 0.5986328125, 0.09564208984375, -0.3583984375, 0.25439453125, 0.200439453125, -0.6005859375, -0.353759765625, 0.2322998046875, 0.0212249755859375, -0.1309814453125, -0.3447265625, -0.5478515625, 0.56787109375, -0.81396484375, 0.410888671875, -0.04638671875, -0.26953125, -0.1529541015625, -0.3349609375, 1.09375, -0.37890625, 0.2021484375, -0.35302734375, 0.28759765625, 0.509765625, -0.0271148681640625, -0.2568359375, -0.37841796875, -0.58544921875, -1.2841796875, 0.55712890625, -0.2073974609375, 0.041229248046875, -0.6953125, -0.30517578125, 1.2958984375, -0.455078125, 0.2412109375, 1.47265625, 0.177001953125, 0.21435546875, -0.4521484375, 0.61181640625, 0.6044921875, -0.43505859375, -0.07476806640625, 0.2271728515625, -0.62158203125, -0.038848876953125, -0.474365234375, -1.2001953125, -0.71875, 0.447021484375, 1.2177734375, -0.444580078125, 0.77197265625, -0.251708984375, -1.0654296875, -0.56884765625, 0.84521484375, -0.060882568359375, 0.256591796875, 0.888671875, 0.1416015625, -0.220947265625, 0.264404296875, -0.154541015625, -0.337890625, -0.6904296875, 0.9970703125, -0.3916015625, -0.08599853515625, 1.2236328125, 0.9052734375, -1.1552734375, -0.81494140625, -0.465087890625, -0.057525634765625, 0.17919921875, -0.91064453125, -0.0112457275390625, 0.5595703125, -0.60888671875, -0.0207366943359375, 0.61572265625, -0.3603515625, 0.3837890625, 0.0994873046875, 0.1588134765625, -0.2374267578125, 0.36669921875, 0.60546875, -0.2452392578125, -0.34033203125, -0.904296875, -0.3857421875, -0.2197265625, 0.007320404052734375, 1.0625, -0.1510009765625, 0.3935546875, 0.1929931640625, -0.0814208984375, 0.7529296875, -0.44091796875, -0.3251953125, 0.2158203125, -0.64013671875, -0.295166015625, -0.20556640625, 0.400146484375, 0.1787109375, 0.78369140625, -0.626953125, -0.00919342041015625, 0.218505859375, 0.43798828125, -0.469482421875, -1.103515625, -0.1787109375, -1.1591796875, -0.42626953125, -0.61962890625, -0.767578125, 0.0220947265625, 0.716796875, 0.057281494140625, -0.64111328125, -0.09588623046875, 0.1610107421875, -0.426513671875, 0.61328125, -0.5830078125, 0.2117919921875, -0.5009765625, -0.266845703125, -0.68701171875, 0.09002685546875, -0.80859375, -0.138671875, -0.50537109375, 0.413818359375, -0.56884765625, 0.33984375, -0.48486328125, 0.408935546875, -0.2744140625, -0.70361328125, -0.35693359375, 0.08843994140625, -0.56640625, 0.9501953125, 0.75341796875, 0.279541015625, 0.36328125, -0.46044921875, -0.328369140625, -0.474365234375, 0.424560546875, 0.07135009765625, 0.02484130859375, -0.34033203125, -0.244384765625, 0.16455078125, -1.0205078125, 0.1898193359375, -0.154052734375, 0.103759765625, 0.097412109375, -0.26123046875, 0.5400390625, 1.361328125, -0.1944580078125, 0.349365234375, -0.055694580078125, 0.42822265625, 0.371826171875, 0.2271728515625, -0.12481689453125, 0.82080078125, -0.278564453125, -0.6064453125, 0.1619873046875, 0.07098388671875, 0.2239990234375, 0.032440185546875, -0.401611328125, -0.72998046875, -0.8359375, -0.30078125, -0.00490570068359375, 0.52392578125, 0.58642578125, -0.15234375, 0.028076171875, -0.517578125, -0.3798828125, -0.5439453125, -1.255859375, -0.87109375, 0.5166015625, -0.190673828125, -0.8056640625, -0.0565185546875, -0.17431640625, -0.1336669921875, 0.0828857421875, 0.29541015625, -0.317138671875, 0.57568359375, -0.407958984375, 0.51318359375, -0.12164306640625, -0.033172607421875, 0.08575439453125, 0.484130859375, -0.58154296875, -0.6630859375, 0.392578125, 0.91748046875, 0.1627197265625, -0.3037109375, -0.720703125, 0.41796875, -0.1314697265625, -0.12457275390625, -0.53173828125, 0.3818359375, -0.08203125, 0.457275390625, -0.79443359375, -0.1103515625, -0.53173828125, 0.62744140625, 0.223388671875, -0.56103515625, -0.64404296875, 0.91552734375, 0.467529296875, -0.28125, 0.283935546875, -0.04327392578125, 0.27685546875, -0.14208984375, 0.1534423828125, -0.32275390625, 0.80029296875, 0.87255859375, 0.9091796875, -0.1287841796875, 0.258544921875, 0.56396484375, 0.438232421875, -0.1573486328125, 0.49267578125, 0.09405517578125, 0.09857177734375, 0.076904296875, -0.1295166015625, -0.2142333984375, -0.369873046875, -0.6328125, 0.325927734375, -0.34716796875, 0.245361328125, 0.0673828125, -0.63134765625, 0.955078125, -0.36572265625, -0.135498046875, 0.0916748046875, -0.66552734375, 0.185546875, 0.57568359375, -0.12841796875, -0.4765625, 0.681640625, 0.65576171875, 0.404296875, 0.44189453125, 0.2222900390625, 0.5947265625, -0.5966796875, 0.1895751953125, 0.27197265625, 0.034210205078125, -0.45947265625, -0.5654296875, -1.021484375, 0.406982421875, -0.77685546875, -0.3740234375, 0.439208984375, -0.80810546875, 0.06964111328125, -0.12298583984375, 0.80517578125, -0.275146484375, 0.157470703125, 0.46923828125, -0.11871337890625, -0.564453125, 0.90283203125, -0.1419677734375, 0.25537109375, -0.23876953125, 1.259765625, -0.006412506103515625, 1.4482421875, 0.80859375, 0.1181640625, 0.01335906982421875, 0.302734375, -0.42626953125, -0.66552734375, -0.304443359375, -0.29345703125, 0.008148193359375, -0.64453125, -0.48486328125, -0.232421875, 0.91357421875, -0.09100341796875, -0.7470703125, -0.262939453125, 0.31396484375, -0.85693359375, 0.493896484375, 0.414306640625, 0.3916015625, -0.0021076202392578125, -0.230224609375, -0.482666015625, -0.603515625, 0.61962890625, -0.63671875, 0.320556640625, -0.6396484375, -0.244384765625, -0.459716796875, -0.673828125, -0.39892578125, -0.1478271484375, -0.1920166015625, -0.98828125, 0.56884765625, 0.2047119140625, 0.4775390625, 0.33740234375, -0.71484375, 0.2578125, 0.75439453125, 1.095703125, 0.0182952880859375, 0.60498046875, 0.462890625, -0.203369140625, 0.12213134765625, -0.2423095703125, 0.4345703125, 0.1707763671875, 0.482421875, -0.26806640625, 0.06396484375, -0.71923828125, -1.13671875, 0.185791015625, 0.4541015625, 0.1781005859375, -0.61328125, -1.1064453125, -0.473388671875, -0.8916015625, -0.10845947265625, -0.84423828125, 0.517578125, -0.316650390625, 0.30322265625, -0.056854248046875, -1.0087890625, 4.39453125, 1.0048828125, 1.064453125, 0.005756378173828125, 0.433349609375, 1.1171875, 0.212646484375, -0.7734375, -0.00690460205078125, -0.400146484375, 1, -0.253662109375, 0.0831298828125, 0.66748046875, 0.25537109375, 0.6484375, -0.8798828125, 0.15185546875, -0.05828857421875, -1.251953125, -0.47216796875, 0.2392578125, -0.12420654296875, 0.77099609375, -0.10614013671875, 0.205810546875, 0.8125, -1.15625, -0.261962890625, -0.81884765625, 0.293701171875, -0.160400390625, 0.5068359375, 0.29248046875, 0.04779052734375, 0.8349609375, -0.309814453125, -0.3037109375, -0.2100830078125, -0.0213623046875, -0.0941162109375, -0.236083984375, 0.258056640625, -0.619140625, -0.373046875, 0.14013671875, -0.483154296875, 0.59716796875, 0.1412353515625, -0.93408203125, 0.50244140625, 0.074951171875, 0.76953125, -0.8671875, -0.5986328125, 0.0000445246696472168, 0.463134765625, -0.251953125, -0.06951904296875, 0.6767578125, 0.395751953125, 0.884765625, -0.3173828125, 0.69384765625, -0.80322265625, 0.93408203125, -0.30908203125, 0.273681640625, -0.72412109375, 0.377685546875, -0.1566162109375, -0.6591796875, -0.423583984375, -0.58544921875, 0.591796875, 0.11773681640625, -0.29443359375, 0.64990234375, 0.86376953125, -0.347900390625, -0.0310211181640625, -0.52099609375, -0.427490234375, -0.295166015625, 0.36767578125, 1.3271484375, -0.42626953125, -0.27294921875, -0.1180419921875, 0.52978515625, 0.330322265625, 0.58251953125, 0.027496337890625, -0.54833984375, -0.431396484375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Tags: games Correct Solution: ``` # import sys # input = sys.stdin.readline Q = int(input()) for _ in range(Q): a, b = map(int, input().split()) S = input() + "X" s = 0 x = x1 = x2 = x3 = xx = 0 for i in range(len(S)): if S[i] == "X": if s < b: pass elif a <= s < 2*b: x += 1 elif a < 2*b and (3*a <= s < a+3*b-1 or 2*a <= s < a+2*b-1): xx += 1 elif a < 2*b and 3*a <= s < a+4*b-1: x3 += 1 elif a < 2*b and 2*a <= s < a+3*b-1: x2 += 1 elif a <= s < a+2*b-1: x1 += 1 else: # print("a, b, s =", a, b, s) print("NO") break s = 0 else: s += 1 else: # print("x, x1, x2, x3 =", x, x1, x2, x3) if xx+x1+x2+x3 >= 2: print("NO") elif xx: print("YES") elif (x + x1 + x2*2 + x3*3) % 2 == 0: print("NO") else: print("YES") ```
106,223
[ 0.2432861328125, 0.25244140625, -0.0284423828125, 0.39697265625, -0.60546875, -0.57177734375, -0.124267578125, 0.179931640625, 0.296142578125, 0.88623046875, 0.82666015625, 0.1943359375, 0.1842041015625, -0.60791015625, -0.51904296875, 0.12939453125, -0.77734375, -0.923828125, -0.388427734375, -0.1505126953125, 0.11309814453125, 0.0036067962646484375, -1.3173828125, -0.00513458251953125, -0.197509765625, 0.83642578125, 0.1290283203125, -0.01087188720703125, 0.9296875, 1.130859375, 0.0889892578125, -0.53564453125, 0.461669921875, -0.8095703125, -0.443603515625, -0.263916015625, 0.83251953125, -0.599609375, -0.06732177734375, -0.439697265625, 0.323486328125, -0.53369140625, 0.347412109375, -0.61376953125, -1.2734375, 0.005489349365234375, -0.2998046875, -0.50732421875, -0.1939697265625, -0.52685546875, -0.04132080078125, -0.385498046875, 0.44482421875, -0.242919921875, 0.1131591796875, 0.09869384765625, 0.2291259765625, 0.1610107421875, -0.6962890625, 0.26171875, 0.245849609375, -0.350830078125, 0.04052734375, -0.79638671875, 0.232421875, 0.018157958984375, 0.199462890625, -0.441650390625, 0.342529296875, -0.74267578125, -0.2227783203125, -0.06903076171875, -0.64306640625, -0.5068359375, -0.055572509765625, 0.435302734375, 0.35791015625, -0.14404296875, -0.84326171875, 0.71630859375, -0.2421875, 0.84423828125, 0.64453125, -0.05474853515625, -0.3134765625, -0.58251953125, 0.43212890625, 0.2276611328125, 0.364013671875, -0.2197265625, -0.12384033203125, 0.49853515625, -0.29541015625, -0.267578125, 0.17578125, 0.86376953125, -0.177001953125, 0.158203125, 0.7451171875, -0.09759521484375, 0.568359375, 0.73681640625, -0.61083984375, 1.0849609375, -0.436279296875, 0.074951171875, 0.427001953125, 0.0109405517578125, -0.1859130859375, -0.5419921875, -0.2724609375, -0.4228515625, 0.60498046875, 0.48046875, -0.5146484375, 0.90576171875, 0.0615234375, 0.58544921875, -0.63525390625, 0.10992431640625, 0.708984375, 0.028839111328125, 0.65087890625, -0.1412353515625, 0.01461029052734375, -0.28173828125, -0.60888671875, 1.0390625, -0.66015625, -0.1875, 0.59375, -0.04638671875, -0.2254638671875, 0.418701171875, -0.31689453125, 0.720703125, -0.150634765625, 0.33544921875, 0.7255859375, -0.5068359375, 0.98486328125, -0.0112762451171875, 0.0811767578125, 1.3583984375, 0.3388671875, -0.1407470703125, 0.416259765625, 0.576171875, -0.83251953125, 0.265869140625, -1.0712890625, 0.498046875, -0.0316162109375, 0.2147216796875, -0.1856689453125, -0.2286376953125, -0.501953125, 0.57421875, 0.36669921875, 0.0225067138671875, -0.1441650390625, 0.4677734375, -0.475341796875, 0.76513671875, -0.339599609375, 0.763671875, -0.439208984375, -0.1793212890625, 0.06060791015625, -0.30419921875, 0.0274200439453125, -0.404052734375, 0.057220458984375, 0.69384765625, 0.419677734375, 1.3134765625, 1.23046875, -0.349609375, 0.48681640625, 0.449462890625, -0.4794921875, 0.44482421875, 0.404541015625, 1.0244140625, 0.4287109375, 0.462890625, -0.07708740234375, 0.0635986328125, -0.78466796875, -0.317626953125, 0.1864013671875, 0.5908203125, -0.399658203125, 0.288818359375, 0.31689453125, 0.0997314453125, -1.0654296875, -0.1409912109375, -0.0579833984375, -0.75341796875, -0.55517578125, 0.416015625, 0.04644775390625, 0.3828125, -0.51123046875, -0.556640625, 0.26513671875, 1.2080078125, -0.3828125, -0.095458984375, 0.51318359375, 0.1256103515625, 0.0880126953125, -0.1456298828125, -0.0869140625, -0.100341796875, -0.6083984375, 1.0771484375, 0.08349609375, -0.15234375, 0.004337310791015625, 0.7216796875, 0.24658203125, 0.84375, -0.66552734375, -0.3193359375, 0.517578125, 1.0771484375, 0.11627197265625, 0.83642578125, 0.58544921875, 1.1611328125, 0.29150390625, 0.728515625, 0.30224609375, 0.283935546875, 0.6591796875, 1.044921875, -0.07086181640625, -0.06689453125, 0.250244140625, 0.38916015625, 0.1929931640625, 0.6025390625, 0.27294921875, 0.53662109375, -0.188720703125, 0.057769775390625, -0.8125, 0.1368408203125, -0.303466796875, 0.53759765625, 0.263427734375, 0.5634765625, -0.428466796875, -0.1690673828125, 0.25341796875, 0.9833984375, -1.060546875, -0.62109375, 0.0430908203125, -0.1282958984375, -0.0501708984375, -0.038116455078125, 0.52880859375, 0.12939453125, 0.55224609375, 0.4462890625, -0.28515625, -0.4560546875, -0.8701171875, -0.7216796875, -0.79248046875, -0.4208984375, -0.56103515625, -0.1527099609375, 0.2415771484375, -1.0810546875, -0.00861358642578125, -0.390625, -0.059173583984375, 0.2420654296875, -0.759765625, 1.0244140625, -0.666015625, 0.36669921875, -0.73193359375, 0.393798828125, 0.2666015625, 1.0947265625, -0.35107421875, -0.0738525390625, -0.06805419921875, -0.355224609375, 0.160400390625, -0.168212890625, 0.34228515625, -0.12152099609375, -0.353759765625, -0.74072265625, -0.433837890625, -0.335693359375, -0.59814453125, 0.324951171875, -0.5791015625, 0.77685546875, 0.66552734375, -0.495849609375, 0.7744140625, 1.0205078125, -0.58349609375, 0.4580078125, 0.075927734375, 0.0177459716796875, -0.71533203125, 1.2958984375, 0.716796875, 0.35791015625, -0.384521484375, -0.5693359375, -0.3935546875, -0.384521484375, 0.352294921875, -0.50537109375, -0.59228515625, 0.70068359375, -0.05267333984375, -1.0576171875, 0.160400390625, -0.98828125, -0.640625, -0.33251953125, -0.3798828125, 0.810546875, 0.79443359375, 0.16357421875, -0.1533203125, -0.321533203125, 0.1978759765625, 0.49365234375, 0.31494140625, -0.7724609375, 0.285400390625, 0.6962890625, 0.11297607421875, 0.370849609375, 0.292236328125, -0.282470703125, -0.10418701171875, 0.0341796875, -0.185791015625, 0.65283203125, 0.1177978515625, 0.214599609375, 0.4931640625, 0.419921875, -0.73779296875, -0.059173583984375, -0.2392578125, 0.51708984375, 0.4521484375, 0.46630859375, 0.248291015625, -0.357666015625, -0.650390625, -1.1513671875, 0.378662109375, 0.07000732421875, 0.7939453125, -0.763671875, 0.927734375, -0.01424407958984375, -0.2347412109375, 0.347412109375, -0.66357421875, 0.1539306640625, 1.1240234375, -0.431640625, 0.367919921875, -0.63427734375, 0.489013671875, 0.25537109375, 0.270751953125, 0.486328125, 0.278564453125, 0.70068359375, -0.2349853515625, -0.56982421875, -0.591796875, -0.1993408203125, -0.053375244140625, -0.75341796875, 0.2666015625, -0.6484375, -0.308349609375, -0.64697265625, 0.3857421875, 0.97021484375, 1.0126953125, -0.022369384765625, 0.65234375, 0.04449462890625, 0.28125, 0.47314453125, -0.57568359375, 0.0972900390625, -0.53173828125, 0.81103515625, 0.490234375, 0.3349609375, -0.70361328125, 0.021331787109375, -0.2099609375, -0.261474609375, 0.152099609375, -0.281005859375, -1.1494140625, 0.0467529296875, -0.192626953125, 0.5390625, -0.487548828125, -0.29052734375, -0.1641845703125, 0.44384765625, 0.48583984375, -0.70556640625, 0.11822509765625, -1.07421875, 0.779296875, 0.25390625, -0.262451171875, -0.39697265625, -0.56396484375, -0.61865234375, -1.0869140625, -0.07196044921875, 0.97412109375, 0.1558837890625, 0.494873046875, -0.93896484375, 0.4384765625, -0.07281494140625, -0.4580078125, 0.08062744140625, -0.291015625, 0.414306640625, -0.12237548828125, 0.70703125, -0.681640625, -0.52685546875, -0.04833984375, -0.92333984375, 0.6650390625, -0.486572265625, 0.330322265625, -0.026702880859375, -0.254150390625, -0.2362060546875, 0.27001953125, -0.2032470703125, 0.392333984375, -0.452880859375, 0.28466796875, -0.7958984375, -0.382080078125, 0.728515625, -0.35546875, -0.10601806640625, 0.71435546875, -0.10003662109375, -0.462890625, 0.09808349609375, 0.52392578125, -0.404296875, 0.429443359375, -0.496826171875, 0.40966796875, -0.2215576171875, -0.43115234375, -0.25, -0.70947265625, 0.86865234375, 0.29345703125, -0.5224609375, -0.445556640625, -1.0068359375, -0.267333984375, 0.026702880859375, -0.1964111328125, 0.560546875, 0.033905029296875, 0.059051513671875, 0.08074951171875, -0.1968994140625, -0.5517578125, -0.08392333984375, -0.29345703125, -0.00732421875, -0.02569580078125, 0.51953125, 0.482177734375, -0.179931640625, -0.5361328125, -0.454833984375, -0.294189453125, 0.09356689453125, -0.498291015625, -0.4560546875, -0.28515625, -0.288818359375, -0.69384765625, 0.1002197265625, -0.08123779296875, 0.46142578125, 0.953125, 0.0721435546875, 0.623046875, 0.320556640625, -0.84375, 1.1298828125, 0.37451171875, -1.091796875, -0.73095703125, 0.359619140625, -0.1285400390625, 0.5322265625, 0.176025390625, -0.515625, -0.826171875, -0.89599609375, 0.168701171875, -0.94189453125, -0.158935546875, -1.1455078125, -0.468994140625, -0.4716796875, 0.35888671875, -0.0592041015625, -0.7060546875, 0.27294921875, -0.9169921875, 0.332275390625, -0.7958984375, 0.10467529296875, -0.6123046875, -0.61767578125, -0.1968994140625, 1.1044921875, 0.12939453125, 0.5986328125, 0.09564208984375, -0.3583984375, 0.25439453125, 0.200439453125, -0.6005859375, -0.353759765625, 0.2322998046875, 0.0212249755859375, -0.1309814453125, -0.3447265625, -0.5478515625, 0.56787109375, -0.81396484375, 0.410888671875, -0.04638671875, -0.26953125, -0.1529541015625, -0.3349609375, 1.09375, -0.37890625, 0.2021484375, -0.35302734375, 0.28759765625, 0.509765625, -0.0271148681640625, -0.2568359375, -0.37841796875, -0.58544921875, -1.2841796875, 0.55712890625, -0.2073974609375, 0.041229248046875, -0.6953125, -0.30517578125, 1.2958984375, -0.455078125, 0.2412109375, 1.47265625, 0.177001953125, 0.21435546875, -0.4521484375, 0.61181640625, 0.6044921875, -0.43505859375, -0.07476806640625, 0.2271728515625, -0.62158203125, -0.038848876953125, -0.474365234375, -1.2001953125, -0.71875, 0.447021484375, 1.2177734375, -0.444580078125, 0.77197265625, -0.251708984375, -1.0654296875, -0.56884765625, 0.84521484375, -0.060882568359375, 0.256591796875, 0.888671875, 0.1416015625, -0.220947265625, 0.264404296875, -0.154541015625, -0.337890625, -0.6904296875, 0.9970703125, -0.3916015625, -0.08599853515625, 1.2236328125, 0.9052734375, -1.1552734375, -0.81494140625, -0.465087890625, -0.057525634765625, 0.17919921875, -0.91064453125, -0.0112457275390625, 0.5595703125, -0.60888671875, -0.0207366943359375, 0.61572265625, -0.3603515625, 0.3837890625, 0.0994873046875, 0.1588134765625, -0.2374267578125, 0.36669921875, 0.60546875, -0.2452392578125, -0.34033203125, -0.904296875, -0.3857421875, -0.2197265625, 0.007320404052734375, 1.0625, -0.1510009765625, 0.3935546875, 0.1929931640625, -0.0814208984375, 0.7529296875, -0.44091796875, -0.3251953125, 0.2158203125, -0.64013671875, -0.295166015625, -0.20556640625, 0.400146484375, 0.1787109375, 0.78369140625, -0.626953125, -0.00919342041015625, 0.218505859375, 0.43798828125, -0.469482421875, -1.103515625, -0.1787109375, -1.1591796875, -0.42626953125, -0.61962890625, -0.767578125, 0.0220947265625, 0.716796875, 0.057281494140625, -0.64111328125, -0.09588623046875, 0.1610107421875, -0.426513671875, 0.61328125, -0.5830078125, 0.2117919921875, -0.5009765625, -0.266845703125, -0.68701171875, 0.09002685546875, -0.80859375, -0.138671875, -0.50537109375, 0.413818359375, -0.56884765625, 0.33984375, -0.48486328125, 0.408935546875, -0.2744140625, -0.70361328125, -0.35693359375, 0.08843994140625, -0.56640625, 0.9501953125, 0.75341796875, 0.279541015625, 0.36328125, -0.46044921875, -0.328369140625, -0.474365234375, 0.424560546875, 0.07135009765625, 0.02484130859375, -0.34033203125, -0.244384765625, 0.16455078125, -1.0205078125, 0.1898193359375, -0.154052734375, 0.103759765625, 0.097412109375, -0.26123046875, 0.5400390625, 1.361328125, -0.1944580078125, 0.349365234375, -0.055694580078125, 0.42822265625, 0.371826171875, 0.2271728515625, -0.12481689453125, 0.82080078125, -0.278564453125, -0.6064453125, 0.1619873046875, 0.07098388671875, 0.2239990234375, 0.032440185546875, -0.401611328125, -0.72998046875, -0.8359375, -0.30078125, -0.00490570068359375, 0.52392578125, 0.58642578125, -0.15234375, 0.028076171875, -0.517578125, -0.3798828125, -0.5439453125, -1.255859375, -0.87109375, 0.5166015625, -0.190673828125, -0.8056640625, -0.0565185546875, -0.17431640625, -0.1336669921875, 0.0828857421875, 0.29541015625, -0.317138671875, 0.57568359375, -0.407958984375, 0.51318359375, -0.12164306640625, -0.033172607421875, 0.08575439453125, 0.484130859375, -0.58154296875, -0.6630859375, 0.392578125, 0.91748046875, 0.1627197265625, -0.3037109375, -0.720703125, 0.41796875, -0.1314697265625, -0.12457275390625, -0.53173828125, 0.3818359375, -0.08203125, 0.457275390625, -0.79443359375, -0.1103515625, -0.53173828125, 0.62744140625, 0.223388671875, -0.56103515625, -0.64404296875, 0.91552734375, 0.467529296875, -0.28125, 0.283935546875, -0.04327392578125, 0.27685546875, -0.14208984375, 0.1534423828125, -0.32275390625, 0.80029296875, 0.87255859375, 0.9091796875, -0.1287841796875, 0.258544921875, 0.56396484375, 0.438232421875, -0.1573486328125, 0.49267578125, 0.09405517578125, 0.09857177734375, 0.076904296875, -0.1295166015625, -0.2142333984375, -0.369873046875, -0.6328125, 0.325927734375, -0.34716796875, 0.245361328125, 0.0673828125, -0.63134765625, 0.955078125, -0.36572265625, -0.135498046875, 0.0916748046875, -0.66552734375, 0.185546875, 0.57568359375, -0.12841796875, -0.4765625, 0.681640625, 0.65576171875, 0.404296875, 0.44189453125, 0.2222900390625, 0.5947265625, -0.5966796875, 0.1895751953125, 0.27197265625, 0.034210205078125, -0.45947265625, -0.5654296875, -1.021484375, 0.406982421875, -0.77685546875, -0.3740234375, 0.439208984375, -0.80810546875, 0.06964111328125, -0.12298583984375, 0.80517578125, -0.275146484375, 0.157470703125, 0.46923828125, -0.11871337890625, -0.564453125, 0.90283203125, -0.1419677734375, 0.25537109375, -0.23876953125, 1.259765625, -0.006412506103515625, 1.4482421875, 0.80859375, 0.1181640625, 0.01335906982421875, 0.302734375, -0.42626953125, -0.66552734375, -0.304443359375, -0.29345703125, 0.008148193359375, -0.64453125, -0.48486328125, -0.232421875, 0.91357421875, -0.09100341796875, -0.7470703125, -0.262939453125, 0.31396484375, -0.85693359375, 0.493896484375, 0.414306640625, 0.3916015625, -0.0021076202392578125, -0.230224609375, -0.482666015625, -0.603515625, 0.61962890625, -0.63671875, 0.320556640625, -0.6396484375, -0.244384765625, -0.459716796875, -0.673828125, -0.39892578125, -0.1478271484375, -0.1920166015625, -0.98828125, 0.56884765625, 0.2047119140625, 0.4775390625, 0.33740234375, -0.71484375, 0.2578125, 0.75439453125, 1.095703125, 0.0182952880859375, 0.60498046875, 0.462890625, -0.203369140625, 0.12213134765625, -0.2423095703125, 0.4345703125, 0.1707763671875, 0.482421875, -0.26806640625, 0.06396484375, -0.71923828125, -1.13671875, 0.185791015625, 0.4541015625, 0.1781005859375, -0.61328125, -1.1064453125, -0.473388671875, -0.8916015625, -0.10845947265625, -0.84423828125, 0.517578125, -0.316650390625, 0.30322265625, -0.056854248046875, -1.0087890625, 4.39453125, 1.0048828125, 1.064453125, 0.005756378173828125, 0.433349609375, 1.1171875, 0.212646484375, -0.7734375, -0.00690460205078125, -0.400146484375, 1, -0.253662109375, 0.0831298828125, 0.66748046875, 0.25537109375, 0.6484375, -0.8798828125, 0.15185546875, -0.05828857421875, -1.251953125, -0.47216796875, 0.2392578125, -0.12420654296875, 0.77099609375, -0.10614013671875, 0.205810546875, 0.8125, -1.15625, -0.261962890625, -0.81884765625, 0.293701171875, -0.160400390625, 0.5068359375, 0.29248046875, 0.04779052734375, 0.8349609375, -0.309814453125, -0.3037109375, -0.2100830078125, -0.0213623046875, -0.0941162109375, -0.236083984375, 0.258056640625, -0.619140625, -0.373046875, 0.14013671875, -0.483154296875, 0.59716796875, 0.1412353515625, -0.93408203125, 0.50244140625, 0.074951171875, 0.76953125, -0.8671875, -0.5986328125, 0.0000445246696472168, 0.463134765625, -0.251953125, -0.06951904296875, 0.6767578125, 0.395751953125, 0.884765625, -0.3173828125, 0.69384765625, -0.80322265625, 0.93408203125, -0.30908203125, 0.273681640625, -0.72412109375, 0.377685546875, -0.1566162109375, -0.6591796875, -0.423583984375, -0.58544921875, 0.591796875, 0.11773681640625, -0.29443359375, 0.64990234375, 0.86376953125, -0.347900390625, -0.0310211181640625, -0.52099609375, -0.427490234375, -0.295166015625, 0.36767578125, 1.3271484375, -0.42626953125, -0.27294921875, -0.1180419921875, 0.52978515625, 0.330322265625, 0.58251953125, 0.027496337890625, -0.54833984375, -0.431396484375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Tags: games Correct Solution: ``` import os, sys # zeilen = [l.strip() for l in sys.stdin.readlines()] q = int(sys.stdin.readline().strip()) for _ in range(q): a, b = map(int, sys.stdin.readline().strip().split()) word = sys.stdin.readline().strip() gaps = sorted([len(gap) for gap in word.split('X') if len(gap)>= b]) if len(gaps) == 0: print('NO') elif gaps[0] < a: print('NO') elif len(gaps) > 1 and gaps[-2] >= 2*b: print('NO') elif gaps[-1] < 2*b: # no problematic, need only count print('YES' if (len(gaps) % 2) else 'NO') else: # exactly one problematic gap p = gaps[-1] if (len(gaps) % 2): # A tries to make this gap into zero or two if p <= (a + 2*b - 2): # short enough for 0 print('YES') elif p < 3*a: # we have to try two print('NO') # not long enough elif p > (a + 4*b - 2): # too long print('NO') else: print('YES') else: # A tries to make this gap into one if p < 2*a: # too short print('NO') elif p > (a + 3*b - 2):# too long print('NO') else: print('YES') ```
106,224
[ 0.2432861328125, 0.25244140625, -0.0284423828125, 0.39697265625, -0.60546875, -0.57177734375, -0.124267578125, 0.179931640625, 0.296142578125, 0.88623046875, 0.82666015625, 0.1943359375, 0.1842041015625, -0.60791015625, -0.51904296875, 0.12939453125, -0.77734375, -0.923828125, -0.388427734375, -0.1505126953125, 0.11309814453125, 0.0036067962646484375, -1.3173828125, -0.00513458251953125, -0.197509765625, 0.83642578125, 0.1290283203125, -0.01087188720703125, 0.9296875, 1.130859375, 0.0889892578125, -0.53564453125, 0.461669921875, -0.8095703125, -0.443603515625, -0.263916015625, 0.83251953125, -0.599609375, -0.06732177734375, -0.439697265625, 0.323486328125, -0.53369140625, 0.347412109375, -0.61376953125, -1.2734375, 0.005489349365234375, -0.2998046875, -0.50732421875, -0.1939697265625, -0.52685546875, -0.04132080078125, -0.385498046875, 0.44482421875, -0.242919921875, 0.1131591796875, 0.09869384765625, 0.2291259765625, 0.1610107421875, -0.6962890625, 0.26171875, 0.245849609375, -0.350830078125, 0.04052734375, -0.79638671875, 0.232421875, 0.018157958984375, 0.199462890625, -0.441650390625, 0.342529296875, -0.74267578125, -0.2227783203125, -0.06903076171875, -0.64306640625, -0.5068359375, -0.055572509765625, 0.435302734375, 0.35791015625, -0.14404296875, -0.84326171875, 0.71630859375, -0.2421875, 0.84423828125, 0.64453125, -0.05474853515625, -0.3134765625, -0.58251953125, 0.43212890625, 0.2276611328125, 0.364013671875, -0.2197265625, -0.12384033203125, 0.49853515625, -0.29541015625, -0.267578125, 0.17578125, 0.86376953125, -0.177001953125, 0.158203125, 0.7451171875, -0.09759521484375, 0.568359375, 0.73681640625, -0.61083984375, 1.0849609375, -0.436279296875, 0.074951171875, 0.427001953125, 0.0109405517578125, -0.1859130859375, -0.5419921875, -0.2724609375, -0.4228515625, 0.60498046875, 0.48046875, -0.5146484375, 0.90576171875, 0.0615234375, 0.58544921875, -0.63525390625, 0.10992431640625, 0.708984375, 0.028839111328125, 0.65087890625, -0.1412353515625, 0.01461029052734375, -0.28173828125, -0.60888671875, 1.0390625, -0.66015625, -0.1875, 0.59375, -0.04638671875, -0.2254638671875, 0.418701171875, -0.31689453125, 0.720703125, -0.150634765625, 0.33544921875, 0.7255859375, -0.5068359375, 0.98486328125, -0.0112762451171875, 0.0811767578125, 1.3583984375, 0.3388671875, -0.1407470703125, 0.416259765625, 0.576171875, -0.83251953125, 0.265869140625, -1.0712890625, 0.498046875, -0.0316162109375, 0.2147216796875, -0.1856689453125, -0.2286376953125, -0.501953125, 0.57421875, 0.36669921875, 0.0225067138671875, -0.1441650390625, 0.4677734375, -0.475341796875, 0.76513671875, -0.339599609375, 0.763671875, -0.439208984375, -0.1793212890625, 0.06060791015625, -0.30419921875, 0.0274200439453125, -0.404052734375, 0.057220458984375, 0.69384765625, 0.419677734375, 1.3134765625, 1.23046875, -0.349609375, 0.48681640625, 0.449462890625, -0.4794921875, 0.44482421875, 0.404541015625, 1.0244140625, 0.4287109375, 0.462890625, -0.07708740234375, 0.0635986328125, -0.78466796875, -0.317626953125, 0.1864013671875, 0.5908203125, -0.399658203125, 0.288818359375, 0.31689453125, 0.0997314453125, -1.0654296875, -0.1409912109375, -0.0579833984375, -0.75341796875, -0.55517578125, 0.416015625, 0.04644775390625, 0.3828125, -0.51123046875, -0.556640625, 0.26513671875, 1.2080078125, -0.3828125, -0.095458984375, 0.51318359375, 0.1256103515625, 0.0880126953125, -0.1456298828125, -0.0869140625, -0.100341796875, -0.6083984375, 1.0771484375, 0.08349609375, -0.15234375, 0.004337310791015625, 0.7216796875, 0.24658203125, 0.84375, -0.66552734375, -0.3193359375, 0.517578125, 1.0771484375, 0.11627197265625, 0.83642578125, 0.58544921875, 1.1611328125, 0.29150390625, 0.728515625, 0.30224609375, 0.283935546875, 0.6591796875, 1.044921875, -0.07086181640625, -0.06689453125, 0.250244140625, 0.38916015625, 0.1929931640625, 0.6025390625, 0.27294921875, 0.53662109375, -0.188720703125, 0.057769775390625, -0.8125, 0.1368408203125, -0.303466796875, 0.53759765625, 0.263427734375, 0.5634765625, -0.428466796875, -0.1690673828125, 0.25341796875, 0.9833984375, -1.060546875, -0.62109375, 0.0430908203125, -0.1282958984375, -0.0501708984375, -0.038116455078125, 0.52880859375, 0.12939453125, 0.55224609375, 0.4462890625, -0.28515625, -0.4560546875, -0.8701171875, -0.7216796875, -0.79248046875, -0.4208984375, -0.56103515625, -0.1527099609375, 0.2415771484375, -1.0810546875, -0.00861358642578125, -0.390625, -0.059173583984375, 0.2420654296875, -0.759765625, 1.0244140625, -0.666015625, 0.36669921875, -0.73193359375, 0.393798828125, 0.2666015625, 1.0947265625, -0.35107421875, -0.0738525390625, -0.06805419921875, -0.355224609375, 0.160400390625, -0.168212890625, 0.34228515625, -0.12152099609375, -0.353759765625, -0.74072265625, -0.433837890625, -0.335693359375, -0.59814453125, 0.324951171875, -0.5791015625, 0.77685546875, 0.66552734375, -0.495849609375, 0.7744140625, 1.0205078125, -0.58349609375, 0.4580078125, 0.075927734375, 0.0177459716796875, -0.71533203125, 1.2958984375, 0.716796875, 0.35791015625, -0.384521484375, -0.5693359375, -0.3935546875, -0.384521484375, 0.352294921875, -0.50537109375, -0.59228515625, 0.70068359375, -0.05267333984375, -1.0576171875, 0.160400390625, -0.98828125, -0.640625, -0.33251953125, -0.3798828125, 0.810546875, 0.79443359375, 0.16357421875, -0.1533203125, -0.321533203125, 0.1978759765625, 0.49365234375, 0.31494140625, -0.7724609375, 0.285400390625, 0.6962890625, 0.11297607421875, 0.370849609375, 0.292236328125, -0.282470703125, -0.10418701171875, 0.0341796875, -0.185791015625, 0.65283203125, 0.1177978515625, 0.214599609375, 0.4931640625, 0.419921875, -0.73779296875, -0.059173583984375, -0.2392578125, 0.51708984375, 0.4521484375, 0.46630859375, 0.248291015625, -0.357666015625, -0.650390625, -1.1513671875, 0.378662109375, 0.07000732421875, 0.7939453125, -0.763671875, 0.927734375, -0.01424407958984375, -0.2347412109375, 0.347412109375, -0.66357421875, 0.1539306640625, 1.1240234375, -0.431640625, 0.367919921875, -0.63427734375, 0.489013671875, 0.25537109375, 0.270751953125, 0.486328125, 0.278564453125, 0.70068359375, -0.2349853515625, -0.56982421875, -0.591796875, -0.1993408203125, -0.053375244140625, -0.75341796875, 0.2666015625, -0.6484375, -0.308349609375, -0.64697265625, 0.3857421875, 0.97021484375, 1.0126953125, -0.022369384765625, 0.65234375, 0.04449462890625, 0.28125, 0.47314453125, -0.57568359375, 0.0972900390625, -0.53173828125, 0.81103515625, 0.490234375, 0.3349609375, -0.70361328125, 0.021331787109375, -0.2099609375, -0.261474609375, 0.152099609375, -0.281005859375, -1.1494140625, 0.0467529296875, -0.192626953125, 0.5390625, -0.487548828125, -0.29052734375, -0.1641845703125, 0.44384765625, 0.48583984375, -0.70556640625, 0.11822509765625, -1.07421875, 0.779296875, 0.25390625, -0.262451171875, -0.39697265625, -0.56396484375, -0.61865234375, -1.0869140625, -0.07196044921875, 0.97412109375, 0.1558837890625, 0.494873046875, -0.93896484375, 0.4384765625, -0.07281494140625, -0.4580078125, 0.08062744140625, -0.291015625, 0.414306640625, -0.12237548828125, 0.70703125, -0.681640625, -0.52685546875, -0.04833984375, -0.92333984375, 0.6650390625, -0.486572265625, 0.330322265625, -0.026702880859375, -0.254150390625, -0.2362060546875, 0.27001953125, -0.2032470703125, 0.392333984375, -0.452880859375, 0.28466796875, -0.7958984375, -0.382080078125, 0.728515625, -0.35546875, -0.10601806640625, 0.71435546875, -0.10003662109375, -0.462890625, 0.09808349609375, 0.52392578125, -0.404296875, 0.429443359375, -0.496826171875, 0.40966796875, -0.2215576171875, -0.43115234375, -0.25, -0.70947265625, 0.86865234375, 0.29345703125, -0.5224609375, -0.445556640625, -1.0068359375, -0.267333984375, 0.026702880859375, -0.1964111328125, 0.560546875, 0.033905029296875, 0.059051513671875, 0.08074951171875, -0.1968994140625, -0.5517578125, -0.08392333984375, -0.29345703125, -0.00732421875, -0.02569580078125, 0.51953125, 0.482177734375, -0.179931640625, -0.5361328125, -0.454833984375, -0.294189453125, 0.09356689453125, -0.498291015625, -0.4560546875, -0.28515625, -0.288818359375, -0.69384765625, 0.1002197265625, -0.08123779296875, 0.46142578125, 0.953125, 0.0721435546875, 0.623046875, 0.320556640625, -0.84375, 1.1298828125, 0.37451171875, -1.091796875, -0.73095703125, 0.359619140625, -0.1285400390625, 0.5322265625, 0.176025390625, -0.515625, -0.826171875, -0.89599609375, 0.168701171875, -0.94189453125, -0.158935546875, -1.1455078125, -0.468994140625, -0.4716796875, 0.35888671875, -0.0592041015625, -0.7060546875, 0.27294921875, -0.9169921875, 0.332275390625, -0.7958984375, 0.10467529296875, -0.6123046875, -0.61767578125, -0.1968994140625, 1.1044921875, 0.12939453125, 0.5986328125, 0.09564208984375, -0.3583984375, 0.25439453125, 0.200439453125, -0.6005859375, -0.353759765625, 0.2322998046875, 0.0212249755859375, -0.1309814453125, -0.3447265625, -0.5478515625, 0.56787109375, -0.81396484375, 0.410888671875, -0.04638671875, -0.26953125, -0.1529541015625, -0.3349609375, 1.09375, -0.37890625, 0.2021484375, -0.35302734375, 0.28759765625, 0.509765625, -0.0271148681640625, -0.2568359375, -0.37841796875, -0.58544921875, -1.2841796875, 0.55712890625, -0.2073974609375, 0.041229248046875, -0.6953125, -0.30517578125, 1.2958984375, -0.455078125, 0.2412109375, 1.47265625, 0.177001953125, 0.21435546875, -0.4521484375, 0.61181640625, 0.6044921875, -0.43505859375, -0.07476806640625, 0.2271728515625, -0.62158203125, -0.038848876953125, -0.474365234375, -1.2001953125, -0.71875, 0.447021484375, 1.2177734375, -0.444580078125, 0.77197265625, -0.251708984375, -1.0654296875, -0.56884765625, 0.84521484375, -0.060882568359375, 0.256591796875, 0.888671875, 0.1416015625, -0.220947265625, 0.264404296875, -0.154541015625, -0.337890625, -0.6904296875, 0.9970703125, -0.3916015625, -0.08599853515625, 1.2236328125, 0.9052734375, -1.1552734375, -0.81494140625, -0.465087890625, -0.057525634765625, 0.17919921875, -0.91064453125, -0.0112457275390625, 0.5595703125, -0.60888671875, -0.0207366943359375, 0.61572265625, -0.3603515625, 0.3837890625, 0.0994873046875, 0.1588134765625, -0.2374267578125, 0.36669921875, 0.60546875, -0.2452392578125, -0.34033203125, -0.904296875, -0.3857421875, -0.2197265625, 0.007320404052734375, 1.0625, -0.1510009765625, 0.3935546875, 0.1929931640625, -0.0814208984375, 0.7529296875, -0.44091796875, -0.3251953125, 0.2158203125, -0.64013671875, -0.295166015625, -0.20556640625, 0.400146484375, 0.1787109375, 0.78369140625, -0.626953125, -0.00919342041015625, 0.218505859375, 0.43798828125, -0.469482421875, -1.103515625, -0.1787109375, -1.1591796875, -0.42626953125, -0.61962890625, -0.767578125, 0.0220947265625, 0.716796875, 0.057281494140625, -0.64111328125, -0.09588623046875, 0.1610107421875, -0.426513671875, 0.61328125, -0.5830078125, 0.2117919921875, -0.5009765625, -0.266845703125, -0.68701171875, 0.09002685546875, -0.80859375, -0.138671875, -0.50537109375, 0.413818359375, -0.56884765625, 0.33984375, -0.48486328125, 0.408935546875, -0.2744140625, -0.70361328125, -0.35693359375, 0.08843994140625, -0.56640625, 0.9501953125, 0.75341796875, 0.279541015625, 0.36328125, -0.46044921875, -0.328369140625, -0.474365234375, 0.424560546875, 0.07135009765625, 0.02484130859375, -0.34033203125, -0.244384765625, 0.16455078125, -1.0205078125, 0.1898193359375, -0.154052734375, 0.103759765625, 0.097412109375, -0.26123046875, 0.5400390625, 1.361328125, -0.1944580078125, 0.349365234375, -0.055694580078125, 0.42822265625, 0.371826171875, 0.2271728515625, -0.12481689453125, 0.82080078125, -0.278564453125, -0.6064453125, 0.1619873046875, 0.07098388671875, 0.2239990234375, 0.032440185546875, -0.401611328125, -0.72998046875, -0.8359375, -0.30078125, -0.00490570068359375, 0.52392578125, 0.58642578125, -0.15234375, 0.028076171875, -0.517578125, -0.3798828125, -0.5439453125, -1.255859375, -0.87109375, 0.5166015625, -0.190673828125, -0.8056640625, -0.0565185546875, -0.17431640625, -0.1336669921875, 0.0828857421875, 0.29541015625, -0.317138671875, 0.57568359375, -0.407958984375, 0.51318359375, -0.12164306640625, -0.033172607421875, 0.08575439453125, 0.484130859375, -0.58154296875, -0.6630859375, 0.392578125, 0.91748046875, 0.1627197265625, -0.3037109375, -0.720703125, 0.41796875, -0.1314697265625, -0.12457275390625, -0.53173828125, 0.3818359375, -0.08203125, 0.457275390625, -0.79443359375, -0.1103515625, -0.53173828125, 0.62744140625, 0.223388671875, -0.56103515625, -0.64404296875, 0.91552734375, 0.467529296875, -0.28125, 0.283935546875, -0.04327392578125, 0.27685546875, -0.14208984375, 0.1534423828125, -0.32275390625, 0.80029296875, 0.87255859375, 0.9091796875, -0.1287841796875, 0.258544921875, 0.56396484375, 0.438232421875, -0.1573486328125, 0.49267578125, 0.09405517578125, 0.09857177734375, 0.076904296875, -0.1295166015625, -0.2142333984375, -0.369873046875, -0.6328125, 0.325927734375, -0.34716796875, 0.245361328125, 0.0673828125, -0.63134765625, 0.955078125, -0.36572265625, -0.135498046875, 0.0916748046875, -0.66552734375, 0.185546875, 0.57568359375, -0.12841796875, -0.4765625, 0.681640625, 0.65576171875, 0.404296875, 0.44189453125, 0.2222900390625, 0.5947265625, -0.5966796875, 0.1895751953125, 0.27197265625, 0.034210205078125, -0.45947265625, -0.5654296875, -1.021484375, 0.406982421875, -0.77685546875, -0.3740234375, 0.439208984375, -0.80810546875, 0.06964111328125, -0.12298583984375, 0.80517578125, -0.275146484375, 0.157470703125, 0.46923828125, -0.11871337890625, -0.564453125, 0.90283203125, -0.1419677734375, 0.25537109375, -0.23876953125, 1.259765625, -0.006412506103515625, 1.4482421875, 0.80859375, 0.1181640625, 0.01335906982421875, 0.302734375, -0.42626953125, -0.66552734375, -0.304443359375, -0.29345703125, 0.008148193359375, -0.64453125, -0.48486328125, -0.232421875, 0.91357421875, -0.09100341796875, -0.7470703125, -0.262939453125, 0.31396484375, -0.85693359375, 0.493896484375, 0.414306640625, 0.3916015625, -0.0021076202392578125, -0.230224609375, -0.482666015625, -0.603515625, 0.61962890625, -0.63671875, 0.320556640625, -0.6396484375, -0.244384765625, -0.459716796875, -0.673828125, -0.39892578125, -0.1478271484375, -0.1920166015625, -0.98828125, 0.56884765625, 0.2047119140625, 0.4775390625, 0.33740234375, -0.71484375, 0.2578125, 0.75439453125, 1.095703125, 0.0182952880859375, 0.60498046875, 0.462890625, -0.203369140625, 0.12213134765625, -0.2423095703125, 0.4345703125, 0.1707763671875, 0.482421875, -0.26806640625, 0.06396484375, -0.71923828125, -1.13671875, 0.185791015625, 0.4541015625, 0.1781005859375, -0.61328125, -1.1064453125, -0.473388671875, -0.8916015625, -0.10845947265625, -0.84423828125, 0.517578125, -0.316650390625, 0.30322265625, -0.056854248046875, -1.0087890625, 4.39453125, 1.0048828125, 1.064453125, 0.005756378173828125, 0.433349609375, 1.1171875, 0.212646484375, -0.7734375, -0.00690460205078125, -0.400146484375, 1, -0.253662109375, 0.0831298828125, 0.66748046875, 0.25537109375, 0.6484375, -0.8798828125, 0.15185546875, -0.05828857421875, -1.251953125, -0.47216796875, 0.2392578125, -0.12420654296875, 0.77099609375, -0.10614013671875, 0.205810546875, 0.8125, -1.15625, -0.261962890625, -0.81884765625, 0.293701171875, -0.160400390625, 0.5068359375, 0.29248046875, 0.04779052734375, 0.8349609375, -0.309814453125, -0.3037109375, -0.2100830078125, -0.0213623046875, -0.0941162109375, -0.236083984375, 0.258056640625, -0.619140625, -0.373046875, 0.14013671875, -0.483154296875, 0.59716796875, 0.1412353515625, -0.93408203125, 0.50244140625, 0.074951171875, 0.76953125, -0.8671875, -0.5986328125, 0.0000445246696472168, 0.463134765625, -0.251953125, -0.06951904296875, 0.6767578125, 0.395751953125, 0.884765625, -0.3173828125, 0.69384765625, -0.80322265625, 0.93408203125, -0.30908203125, 0.273681640625, -0.72412109375, 0.377685546875, -0.1566162109375, -0.6591796875, -0.423583984375, -0.58544921875, 0.591796875, 0.11773681640625, -0.29443359375, 0.64990234375, 0.86376953125, -0.347900390625, -0.0310211181640625, -0.52099609375, -0.427490234375, -0.295166015625, 0.36767578125, 1.3271484375, -0.42626953125, -0.27294921875, -0.1180419921875, 0.52978515625, 0.330322265625, 0.58251953125, 0.027496337890625, -0.54833984375, -0.431396484375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Tags: games Correct Solution: ``` import sys input = sys.stdin.readline q=int(input()) for testcases in range(q): a,b=map(int,input().split()) S=input().strip() S+="X" T=[] NOW=0 for s in S: if s==".": NOW+=1 else: if NOW!=0: T.append(NOW) NOW=0 count=0 noflag=0 other=[] for t in T: if b<=t<a: noflag=1 break if a<=t<2*b: count+=1 elif t>=2*b: other.append(t) if len(other)>=2: noflag=1 if noflag==1: print("NO") continue if len(other)==0: if count%2==1: print("YES") else: print("NO") continue OTHER=other[0] for left in range(OTHER-a+1): right=OTHER-a-left if left>=2*b or right>=2*b or b<=left<a or b<=right<a: continue count2=count if left>=a: count2+=1 if right>=a: count2+=1 if count2%2==0: print("YES") break else: print("NO") ```
106,225
[ 0.2432861328125, 0.25244140625, -0.0284423828125, 0.39697265625, -0.60546875, -0.57177734375, -0.124267578125, 0.179931640625, 0.296142578125, 0.88623046875, 0.82666015625, 0.1943359375, 0.1842041015625, -0.60791015625, -0.51904296875, 0.12939453125, -0.77734375, -0.923828125, -0.388427734375, -0.1505126953125, 0.11309814453125, 0.0036067962646484375, -1.3173828125, -0.00513458251953125, -0.197509765625, 0.83642578125, 0.1290283203125, -0.01087188720703125, 0.9296875, 1.130859375, 0.0889892578125, -0.53564453125, 0.461669921875, -0.8095703125, -0.443603515625, -0.263916015625, 0.83251953125, -0.599609375, -0.06732177734375, -0.439697265625, 0.323486328125, -0.53369140625, 0.347412109375, -0.61376953125, -1.2734375, 0.005489349365234375, -0.2998046875, -0.50732421875, -0.1939697265625, -0.52685546875, -0.04132080078125, -0.385498046875, 0.44482421875, -0.242919921875, 0.1131591796875, 0.09869384765625, 0.2291259765625, 0.1610107421875, -0.6962890625, 0.26171875, 0.245849609375, -0.350830078125, 0.04052734375, -0.79638671875, 0.232421875, 0.018157958984375, 0.199462890625, -0.441650390625, 0.342529296875, -0.74267578125, -0.2227783203125, -0.06903076171875, -0.64306640625, -0.5068359375, -0.055572509765625, 0.435302734375, 0.35791015625, -0.14404296875, -0.84326171875, 0.71630859375, -0.2421875, 0.84423828125, 0.64453125, -0.05474853515625, -0.3134765625, -0.58251953125, 0.43212890625, 0.2276611328125, 0.364013671875, -0.2197265625, -0.12384033203125, 0.49853515625, -0.29541015625, -0.267578125, 0.17578125, 0.86376953125, -0.177001953125, 0.158203125, 0.7451171875, -0.09759521484375, 0.568359375, 0.73681640625, -0.61083984375, 1.0849609375, -0.436279296875, 0.074951171875, 0.427001953125, 0.0109405517578125, -0.1859130859375, -0.5419921875, -0.2724609375, -0.4228515625, 0.60498046875, 0.48046875, -0.5146484375, 0.90576171875, 0.0615234375, 0.58544921875, -0.63525390625, 0.10992431640625, 0.708984375, 0.028839111328125, 0.65087890625, -0.1412353515625, 0.01461029052734375, -0.28173828125, -0.60888671875, 1.0390625, -0.66015625, -0.1875, 0.59375, -0.04638671875, -0.2254638671875, 0.418701171875, -0.31689453125, 0.720703125, -0.150634765625, 0.33544921875, 0.7255859375, -0.5068359375, 0.98486328125, -0.0112762451171875, 0.0811767578125, 1.3583984375, 0.3388671875, -0.1407470703125, 0.416259765625, 0.576171875, -0.83251953125, 0.265869140625, -1.0712890625, 0.498046875, -0.0316162109375, 0.2147216796875, -0.1856689453125, -0.2286376953125, -0.501953125, 0.57421875, 0.36669921875, 0.0225067138671875, -0.1441650390625, 0.4677734375, -0.475341796875, 0.76513671875, -0.339599609375, 0.763671875, -0.439208984375, -0.1793212890625, 0.06060791015625, -0.30419921875, 0.0274200439453125, -0.404052734375, 0.057220458984375, 0.69384765625, 0.419677734375, 1.3134765625, 1.23046875, -0.349609375, 0.48681640625, 0.449462890625, -0.4794921875, 0.44482421875, 0.404541015625, 1.0244140625, 0.4287109375, 0.462890625, -0.07708740234375, 0.0635986328125, -0.78466796875, -0.317626953125, 0.1864013671875, 0.5908203125, -0.399658203125, 0.288818359375, 0.31689453125, 0.0997314453125, -1.0654296875, -0.1409912109375, -0.0579833984375, -0.75341796875, -0.55517578125, 0.416015625, 0.04644775390625, 0.3828125, -0.51123046875, -0.556640625, 0.26513671875, 1.2080078125, -0.3828125, -0.095458984375, 0.51318359375, 0.1256103515625, 0.0880126953125, -0.1456298828125, -0.0869140625, -0.100341796875, -0.6083984375, 1.0771484375, 0.08349609375, -0.15234375, 0.004337310791015625, 0.7216796875, 0.24658203125, 0.84375, -0.66552734375, -0.3193359375, 0.517578125, 1.0771484375, 0.11627197265625, 0.83642578125, 0.58544921875, 1.1611328125, 0.29150390625, 0.728515625, 0.30224609375, 0.283935546875, 0.6591796875, 1.044921875, -0.07086181640625, -0.06689453125, 0.250244140625, 0.38916015625, 0.1929931640625, 0.6025390625, 0.27294921875, 0.53662109375, -0.188720703125, 0.057769775390625, -0.8125, 0.1368408203125, -0.303466796875, 0.53759765625, 0.263427734375, 0.5634765625, -0.428466796875, -0.1690673828125, 0.25341796875, 0.9833984375, -1.060546875, -0.62109375, 0.0430908203125, -0.1282958984375, -0.0501708984375, -0.038116455078125, 0.52880859375, 0.12939453125, 0.55224609375, 0.4462890625, -0.28515625, -0.4560546875, -0.8701171875, -0.7216796875, -0.79248046875, -0.4208984375, -0.56103515625, -0.1527099609375, 0.2415771484375, -1.0810546875, -0.00861358642578125, -0.390625, -0.059173583984375, 0.2420654296875, -0.759765625, 1.0244140625, -0.666015625, 0.36669921875, -0.73193359375, 0.393798828125, 0.2666015625, 1.0947265625, -0.35107421875, -0.0738525390625, -0.06805419921875, -0.355224609375, 0.160400390625, -0.168212890625, 0.34228515625, -0.12152099609375, -0.353759765625, -0.74072265625, -0.433837890625, -0.335693359375, -0.59814453125, 0.324951171875, -0.5791015625, 0.77685546875, 0.66552734375, -0.495849609375, 0.7744140625, 1.0205078125, -0.58349609375, 0.4580078125, 0.075927734375, 0.0177459716796875, -0.71533203125, 1.2958984375, 0.716796875, 0.35791015625, -0.384521484375, -0.5693359375, -0.3935546875, -0.384521484375, 0.352294921875, -0.50537109375, -0.59228515625, 0.70068359375, -0.05267333984375, -1.0576171875, 0.160400390625, -0.98828125, -0.640625, -0.33251953125, -0.3798828125, 0.810546875, 0.79443359375, 0.16357421875, -0.1533203125, -0.321533203125, 0.1978759765625, 0.49365234375, 0.31494140625, -0.7724609375, 0.285400390625, 0.6962890625, 0.11297607421875, 0.370849609375, 0.292236328125, -0.282470703125, -0.10418701171875, 0.0341796875, -0.185791015625, 0.65283203125, 0.1177978515625, 0.214599609375, 0.4931640625, 0.419921875, -0.73779296875, -0.059173583984375, -0.2392578125, 0.51708984375, 0.4521484375, 0.46630859375, 0.248291015625, -0.357666015625, -0.650390625, -1.1513671875, 0.378662109375, 0.07000732421875, 0.7939453125, -0.763671875, 0.927734375, -0.01424407958984375, -0.2347412109375, 0.347412109375, -0.66357421875, 0.1539306640625, 1.1240234375, -0.431640625, 0.367919921875, -0.63427734375, 0.489013671875, 0.25537109375, 0.270751953125, 0.486328125, 0.278564453125, 0.70068359375, -0.2349853515625, -0.56982421875, -0.591796875, -0.1993408203125, -0.053375244140625, -0.75341796875, 0.2666015625, -0.6484375, -0.308349609375, -0.64697265625, 0.3857421875, 0.97021484375, 1.0126953125, -0.022369384765625, 0.65234375, 0.04449462890625, 0.28125, 0.47314453125, -0.57568359375, 0.0972900390625, -0.53173828125, 0.81103515625, 0.490234375, 0.3349609375, -0.70361328125, 0.021331787109375, -0.2099609375, -0.261474609375, 0.152099609375, -0.281005859375, -1.1494140625, 0.0467529296875, -0.192626953125, 0.5390625, -0.487548828125, -0.29052734375, -0.1641845703125, 0.44384765625, 0.48583984375, -0.70556640625, 0.11822509765625, -1.07421875, 0.779296875, 0.25390625, -0.262451171875, -0.39697265625, -0.56396484375, -0.61865234375, -1.0869140625, -0.07196044921875, 0.97412109375, 0.1558837890625, 0.494873046875, -0.93896484375, 0.4384765625, -0.07281494140625, -0.4580078125, 0.08062744140625, -0.291015625, 0.414306640625, -0.12237548828125, 0.70703125, -0.681640625, -0.52685546875, -0.04833984375, -0.92333984375, 0.6650390625, -0.486572265625, 0.330322265625, -0.026702880859375, -0.254150390625, -0.2362060546875, 0.27001953125, -0.2032470703125, 0.392333984375, -0.452880859375, 0.28466796875, -0.7958984375, -0.382080078125, 0.728515625, -0.35546875, -0.10601806640625, 0.71435546875, -0.10003662109375, -0.462890625, 0.09808349609375, 0.52392578125, -0.404296875, 0.429443359375, -0.496826171875, 0.40966796875, -0.2215576171875, -0.43115234375, -0.25, -0.70947265625, 0.86865234375, 0.29345703125, -0.5224609375, -0.445556640625, -1.0068359375, -0.267333984375, 0.026702880859375, -0.1964111328125, 0.560546875, 0.033905029296875, 0.059051513671875, 0.08074951171875, -0.1968994140625, -0.5517578125, -0.08392333984375, -0.29345703125, -0.00732421875, -0.02569580078125, 0.51953125, 0.482177734375, -0.179931640625, -0.5361328125, -0.454833984375, -0.294189453125, 0.09356689453125, -0.498291015625, -0.4560546875, -0.28515625, -0.288818359375, -0.69384765625, 0.1002197265625, -0.08123779296875, 0.46142578125, 0.953125, 0.0721435546875, 0.623046875, 0.320556640625, -0.84375, 1.1298828125, 0.37451171875, -1.091796875, -0.73095703125, 0.359619140625, -0.1285400390625, 0.5322265625, 0.176025390625, -0.515625, -0.826171875, -0.89599609375, 0.168701171875, -0.94189453125, -0.158935546875, -1.1455078125, -0.468994140625, -0.4716796875, 0.35888671875, -0.0592041015625, -0.7060546875, 0.27294921875, -0.9169921875, 0.332275390625, -0.7958984375, 0.10467529296875, -0.6123046875, -0.61767578125, -0.1968994140625, 1.1044921875, 0.12939453125, 0.5986328125, 0.09564208984375, -0.3583984375, 0.25439453125, 0.200439453125, -0.6005859375, -0.353759765625, 0.2322998046875, 0.0212249755859375, -0.1309814453125, -0.3447265625, -0.5478515625, 0.56787109375, -0.81396484375, 0.410888671875, -0.04638671875, -0.26953125, -0.1529541015625, -0.3349609375, 1.09375, -0.37890625, 0.2021484375, -0.35302734375, 0.28759765625, 0.509765625, -0.0271148681640625, -0.2568359375, -0.37841796875, -0.58544921875, -1.2841796875, 0.55712890625, -0.2073974609375, 0.041229248046875, -0.6953125, -0.30517578125, 1.2958984375, -0.455078125, 0.2412109375, 1.47265625, 0.177001953125, 0.21435546875, -0.4521484375, 0.61181640625, 0.6044921875, -0.43505859375, -0.07476806640625, 0.2271728515625, -0.62158203125, -0.038848876953125, -0.474365234375, -1.2001953125, -0.71875, 0.447021484375, 1.2177734375, -0.444580078125, 0.77197265625, -0.251708984375, -1.0654296875, -0.56884765625, 0.84521484375, -0.060882568359375, 0.256591796875, 0.888671875, 0.1416015625, -0.220947265625, 0.264404296875, -0.154541015625, -0.337890625, -0.6904296875, 0.9970703125, -0.3916015625, -0.08599853515625, 1.2236328125, 0.9052734375, -1.1552734375, -0.81494140625, -0.465087890625, -0.057525634765625, 0.17919921875, -0.91064453125, -0.0112457275390625, 0.5595703125, -0.60888671875, -0.0207366943359375, 0.61572265625, -0.3603515625, 0.3837890625, 0.0994873046875, 0.1588134765625, -0.2374267578125, 0.36669921875, 0.60546875, -0.2452392578125, -0.34033203125, -0.904296875, -0.3857421875, -0.2197265625, 0.007320404052734375, 1.0625, -0.1510009765625, 0.3935546875, 0.1929931640625, -0.0814208984375, 0.7529296875, -0.44091796875, -0.3251953125, 0.2158203125, -0.64013671875, -0.295166015625, -0.20556640625, 0.400146484375, 0.1787109375, 0.78369140625, -0.626953125, -0.00919342041015625, 0.218505859375, 0.43798828125, -0.469482421875, -1.103515625, -0.1787109375, -1.1591796875, -0.42626953125, -0.61962890625, -0.767578125, 0.0220947265625, 0.716796875, 0.057281494140625, -0.64111328125, -0.09588623046875, 0.1610107421875, -0.426513671875, 0.61328125, -0.5830078125, 0.2117919921875, -0.5009765625, -0.266845703125, -0.68701171875, 0.09002685546875, -0.80859375, -0.138671875, -0.50537109375, 0.413818359375, -0.56884765625, 0.33984375, -0.48486328125, 0.408935546875, -0.2744140625, -0.70361328125, -0.35693359375, 0.08843994140625, -0.56640625, 0.9501953125, 0.75341796875, 0.279541015625, 0.36328125, -0.46044921875, -0.328369140625, -0.474365234375, 0.424560546875, 0.07135009765625, 0.02484130859375, -0.34033203125, -0.244384765625, 0.16455078125, -1.0205078125, 0.1898193359375, -0.154052734375, 0.103759765625, 0.097412109375, -0.26123046875, 0.5400390625, 1.361328125, -0.1944580078125, 0.349365234375, -0.055694580078125, 0.42822265625, 0.371826171875, 0.2271728515625, -0.12481689453125, 0.82080078125, -0.278564453125, -0.6064453125, 0.1619873046875, 0.07098388671875, 0.2239990234375, 0.032440185546875, -0.401611328125, -0.72998046875, -0.8359375, -0.30078125, -0.00490570068359375, 0.52392578125, 0.58642578125, -0.15234375, 0.028076171875, -0.517578125, -0.3798828125, -0.5439453125, -1.255859375, -0.87109375, 0.5166015625, -0.190673828125, -0.8056640625, -0.0565185546875, -0.17431640625, -0.1336669921875, 0.0828857421875, 0.29541015625, -0.317138671875, 0.57568359375, -0.407958984375, 0.51318359375, -0.12164306640625, -0.033172607421875, 0.08575439453125, 0.484130859375, -0.58154296875, -0.6630859375, 0.392578125, 0.91748046875, 0.1627197265625, -0.3037109375, -0.720703125, 0.41796875, -0.1314697265625, -0.12457275390625, -0.53173828125, 0.3818359375, -0.08203125, 0.457275390625, -0.79443359375, -0.1103515625, -0.53173828125, 0.62744140625, 0.223388671875, -0.56103515625, -0.64404296875, 0.91552734375, 0.467529296875, -0.28125, 0.283935546875, -0.04327392578125, 0.27685546875, -0.14208984375, 0.1534423828125, -0.32275390625, 0.80029296875, 0.87255859375, 0.9091796875, -0.1287841796875, 0.258544921875, 0.56396484375, 0.438232421875, -0.1573486328125, 0.49267578125, 0.09405517578125, 0.09857177734375, 0.076904296875, -0.1295166015625, -0.2142333984375, -0.369873046875, -0.6328125, 0.325927734375, -0.34716796875, 0.245361328125, 0.0673828125, -0.63134765625, 0.955078125, -0.36572265625, -0.135498046875, 0.0916748046875, -0.66552734375, 0.185546875, 0.57568359375, -0.12841796875, -0.4765625, 0.681640625, 0.65576171875, 0.404296875, 0.44189453125, 0.2222900390625, 0.5947265625, -0.5966796875, 0.1895751953125, 0.27197265625, 0.034210205078125, -0.45947265625, -0.5654296875, -1.021484375, 0.406982421875, -0.77685546875, -0.3740234375, 0.439208984375, -0.80810546875, 0.06964111328125, -0.12298583984375, 0.80517578125, -0.275146484375, 0.157470703125, 0.46923828125, -0.11871337890625, -0.564453125, 0.90283203125, -0.1419677734375, 0.25537109375, -0.23876953125, 1.259765625, -0.006412506103515625, 1.4482421875, 0.80859375, 0.1181640625, 0.01335906982421875, 0.302734375, -0.42626953125, -0.66552734375, -0.304443359375, -0.29345703125, 0.008148193359375, -0.64453125, -0.48486328125, -0.232421875, 0.91357421875, -0.09100341796875, -0.7470703125, -0.262939453125, 0.31396484375, -0.85693359375, 0.493896484375, 0.414306640625, 0.3916015625, -0.0021076202392578125, -0.230224609375, -0.482666015625, -0.603515625, 0.61962890625, -0.63671875, 0.320556640625, -0.6396484375, -0.244384765625, -0.459716796875, -0.673828125, -0.39892578125, -0.1478271484375, -0.1920166015625, -0.98828125, 0.56884765625, 0.2047119140625, 0.4775390625, 0.33740234375, -0.71484375, 0.2578125, 0.75439453125, 1.095703125, 0.0182952880859375, 0.60498046875, 0.462890625, -0.203369140625, 0.12213134765625, -0.2423095703125, 0.4345703125, 0.1707763671875, 0.482421875, -0.26806640625, 0.06396484375, -0.71923828125, -1.13671875, 0.185791015625, 0.4541015625, 0.1781005859375, -0.61328125, -1.1064453125, -0.473388671875, -0.8916015625, -0.10845947265625, -0.84423828125, 0.517578125, -0.316650390625, 0.30322265625, -0.056854248046875, -1.0087890625, 4.39453125, 1.0048828125, 1.064453125, 0.005756378173828125, 0.433349609375, 1.1171875, 0.212646484375, -0.7734375, -0.00690460205078125, -0.400146484375, 1, -0.253662109375, 0.0831298828125, 0.66748046875, 0.25537109375, 0.6484375, -0.8798828125, 0.15185546875, -0.05828857421875, -1.251953125, -0.47216796875, 0.2392578125, -0.12420654296875, 0.77099609375, -0.10614013671875, 0.205810546875, 0.8125, -1.15625, -0.261962890625, -0.81884765625, 0.293701171875, -0.160400390625, 0.5068359375, 0.29248046875, 0.04779052734375, 0.8349609375, -0.309814453125, -0.3037109375, -0.2100830078125, -0.0213623046875, -0.0941162109375, -0.236083984375, 0.258056640625, -0.619140625, -0.373046875, 0.14013671875, -0.483154296875, 0.59716796875, 0.1412353515625, -0.93408203125, 0.50244140625, 0.074951171875, 0.76953125, -0.8671875, -0.5986328125, 0.0000445246696472168, 0.463134765625, -0.251953125, -0.06951904296875, 0.6767578125, 0.395751953125, 0.884765625, -0.3173828125, 0.69384765625, -0.80322265625, 0.93408203125, -0.30908203125, 0.273681640625, -0.72412109375, 0.377685546875, -0.1566162109375, -0.6591796875, -0.423583984375, -0.58544921875, 0.591796875, 0.11773681640625, -0.29443359375, 0.64990234375, 0.86376953125, -0.347900390625, -0.0310211181640625, -0.52099609375, -0.427490234375, -0.295166015625, 0.36767578125, 1.3271484375, -0.42626953125, -0.27294921875, -0.1180419921875, 0.52978515625, 0.330322265625, 0.58251953125, 0.027496337890625, -0.54833984375, -0.431396484375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Tags: games Correct Solution: ``` def sol(): a, b = map(int, input().split()) s = input().replace("X", " ") small_segs = 0 critical_region = -1 for p in map(len, s.split()): if p < b: continue if p < a and p >= b: return False if ((p - a) % 2 == 0 and (p >= a + 4 * b)) or ((p - a) % 2 == 1 and p >= a + 4 * b - 1): return False if p >= 2*b: if critical_region != -1: return False critical_region = p elif p >= a: small_segs += 1 if critical_region == -1: return small_segs % 2 == 1 can = [0] * 3 for l in range(critical_region+1-a): r = critical_region - l - a if (l >= b and l < a) or l >= 2 * b: continue if (r >= b and r < a) or r >= 2 * b: continue canl = int(l >= a) canr = int(r >= a) can[canl + canr] = 1 for choice, val in enumerate(can): if val and (small_segs + choice) % 2 == 0: return True return False n = int(input()) for _ in range(n): print("YES" if sol() else "NO") ```
106,226
[ 0.2432861328125, 0.25244140625, -0.0284423828125, 0.39697265625, -0.60546875, -0.57177734375, -0.124267578125, 0.179931640625, 0.296142578125, 0.88623046875, 0.82666015625, 0.1943359375, 0.1842041015625, -0.60791015625, -0.51904296875, 0.12939453125, -0.77734375, -0.923828125, -0.388427734375, -0.1505126953125, 0.11309814453125, 0.0036067962646484375, -1.3173828125, -0.00513458251953125, -0.197509765625, 0.83642578125, 0.1290283203125, -0.01087188720703125, 0.9296875, 1.130859375, 0.0889892578125, -0.53564453125, 0.461669921875, -0.8095703125, -0.443603515625, -0.263916015625, 0.83251953125, -0.599609375, -0.06732177734375, -0.439697265625, 0.323486328125, -0.53369140625, 0.347412109375, -0.61376953125, -1.2734375, 0.005489349365234375, -0.2998046875, -0.50732421875, -0.1939697265625, -0.52685546875, -0.04132080078125, -0.385498046875, 0.44482421875, -0.242919921875, 0.1131591796875, 0.09869384765625, 0.2291259765625, 0.1610107421875, -0.6962890625, 0.26171875, 0.245849609375, -0.350830078125, 0.04052734375, -0.79638671875, 0.232421875, 0.018157958984375, 0.199462890625, -0.441650390625, 0.342529296875, -0.74267578125, -0.2227783203125, -0.06903076171875, -0.64306640625, -0.5068359375, -0.055572509765625, 0.435302734375, 0.35791015625, -0.14404296875, -0.84326171875, 0.71630859375, -0.2421875, 0.84423828125, 0.64453125, -0.05474853515625, -0.3134765625, -0.58251953125, 0.43212890625, 0.2276611328125, 0.364013671875, -0.2197265625, -0.12384033203125, 0.49853515625, -0.29541015625, -0.267578125, 0.17578125, 0.86376953125, -0.177001953125, 0.158203125, 0.7451171875, -0.09759521484375, 0.568359375, 0.73681640625, -0.61083984375, 1.0849609375, -0.436279296875, 0.074951171875, 0.427001953125, 0.0109405517578125, -0.1859130859375, -0.5419921875, -0.2724609375, -0.4228515625, 0.60498046875, 0.48046875, -0.5146484375, 0.90576171875, 0.0615234375, 0.58544921875, -0.63525390625, 0.10992431640625, 0.708984375, 0.028839111328125, 0.65087890625, -0.1412353515625, 0.01461029052734375, -0.28173828125, -0.60888671875, 1.0390625, -0.66015625, -0.1875, 0.59375, -0.04638671875, -0.2254638671875, 0.418701171875, -0.31689453125, 0.720703125, -0.150634765625, 0.33544921875, 0.7255859375, -0.5068359375, 0.98486328125, -0.0112762451171875, 0.0811767578125, 1.3583984375, 0.3388671875, -0.1407470703125, 0.416259765625, 0.576171875, -0.83251953125, 0.265869140625, -1.0712890625, 0.498046875, -0.0316162109375, 0.2147216796875, -0.1856689453125, -0.2286376953125, -0.501953125, 0.57421875, 0.36669921875, 0.0225067138671875, -0.1441650390625, 0.4677734375, -0.475341796875, 0.76513671875, -0.339599609375, 0.763671875, -0.439208984375, -0.1793212890625, 0.06060791015625, -0.30419921875, 0.0274200439453125, -0.404052734375, 0.057220458984375, 0.69384765625, 0.419677734375, 1.3134765625, 1.23046875, -0.349609375, 0.48681640625, 0.449462890625, -0.4794921875, 0.44482421875, 0.404541015625, 1.0244140625, 0.4287109375, 0.462890625, -0.07708740234375, 0.0635986328125, -0.78466796875, -0.317626953125, 0.1864013671875, 0.5908203125, -0.399658203125, 0.288818359375, 0.31689453125, 0.0997314453125, -1.0654296875, -0.1409912109375, -0.0579833984375, -0.75341796875, -0.55517578125, 0.416015625, 0.04644775390625, 0.3828125, -0.51123046875, -0.556640625, 0.26513671875, 1.2080078125, -0.3828125, -0.095458984375, 0.51318359375, 0.1256103515625, 0.0880126953125, -0.1456298828125, -0.0869140625, -0.100341796875, -0.6083984375, 1.0771484375, 0.08349609375, -0.15234375, 0.004337310791015625, 0.7216796875, 0.24658203125, 0.84375, -0.66552734375, -0.3193359375, 0.517578125, 1.0771484375, 0.11627197265625, 0.83642578125, 0.58544921875, 1.1611328125, 0.29150390625, 0.728515625, 0.30224609375, 0.283935546875, 0.6591796875, 1.044921875, -0.07086181640625, -0.06689453125, 0.250244140625, 0.38916015625, 0.1929931640625, 0.6025390625, 0.27294921875, 0.53662109375, -0.188720703125, 0.057769775390625, -0.8125, 0.1368408203125, -0.303466796875, 0.53759765625, 0.263427734375, 0.5634765625, -0.428466796875, -0.1690673828125, 0.25341796875, 0.9833984375, -1.060546875, -0.62109375, 0.0430908203125, -0.1282958984375, -0.0501708984375, -0.038116455078125, 0.52880859375, 0.12939453125, 0.55224609375, 0.4462890625, -0.28515625, -0.4560546875, -0.8701171875, -0.7216796875, -0.79248046875, -0.4208984375, -0.56103515625, -0.1527099609375, 0.2415771484375, -1.0810546875, -0.00861358642578125, -0.390625, -0.059173583984375, 0.2420654296875, -0.759765625, 1.0244140625, -0.666015625, 0.36669921875, -0.73193359375, 0.393798828125, 0.2666015625, 1.0947265625, -0.35107421875, -0.0738525390625, -0.06805419921875, -0.355224609375, 0.160400390625, -0.168212890625, 0.34228515625, -0.12152099609375, -0.353759765625, -0.74072265625, -0.433837890625, -0.335693359375, -0.59814453125, 0.324951171875, -0.5791015625, 0.77685546875, 0.66552734375, -0.495849609375, 0.7744140625, 1.0205078125, -0.58349609375, 0.4580078125, 0.075927734375, 0.0177459716796875, -0.71533203125, 1.2958984375, 0.716796875, 0.35791015625, -0.384521484375, -0.5693359375, -0.3935546875, -0.384521484375, 0.352294921875, -0.50537109375, -0.59228515625, 0.70068359375, -0.05267333984375, -1.0576171875, 0.160400390625, -0.98828125, -0.640625, -0.33251953125, -0.3798828125, 0.810546875, 0.79443359375, 0.16357421875, -0.1533203125, -0.321533203125, 0.1978759765625, 0.49365234375, 0.31494140625, -0.7724609375, 0.285400390625, 0.6962890625, 0.11297607421875, 0.370849609375, 0.292236328125, -0.282470703125, -0.10418701171875, 0.0341796875, -0.185791015625, 0.65283203125, 0.1177978515625, 0.214599609375, 0.4931640625, 0.419921875, -0.73779296875, -0.059173583984375, -0.2392578125, 0.51708984375, 0.4521484375, 0.46630859375, 0.248291015625, -0.357666015625, -0.650390625, -1.1513671875, 0.378662109375, 0.07000732421875, 0.7939453125, -0.763671875, 0.927734375, -0.01424407958984375, -0.2347412109375, 0.347412109375, -0.66357421875, 0.1539306640625, 1.1240234375, -0.431640625, 0.367919921875, -0.63427734375, 0.489013671875, 0.25537109375, 0.270751953125, 0.486328125, 0.278564453125, 0.70068359375, -0.2349853515625, -0.56982421875, -0.591796875, -0.1993408203125, -0.053375244140625, -0.75341796875, 0.2666015625, -0.6484375, -0.308349609375, -0.64697265625, 0.3857421875, 0.97021484375, 1.0126953125, -0.022369384765625, 0.65234375, 0.04449462890625, 0.28125, 0.47314453125, -0.57568359375, 0.0972900390625, -0.53173828125, 0.81103515625, 0.490234375, 0.3349609375, -0.70361328125, 0.021331787109375, -0.2099609375, -0.261474609375, 0.152099609375, -0.281005859375, -1.1494140625, 0.0467529296875, -0.192626953125, 0.5390625, -0.487548828125, -0.29052734375, -0.1641845703125, 0.44384765625, 0.48583984375, -0.70556640625, 0.11822509765625, -1.07421875, 0.779296875, 0.25390625, -0.262451171875, -0.39697265625, -0.56396484375, -0.61865234375, -1.0869140625, -0.07196044921875, 0.97412109375, 0.1558837890625, 0.494873046875, -0.93896484375, 0.4384765625, -0.07281494140625, -0.4580078125, 0.08062744140625, -0.291015625, 0.414306640625, -0.12237548828125, 0.70703125, -0.681640625, -0.52685546875, -0.04833984375, -0.92333984375, 0.6650390625, -0.486572265625, 0.330322265625, -0.026702880859375, -0.254150390625, -0.2362060546875, 0.27001953125, -0.2032470703125, 0.392333984375, -0.452880859375, 0.28466796875, -0.7958984375, -0.382080078125, 0.728515625, -0.35546875, -0.10601806640625, 0.71435546875, -0.10003662109375, -0.462890625, 0.09808349609375, 0.52392578125, -0.404296875, 0.429443359375, -0.496826171875, 0.40966796875, -0.2215576171875, -0.43115234375, -0.25, -0.70947265625, 0.86865234375, 0.29345703125, -0.5224609375, -0.445556640625, -1.0068359375, -0.267333984375, 0.026702880859375, -0.1964111328125, 0.560546875, 0.033905029296875, 0.059051513671875, 0.08074951171875, -0.1968994140625, -0.5517578125, -0.08392333984375, -0.29345703125, -0.00732421875, -0.02569580078125, 0.51953125, 0.482177734375, -0.179931640625, -0.5361328125, -0.454833984375, -0.294189453125, 0.09356689453125, -0.498291015625, -0.4560546875, -0.28515625, -0.288818359375, -0.69384765625, 0.1002197265625, -0.08123779296875, 0.46142578125, 0.953125, 0.0721435546875, 0.623046875, 0.320556640625, -0.84375, 1.1298828125, 0.37451171875, -1.091796875, -0.73095703125, 0.359619140625, -0.1285400390625, 0.5322265625, 0.176025390625, -0.515625, -0.826171875, -0.89599609375, 0.168701171875, -0.94189453125, -0.158935546875, -1.1455078125, -0.468994140625, -0.4716796875, 0.35888671875, -0.0592041015625, -0.7060546875, 0.27294921875, -0.9169921875, 0.332275390625, -0.7958984375, 0.10467529296875, -0.6123046875, -0.61767578125, -0.1968994140625, 1.1044921875, 0.12939453125, 0.5986328125, 0.09564208984375, -0.3583984375, 0.25439453125, 0.200439453125, -0.6005859375, -0.353759765625, 0.2322998046875, 0.0212249755859375, -0.1309814453125, -0.3447265625, -0.5478515625, 0.56787109375, -0.81396484375, 0.410888671875, -0.04638671875, -0.26953125, -0.1529541015625, -0.3349609375, 1.09375, -0.37890625, 0.2021484375, -0.35302734375, 0.28759765625, 0.509765625, -0.0271148681640625, -0.2568359375, -0.37841796875, -0.58544921875, -1.2841796875, 0.55712890625, -0.2073974609375, 0.041229248046875, -0.6953125, -0.30517578125, 1.2958984375, -0.455078125, 0.2412109375, 1.47265625, 0.177001953125, 0.21435546875, -0.4521484375, 0.61181640625, 0.6044921875, -0.43505859375, -0.07476806640625, 0.2271728515625, -0.62158203125, -0.038848876953125, -0.474365234375, -1.2001953125, -0.71875, 0.447021484375, 1.2177734375, -0.444580078125, 0.77197265625, -0.251708984375, -1.0654296875, -0.56884765625, 0.84521484375, -0.060882568359375, 0.256591796875, 0.888671875, 0.1416015625, -0.220947265625, 0.264404296875, -0.154541015625, -0.337890625, -0.6904296875, 0.9970703125, -0.3916015625, -0.08599853515625, 1.2236328125, 0.9052734375, -1.1552734375, -0.81494140625, -0.465087890625, -0.057525634765625, 0.17919921875, -0.91064453125, -0.0112457275390625, 0.5595703125, -0.60888671875, -0.0207366943359375, 0.61572265625, -0.3603515625, 0.3837890625, 0.0994873046875, 0.1588134765625, -0.2374267578125, 0.36669921875, 0.60546875, -0.2452392578125, -0.34033203125, -0.904296875, -0.3857421875, -0.2197265625, 0.007320404052734375, 1.0625, -0.1510009765625, 0.3935546875, 0.1929931640625, -0.0814208984375, 0.7529296875, -0.44091796875, -0.3251953125, 0.2158203125, -0.64013671875, -0.295166015625, -0.20556640625, 0.400146484375, 0.1787109375, 0.78369140625, -0.626953125, -0.00919342041015625, 0.218505859375, 0.43798828125, -0.469482421875, -1.103515625, -0.1787109375, -1.1591796875, -0.42626953125, -0.61962890625, -0.767578125, 0.0220947265625, 0.716796875, 0.057281494140625, -0.64111328125, -0.09588623046875, 0.1610107421875, -0.426513671875, 0.61328125, -0.5830078125, 0.2117919921875, -0.5009765625, -0.266845703125, -0.68701171875, 0.09002685546875, -0.80859375, -0.138671875, -0.50537109375, 0.413818359375, -0.56884765625, 0.33984375, -0.48486328125, 0.408935546875, -0.2744140625, -0.70361328125, -0.35693359375, 0.08843994140625, -0.56640625, 0.9501953125, 0.75341796875, 0.279541015625, 0.36328125, -0.46044921875, -0.328369140625, -0.474365234375, 0.424560546875, 0.07135009765625, 0.02484130859375, -0.34033203125, -0.244384765625, 0.16455078125, -1.0205078125, 0.1898193359375, -0.154052734375, 0.103759765625, 0.097412109375, -0.26123046875, 0.5400390625, 1.361328125, -0.1944580078125, 0.349365234375, -0.055694580078125, 0.42822265625, 0.371826171875, 0.2271728515625, -0.12481689453125, 0.82080078125, -0.278564453125, -0.6064453125, 0.1619873046875, 0.07098388671875, 0.2239990234375, 0.032440185546875, -0.401611328125, -0.72998046875, -0.8359375, -0.30078125, -0.00490570068359375, 0.52392578125, 0.58642578125, -0.15234375, 0.028076171875, -0.517578125, -0.3798828125, -0.5439453125, -1.255859375, -0.87109375, 0.5166015625, -0.190673828125, -0.8056640625, -0.0565185546875, -0.17431640625, -0.1336669921875, 0.0828857421875, 0.29541015625, -0.317138671875, 0.57568359375, -0.407958984375, 0.51318359375, -0.12164306640625, -0.033172607421875, 0.08575439453125, 0.484130859375, -0.58154296875, -0.6630859375, 0.392578125, 0.91748046875, 0.1627197265625, -0.3037109375, -0.720703125, 0.41796875, -0.1314697265625, -0.12457275390625, -0.53173828125, 0.3818359375, -0.08203125, 0.457275390625, -0.79443359375, -0.1103515625, -0.53173828125, 0.62744140625, 0.223388671875, -0.56103515625, -0.64404296875, 0.91552734375, 0.467529296875, -0.28125, 0.283935546875, -0.04327392578125, 0.27685546875, -0.14208984375, 0.1534423828125, -0.32275390625, 0.80029296875, 0.87255859375, 0.9091796875, -0.1287841796875, 0.258544921875, 0.56396484375, 0.438232421875, -0.1573486328125, 0.49267578125, 0.09405517578125, 0.09857177734375, 0.076904296875, -0.1295166015625, -0.2142333984375, -0.369873046875, -0.6328125, 0.325927734375, -0.34716796875, 0.245361328125, 0.0673828125, -0.63134765625, 0.955078125, -0.36572265625, -0.135498046875, 0.0916748046875, -0.66552734375, 0.185546875, 0.57568359375, -0.12841796875, -0.4765625, 0.681640625, 0.65576171875, 0.404296875, 0.44189453125, 0.2222900390625, 0.5947265625, -0.5966796875, 0.1895751953125, 0.27197265625, 0.034210205078125, -0.45947265625, -0.5654296875, -1.021484375, 0.406982421875, -0.77685546875, -0.3740234375, 0.439208984375, -0.80810546875, 0.06964111328125, -0.12298583984375, 0.80517578125, -0.275146484375, 0.157470703125, 0.46923828125, -0.11871337890625, -0.564453125, 0.90283203125, -0.1419677734375, 0.25537109375, -0.23876953125, 1.259765625, -0.006412506103515625, 1.4482421875, 0.80859375, 0.1181640625, 0.01335906982421875, 0.302734375, -0.42626953125, -0.66552734375, -0.304443359375, -0.29345703125, 0.008148193359375, -0.64453125, -0.48486328125, -0.232421875, 0.91357421875, -0.09100341796875, -0.7470703125, -0.262939453125, 0.31396484375, -0.85693359375, 0.493896484375, 0.414306640625, 0.3916015625, -0.0021076202392578125, -0.230224609375, -0.482666015625, -0.603515625, 0.61962890625, -0.63671875, 0.320556640625, -0.6396484375, -0.244384765625, -0.459716796875, -0.673828125, -0.39892578125, -0.1478271484375, -0.1920166015625, -0.98828125, 0.56884765625, 0.2047119140625, 0.4775390625, 0.33740234375, -0.71484375, 0.2578125, 0.75439453125, 1.095703125, 0.0182952880859375, 0.60498046875, 0.462890625, -0.203369140625, 0.12213134765625, -0.2423095703125, 0.4345703125, 0.1707763671875, 0.482421875, -0.26806640625, 0.06396484375, -0.71923828125, -1.13671875, 0.185791015625, 0.4541015625, 0.1781005859375, -0.61328125, -1.1064453125, -0.473388671875, -0.8916015625, -0.10845947265625, -0.84423828125, 0.517578125, -0.316650390625, 0.30322265625, -0.056854248046875, -1.0087890625, 4.39453125, 1.0048828125, 1.064453125, 0.005756378173828125, 0.433349609375, 1.1171875, 0.212646484375, -0.7734375, -0.00690460205078125, -0.400146484375, 1, -0.253662109375, 0.0831298828125, 0.66748046875, 0.25537109375, 0.6484375, -0.8798828125, 0.15185546875, -0.05828857421875, -1.251953125, -0.47216796875, 0.2392578125, -0.12420654296875, 0.77099609375, -0.10614013671875, 0.205810546875, 0.8125, -1.15625, -0.261962890625, -0.81884765625, 0.293701171875, -0.160400390625, 0.5068359375, 0.29248046875, 0.04779052734375, 0.8349609375, -0.309814453125, -0.3037109375, -0.2100830078125, -0.0213623046875, -0.0941162109375, -0.236083984375, 0.258056640625, -0.619140625, -0.373046875, 0.14013671875, -0.483154296875, 0.59716796875, 0.1412353515625, -0.93408203125, 0.50244140625, 0.074951171875, 0.76953125, -0.8671875, -0.5986328125, 0.0000445246696472168, 0.463134765625, -0.251953125, -0.06951904296875, 0.6767578125, 0.395751953125, 0.884765625, -0.3173828125, 0.69384765625, -0.80322265625, 0.93408203125, -0.30908203125, 0.273681640625, -0.72412109375, 0.377685546875, -0.1566162109375, -0.6591796875, -0.423583984375, -0.58544921875, 0.591796875, 0.11773681640625, -0.29443359375, 0.64990234375, 0.86376953125, -0.347900390625, -0.0310211181640625, -0.52099609375, -0.427490234375, -0.295166015625, 0.36767578125, 1.3271484375, -0.42626953125, -0.27294921875, -0.1180419921875, 0.52978515625, 0.330322265625, 0.58251953125, 0.027496337890625, -0.54833984375, -0.431396484375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Tags: games Correct Solution: ``` q = int(input()) for rwer in range(q): a, b = map(int,input().split()) s = input() tab = [] count = 0 for i in range(len(s)): if s[i] == '.': count += 1 if s[i] == 'X': if count > 0: tab.append(count) count = 0 if count > 0: tab.append(count) #print(tab) bat = [j for j in tab if j >= b] tab = bat.copy() if len(tab) == 0: print("no") else: roomb = 0 for i in tab: if i >= 2*b: roomb += 1 if roomb > 1: print("no") else: alice = 1 for i in tab: if i < a: alice = 0 break if alice == 0: print("no") else: if roomb == 0: if len(tab) % 2 == 1: print("yes") else: print("no") if roomb == 1: jednostrzaly = len(tab) - 1 duzy = max(tab) #alice gra w duzym i co ona tam moze zrobic? if duzy >= (a + 4*b - 1): print("no") else: if jednostrzaly % 2 == 0: #jesli alice da rade zostawic 0 albo 2 sloty to wygrala if duzy <= a + 2 * b - 2: ########poprawka z -1 print("yes") elif duzy >= 3 * a: print("yes") else: print("no") if jednostrzaly % 2 == 1: #alice musi zostawic 1 slota if duzy >= 2*a and duzy <= (a + 3*b-2): print("yes") else: print("no") ```
106,227
[ 0.2432861328125, 0.25244140625, -0.0284423828125, 0.39697265625, -0.60546875, -0.57177734375, -0.124267578125, 0.179931640625, 0.296142578125, 0.88623046875, 0.82666015625, 0.1943359375, 0.1842041015625, -0.60791015625, -0.51904296875, 0.12939453125, -0.77734375, -0.923828125, -0.388427734375, -0.1505126953125, 0.11309814453125, 0.0036067962646484375, -1.3173828125, -0.00513458251953125, -0.197509765625, 0.83642578125, 0.1290283203125, -0.01087188720703125, 0.9296875, 1.130859375, 0.0889892578125, -0.53564453125, 0.461669921875, -0.8095703125, -0.443603515625, -0.263916015625, 0.83251953125, -0.599609375, -0.06732177734375, -0.439697265625, 0.323486328125, -0.53369140625, 0.347412109375, -0.61376953125, -1.2734375, 0.005489349365234375, -0.2998046875, -0.50732421875, -0.1939697265625, -0.52685546875, -0.04132080078125, -0.385498046875, 0.44482421875, -0.242919921875, 0.1131591796875, 0.09869384765625, 0.2291259765625, 0.1610107421875, -0.6962890625, 0.26171875, 0.245849609375, -0.350830078125, 0.04052734375, -0.79638671875, 0.232421875, 0.018157958984375, 0.199462890625, -0.441650390625, 0.342529296875, -0.74267578125, -0.2227783203125, -0.06903076171875, -0.64306640625, -0.5068359375, -0.055572509765625, 0.435302734375, 0.35791015625, -0.14404296875, -0.84326171875, 0.71630859375, -0.2421875, 0.84423828125, 0.64453125, -0.05474853515625, -0.3134765625, -0.58251953125, 0.43212890625, 0.2276611328125, 0.364013671875, -0.2197265625, -0.12384033203125, 0.49853515625, -0.29541015625, -0.267578125, 0.17578125, 0.86376953125, -0.177001953125, 0.158203125, 0.7451171875, -0.09759521484375, 0.568359375, 0.73681640625, -0.61083984375, 1.0849609375, -0.436279296875, 0.074951171875, 0.427001953125, 0.0109405517578125, -0.1859130859375, -0.5419921875, -0.2724609375, -0.4228515625, 0.60498046875, 0.48046875, -0.5146484375, 0.90576171875, 0.0615234375, 0.58544921875, -0.63525390625, 0.10992431640625, 0.708984375, 0.028839111328125, 0.65087890625, -0.1412353515625, 0.01461029052734375, -0.28173828125, -0.60888671875, 1.0390625, -0.66015625, -0.1875, 0.59375, -0.04638671875, -0.2254638671875, 0.418701171875, -0.31689453125, 0.720703125, -0.150634765625, 0.33544921875, 0.7255859375, -0.5068359375, 0.98486328125, -0.0112762451171875, 0.0811767578125, 1.3583984375, 0.3388671875, -0.1407470703125, 0.416259765625, 0.576171875, -0.83251953125, 0.265869140625, -1.0712890625, 0.498046875, -0.0316162109375, 0.2147216796875, -0.1856689453125, -0.2286376953125, -0.501953125, 0.57421875, 0.36669921875, 0.0225067138671875, -0.1441650390625, 0.4677734375, -0.475341796875, 0.76513671875, -0.339599609375, 0.763671875, -0.439208984375, -0.1793212890625, 0.06060791015625, -0.30419921875, 0.0274200439453125, -0.404052734375, 0.057220458984375, 0.69384765625, 0.419677734375, 1.3134765625, 1.23046875, -0.349609375, 0.48681640625, 0.449462890625, -0.4794921875, 0.44482421875, 0.404541015625, 1.0244140625, 0.4287109375, 0.462890625, -0.07708740234375, 0.0635986328125, -0.78466796875, -0.317626953125, 0.1864013671875, 0.5908203125, -0.399658203125, 0.288818359375, 0.31689453125, 0.0997314453125, -1.0654296875, -0.1409912109375, -0.0579833984375, -0.75341796875, -0.55517578125, 0.416015625, 0.04644775390625, 0.3828125, -0.51123046875, -0.556640625, 0.26513671875, 1.2080078125, -0.3828125, -0.095458984375, 0.51318359375, 0.1256103515625, 0.0880126953125, -0.1456298828125, -0.0869140625, -0.100341796875, -0.6083984375, 1.0771484375, 0.08349609375, -0.15234375, 0.004337310791015625, 0.7216796875, 0.24658203125, 0.84375, -0.66552734375, -0.3193359375, 0.517578125, 1.0771484375, 0.11627197265625, 0.83642578125, 0.58544921875, 1.1611328125, 0.29150390625, 0.728515625, 0.30224609375, 0.283935546875, 0.6591796875, 1.044921875, -0.07086181640625, -0.06689453125, 0.250244140625, 0.38916015625, 0.1929931640625, 0.6025390625, 0.27294921875, 0.53662109375, -0.188720703125, 0.057769775390625, -0.8125, 0.1368408203125, -0.303466796875, 0.53759765625, 0.263427734375, 0.5634765625, -0.428466796875, -0.1690673828125, 0.25341796875, 0.9833984375, -1.060546875, -0.62109375, 0.0430908203125, -0.1282958984375, -0.0501708984375, -0.038116455078125, 0.52880859375, 0.12939453125, 0.55224609375, 0.4462890625, -0.28515625, -0.4560546875, -0.8701171875, -0.7216796875, -0.79248046875, -0.4208984375, -0.56103515625, -0.1527099609375, 0.2415771484375, -1.0810546875, -0.00861358642578125, -0.390625, -0.059173583984375, 0.2420654296875, -0.759765625, 1.0244140625, -0.666015625, 0.36669921875, -0.73193359375, 0.393798828125, 0.2666015625, 1.0947265625, -0.35107421875, -0.0738525390625, -0.06805419921875, -0.355224609375, 0.160400390625, -0.168212890625, 0.34228515625, -0.12152099609375, -0.353759765625, -0.74072265625, -0.433837890625, -0.335693359375, -0.59814453125, 0.324951171875, -0.5791015625, 0.77685546875, 0.66552734375, -0.495849609375, 0.7744140625, 1.0205078125, -0.58349609375, 0.4580078125, 0.075927734375, 0.0177459716796875, -0.71533203125, 1.2958984375, 0.716796875, 0.35791015625, -0.384521484375, -0.5693359375, -0.3935546875, -0.384521484375, 0.352294921875, -0.50537109375, -0.59228515625, 0.70068359375, -0.05267333984375, -1.0576171875, 0.160400390625, -0.98828125, -0.640625, -0.33251953125, -0.3798828125, 0.810546875, 0.79443359375, 0.16357421875, -0.1533203125, -0.321533203125, 0.1978759765625, 0.49365234375, 0.31494140625, -0.7724609375, 0.285400390625, 0.6962890625, 0.11297607421875, 0.370849609375, 0.292236328125, -0.282470703125, -0.10418701171875, 0.0341796875, -0.185791015625, 0.65283203125, 0.1177978515625, 0.214599609375, 0.4931640625, 0.419921875, -0.73779296875, -0.059173583984375, -0.2392578125, 0.51708984375, 0.4521484375, 0.46630859375, 0.248291015625, -0.357666015625, -0.650390625, -1.1513671875, 0.378662109375, 0.07000732421875, 0.7939453125, -0.763671875, 0.927734375, -0.01424407958984375, -0.2347412109375, 0.347412109375, -0.66357421875, 0.1539306640625, 1.1240234375, -0.431640625, 0.367919921875, -0.63427734375, 0.489013671875, 0.25537109375, 0.270751953125, 0.486328125, 0.278564453125, 0.70068359375, -0.2349853515625, -0.56982421875, -0.591796875, -0.1993408203125, -0.053375244140625, -0.75341796875, 0.2666015625, -0.6484375, -0.308349609375, -0.64697265625, 0.3857421875, 0.97021484375, 1.0126953125, -0.022369384765625, 0.65234375, 0.04449462890625, 0.28125, 0.47314453125, -0.57568359375, 0.0972900390625, -0.53173828125, 0.81103515625, 0.490234375, 0.3349609375, -0.70361328125, 0.021331787109375, -0.2099609375, -0.261474609375, 0.152099609375, -0.281005859375, -1.1494140625, 0.0467529296875, -0.192626953125, 0.5390625, -0.487548828125, -0.29052734375, -0.1641845703125, 0.44384765625, 0.48583984375, -0.70556640625, 0.11822509765625, -1.07421875, 0.779296875, 0.25390625, -0.262451171875, -0.39697265625, -0.56396484375, -0.61865234375, -1.0869140625, -0.07196044921875, 0.97412109375, 0.1558837890625, 0.494873046875, -0.93896484375, 0.4384765625, -0.07281494140625, -0.4580078125, 0.08062744140625, -0.291015625, 0.414306640625, -0.12237548828125, 0.70703125, -0.681640625, -0.52685546875, -0.04833984375, -0.92333984375, 0.6650390625, -0.486572265625, 0.330322265625, -0.026702880859375, -0.254150390625, -0.2362060546875, 0.27001953125, -0.2032470703125, 0.392333984375, -0.452880859375, 0.28466796875, -0.7958984375, -0.382080078125, 0.728515625, -0.35546875, -0.10601806640625, 0.71435546875, -0.10003662109375, -0.462890625, 0.09808349609375, 0.52392578125, -0.404296875, 0.429443359375, -0.496826171875, 0.40966796875, -0.2215576171875, -0.43115234375, -0.25, -0.70947265625, 0.86865234375, 0.29345703125, -0.5224609375, -0.445556640625, -1.0068359375, -0.267333984375, 0.026702880859375, -0.1964111328125, 0.560546875, 0.033905029296875, 0.059051513671875, 0.08074951171875, -0.1968994140625, -0.5517578125, -0.08392333984375, -0.29345703125, -0.00732421875, -0.02569580078125, 0.51953125, 0.482177734375, -0.179931640625, -0.5361328125, -0.454833984375, -0.294189453125, 0.09356689453125, -0.498291015625, -0.4560546875, -0.28515625, -0.288818359375, -0.69384765625, 0.1002197265625, -0.08123779296875, 0.46142578125, 0.953125, 0.0721435546875, 0.623046875, 0.320556640625, -0.84375, 1.1298828125, 0.37451171875, -1.091796875, -0.73095703125, 0.359619140625, -0.1285400390625, 0.5322265625, 0.176025390625, -0.515625, -0.826171875, -0.89599609375, 0.168701171875, -0.94189453125, -0.158935546875, -1.1455078125, -0.468994140625, -0.4716796875, 0.35888671875, -0.0592041015625, -0.7060546875, 0.27294921875, -0.9169921875, 0.332275390625, -0.7958984375, 0.10467529296875, -0.6123046875, -0.61767578125, -0.1968994140625, 1.1044921875, 0.12939453125, 0.5986328125, 0.09564208984375, -0.3583984375, 0.25439453125, 0.200439453125, -0.6005859375, -0.353759765625, 0.2322998046875, 0.0212249755859375, -0.1309814453125, -0.3447265625, -0.5478515625, 0.56787109375, -0.81396484375, 0.410888671875, -0.04638671875, -0.26953125, -0.1529541015625, -0.3349609375, 1.09375, -0.37890625, 0.2021484375, -0.35302734375, 0.28759765625, 0.509765625, -0.0271148681640625, -0.2568359375, -0.37841796875, -0.58544921875, -1.2841796875, 0.55712890625, -0.2073974609375, 0.041229248046875, -0.6953125, -0.30517578125, 1.2958984375, -0.455078125, 0.2412109375, 1.47265625, 0.177001953125, 0.21435546875, -0.4521484375, 0.61181640625, 0.6044921875, -0.43505859375, -0.07476806640625, 0.2271728515625, -0.62158203125, -0.038848876953125, -0.474365234375, -1.2001953125, -0.71875, 0.447021484375, 1.2177734375, -0.444580078125, 0.77197265625, -0.251708984375, -1.0654296875, -0.56884765625, 0.84521484375, -0.060882568359375, 0.256591796875, 0.888671875, 0.1416015625, -0.220947265625, 0.264404296875, -0.154541015625, -0.337890625, -0.6904296875, 0.9970703125, -0.3916015625, -0.08599853515625, 1.2236328125, 0.9052734375, -1.1552734375, -0.81494140625, -0.465087890625, -0.057525634765625, 0.17919921875, -0.91064453125, -0.0112457275390625, 0.5595703125, -0.60888671875, -0.0207366943359375, 0.61572265625, -0.3603515625, 0.3837890625, 0.0994873046875, 0.1588134765625, -0.2374267578125, 0.36669921875, 0.60546875, -0.2452392578125, -0.34033203125, -0.904296875, -0.3857421875, -0.2197265625, 0.007320404052734375, 1.0625, -0.1510009765625, 0.3935546875, 0.1929931640625, -0.0814208984375, 0.7529296875, -0.44091796875, -0.3251953125, 0.2158203125, -0.64013671875, -0.295166015625, -0.20556640625, 0.400146484375, 0.1787109375, 0.78369140625, -0.626953125, -0.00919342041015625, 0.218505859375, 0.43798828125, -0.469482421875, -1.103515625, -0.1787109375, -1.1591796875, -0.42626953125, -0.61962890625, -0.767578125, 0.0220947265625, 0.716796875, 0.057281494140625, -0.64111328125, -0.09588623046875, 0.1610107421875, -0.426513671875, 0.61328125, -0.5830078125, 0.2117919921875, -0.5009765625, -0.266845703125, -0.68701171875, 0.09002685546875, -0.80859375, -0.138671875, -0.50537109375, 0.413818359375, -0.56884765625, 0.33984375, -0.48486328125, 0.408935546875, -0.2744140625, -0.70361328125, -0.35693359375, 0.08843994140625, -0.56640625, 0.9501953125, 0.75341796875, 0.279541015625, 0.36328125, -0.46044921875, -0.328369140625, -0.474365234375, 0.424560546875, 0.07135009765625, 0.02484130859375, -0.34033203125, -0.244384765625, 0.16455078125, -1.0205078125, 0.1898193359375, -0.154052734375, 0.103759765625, 0.097412109375, -0.26123046875, 0.5400390625, 1.361328125, -0.1944580078125, 0.349365234375, -0.055694580078125, 0.42822265625, 0.371826171875, 0.2271728515625, -0.12481689453125, 0.82080078125, -0.278564453125, -0.6064453125, 0.1619873046875, 0.07098388671875, 0.2239990234375, 0.032440185546875, -0.401611328125, -0.72998046875, -0.8359375, -0.30078125, -0.00490570068359375, 0.52392578125, 0.58642578125, -0.15234375, 0.028076171875, -0.517578125, -0.3798828125, -0.5439453125, -1.255859375, -0.87109375, 0.5166015625, -0.190673828125, -0.8056640625, -0.0565185546875, -0.17431640625, -0.1336669921875, 0.0828857421875, 0.29541015625, -0.317138671875, 0.57568359375, -0.407958984375, 0.51318359375, -0.12164306640625, -0.033172607421875, 0.08575439453125, 0.484130859375, -0.58154296875, -0.6630859375, 0.392578125, 0.91748046875, 0.1627197265625, -0.3037109375, -0.720703125, 0.41796875, -0.1314697265625, -0.12457275390625, -0.53173828125, 0.3818359375, -0.08203125, 0.457275390625, -0.79443359375, -0.1103515625, -0.53173828125, 0.62744140625, 0.223388671875, -0.56103515625, -0.64404296875, 0.91552734375, 0.467529296875, -0.28125, 0.283935546875, -0.04327392578125, 0.27685546875, -0.14208984375, 0.1534423828125, -0.32275390625, 0.80029296875, 0.87255859375, 0.9091796875, -0.1287841796875, 0.258544921875, 0.56396484375, 0.438232421875, -0.1573486328125, 0.49267578125, 0.09405517578125, 0.09857177734375, 0.076904296875, -0.1295166015625, -0.2142333984375, -0.369873046875, -0.6328125, 0.325927734375, -0.34716796875, 0.245361328125, 0.0673828125, -0.63134765625, 0.955078125, -0.36572265625, -0.135498046875, 0.0916748046875, -0.66552734375, 0.185546875, 0.57568359375, -0.12841796875, -0.4765625, 0.681640625, 0.65576171875, 0.404296875, 0.44189453125, 0.2222900390625, 0.5947265625, -0.5966796875, 0.1895751953125, 0.27197265625, 0.034210205078125, -0.45947265625, -0.5654296875, -1.021484375, 0.406982421875, -0.77685546875, -0.3740234375, 0.439208984375, -0.80810546875, 0.06964111328125, -0.12298583984375, 0.80517578125, -0.275146484375, 0.157470703125, 0.46923828125, -0.11871337890625, -0.564453125, 0.90283203125, -0.1419677734375, 0.25537109375, -0.23876953125, 1.259765625, -0.006412506103515625, 1.4482421875, 0.80859375, 0.1181640625, 0.01335906982421875, 0.302734375, -0.42626953125, -0.66552734375, -0.304443359375, -0.29345703125, 0.008148193359375, -0.64453125, -0.48486328125, -0.232421875, 0.91357421875, -0.09100341796875, -0.7470703125, -0.262939453125, 0.31396484375, -0.85693359375, 0.493896484375, 0.414306640625, 0.3916015625, -0.0021076202392578125, -0.230224609375, -0.482666015625, -0.603515625, 0.61962890625, -0.63671875, 0.320556640625, -0.6396484375, -0.244384765625, -0.459716796875, -0.673828125, -0.39892578125, -0.1478271484375, -0.1920166015625, -0.98828125, 0.56884765625, 0.2047119140625, 0.4775390625, 0.33740234375, -0.71484375, 0.2578125, 0.75439453125, 1.095703125, 0.0182952880859375, 0.60498046875, 0.462890625, -0.203369140625, 0.12213134765625, -0.2423095703125, 0.4345703125, 0.1707763671875, 0.482421875, -0.26806640625, 0.06396484375, -0.71923828125, -1.13671875, 0.185791015625, 0.4541015625, 0.1781005859375, -0.61328125, -1.1064453125, -0.473388671875, -0.8916015625, -0.10845947265625, -0.84423828125, 0.517578125, -0.316650390625, 0.30322265625, -0.056854248046875, -1.0087890625, 4.39453125, 1.0048828125, 1.064453125, 0.005756378173828125, 0.433349609375, 1.1171875, 0.212646484375, -0.7734375, -0.00690460205078125, -0.400146484375, 1, -0.253662109375, 0.0831298828125, 0.66748046875, 0.25537109375, 0.6484375, -0.8798828125, 0.15185546875, -0.05828857421875, -1.251953125, -0.47216796875, 0.2392578125, -0.12420654296875, 0.77099609375, -0.10614013671875, 0.205810546875, 0.8125, -1.15625, -0.261962890625, -0.81884765625, 0.293701171875, -0.160400390625, 0.5068359375, 0.29248046875, 0.04779052734375, 0.8349609375, -0.309814453125, -0.3037109375, -0.2100830078125, -0.0213623046875, -0.0941162109375, -0.236083984375, 0.258056640625, -0.619140625, -0.373046875, 0.14013671875, -0.483154296875, 0.59716796875, 0.1412353515625, -0.93408203125, 0.50244140625, 0.074951171875, 0.76953125, -0.8671875, -0.5986328125, 0.0000445246696472168, 0.463134765625, -0.251953125, -0.06951904296875, 0.6767578125, 0.395751953125, 0.884765625, -0.3173828125, 0.69384765625, -0.80322265625, 0.93408203125, -0.30908203125, 0.273681640625, -0.72412109375, 0.377685546875, -0.1566162109375, -0.6591796875, -0.423583984375, -0.58544921875, 0.591796875, 0.11773681640625, -0.29443359375, 0.64990234375, 0.86376953125, -0.347900390625, -0.0310211181640625, -0.52099609375, -0.427490234375, -0.295166015625, 0.36767578125, 1.3271484375, -0.42626953125, -0.27294921875, -0.1180419921875, 0.52978515625, 0.330322265625, 0.58251953125, 0.027496337890625, -0.54833984375, -0.431396484375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Tags: games Correct Solution: ``` def removeX(s,p): if (p==len(s)): return s while s[p]!='X': p+=1 if (p==len(s)): return s j=0 while s[p+j]=='X': j+=1 if (p+j==len(s)): break return removeX(s[0:p+1]+s[p+j:],p+1) def doable(lenght,a,b,parity): for x in range((lenght-a)//2+1): y=lenght-a-x #print(x,y) if ((not((x>=b) & (x<a)))&(not(x>=2*b))&(not((y>=b) & (y<a)))&(not(y>=2*b))): e=0 #print('oui') if((x>=a)&(x<2*b)): e+=1 if((y>=a)&(y<2*b)): e+=1 if((parity+e)%2==0): return 1 return 0 for i in range(int(input())): a,b=[int(x) for x in input().split()] v=[0,0,0] s=removeX(input(),0) for y in s.split('X'): k=len(y) if ((k>=b) & (k<a)): v[0]+=1 elif ((k>=a) & (k<2*b)): v[1]+=1 elif (k>=2*b): v[2]+=1 lenght=k #print(v) if ((v[0]>0) | (v[2]>1)): print('NO') elif (v[2]==1): if (lenght-a>=4*b): print('NO') else: if (doable(lenght,a,b,v[1]%2)==1): print('YES') else: print('NO') else: if (v[1]%2==0): print('NO') else: print('YES') ```
106,228
[ 0.2432861328125, 0.25244140625, -0.0284423828125, 0.39697265625, -0.60546875, -0.57177734375, -0.124267578125, 0.179931640625, 0.296142578125, 0.88623046875, 0.82666015625, 0.1943359375, 0.1842041015625, -0.60791015625, -0.51904296875, 0.12939453125, -0.77734375, -0.923828125, -0.388427734375, -0.1505126953125, 0.11309814453125, 0.0036067962646484375, -1.3173828125, -0.00513458251953125, -0.197509765625, 0.83642578125, 0.1290283203125, -0.01087188720703125, 0.9296875, 1.130859375, 0.0889892578125, -0.53564453125, 0.461669921875, -0.8095703125, -0.443603515625, -0.263916015625, 0.83251953125, -0.599609375, -0.06732177734375, -0.439697265625, 0.323486328125, -0.53369140625, 0.347412109375, -0.61376953125, -1.2734375, 0.005489349365234375, -0.2998046875, -0.50732421875, -0.1939697265625, -0.52685546875, -0.04132080078125, -0.385498046875, 0.44482421875, -0.242919921875, 0.1131591796875, 0.09869384765625, 0.2291259765625, 0.1610107421875, -0.6962890625, 0.26171875, 0.245849609375, -0.350830078125, 0.04052734375, -0.79638671875, 0.232421875, 0.018157958984375, 0.199462890625, -0.441650390625, 0.342529296875, -0.74267578125, -0.2227783203125, -0.06903076171875, -0.64306640625, -0.5068359375, -0.055572509765625, 0.435302734375, 0.35791015625, -0.14404296875, -0.84326171875, 0.71630859375, -0.2421875, 0.84423828125, 0.64453125, -0.05474853515625, -0.3134765625, -0.58251953125, 0.43212890625, 0.2276611328125, 0.364013671875, -0.2197265625, -0.12384033203125, 0.49853515625, -0.29541015625, -0.267578125, 0.17578125, 0.86376953125, -0.177001953125, 0.158203125, 0.7451171875, -0.09759521484375, 0.568359375, 0.73681640625, -0.61083984375, 1.0849609375, -0.436279296875, 0.074951171875, 0.427001953125, 0.0109405517578125, -0.1859130859375, -0.5419921875, -0.2724609375, -0.4228515625, 0.60498046875, 0.48046875, -0.5146484375, 0.90576171875, 0.0615234375, 0.58544921875, -0.63525390625, 0.10992431640625, 0.708984375, 0.028839111328125, 0.65087890625, -0.1412353515625, 0.01461029052734375, -0.28173828125, -0.60888671875, 1.0390625, -0.66015625, -0.1875, 0.59375, -0.04638671875, -0.2254638671875, 0.418701171875, -0.31689453125, 0.720703125, -0.150634765625, 0.33544921875, 0.7255859375, -0.5068359375, 0.98486328125, -0.0112762451171875, 0.0811767578125, 1.3583984375, 0.3388671875, -0.1407470703125, 0.416259765625, 0.576171875, -0.83251953125, 0.265869140625, -1.0712890625, 0.498046875, -0.0316162109375, 0.2147216796875, -0.1856689453125, -0.2286376953125, -0.501953125, 0.57421875, 0.36669921875, 0.0225067138671875, -0.1441650390625, 0.4677734375, -0.475341796875, 0.76513671875, -0.339599609375, 0.763671875, -0.439208984375, -0.1793212890625, 0.06060791015625, -0.30419921875, 0.0274200439453125, -0.404052734375, 0.057220458984375, 0.69384765625, 0.419677734375, 1.3134765625, 1.23046875, -0.349609375, 0.48681640625, 0.449462890625, -0.4794921875, 0.44482421875, 0.404541015625, 1.0244140625, 0.4287109375, 0.462890625, -0.07708740234375, 0.0635986328125, -0.78466796875, -0.317626953125, 0.1864013671875, 0.5908203125, -0.399658203125, 0.288818359375, 0.31689453125, 0.0997314453125, -1.0654296875, -0.1409912109375, -0.0579833984375, -0.75341796875, -0.55517578125, 0.416015625, 0.04644775390625, 0.3828125, -0.51123046875, -0.556640625, 0.26513671875, 1.2080078125, -0.3828125, -0.095458984375, 0.51318359375, 0.1256103515625, 0.0880126953125, -0.1456298828125, -0.0869140625, -0.100341796875, -0.6083984375, 1.0771484375, 0.08349609375, -0.15234375, 0.004337310791015625, 0.7216796875, 0.24658203125, 0.84375, -0.66552734375, -0.3193359375, 0.517578125, 1.0771484375, 0.11627197265625, 0.83642578125, 0.58544921875, 1.1611328125, 0.29150390625, 0.728515625, 0.30224609375, 0.283935546875, 0.6591796875, 1.044921875, -0.07086181640625, -0.06689453125, 0.250244140625, 0.38916015625, 0.1929931640625, 0.6025390625, 0.27294921875, 0.53662109375, -0.188720703125, 0.057769775390625, -0.8125, 0.1368408203125, -0.303466796875, 0.53759765625, 0.263427734375, 0.5634765625, -0.428466796875, -0.1690673828125, 0.25341796875, 0.9833984375, -1.060546875, -0.62109375, 0.0430908203125, -0.1282958984375, -0.0501708984375, -0.038116455078125, 0.52880859375, 0.12939453125, 0.55224609375, 0.4462890625, -0.28515625, -0.4560546875, -0.8701171875, -0.7216796875, -0.79248046875, -0.4208984375, -0.56103515625, -0.1527099609375, 0.2415771484375, -1.0810546875, -0.00861358642578125, -0.390625, -0.059173583984375, 0.2420654296875, -0.759765625, 1.0244140625, -0.666015625, 0.36669921875, -0.73193359375, 0.393798828125, 0.2666015625, 1.0947265625, -0.35107421875, -0.0738525390625, -0.06805419921875, -0.355224609375, 0.160400390625, -0.168212890625, 0.34228515625, -0.12152099609375, -0.353759765625, -0.74072265625, -0.433837890625, -0.335693359375, -0.59814453125, 0.324951171875, -0.5791015625, 0.77685546875, 0.66552734375, -0.495849609375, 0.7744140625, 1.0205078125, -0.58349609375, 0.4580078125, 0.075927734375, 0.0177459716796875, -0.71533203125, 1.2958984375, 0.716796875, 0.35791015625, -0.384521484375, -0.5693359375, -0.3935546875, -0.384521484375, 0.352294921875, -0.50537109375, -0.59228515625, 0.70068359375, -0.05267333984375, -1.0576171875, 0.160400390625, -0.98828125, -0.640625, -0.33251953125, -0.3798828125, 0.810546875, 0.79443359375, 0.16357421875, -0.1533203125, -0.321533203125, 0.1978759765625, 0.49365234375, 0.31494140625, -0.7724609375, 0.285400390625, 0.6962890625, 0.11297607421875, 0.370849609375, 0.292236328125, -0.282470703125, -0.10418701171875, 0.0341796875, -0.185791015625, 0.65283203125, 0.1177978515625, 0.214599609375, 0.4931640625, 0.419921875, -0.73779296875, -0.059173583984375, -0.2392578125, 0.51708984375, 0.4521484375, 0.46630859375, 0.248291015625, -0.357666015625, -0.650390625, -1.1513671875, 0.378662109375, 0.07000732421875, 0.7939453125, -0.763671875, 0.927734375, -0.01424407958984375, -0.2347412109375, 0.347412109375, -0.66357421875, 0.1539306640625, 1.1240234375, -0.431640625, 0.367919921875, -0.63427734375, 0.489013671875, 0.25537109375, 0.270751953125, 0.486328125, 0.278564453125, 0.70068359375, -0.2349853515625, -0.56982421875, -0.591796875, -0.1993408203125, -0.053375244140625, -0.75341796875, 0.2666015625, -0.6484375, -0.308349609375, -0.64697265625, 0.3857421875, 0.97021484375, 1.0126953125, -0.022369384765625, 0.65234375, 0.04449462890625, 0.28125, 0.47314453125, -0.57568359375, 0.0972900390625, -0.53173828125, 0.81103515625, 0.490234375, 0.3349609375, -0.70361328125, 0.021331787109375, -0.2099609375, -0.261474609375, 0.152099609375, -0.281005859375, -1.1494140625, 0.0467529296875, -0.192626953125, 0.5390625, -0.487548828125, -0.29052734375, -0.1641845703125, 0.44384765625, 0.48583984375, -0.70556640625, 0.11822509765625, -1.07421875, 0.779296875, 0.25390625, -0.262451171875, -0.39697265625, -0.56396484375, -0.61865234375, -1.0869140625, -0.07196044921875, 0.97412109375, 0.1558837890625, 0.494873046875, -0.93896484375, 0.4384765625, -0.07281494140625, -0.4580078125, 0.08062744140625, -0.291015625, 0.414306640625, -0.12237548828125, 0.70703125, -0.681640625, -0.52685546875, -0.04833984375, -0.92333984375, 0.6650390625, -0.486572265625, 0.330322265625, -0.026702880859375, -0.254150390625, -0.2362060546875, 0.27001953125, -0.2032470703125, 0.392333984375, -0.452880859375, 0.28466796875, -0.7958984375, -0.382080078125, 0.728515625, -0.35546875, -0.10601806640625, 0.71435546875, -0.10003662109375, -0.462890625, 0.09808349609375, 0.52392578125, -0.404296875, 0.429443359375, -0.496826171875, 0.40966796875, -0.2215576171875, -0.43115234375, -0.25, -0.70947265625, 0.86865234375, 0.29345703125, -0.5224609375, -0.445556640625, -1.0068359375, -0.267333984375, 0.026702880859375, -0.1964111328125, 0.560546875, 0.033905029296875, 0.059051513671875, 0.08074951171875, -0.1968994140625, -0.5517578125, -0.08392333984375, -0.29345703125, -0.00732421875, -0.02569580078125, 0.51953125, 0.482177734375, -0.179931640625, -0.5361328125, -0.454833984375, -0.294189453125, 0.09356689453125, -0.498291015625, -0.4560546875, -0.28515625, -0.288818359375, -0.69384765625, 0.1002197265625, -0.08123779296875, 0.46142578125, 0.953125, 0.0721435546875, 0.623046875, 0.320556640625, -0.84375, 1.1298828125, 0.37451171875, -1.091796875, -0.73095703125, 0.359619140625, -0.1285400390625, 0.5322265625, 0.176025390625, -0.515625, -0.826171875, -0.89599609375, 0.168701171875, -0.94189453125, -0.158935546875, -1.1455078125, -0.468994140625, -0.4716796875, 0.35888671875, -0.0592041015625, -0.7060546875, 0.27294921875, -0.9169921875, 0.332275390625, -0.7958984375, 0.10467529296875, -0.6123046875, -0.61767578125, -0.1968994140625, 1.1044921875, 0.12939453125, 0.5986328125, 0.09564208984375, -0.3583984375, 0.25439453125, 0.200439453125, -0.6005859375, -0.353759765625, 0.2322998046875, 0.0212249755859375, -0.1309814453125, -0.3447265625, -0.5478515625, 0.56787109375, -0.81396484375, 0.410888671875, -0.04638671875, -0.26953125, -0.1529541015625, -0.3349609375, 1.09375, -0.37890625, 0.2021484375, -0.35302734375, 0.28759765625, 0.509765625, -0.0271148681640625, -0.2568359375, -0.37841796875, -0.58544921875, -1.2841796875, 0.55712890625, -0.2073974609375, 0.041229248046875, -0.6953125, -0.30517578125, 1.2958984375, -0.455078125, 0.2412109375, 1.47265625, 0.177001953125, 0.21435546875, -0.4521484375, 0.61181640625, 0.6044921875, -0.43505859375, -0.07476806640625, 0.2271728515625, -0.62158203125, -0.038848876953125, -0.474365234375, -1.2001953125, -0.71875, 0.447021484375, 1.2177734375, -0.444580078125, 0.77197265625, -0.251708984375, -1.0654296875, -0.56884765625, 0.84521484375, -0.060882568359375, 0.256591796875, 0.888671875, 0.1416015625, -0.220947265625, 0.264404296875, -0.154541015625, -0.337890625, -0.6904296875, 0.9970703125, -0.3916015625, -0.08599853515625, 1.2236328125, 0.9052734375, -1.1552734375, -0.81494140625, -0.465087890625, -0.057525634765625, 0.17919921875, -0.91064453125, -0.0112457275390625, 0.5595703125, -0.60888671875, -0.0207366943359375, 0.61572265625, -0.3603515625, 0.3837890625, 0.0994873046875, 0.1588134765625, -0.2374267578125, 0.36669921875, 0.60546875, -0.2452392578125, -0.34033203125, -0.904296875, -0.3857421875, -0.2197265625, 0.007320404052734375, 1.0625, -0.1510009765625, 0.3935546875, 0.1929931640625, -0.0814208984375, 0.7529296875, -0.44091796875, -0.3251953125, 0.2158203125, -0.64013671875, -0.295166015625, -0.20556640625, 0.400146484375, 0.1787109375, 0.78369140625, -0.626953125, -0.00919342041015625, 0.218505859375, 0.43798828125, -0.469482421875, -1.103515625, -0.1787109375, -1.1591796875, -0.42626953125, -0.61962890625, -0.767578125, 0.0220947265625, 0.716796875, 0.057281494140625, -0.64111328125, -0.09588623046875, 0.1610107421875, -0.426513671875, 0.61328125, -0.5830078125, 0.2117919921875, -0.5009765625, -0.266845703125, -0.68701171875, 0.09002685546875, -0.80859375, -0.138671875, -0.50537109375, 0.413818359375, -0.56884765625, 0.33984375, -0.48486328125, 0.408935546875, -0.2744140625, -0.70361328125, -0.35693359375, 0.08843994140625, -0.56640625, 0.9501953125, 0.75341796875, 0.279541015625, 0.36328125, -0.46044921875, -0.328369140625, -0.474365234375, 0.424560546875, 0.07135009765625, 0.02484130859375, -0.34033203125, -0.244384765625, 0.16455078125, -1.0205078125, 0.1898193359375, -0.154052734375, 0.103759765625, 0.097412109375, -0.26123046875, 0.5400390625, 1.361328125, -0.1944580078125, 0.349365234375, -0.055694580078125, 0.42822265625, 0.371826171875, 0.2271728515625, -0.12481689453125, 0.82080078125, -0.278564453125, -0.6064453125, 0.1619873046875, 0.07098388671875, 0.2239990234375, 0.032440185546875, -0.401611328125, -0.72998046875, -0.8359375, -0.30078125, -0.00490570068359375, 0.52392578125, 0.58642578125, -0.15234375, 0.028076171875, -0.517578125, -0.3798828125, -0.5439453125, -1.255859375, -0.87109375, 0.5166015625, -0.190673828125, -0.8056640625, -0.0565185546875, -0.17431640625, -0.1336669921875, 0.0828857421875, 0.29541015625, -0.317138671875, 0.57568359375, -0.407958984375, 0.51318359375, -0.12164306640625, -0.033172607421875, 0.08575439453125, 0.484130859375, -0.58154296875, -0.6630859375, 0.392578125, 0.91748046875, 0.1627197265625, -0.3037109375, -0.720703125, 0.41796875, -0.1314697265625, -0.12457275390625, -0.53173828125, 0.3818359375, -0.08203125, 0.457275390625, -0.79443359375, -0.1103515625, -0.53173828125, 0.62744140625, 0.223388671875, -0.56103515625, -0.64404296875, 0.91552734375, 0.467529296875, -0.28125, 0.283935546875, -0.04327392578125, 0.27685546875, -0.14208984375, 0.1534423828125, -0.32275390625, 0.80029296875, 0.87255859375, 0.9091796875, -0.1287841796875, 0.258544921875, 0.56396484375, 0.438232421875, -0.1573486328125, 0.49267578125, 0.09405517578125, 0.09857177734375, 0.076904296875, -0.1295166015625, -0.2142333984375, -0.369873046875, -0.6328125, 0.325927734375, -0.34716796875, 0.245361328125, 0.0673828125, -0.63134765625, 0.955078125, -0.36572265625, -0.135498046875, 0.0916748046875, -0.66552734375, 0.185546875, 0.57568359375, -0.12841796875, -0.4765625, 0.681640625, 0.65576171875, 0.404296875, 0.44189453125, 0.2222900390625, 0.5947265625, -0.5966796875, 0.1895751953125, 0.27197265625, 0.034210205078125, -0.45947265625, -0.5654296875, -1.021484375, 0.406982421875, -0.77685546875, -0.3740234375, 0.439208984375, -0.80810546875, 0.06964111328125, -0.12298583984375, 0.80517578125, -0.275146484375, 0.157470703125, 0.46923828125, -0.11871337890625, -0.564453125, 0.90283203125, -0.1419677734375, 0.25537109375, -0.23876953125, 1.259765625, -0.006412506103515625, 1.4482421875, 0.80859375, 0.1181640625, 0.01335906982421875, 0.302734375, -0.42626953125, -0.66552734375, -0.304443359375, -0.29345703125, 0.008148193359375, -0.64453125, -0.48486328125, -0.232421875, 0.91357421875, -0.09100341796875, -0.7470703125, -0.262939453125, 0.31396484375, -0.85693359375, 0.493896484375, 0.414306640625, 0.3916015625, -0.0021076202392578125, -0.230224609375, -0.482666015625, -0.603515625, 0.61962890625, -0.63671875, 0.320556640625, -0.6396484375, -0.244384765625, -0.459716796875, -0.673828125, -0.39892578125, -0.1478271484375, -0.1920166015625, -0.98828125, 0.56884765625, 0.2047119140625, 0.4775390625, 0.33740234375, -0.71484375, 0.2578125, 0.75439453125, 1.095703125, 0.0182952880859375, 0.60498046875, 0.462890625, -0.203369140625, 0.12213134765625, -0.2423095703125, 0.4345703125, 0.1707763671875, 0.482421875, -0.26806640625, 0.06396484375, -0.71923828125, -1.13671875, 0.185791015625, 0.4541015625, 0.1781005859375, -0.61328125, -1.1064453125, -0.473388671875, -0.8916015625, -0.10845947265625, -0.84423828125, 0.517578125, -0.316650390625, 0.30322265625, -0.056854248046875, -1.0087890625, 4.39453125, 1.0048828125, 1.064453125, 0.005756378173828125, 0.433349609375, 1.1171875, 0.212646484375, -0.7734375, -0.00690460205078125, -0.400146484375, 1, -0.253662109375, 0.0831298828125, 0.66748046875, 0.25537109375, 0.6484375, -0.8798828125, 0.15185546875, -0.05828857421875, -1.251953125, -0.47216796875, 0.2392578125, -0.12420654296875, 0.77099609375, -0.10614013671875, 0.205810546875, 0.8125, -1.15625, -0.261962890625, -0.81884765625, 0.293701171875, -0.160400390625, 0.5068359375, 0.29248046875, 0.04779052734375, 0.8349609375, -0.309814453125, -0.3037109375, -0.2100830078125, -0.0213623046875, -0.0941162109375, -0.236083984375, 0.258056640625, -0.619140625, -0.373046875, 0.14013671875, -0.483154296875, 0.59716796875, 0.1412353515625, -0.93408203125, 0.50244140625, 0.074951171875, 0.76953125, -0.8671875, -0.5986328125, 0.0000445246696472168, 0.463134765625, -0.251953125, -0.06951904296875, 0.6767578125, 0.395751953125, 0.884765625, -0.3173828125, 0.69384765625, -0.80322265625, 0.93408203125, -0.30908203125, 0.273681640625, -0.72412109375, 0.377685546875, -0.1566162109375, -0.6591796875, -0.423583984375, -0.58544921875, 0.591796875, 0.11773681640625, -0.29443359375, 0.64990234375, 0.86376953125, -0.347900390625, -0.0310211181640625, -0.52099609375, -0.427490234375, -0.295166015625, 0.36767578125, 1.3271484375, -0.42626953125, -0.27294921875, -0.1180419921875, 0.52978515625, 0.330322265625, 0.58251953125, 0.027496337890625, -0.54833984375, -0.431396484375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Submitted Solution: ``` import sys input = lambda: sys.stdin.readline().rstrip() Q = int(input()) for _ in range(Q): a, b = map(int, input().split()) S = input() + "X" s = 0 x = x1 = x2 = x3 = xx = 0 for i in range(len(S)): if S[i] == "X": if s < b: pass elif a <= s < 2*b: x += 1 elif a < 2*b and (3*a <= s < a+3*b-1 or 2*a <= s < a+2*b-1): xx += 1 elif a < 2*b and 3*a <= s < a+4*b-1: x3 += 1 elif a < 2*b and 2*a <= s < a+3*b-1: x2 += 1 elif a <= s < a+2*b-1: x1 += 1 else: # print("a, b, s =", a, b, s) print("NO") break s = 0 else: s += 1 else: # print("x, x1, x2, x3 =", x, x1, x2, x3) if xx+x1+x2+x3 >= 2: print("NO") elif xx: print("YES") elif (x + x1 + x2*2 + x3*3) % 2 == 0: print("NO") else: print("YES") ``` Yes
106,229
[ 0.44287109375, 0.240478515625, -0.087890625, 0.341552734375, -0.591796875, -0.5078125, -0.1556396484375, 0.25732421875, 0.2320556640625, 0.87841796875, 0.70458984375, 0.2056884765625, 0.13916015625, -0.640625, -0.50146484375, -0.04205322265625, -0.654296875, -0.849609375, -0.380859375, -0.224365234375, 0.0240325927734375, -0.1005859375, -1.3369140625, 0.0732421875, -0.2235107421875, 0.7412109375, 0.1297607421875, -0.041015625, 0.88623046875, 1.02734375, -0.01287841796875, -0.466796875, 0.5283203125, -0.65869140625, -0.421142578125, -0.397705078125, 0.76708984375, -0.69775390625, -0.2042236328125, -0.515625, 0.24169921875, -0.423828125, 0.45751953125, -0.60791015625, -1.3544921875, 0.0294342041015625, -0.193115234375, -0.50634765625, -0.216552734375, -0.48974609375, 0.10821533203125, -0.395263671875, 0.303955078125, -0.290283203125, 0.22119140625, 0.272216796875, 0.058868408203125, 0.0958251953125, -0.765625, 0.1998291015625, 0.338623046875, -0.24658203125, -0.019744873046875, -0.92822265625, 0.0936279296875, 0.044525146484375, 0.225830078125, -0.462890625, 0.2509765625, -0.5712890625, -0.205810546875, -0.1949462890625, -0.64697265625, -0.317626953125, -0.1839599609375, 0.428466796875, 0.361328125, -0.10089111328125, -0.95947265625, 0.7646484375, -0.230224609375, 0.94482421875, 0.63525390625, 0.008575439453125, -0.306884765625, -0.478271484375, 0.47021484375, 0.26513671875, 0.43359375, -0.259033203125, -0.054290771484375, 0.5107421875, -0.331787109375, -0.167724609375, 0.34814453125, 0.8525390625, -0.1483154296875, 0.124267578125, 0.6689453125, -0.1033935546875, 0.57763671875, 0.69287109375, -0.50634765625, 1.12890625, -0.447021484375, -0.009674072265625, 0.380126953125, -0.0626220703125, -0.0260467529296875, -0.5029296875, -0.192626953125, -0.473876953125, 0.66015625, 0.382568359375, -0.564453125, 0.876953125, 0.10308837890625, 0.413818359375, -0.61572265625, -0.002712249755859375, 0.72119140625, -0.029205322265625, 0.54931640625, -0.0478515625, 0.1151123046875, -0.276123046875, -0.6298828125, 1.001953125, -0.56494140625, -0.2529296875, 0.57421875, -0.064208984375, -0.25244140625, 0.362548828125, -0.2763671875, 0.75, -0.151611328125, 0.461669921875, 0.76953125, -0.62841796875, 0.9716796875, -0.0301666259765625, 0.2265625, 1.4716796875, 0.24951171875, -0.2176513671875, 0.3701171875, 0.5263671875, -0.85595703125, 0.3525390625, -1.05078125, 0.6015625, -0.045562744140625, 0.200927734375, -0.266357421875, -0.2261962890625, -0.333984375, 0.52392578125, 0.335205078125, -0.0050048828125, -0.14208984375, 0.5625, -0.54736328125, 0.72705078125, -0.328125, 0.6953125, -0.386962890625, -0.2027587890625, -0.005481719970703125, -0.266845703125, 0.06683349609375, -0.376708984375, 0.14501953125, 0.7578125, 0.5234375, 1.35546875, 1.2919921875, -0.226318359375, 0.364990234375, 0.423095703125, -0.52685546875, 0.3935546875, 0.38330078125, 1.0556640625, 0.416748046875, 0.461181640625, 0.0469970703125, 0.093017578125, -0.7236328125, -0.385009765625, 0.1390380859375, 0.67041015625, -0.475341796875, 0.3740234375, 0.248779296875, 0.1494140625, -0.91796875, -0.210693359375, 0.0303802490234375, -0.8173828125, -0.54638671875, 0.41015625, 0.03704833984375, 0.4140625, -0.65185546875, -0.638671875, 0.1275634765625, 1.146484375, -0.341796875, -0.109619140625, 0.4697265625, 0.30615234375, 0.0167999267578125, -0.22119140625, 0.00995635986328125, -0.014801025390625, -0.6767578125, 0.98046875, 0.039337158203125, -0.148681640625, 0.11639404296875, 0.70849609375, 0.1844482421875, 0.75146484375, -0.626953125, -0.384521484375, 0.4619140625, 1.0947265625, 0.09918212890625, 0.74462890625, 0.55419921875, 1.1552734375, 0.326904296875, 0.86474609375, 0.306884765625, 0.264892578125, 0.76708984375, 0.91015625, -0.2357177734375, -0.01302337646484375, 0.221435546875, 0.467529296875, 0.1466064453125, 0.638671875, 0.29638671875, 0.44775390625, -0.18115234375, 0.032867431640625, -0.6728515625, 0.1142578125, -0.2978515625, 0.50439453125, 0.2052001953125, 0.6064453125, -0.442626953125, -0.1087646484375, 0.3681640625, 0.978515625, -1.1103515625, -0.6884765625, 0.042022705078125, -0.03961181640625, -0.0960693359375, 0.051849365234375, 0.57666015625, 0.0285797119140625, 0.42529296875, 0.408203125, -0.366455078125, -0.63623046875, -0.7861328125, -0.740234375, -0.896484375, -0.40185546875, -0.5849609375, -0.234619140625, 0.1978759765625, -0.978515625, -0.07916259765625, -0.5234375, -0.047027587890625, 0.1627197265625, -0.5322265625, 1.03125, -0.5634765625, 0.5048828125, -0.81396484375, 0.235595703125, 0.427001953125, 1.072265625, -0.430908203125, -0.108642578125, -0.1849365234375, -0.31787109375, 0.196044921875, -0.17626953125, 0.4287109375, -0.0341796875, -0.43115234375, -0.7578125, -0.4189453125, -0.16748046875, -0.476318359375, 0.2705078125, -0.6591796875, 0.80517578125, 0.5, -0.52197265625, 0.673828125, 1.0166015625, -0.59716796875, 0.53466796875, 0.1663818359375, 0.1090087890625, -0.65869140625, 1.3125, 0.6787109375, 0.400390625, -0.42138671875, -0.533203125, -0.3681640625, -0.281005859375, 0.338623046875, -0.546875, -0.63623046875, 0.6552734375, 0.0238494873046875, -1.0849609375, 0.1781005859375, -1.0458984375, -0.619140625, -0.237060546875, -0.496826171875, 0.84423828125, 0.80908203125, 0.254638671875, -0.05657958984375, -0.400390625, 0.1473388671875, 0.42138671875, 0.40576171875, -0.8291015625, 0.263671875, 0.7724609375, 0.05462646484375, 0.34521484375, 0.343994140625, -0.3359375, -0.031402587890625, -0.01007080078125, -0.2374267578125, 0.65625, 0.108642578125, 0.2283935546875, 0.390625, 0.472900390625, -0.826171875, -0.1346435546875, -0.30712890625, 0.515625, 0.45068359375, 0.56982421875, 0.305419921875, -0.258544921875, -0.72216796875, -1.0166015625, 0.368896484375, 0.062347412109375, 0.7314453125, -0.5927734375, 0.89990234375, -0.059295654296875, -0.3046875, 0.488525390625, -0.66357421875, 0.0909423828125, 1.1416015625, -0.301513671875, 0.4501953125, -0.70166015625, 0.44921875, 0.12115478515625, 0.138671875, 0.49267578125, 0.23193359375, 0.77294921875, -0.27099609375, -0.54150390625, -0.485595703125, -0.1568603515625, -0.0576171875, -0.7685546875, 0.2191162109375, -0.57080078125, -0.412841796875, -0.7265625, 0.4306640625, 0.82275390625, 1.0576171875, -0.01462554931640625, 0.59326171875, -0.1046142578125, 0.29931640625, 0.56005859375, -0.52392578125, 0.16845703125, -0.5673828125, 0.70751953125, 0.48779296875, 0.171875, -0.62451171875, 0.061126708984375, -0.2076416015625, -0.23046875, 0.12109375, -0.319580078125, -1.0693359375, 0.25537109375, -0.171630859375, 0.59228515625, -0.59765625, -0.344970703125, -0.11004638671875, 0.467529296875, 0.5439453125, -0.73779296875, 0.2127685546875, -1.1064453125, 0.68310546875, 0.359619140625, -0.250732421875, -0.388916015625, -0.5078125, -0.79638671875, -1.095703125, -0.06903076171875, 1.0439453125, 0.11712646484375, 0.380615234375, -1.15625, 0.400634765625, -0.051910400390625, -0.54736328125, 0.1885986328125, -0.3291015625, 0.283935546875, -0.0477294921875, 0.728515625, -0.73974609375, -0.564453125, -0.0182342529296875, -0.95263671875, 0.57080078125, -0.443359375, 0.4169921875, -0.0197601318359375, -0.16552734375, -0.115234375, 0.378662109375, -0.187744140625, 0.28515625, -0.345703125, 0.30908203125, -0.89794921875, -0.4453125, 0.6748046875, -0.2196044921875, -0.179443359375, 0.7548828125, -0.2169189453125, -0.5322265625, 0.1552734375, 0.48486328125, -0.3779296875, 0.537109375, -0.39892578125, 0.408935546875, -0.172119140625, -0.404296875, -0.177001953125, -0.70849609375, 0.8623046875, 0.210205078125, -0.57373046875, -0.474853515625, -0.92138671875, -0.185546875, 0.00908660888671875, -0.196044921875, 0.60400390625, 0.1722412109375, 0.08056640625, -0.06256103515625, -0.221923828125, -0.5810546875, -0.0670166015625, -0.348388671875, 0.01152801513671875, 0.047821044921875, 0.4052734375, 0.404296875, -0.056060791015625, -0.5, -0.4111328125, -0.2340087890625, 0.1390380859375, -0.54345703125, -0.375, -0.235595703125, -0.2890625, -0.63916015625, 0.280517578125, -0.1246337890625, 0.51611328125, 1.0166015625, -0.01617431640625, 0.65869140625, 0.304931640625, -0.9775390625, 1.13671875, 0.203125, -1.2138671875, -0.69677734375, 0.299560546875, 0.10009765625, 0.68359375, 0.1942138671875, -0.481201171875, -0.8681640625, -0.9501953125, 0.2027587890625, -0.88720703125, -0.245849609375, -1.212890625, -0.5361328125, -0.378662109375, 0.4365234375, -0.0665283203125, -0.67724609375, 0.2626953125, -1.0625, 0.38134765625, -0.95947265625, 0.104248046875, -0.7236328125, -0.4853515625, -0.2052001953125, 1.060546875, 0.23876953125, 0.625, 0.0013666152954101562, -0.30126953125, 0.1019287109375, 0.1982421875, -0.5126953125, -0.475830078125, 0.201171875, -0.051849365234375, -0.277099609375, -0.291259765625, -0.5068359375, 0.61474609375, -0.72216796875, 0.42919921875, -0.051910400390625, -0.298583984375, -0.12005615234375, -0.41796875, 1.0888671875, -0.348876953125, 0.1973876953125, -0.4853515625, 0.226806640625, 0.6552734375, -0.2210693359375, -0.30322265625, -0.3466796875, -0.491455078125, -1.25390625, 0.490234375, -0.368408203125, 0.080810546875, -0.7939453125, -0.2174072265625, 1.3291015625, -0.564453125, 0.268310546875, 1.455078125, 0.1661376953125, 0.2191162109375, -0.498046875, 0.671875, 0.7080078125, -0.428955078125, -0.1109619140625, 0.12261962890625, -0.65869140625, -0.118896484375, -0.394775390625, -1.1728515625, -0.77197265625, 0.457275390625, 1.154296875, -0.45263671875, 0.88037109375, -0.24462890625, -1.107421875, -0.591796875, 0.78955078125, -0.1331787109375, 0.240234375, 0.86181640625, 0.28466796875, -0.254150390625, 0.285400390625, -0.107177734375, -0.38134765625, -0.59326171875, 1.177734375, -0.328125, -0.11663818359375, 1.2236328125, 0.87646484375, -1.130859375, -0.82861328125, -0.393310546875, -0.06707763671875, 0.26708984375, -0.8798828125, 0.146728515625, 0.420166015625, -0.56787109375, 0.126708984375, 0.48681640625, -0.3681640625, 0.40625, 0.037567138671875, 0.274169921875, -0.34228515625, 0.313720703125, 0.703125, -0.21435546875, -0.3544921875, -0.9794921875, -0.33642578125, -0.230224609375, -0.0576171875, 0.95654296875, -0.20947265625, 0.405029296875, 0.35205078125, -0.1539306640625, 0.66748046875, -0.609375, -0.28955078125, 0.26220703125, -0.72412109375, -0.310302734375, -0.322265625, 0.44140625, 0.1602783203125, 0.751953125, -0.58056640625, 0.0267333984375, 0.27490234375, 0.44384765625, -0.397705078125, -0.935546875, -0.273193359375, -1.1533203125, -0.55517578125, -0.50390625, -0.6923828125, -0.01372528076171875, 0.57275390625, 0.176513671875, -0.623046875, -0.041595458984375, 0.2249755859375, -0.311279296875, 0.6923828125, -0.59326171875, 0.22021484375, -0.64794921875, -0.344482421875, -0.59619140625, 0.06280517578125, -0.83984375, -0.142333984375, -0.414794921875, 0.394775390625, -0.431396484375, 0.341552734375, -0.4091796875, 0.396484375, -0.1715087890625, -0.63134765625, -0.1396484375, 0.1719970703125, -0.673828125, 1.046875, 0.57080078125, 0.1455078125, 0.34521484375, -0.4990234375, -0.296630859375, -0.31298828125, 0.6123046875, 0.14013671875, -0.0026798248291015625, -0.297607421875, -0.07452392578125, 0.026336669921875, -1.0908203125, 0.29443359375, -0.13232421875, 0.0850830078125, 0.0972900390625, -0.23876953125, 0.465576171875, 1.2509765625, -0.3701171875, 0.39599609375, -0.090087890625, 0.397705078125, 0.443359375, 0.2335205078125, -0.092041015625, 0.8212890625, -0.20361328125, -0.58154296875, 0.1402587890625, 0.1871337890625, 0.1578369140625, 0.04315185546875, -0.388916015625, -0.8583984375, -0.9638671875, -0.224609375, -0.11358642578125, 0.432373046875, 0.5634765625, -0.2274169921875, 0.0099639892578125, -0.3720703125, -0.32470703125, -0.32177734375, -1.3505859375, -0.86767578125, 0.66162109375, -0.126708984375, -0.84375, 0.0214385986328125, -0.202880859375, -0.0936279296875, 0.10711669921875, 0.283447265625, -0.3759765625, 0.48193359375, -0.392822265625, 0.49658203125, -0.2587890625, -0.2227783203125, 0.0252685546875, 0.435791015625, -0.67578125, -0.71240234375, 0.27685546875, 0.9208984375, 0.0303192138671875, -0.35888671875, -0.66796875, 0.4404296875, -0.1474609375, -0.08502197265625, -0.52197265625, 0.399658203125, 0.0001615285873413086, 0.5009765625, -0.69189453125, 0.006313323974609375, -0.56640625, 0.48974609375, 0.1572265625, -0.669921875, -0.57470703125, 0.83935546875, 0.49755859375, -0.3330078125, 0.35302734375, -0.130615234375, 0.419189453125, -0.12493896484375, 0.06219482421875, -0.28662109375, 0.84521484375, 0.81494140625, 0.95068359375, -0.067138671875, 0.395751953125, 0.5986328125, 0.376708984375, 0.0181427001953125, 0.446533203125, 0.039947509765625, 0.014404296875, 0.063720703125, -0.1151123046875, -0.1099853515625, -0.300048828125, -0.67578125, 0.326904296875, -0.33154296875, 0.1650390625, -0.09881591796875, -0.720703125, 0.98486328125, -0.24951171875, -0.0738525390625, 0.09588623046875, -0.6376953125, 0.2421875, 0.6767578125, -0.225341796875, -0.3984375, 0.7119140625, 0.8173828125, 0.54443359375, 0.4677734375, 0.2327880859375, 0.55322265625, -0.68310546875, 0.127197265625, 0.402587890625, -0.0428466796875, -0.3056640625, -0.5673828125, -1.072265625, 0.494873046875, -0.654296875, -0.35400390625, 0.401123046875, -0.8837890625, 0.162353515625, -0.1458740234375, 0.8740234375, -0.354736328125, 0.1397705078125, 0.447509765625, -0.11798095703125, -0.541015625, 0.9404296875, -0.0107269287109375, 0.26220703125, -0.1514892578125, 1.31640625, 0.01111602783203125, 1.44140625, 0.93310546875, 0.041229248046875, 0.08380126953125, 0.462158203125, -0.380126953125, -0.62451171875, -0.27001953125, -0.414794921875, -0.116455078125, -0.724609375, -0.56005859375, -0.2900390625, 0.91455078125, -0.009185791015625, -0.78271484375, -0.332763671875, 0.266845703125, -0.8154296875, 0.414794921875, 0.288818359375, 0.39453125, 0.142822265625, -0.0806884765625, -0.48193359375, -0.5888671875, 0.5947265625, -0.529296875, 0.29638671875, -0.64892578125, -0.2310791015625, -0.4580078125, -0.66845703125, -0.312255859375, -0.2247314453125, -0.2442626953125, -0.8076171875, 0.50048828125, 0.263916015625, 0.4189453125, 0.261474609375, -0.5830078125, 0.1409912109375, 0.82470703125, 1.0947265625, -0.03179931640625, 0.7392578125, 0.417236328125, -0.253173828125, 0.06463623046875, -0.38525390625, 0.42822265625, 0.12322998046875, 0.431884765625, -0.341796875, 0.147216796875, -0.76904296875, -1.0498046875, 0.1356201171875, 0.521484375, 0.057861328125, -0.5693359375, -1.109375, -0.57861328125, -0.90283203125, -0.18212890625, -0.884765625, 0.67529296875, -0.286865234375, 0.1175537109375, -0.08203125, -0.9853515625, 4.38671875, 0.80078125, 0.931640625, 0.1728515625, 0.385009765625, 0.89501953125, 0.265625, -0.8046875, 0.00147247314453125, -0.393798828125, 0.93017578125, -0.29248046875, 0.1124267578125, 0.67529296875, 0.3193359375, 0.5498046875, -0.7685546875, -0.0239715576171875, 0.062469482421875, -1.2998046875, -0.56103515625, 0.29638671875, -0.09124755859375, 0.68310546875, -0.03411865234375, 0.1568603515625, 0.91064453125, -1.205078125, -0.372802734375, -0.83349609375, 0.429443359375, -0.150146484375, 0.68408203125, 0.260986328125, 0.00945281982421875, 0.74169921875, -0.2462158203125, -0.411376953125, -0.28662109375, 0.08343505859375, -0.2210693359375, -0.197509765625, 0.32177734375, -0.541015625, -0.281005859375, 0.2353515625, -0.6220703125, 0.71435546875, 0.08123779296875, -1.0068359375, 0.57275390625, 0.126220703125, 0.78125, -0.78125, -0.6689453125, 0.07940673828125, 0.458740234375, -0.12890625, -0.12188720703125, 0.6162109375, 0.317626953125, 0.8671875, -0.373779296875, 0.85400390625, -1.03515625, 0.837890625, -0.2275390625, 0.266845703125, -0.7294921875, 0.258544921875, -0.273681640625, -0.564453125, -0.331787109375, -0.66455078125, 0.5625, 0.1656494140625, -0.39453125, 0.61669921875, 0.7998046875, -0.383056640625, -0.0288543701171875, -0.437255859375, -0.33544921875, -0.332763671875, 0.578125, 1.2470703125, -0.429443359375, -0.267333984375, -0.1485595703125, 0.625, 0.431640625, 0.63525390625, 0.10198974609375, -0.54150390625, -0.450927734375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Submitted Solution: ``` def solve(a, b, s): l = map(lambda x: len(x), s.split('X')) tot = 0 mx = 0 for j in l: if j < b: continue if j < a: return 'NO' if j >= 2 * b: if mx > 0: return 'NO' mx = j tot += 1 if mx > 0: if a < 2 * b: one = mx >= a and mx <= a + 2 * b - 2 two = mx >= 2 * a and mx <= a + 3 * b - 2 three = mx >= 3 * a and mx <= a + 4 * b - 2 if not (one or two or three): return 'NO' if (one and two) or (two and three): return 'YES' if two: tot += 1 if a >= 2 * b: if not (mx >= a and mx <= a + 2 * b - 2): return 'NO' if tot % 2 == 1: return 'YES' else: return 'NO' q = int(input()) for i in range(q): a, b = map(int, input().split()) s = input() print(solve(a, b, s)) ``` Yes
106,230
[ 0.44287109375, 0.240478515625, -0.087890625, 0.341552734375, -0.591796875, -0.5078125, -0.1556396484375, 0.25732421875, 0.2320556640625, 0.87841796875, 0.70458984375, 0.2056884765625, 0.13916015625, -0.640625, -0.50146484375, -0.04205322265625, -0.654296875, -0.849609375, -0.380859375, -0.224365234375, 0.0240325927734375, -0.1005859375, -1.3369140625, 0.0732421875, -0.2235107421875, 0.7412109375, 0.1297607421875, -0.041015625, 0.88623046875, 1.02734375, -0.01287841796875, -0.466796875, 0.5283203125, -0.65869140625, -0.421142578125, -0.397705078125, 0.76708984375, -0.69775390625, -0.2042236328125, -0.515625, 0.24169921875, -0.423828125, 0.45751953125, -0.60791015625, -1.3544921875, 0.0294342041015625, -0.193115234375, -0.50634765625, -0.216552734375, -0.48974609375, 0.10821533203125, -0.395263671875, 0.303955078125, -0.290283203125, 0.22119140625, 0.272216796875, 0.058868408203125, 0.0958251953125, -0.765625, 0.1998291015625, 0.338623046875, -0.24658203125, -0.019744873046875, -0.92822265625, 0.0936279296875, 0.044525146484375, 0.225830078125, -0.462890625, 0.2509765625, -0.5712890625, -0.205810546875, -0.1949462890625, -0.64697265625, -0.317626953125, -0.1839599609375, 0.428466796875, 0.361328125, -0.10089111328125, -0.95947265625, 0.7646484375, -0.230224609375, 0.94482421875, 0.63525390625, 0.008575439453125, -0.306884765625, -0.478271484375, 0.47021484375, 0.26513671875, 0.43359375, -0.259033203125, -0.054290771484375, 0.5107421875, -0.331787109375, -0.167724609375, 0.34814453125, 0.8525390625, -0.1483154296875, 0.124267578125, 0.6689453125, -0.1033935546875, 0.57763671875, 0.69287109375, -0.50634765625, 1.12890625, -0.447021484375, -0.009674072265625, 0.380126953125, -0.0626220703125, -0.0260467529296875, -0.5029296875, -0.192626953125, -0.473876953125, 0.66015625, 0.382568359375, -0.564453125, 0.876953125, 0.10308837890625, 0.413818359375, -0.61572265625, -0.002712249755859375, 0.72119140625, -0.029205322265625, 0.54931640625, -0.0478515625, 0.1151123046875, -0.276123046875, -0.6298828125, 1.001953125, -0.56494140625, -0.2529296875, 0.57421875, -0.064208984375, -0.25244140625, 0.362548828125, -0.2763671875, 0.75, -0.151611328125, 0.461669921875, 0.76953125, -0.62841796875, 0.9716796875, -0.0301666259765625, 0.2265625, 1.4716796875, 0.24951171875, -0.2176513671875, 0.3701171875, 0.5263671875, -0.85595703125, 0.3525390625, -1.05078125, 0.6015625, -0.045562744140625, 0.200927734375, -0.266357421875, -0.2261962890625, -0.333984375, 0.52392578125, 0.335205078125, -0.0050048828125, -0.14208984375, 0.5625, -0.54736328125, 0.72705078125, -0.328125, 0.6953125, -0.386962890625, -0.2027587890625, -0.005481719970703125, -0.266845703125, 0.06683349609375, -0.376708984375, 0.14501953125, 0.7578125, 0.5234375, 1.35546875, 1.2919921875, -0.226318359375, 0.364990234375, 0.423095703125, -0.52685546875, 0.3935546875, 0.38330078125, 1.0556640625, 0.416748046875, 0.461181640625, 0.0469970703125, 0.093017578125, -0.7236328125, -0.385009765625, 0.1390380859375, 0.67041015625, -0.475341796875, 0.3740234375, 0.248779296875, 0.1494140625, -0.91796875, -0.210693359375, 0.0303802490234375, -0.8173828125, -0.54638671875, 0.41015625, 0.03704833984375, 0.4140625, -0.65185546875, -0.638671875, 0.1275634765625, 1.146484375, -0.341796875, -0.109619140625, 0.4697265625, 0.30615234375, 0.0167999267578125, -0.22119140625, 0.00995635986328125, -0.014801025390625, -0.6767578125, 0.98046875, 0.039337158203125, -0.148681640625, 0.11639404296875, 0.70849609375, 0.1844482421875, 0.75146484375, -0.626953125, -0.384521484375, 0.4619140625, 1.0947265625, 0.09918212890625, 0.74462890625, 0.55419921875, 1.1552734375, 0.326904296875, 0.86474609375, 0.306884765625, 0.264892578125, 0.76708984375, 0.91015625, -0.2357177734375, -0.01302337646484375, 0.221435546875, 0.467529296875, 0.1466064453125, 0.638671875, 0.29638671875, 0.44775390625, -0.18115234375, 0.032867431640625, -0.6728515625, 0.1142578125, -0.2978515625, 0.50439453125, 0.2052001953125, 0.6064453125, -0.442626953125, -0.1087646484375, 0.3681640625, 0.978515625, -1.1103515625, -0.6884765625, 0.042022705078125, -0.03961181640625, -0.0960693359375, 0.051849365234375, 0.57666015625, 0.0285797119140625, 0.42529296875, 0.408203125, -0.366455078125, -0.63623046875, -0.7861328125, -0.740234375, -0.896484375, -0.40185546875, -0.5849609375, -0.234619140625, 0.1978759765625, -0.978515625, -0.07916259765625, -0.5234375, -0.047027587890625, 0.1627197265625, -0.5322265625, 1.03125, -0.5634765625, 0.5048828125, -0.81396484375, 0.235595703125, 0.427001953125, 1.072265625, -0.430908203125, -0.108642578125, -0.1849365234375, -0.31787109375, 0.196044921875, -0.17626953125, 0.4287109375, -0.0341796875, -0.43115234375, -0.7578125, -0.4189453125, -0.16748046875, -0.476318359375, 0.2705078125, -0.6591796875, 0.80517578125, 0.5, -0.52197265625, 0.673828125, 1.0166015625, -0.59716796875, 0.53466796875, 0.1663818359375, 0.1090087890625, -0.65869140625, 1.3125, 0.6787109375, 0.400390625, -0.42138671875, -0.533203125, -0.3681640625, -0.281005859375, 0.338623046875, -0.546875, -0.63623046875, 0.6552734375, 0.0238494873046875, -1.0849609375, 0.1781005859375, -1.0458984375, -0.619140625, -0.237060546875, -0.496826171875, 0.84423828125, 0.80908203125, 0.254638671875, -0.05657958984375, -0.400390625, 0.1473388671875, 0.42138671875, 0.40576171875, -0.8291015625, 0.263671875, 0.7724609375, 0.05462646484375, 0.34521484375, 0.343994140625, -0.3359375, -0.031402587890625, -0.01007080078125, -0.2374267578125, 0.65625, 0.108642578125, 0.2283935546875, 0.390625, 0.472900390625, -0.826171875, -0.1346435546875, -0.30712890625, 0.515625, 0.45068359375, 0.56982421875, 0.305419921875, -0.258544921875, -0.72216796875, -1.0166015625, 0.368896484375, 0.062347412109375, 0.7314453125, -0.5927734375, 0.89990234375, -0.059295654296875, -0.3046875, 0.488525390625, -0.66357421875, 0.0909423828125, 1.1416015625, -0.301513671875, 0.4501953125, -0.70166015625, 0.44921875, 0.12115478515625, 0.138671875, 0.49267578125, 0.23193359375, 0.77294921875, -0.27099609375, -0.54150390625, -0.485595703125, -0.1568603515625, -0.0576171875, -0.7685546875, 0.2191162109375, -0.57080078125, -0.412841796875, -0.7265625, 0.4306640625, 0.82275390625, 1.0576171875, -0.01462554931640625, 0.59326171875, -0.1046142578125, 0.29931640625, 0.56005859375, -0.52392578125, 0.16845703125, -0.5673828125, 0.70751953125, 0.48779296875, 0.171875, -0.62451171875, 0.061126708984375, -0.2076416015625, -0.23046875, 0.12109375, -0.319580078125, -1.0693359375, 0.25537109375, -0.171630859375, 0.59228515625, -0.59765625, -0.344970703125, -0.11004638671875, 0.467529296875, 0.5439453125, -0.73779296875, 0.2127685546875, -1.1064453125, 0.68310546875, 0.359619140625, -0.250732421875, -0.388916015625, -0.5078125, -0.79638671875, -1.095703125, -0.06903076171875, 1.0439453125, 0.11712646484375, 0.380615234375, -1.15625, 0.400634765625, -0.051910400390625, -0.54736328125, 0.1885986328125, -0.3291015625, 0.283935546875, -0.0477294921875, 0.728515625, -0.73974609375, -0.564453125, -0.0182342529296875, -0.95263671875, 0.57080078125, -0.443359375, 0.4169921875, -0.0197601318359375, -0.16552734375, -0.115234375, 0.378662109375, -0.187744140625, 0.28515625, -0.345703125, 0.30908203125, -0.89794921875, -0.4453125, 0.6748046875, -0.2196044921875, -0.179443359375, 0.7548828125, -0.2169189453125, -0.5322265625, 0.1552734375, 0.48486328125, -0.3779296875, 0.537109375, -0.39892578125, 0.408935546875, -0.172119140625, -0.404296875, -0.177001953125, -0.70849609375, 0.8623046875, 0.210205078125, -0.57373046875, -0.474853515625, -0.92138671875, -0.185546875, 0.00908660888671875, -0.196044921875, 0.60400390625, 0.1722412109375, 0.08056640625, -0.06256103515625, -0.221923828125, -0.5810546875, -0.0670166015625, -0.348388671875, 0.01152801513671875, 0.047821044921875, 0.4052734375, 0.404296875, -0.056060791015625, -0.5, -0.4111328125, -0.2340087890625, 0.1390380859375, -0.54345703125, -0.375, -0.235595703125, -0.2890625, -0.63916015625, 0.280517578125, -0.1246337890625, 0.51611328125, 1.0166015625, -0.01617431640625, 0.65869140625, 0.304931640625, -0.9775390625, 1.13671875, 0.203125, -1.2138671875, -0.69677734375, 0.299560546875, 0.10009765625, 0.68359375, 0.1942138671875, -0.481201171875, -0.8681640625, -0.9501953125, 0.2027587890625, -0.88720703125, -0.245849609375, -1.212890625, -0.5361328125, -0.378662109375, 0.4365234375, -0.0665283203125, -0.67724609375, 0.2626953125, -1.0625, 0.38134765625, -0.95947265625, 0.104248046875, -0.7236328125, -0.4853515625, -0.2052001953125, 1.060546875, 0.23876953125, 0.625, 0.0013666152954101562, -0.30126953125, 0.1019287109375, 0.1982421875, -0.5126953125, -0.475830078125, 0.201171875, -0.051849365234375, -0.277099609375, -0.291259765625, -0.5068359375, 0.61474609375, -0.72216796875, 0.42919921875, -0.051910400390625, -0.298583984375, -0.12005615234375, -0.41796875, 1.0888671875, -0.348876953125, 0.1973876953125, -0.4853515625, 0.226806640625, 0.6552734375, -0.2210693359375, -0.30322265625, -0.3466796875, -0.491455078125, -1.25390625, 0.490234375, -0.368408203125, 0.080810546875, -0.7939453125, -0.2174072265625, 1.3291015625, -0.564453125, 0.268310546875, 1.455078125, 0.1661376953125, 0.2191162109375, -0.498046875, 0.671875, 0.7080078125, -0.428955078125, -0.1109619140625, 0.12261962890625, -0.65869140625, -0.118896484375, -0.394775390625, -1.1728515625, -0.77197265625, 0.457275390625, 1.154296875, -0.45263671875, 0.88037109375, -0.24462890625, -1.107421875, -0.591796875, 0.78955078125, -0.1331787109375, 0.240234375, 0.86181640625, 0.28466796875, -0.254150390625, 0.285400390625, -0.107177734375, -0.38134765625, -0.59326171875, 1.177734375, -0.328125, -0.11663818359375, 1.2236328125, 0.87646484375, -1.130859375, -0.82861328125, -0.393310546875, -0.06707763671875, 0.26708984375, -0.8798828125, 0.146728515625, 0.420166015625, -0.56787109375, 0.126708984375, 0.48681640625, -0.3681640625, 0.40625, 0.037567138671875, 0.274169921875, -0.34228515625, 0.313720703125, 0.703125, -0.21435546875, -0.3544921875, -0.9794921875, -0.33642578125, -0.230224609375, -0.0576171875, 0.95654296875, -0.20947265625, 0.405029296875, 0.35205078125, -0.1539306640625, 0.66748046875, -0.609375, -0.28955078125, 0.26220703125, -0.72412109375, -0.310302734375, -0.322265625, 0.44140625, 0.1602783203125, 0.751953125, -0.58056640625, 0.0267333984375, 0.27490234375, 0.44384765625, -0.397705078125, -0.935546875, -0.273193359375, -1.1533203125, -0.55517578125, -0.50390625, -0.6923828125, -0.01372528076171875, 0.57275390625, 0.176513671875, -0.623046875, -0.041595458984375, 0.2249755859375, -0.311279296875, 0.6923828125, -0.59326171875, 0.22021484375, -0.64794921875, -0.344482421875, -0.59619140625, 0.06280517578125, -0.83984375, -0.142333984375, -0.414794921875, 0.394775390625, -0.431396484375, 0.341552734375, -0.4091796875, 0.396484375, -0.1715087890625, -0.63134765625, -0.1396484375, 0.1719970703125, -0.673828125, 1.046875, 0.57080078125, 0.1455078125, 0.34521484375, -0.4990234375, -0.296630859375, -0.31298828125, 0.6123046875, 0.14013671875, -0.0026798248291015625, -0.297607421875, -0.07452392578125, 0.026336669921875, -1.0908203125, 0.29443359375, -0.13232421875, 0.0850830078125, 0.0972900390625, -0.23876953125, 0.465576171875, 1.2509765625, -0.3701171875, 0.39599609375, -0.090087890625, 0.397705078125, 0.443359375, 0.2335205078125, -0.092041015625, 0.8212890625, -0.20361328125, -0.58154296875, 0.1402587890625, 0.1871337890625, 0.1578369140625, 0.04315185546875, -0.388916015625, -0.8583984375, -0.9638671875, -0.224609375, -0.11358642578125, 0.432373046875, 0.5634765625, -0.2274169921875, 0.0099639892578125, -0.3720703125, -0.32470703125, -0.32177734375, -1.3505859375, -0.86767578125, 0.66162109375, -0.126708984375, -0.84375, 0.0214385986328125, -0.202880859375, -0.0936279296875, 0.10711669921875, 0.283447265625, -0.3759765625, 0.48193359375, -0.392822265625, 0.49658203125, -0.2587890625, -0.2227783203125, 0.0252685546875, 0.435791015625, -0.67578125, -0.71240234375, 0.27685546875, 0.9208984375, 0.0303192138671875, -0.35888671875, -0.66796875, 0.4404296875, -0.1474609375, -0.08502197265625, -0.52197265625, 0.399658203125, 0.0001615285873413086, 0.5009765625, -0.69189453125, 0.006313323974609375, -0.56640625, 0.48974609375, 0.1572265625, -0.669921875, -0.57470703125, 0.83935546875, 0.49755859375, -0.3330078125, 0.35302734375, -0.130615234375, 0.419189453125, -0.12493896484375, 0.06219482421875, -0.28662109375, 0.84521484375, 0.81494140625, 0.95068359375, -0.067138671875, 0.395751953125, 0.5986328125, 0.376708984375, 0.0181427001953125, 0.446533203125, 0.039947509765625, 0.014404296875, 0.063720703125, -0.1151123046875, -0.1099853515625, -0.300048828125, -0.67578125, 0.326904296875, -0.33154296875, 0.1650390625, -0.09881591796875, -0.720703125, 0.98486328125, -0.24951171875, -0.0738525390625, 0.09588623046875, -0.6376953125, 0.2421875, 0.6767578125, -0.225341796875, -0.3984375, 0.7119140625, 0.8173828125, 0.54443359375, 0.4677734375, 0.2327880859375, 0.55322265625, -0.68310546875, 0.127197265625, 0.402587890625, -0.0428466796875, -0.3056640625, -0.5673828125, -1.072265625, 0.494873046875, -0.654296875, -0.35400390625, 0.401123046875, -0.8837890625, 0.162353515625, -0.1458740234375, 0.8740234375, -0.354736328125, 0.1397705078125, 0.447509765625, -0.11798095703125, -0.541015625, 0.9404296875, -0.0107269287109375, 0.26220703125, -0.1514892578125, 1.31640625, 0.01111602783203125, 1.44140625, 0.93310546875, 0.041229248046875, 0.08380126953125, 0.462158203125, -0.380126953125, -0.62451171875, -0.27001953125, -0.414794921875, -0.116455078125, -0.724609375, -0.56005859375, -0.2900390625, 0.91455078125, -0.009185791015625, -0.78271484375, -0.332763671875, 0.266845703125, -0.8154296875, 0.414794921875, 0.288818359375, 0.39453125, 0.142822265625, -0.0806884765625, -0.48193359375, -0.5888671875, 0.5947265625, -0.529296875, 0.29638671875, -0.64892578125, -0.2310791015625, -0.4580078125, -0.66845703125, -0.312255859375, -0.2247314453125, -0.2442626953125, -0.8076171875, 0.50048828125, 0.263916015625, 0.4189453125, 0.261474609375, -0.5830078125, 0.1409912109375, 0.82470703125, 1.0947265625, -0.03179931640625, 0.7392578125, 0.417236328125, -0.253173828125, 0.06463623046875, -0.38525390625, 0.42822265625, 0.12322998046875, 0.431884765625, -0.341796875, 0.147216796875, -0.76904296875, -1.0498046875, 0.1356201171875, 0.521484375, 0.057861328125, -0.5693359375, -1.109375, -0.57861328125, -0.90283203125, -0.18212890625, -0.884765625, 0.67529296875, -0.286865234375, 0.1175537109375, -0.08203125, -0.9853515625, 4.38671875, 0.80078125, 0.931640625, 0.1728515625, 0.385009765625, 0.89501953125, 0.265625, -0.8046875, 0.00147247314453125, -0.393798828125, 0.93017578125, -0.29248046875, 0.1124267578125, 0.67529296875, 0.3193359375, 0.5498046875, -0.7685546875, -0.0239715576171875, 0.062469482421875, -1.2998046875, -0.56103515625, 0.29638671875, -0.09124755859375, 0.68310546875, -0.03411865234375, 0.1568603515625, 0.91064453125, -1.205078125, -0.372802734375, -0.83349609375, 0.429443359375, -0.150146484375, 0.68408203125, 0.260986328125, 0.00945281982421875, 0.74169921875, -0.2462158203125, -0.411376953125, -0.28662109375, 0.08343505859375, -0.2210693359375, -0.197509765625, 0.32177734375, -0.541015625, -0.281005859375, 0.2353515625, -0.6220703125, 0.71435546875, 0.08123779296875, -1.0068359375, 0.57275390625, 0.126220703125, 0.78125, -0.78125, -0.6689453125, 0.07940673828125, 0.458740234375, -0.12890625, -0.12188720703125, 0.6162109375, 0.317626953125, 0.8671875, -0.373779296875, 0.85400390625, -1.03515625, 0.837890625, -0.2275390625, 0.266845703125, -0.7294921875, 0.258544921875, -0.273681640625, -0.564453125, -0.331787109375, -0.66455078125, 0.5625, 0.1656494140625, -0.39453125, 0.61669921875, 0.7998046875, -0.383056640625, -0.0288543701171875, -0.437255859375, -0.33544921875, -0.332763671875, 0.578125, 1.2470703125, -0.429443359375, -0.267333984375, -0.1485595703125, 0.625, 0.431640625, 0.63525390625, 0.10198974609375, -0.54150390625, -0.450927734375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Submitted Solution: ``` def main(): import sys input = sys.stdin.readline q = int(input()) for _ in range(q): a, b = map(int, input().split()) S = input().rstrip('\n') S += '!' win = 1 cnt = 0 flg = 0 num = 0 for s in S: if s == '.': cnt += 1 else: if cnt: if b <= cnt < a: win = 0 break elif cnt < b: pass elif cnt < 2*b: num += 1 else: num += 1 if flg: flg = 2 win = 0 break else: flg = 1 tmp = cnt cnt = 0 if flg == 1: if num % 2 == 0: if a >= 2*b: win = 0 else: if not 2*a <= tmp <= a+3*b-2: win = 0 else: if tmp <= a+2*b-2: pass elif 3*a <= tmp <= a+4*b-2: pass else: win = 0 elif flg == 0: if num % 2 == 0: win = 0 if win: print('Yes') else: print('No') if __name__ == '__main__': main() ``` Yes
106,231
[ 0.44287109375, 0.240478515625, -0.087890625, 0.341552734375, -0.591796875, -0.5078125, -0.1556396484375, 0.25732421875, 0.2320556640625, 0.87841796875, 0.70458984375, 0.2056884765625, 0.13916015625, -0.640625, -0.50146484375, -0.04205322265625, -0.654296875, -0.849609375, -0.380859375, -0.224365234375, 0.0240325927734375, -0.1005859375, -1.3369140625, 0.0732421875, -0.2235107421875, 0.7412109375, 0.1297607421875, -0.041015625, 0.88623046875, 1.02734375, -0.01287841796875, -0.466796875, 0.5283203125, -0.65869140625, -0.421142578125, -0.397705078125, 0.76708984375, -0.69775390625, -0.2042236328125, -0.515625, 0.24169921875, -0.423828125, 0.45751953125, -0.60791015625, -1.3544921875, 0.0294342041015625, -0.193115234375, -0.50634765625, -0.216552734375, -0.48974609375, 0.10821533203125, -0.395263671875, 0.303955078125, -0.290283203125, 0.22119140625, 0.272216796875, 0.058868408203125, 0.0958251953125, -0.765625, 0.1998291015625, 0.338623046875, -0.24658203125, -0.019744873046875, -0.92822265625, 0.0936279296875, 0.044525146484375, 0.225830078125, -0.462890625, 0.2509765625, -0.5712890625, -0.205810546875, -0.1949462890625, -0.64697265625, -0.317626953125, -0.1839599609375, 0.428466796875, 0.361328125, -0.10089111328125, -0.95947265625, 0.7646484375, -0.230224609375, 0.94482421875, 0.63525390625, 0.008575439453125, -0.306884765625, -0.478271484375, 0.47021484375, 0.26513671875, 0.43359375, -0.259033203125, -0.054290771484375, 0.5107421875, -0.331787109375, -0.167724609375, 0.34814453125, 0.8525390625, -0.1483154296875, 0.124267578125, 0.6689453125, -0.1033935546875, 0.57763671875, 0.69287109375, -0.50634765625, 1.12890625, -0.447021484375, -0.009674072265625, 0.380126953125, -0.0626220703125, -0.0260467529296875, -0.5029296875, -0.192626953125, -0.473876953125, 0.66015625, 0.382568359375, -0.564453125, 0.876953125, 0.10308837890625, 0.413818359375, -0.61572265625, -0.002712249755859375, 0.72119140625, -0.029205322265625, 0.54931640625, -0.0478515625, 0.1151123046875, -0.276123046875, -0.6298828125, 1.001953125, -0.56494140625, -0.2529296875, 0.57421875, -0.064208984375, -0.25244140625, 0.362548828125, -0.2763671875, 0.75, -0.151611328125, 0.461669921875, 0.76953125, -0.62841796875, 0.9716796875, -0.0301666259765625, 0.2265625, 1.4716796875, 0.24951171875, -0.2176513671875, 0.3701171875, 0.5263671875, -0.85595703125, 0.3525390625, -1.05078125, 0.6015625, -0.045562744140625, 0.200927734375, -0.266357421875, -0.2261962890625, -0.333984375, 0.52392578125, 0.335205078125, -0.0050048828125, -0.14208984375, 0.5625, -0.54736328125, 0.72705078125, -0.328125, 0.6953125, -0.386962890625, -0.2027587890625, -0.005481719970703125, -0.266845703125, 0.06683349609375, -0.376708984375, 0.14501953125, 0.7578125, 0.5234375, 1.35546875, 1.2919921875, -0.226318359375, 0.364990234375, 0.423095703125, -0.52685546875, 0.3935546875, 0.38330078125, 1.0556640625, 0.416748046875, 0.461181640625, 0.0469970703125, 0.093017578125, -0.7236328125, -0.385009765625, 0.1390380859375, 0.67041015625, -0.475341796875, 0.3740234375, 0.248779296875, 0.1494140625, -0.91796875, -0.210693359375, 0.0303802490234375, -0.8173828125, -0.54638671875, 0.41015625, 0.03704833984375, 0.4140625, -0.65185546875, -0.638671875, 0.1275634765625, 1.146484375, -0.341796875, -0.109619140625, 0.4697265625, 0.30615234375, 0.0167999267578125, -0.22119140625, 0.00995635986328125, -0.014801025390625, -0.6767578125, 0.98046875, 0.039337158203125, -0.148681640625, 0.11639404296875, 0.70849609375, 0.1844482421875, 0.75146484375, -0.626953125, -0.384521484375, 0.4619140625, 1.0947265625, 0.09918212890625, 0.74462890625, 0.55419921875, 1.1552734375, 0.326904296875, 0.86474609375, 0.306884765625, 0.264892578125, 0.76708984375, 0.91015625, -0.2357177734375, -0.01302337646484375, 0.221435546875, 0.467529296875, 0.1466064453125, 0.638671875, 0.29638671875, 0.44775390625, -0.18115234375, 0.032867431640625, -0.6728515625, 0.1142578125, -0.2978515625, 0.50439453125, 0.2052001953125, 0.6064453125, -0.442626953125, -0.1087646484375, 0.3681640625, 0.978515625, -1.1103515625, -0.6884765625, 0.042022705078125, -0.03961181640625, -0.0960693359375, 0.051849365234375, 0.57666015625, 0.0285797119140625, 0.42529296875, 0.408203125, -0.366455078125, -0.63623046875, -0.7861328125, -0.740234375, -0.896484375, -0.40185546875, -0.5849609375, -0.234619140625, 0.1978759765625, -0.978515625, -0.07916259765625, -0.5234375, -0.047027587890625, 0.1627197265625, -0.5322265625, 1.03125, -0.5634765625, 0.5048828125, -0.81396484375, 0.235595703125, 0.427001953125, 1.072265625, -0.430908203125, -0.108642578125, -0.1849365234375, -0.31787109375, 0.196044921875, -0.17626953125, 0.4287109375, -0.0341796875, -0.43115234375, -0.7578125, -0.4189453125, -0.16748046875, -0.476318359375, 0.2705078125, -0.6591796875, 0.80517578125, 0.5, -0.52197265625, 0.673828125, 1.0166015625, -0.59716796875, 0.53466796875, 0.1663818359375, 0.1090087890625, -0.65869140625, 1.3125, 0.6787109375, 0.400390625, -0.42138671875, -0.533203125, -0.3681640625, -0.281005859375, 0.338623046875, -0.546875, -0.63623046875, 0.6552734375, 0.0238494873046875, -1.0849609375, 0.1781005859375, -1.0458984375, -0.619140625, -0.237060546875, -0.496826171875, 0.84423828125, 0.80908203125, 0.254638671875, -0.05657958984375, -0.400390625, 0.1473388671875, 0.42138671875, 0.40576171875, -0.8291015625, 0.263671875, 0.7724609375, 0.05462646484375, 0.34521484375, 0.343994140625, -0.3359375, -0.031402587890625, -0.01007080078125, -0.2374267578125, 0.65625, 0.108642578125, 0.2283935546875, 0.390625, 0.472900390625, -0.826171875, -0.1346435546875, -0.30712890625, 0.515625, 0.45068359375, 0.56982421875, 0.305419921875, -0.258544921875, -0.72216796875, -1.0166015625, 0.368896484375, 0.062347412109375, 0.7314453125, -0.5927734375, 0.89990234375, -0.059295654296875, -0.3046875, 0.488525390625, -0.66357421875, 0.0909423828125, 1.1416015625, -0.301513671875, 0.4501953125, -0.70166015625, 0.44921875, 0.12115478515625, 0.138671875, 0.49267578125, 0.23193359375, 0.77294921875, -0.27099609375, -0.54150390625, -0.485595703125, -0.1568603515625, -0.0576171875, -0.7685546875, 0.2191162109375, -0.57080078125, -0.412841796875, -0.7265625, 0.4306640625, 0.82275390625, 1.0576171875, -0.01462554931640625, 0.59326171875, -0.1046142578125, 0.29931640625, 0.56005859375, -0.52392578125, 0.16845703125, -0.5673828125, 0.70751953125, 0.48779296875, 0.171875, -0.62451171875, 0.061126708984375, -0.2076416015625, -0.23046875, 0.12109375, -0.319580078125, -1.0693359375, 0.25537109375, -0.171630859375, 0.59228515625, -0.59765625, -0.344970703125, -0.11004638671875, 0.467529296875, 0.5439453125, -0.73779296875, 0.2127685546875, -1.1064453125, 0.68310546875, 0.359619140625, -0.250732421875, -0.388916015625, -0.5078125, -0.79638671875, -1.095703125, -0.06903076171875, 1.0439453125, 0.11712646484375, 0.380615234375, -1.15625, 0.400634765625, -0.051910400390625, -0.54736328125, 0.1885986328125, -0.3291015625, 0.283935546875, -0.0477294921875, 0.728515625, -0.73974609375, -0.564453125, -0.0182342529296875, -0.95263671875, 0.57080078125, -0.443359375, 0.4169921875, -0.0197601318359375, -0.16552734375, -0.115234375, 0.378662109375, -0.187744140625, 0.28515625, -0.345703125, 0.30908203125, -0.89794921875, -0.4453125, 0.6748046875, -0.2196044921875, -0.179443359375, 0.7548828125, -0.2169189453125, -0.5322265625, 0.1552734375, 0.48486328125, -0.3779296875, 0.537109375, -0.39892578125, 0.408935546875, -0.172119140625, -0.404296875, -0.177001953125, -0.70849609375, 0.8623046875, 0.210205078125, -0.57373046875, -0.474853515625, -0.92138671875, -0.185546875, 0.00908660888671875, -0.196044921875, 0.60400390625, 0.1722412109375, 0.08056640625, -0.06256103515625, -0.221923828125, -0.5810546875, -0.0670166015625, -0.348388671875, 0.01152801513671875, 0.047821044921875, 0.4052734375, 0.404296875, -0.056060791015625, -0.5, -0.4111328125, -0.2340087890625, 0.1390380859375, -0.54345703125, -0.375, -0.235595703125, -0.2890625, -0.63916015625, 0.280517578125, -0.1246337890625, 0.51611328125, 1.0166015625, -0.01617431640625, 0.65869140625, 0.304931640625, -0.9775390625, 1.13671875, 0.203125, -1.2138671875, -0.69677734375, 0.299560546875, 0.10009765625, 0.68359375, 0.1942138671875, -0.481201171875, -0.8681640625, -0.9501953125, 0.2027587890625, -0.88720703125, -0.245849609375, -1.212890625, -0.5361328125, -0.378662109375, 0.4365234375, -0.0665283203125, -0.67724609375, 0.2626953125, -1.0625, 0.38134765625, -0.95947265625, 0.104248046875, -0.7236328125, -0.4853515625, -0.2052001953125, 1.060546875, 0.23876953125, 0.625, 0.0013666152954101562, -0.30126953125, 0.1019287109375, 0.1982421875, -0.5126953125, -0.475830078125, 0.201171875, -0.051849365234375, -0.277099609375, -0.291259765625, -0.5068359375, 0.61474609375, -0.72216796875, 0.42919921875, -0.051910400390625, -0.298583984375, -0.12005615234375, -0.41796875, 1.0888671875, -0.348876953125, 0.1973876953125, -0.4853515625, 0.226806640625, 0.6552734375, -0.2210693359375, -0.30322265625, -0.3466796875, -0.491455078125, -1.25390625, 0.490234375, -0.368408203125, 0.080810546875, -0.7939453125, -0.2174072265625, 1.3291015625, -0.564453125, 0.268310546875, 1.455078125, 0.1661376953125, 0.2191162109375, -0.498046875, 0.671875, 0.7080078125, -0.428955078125, -0.1109619140625, 0.12261962890625, -0.65869140625, -0.118896484375, -0.394775390625, -1.1728515625, -0.77197265625, 0.457275390625, 1.154296875, -0.45263671875, 0.88037109375, -0.24462890625, -1.107421875, -0.591796875, 0.78955078125, -0.1331787109375, 0.240234375, 0.86181640625, 0.28466796875, -0.254150390625, 0.285400390625, -0.107177734375, -0.38134765625, -0.59326171875, 1.177734375, -0.328125, -0.11663818359375, 1.2236328125, 0.87646484375, -1.130859375, -0.82861328125, -0.393310546875, -0.06707763671875, 0.26708984375, -0.8798828125, 0.146728515625, 0.420166015625, -0.56787109375, 0.126708984375, 0.48681640625, -0.3681640625, 0.40625, 0.037567138671875, 0.274169921875, -0.34228515625, 0.313720703125, 0.703125, -0.21435546875, -0.3544921875, -0.9794921875, -0.33642578125, -0.230224609375, -0.0576171875, 0.95654296875, -0.20947265625, 0.405029296875, 0.35205078125, -0.1539306640625, 0.66748046875, -0.609375, -0.28955078125, 0.26220703125, -0.72412109375, -0.310302734375, -0.322265625, 0.44140625, 0.1602783203125, 0.751953125, -0.58056640625, 0.0267333984375, 0.27490234375, 0.44384765625, -0.397705078125, -0.935546875, -0.273193359375, -1.1533203125, -0.55517578125, -0.50390625, -0.6923828125, -0.01372528076171875, 0.57275390625, 0.176513671875, -0.623046875, -0.041595458984375, 0.2249755859375, -0.311279296875, 0.6923828125, -0.59326171875, 0.22021484375, -0.64794921875, -0.344482421875, -0.59619140625, 0.06280517578125, -0.83984375, -0.142333984375, -0.414794921875, 0.394775390625, -0.431396484375, 0.341552734375, -0.4091796875, 0.396484375, -0.1715087890625, -0.63134765625, -0.1396484375, 0.1719970703125, -0.673828125, 1.046875, 0.57080078125, 0.1455078125, 0.34521484375, -0.4990234375, -0.296630859375, -0.31298828125, 0.6123046875, 0.14013671875, -0.0026798248291015625, -0.297607421875, -0.07452392578125, 0.026336669921875, -1.0908203125, 0.29443359375, -0.13232421875, 0.0850830078125, 0.0972900390625, -0.23876953125, 0.465576171875, 1.2509765625, -0.3701171875, 0.39599609375, -0.090087890625, 0.397705078125, 0.443359375, 0.2335205078125, -0.092041015625, 0.8212890625, -0.20361328125, -0.58154296875, 0.1402587890625, 0.1871337890625, 0.1578369140625, 0.04315185546875, -0.388916015625, -0.8583984375, -0.9638671875, -0.224609375, -0.11358642578125, 0.432373046875, 0.5634765625, -0.2274169921875, 0.0099639892578125, -0.3720703125, -0.32470703125, -0.32177734375, -1.3505859375, -0.86767578125, 0.66162109375, -0.126708984375, -0.84375, 0.0214385986328125, -0.202880859375, -0.0936279296875, 0.10711669921875, 0.283447265625, -0.3759765625, 0.48193359375, -0.392822265625, 0.49658203125, -0.2587890625, -0.2227783203125, 0.0252685546875, 0.435791015625, -0.67578125, -0.71240234375, 0.27685546875, 0.9208984375, 0.0303192138671875, -0.35888671875, -0.66796875, 0.4404296875, -0.1474609375, -0.08502197265625, -0.52197265625, 0.399658203125, 0.0001615285873413086, 0.5009765625, -0.69189453125, 0.006313323974609375, -0.56640625, 0.48974609375, 0.1572265625, -0.669921875, -0.57470703125, 0.83935546875, 0.49755859375, -0.3330078125, 0.35302734375, -0.130615234375, 0.419189453125, -0.12493896484375, 0.06219482421875, -0.28662109375, 0.84521484375, 0.81494140625, 0.95068359375, -0.067138671875, 0.395751953125, 0.5986328125, 0.376708984375, 0.0181427001953125, 0.446533203125, 0.039947509765625, 0.014404296875, 0.063720703125, -0.1151123046875, -0.1099853515625, -0.300048828125, -0.67578125, 0.326904296875, -0.33154296875, 0.1650390625, -0.09881591796875, -0.720703125, 0.98486328125, -0.24951171875, -0.0738525390625, 0.09588623046875, -0.6376953125, 0.2421875, 0.6767578125, -0.225341796875, -0.3984375, 0.7119140625, 0.8173828125, 0.54443359375, 0.4677734375, 0.2327880859375, 0.55322265625, -0.68310546875, 0.127197265625, 0.402587890625, -0.0428466796875, -0.3056640625, -0.5673828125, -1.072265625, 0.494873046875, -0.654296875, -0.35400390625, 0.401123046875, -0.8837890625, 0.162353515625, -0.1458740234375, 0.8740234375, -0.354736328125, 0.1397705078125, 0.447509765625, -0.11798095703125, -0.541015625, 0.9404296875, -0.0107269287109375, 0.26220703125, -0.1514892578125, 1.31640625, 0.01111602783203125, 1.44140625, 0.93310546875, 0.041229248046875, 0.08380126953125, 0.462158203125, -0.380126953125, -0.62451171875, -0.27001953125, -0.414794921875, -0.116455078125, -0.724609375, -0.56005859375, -0.2900390625, 0.91455078125, -0.009185791015625, -0.78271484375, -0.332763671875, 0.266845703125, -0.8154296875, 0.414794921875, 0.288818359375, 0.39453125, 0.142822265625, -0.0806884765625, -0.48193359375, -0.5888671875, 0.5947265625, -0.529296875, 0.29638671875, -0.64892578125, -0.2310791015625, -0.4580078125, -0.66845703125, -0.312255859375, -0.2247314453125, -0.2442626953125, -0.8076171875, 0.50048828125, 0.263916015625, 0.4189453125, 0.261474609375, -0.5830078125, 0.1409912109375, 0.82470703125, 1.0947265625, -0.03179931640625, 0.7392578125, 0.417236328125, -0.253173828125, 0.06463623046875, -0.38525390625, 0.42822265625, 0.12322998046875, 0.431884765625, -0.341796875, 0.147216796875, -0.76904296875, -1.0498046875, 0.1356201171875, 0.521484375, 0.057861328125, -0.5693359375, -1.109375, -0.57861328125, -0.90283203125, -0.18212890625, -0.884765625, 0.67529296875, -0.286865234375, 0.1175537109375, -0.08203125, -0.9853515625, 4.38671875, 0.80078125, 0.931640625, 0.1728515625, 0.385009765625, 0.89501953125, 0.265625, -0.8046875, 0.00147247314453125, -0.393798828125, 0.93017578125, -0.29248046875, 0.1124267578125, 0.67529296875, 0.3193359375, 0.5498046875, -0.7685546875, -0.0239715576171875, 0.062469482421875, -1.2998046875, -0.56103515625, 0.29638671875, -0.09124755859375, 0.68310546875, -0.03411865234375, 0.1568603515625, 0.91064453125, -1.205078125, -0.372802734375, -0.83349609375, 0.429443359375, -0.150146484375, 0.68408203125, 0.260986328125, 0.00945281982421875, 0.74169921875, -0.2462158203125, -0.411376953125, -0.28662109375, 0.08343505859375, -0.2210693359375, -0.197509765625, 0.32177734375, -0.541015625, -0.281005859375, 0.2353515625, -0.6220703125, 0.71435546875, 0.08123779296875, -1.0068359375, 0.57275390625, 0.126220703125, 0.78125, -0.78125, -0.6689453125, 0.07940673828125, 0.458740234375, -0.12890625, -0.12188720703125, 0.6162109375, 0.317626953125, 0.8671875, -0.373779296875, 0.85400390625, -1.03515625, 0.837890625, -0.2275390625, 0.266845703125, -0.7294921875, 0.258544921875, -0.273681640625, -0.564453125, -0.331787109375, -0.66455078125, 0.5625, 0.1656494140625, -0.39453125, 0.61669921875, 0.7998046875, -0.383056640625, -0.0288543701171875, -0.437255859375, -0.33544921875, -0.332763671875, 0.578125, 1.2470703125, -0.429443359375, -0.267333984375, -0.1485595703125, 0.625, 0.431640625, 0.63525390625, 0.10198974609375, -0.54150390625, -0.450927734375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Submitted Solution: ``` q = int(input()) for i in range(q): a, b = [int(item) for item in input().split()] s = input().rstrip() + "#" cnt = 0 bob_world = 0 alice_world = 0 length = 0 bob_winning = False for ch in s: if ch == ".": cnt += 1 else: if cnt < b: pass elif b <= cnt < a: bob_winning = True break elif a <= cnt < b * 2: alice_world += 1 elif cnt >= b * 2: length = cnt bob_world += 1 if bob_world >= 2: bob_winning = True break cnt = 0 if bob_winning: print("No") else: if length == 0: if alice_world % 2 == 1: print("Yes") else: print("No") continue possibility = set() for i in range(length - a + 1): l = i; r = length - a - i if b <= l < a or b <= r < a: continue if l >= b * 2 or r >= b * 2: continue val = 0 if a <= l < b * 2: val += 1 if a <= r < b * 2: val += 1 possibility.add(val + 1) alice_win = False for item in possibility: if (alice_world + item) % 2 == 1: alice_win = True if alice_win: print("Yes") else: print("No") ``` Yes
106,232
[ 0.44287109375, 0.240478515625, -0.087890625, 0.341552734375, -0.591796875, -0.5078125, -0.1556396484375, 0.25732421875, 0.2320556640625, 0.87841796875, 0.70458984375, 0.2056884765625, 0.13916015625, -0.640625, -0.50146484375, -0.04205322265625, -0.654296875, -0.849609375, -0.380859375, -0.224365234375, 0.0240325927734375, -0.1005859375, -1.3369140625, 0.0732421875, -0.2235107421875, 0.7412109375, 0.1297607421875, -0.041015625, 0.88623046875, 1.02734375, -0.01287841796875, -0.466796875, 0.5283203125, -0.65869140625, -0.421142578125, -0.397705078125, 0.76708984375, -0.69775390625, -0.2042236328125, -0.515625, 0.24169921875, -0.423828125, 0.45751953125, -0.60791015625, -1.3544921875, 0.0294342041015625, -0.193115234375, -0.50634765625, -0.216552734375, -0.48974609375, 0.10821533203125, -0.395263671875, 0.303955078125, -0.290283203125, 0.22119140625, 0.272216796875, 0.058868408203125, 0.0958251953125, -0.765625, 0.1998291015625, 0.338623046875, -0.24658203125, -0.019744873046875, -0.92822265625, 0.0936279296875, 0.044525146484375, 0.225830078125, -0.462890625, 0.2509765625, -0.5712890625, -0.205810546875, -0.1949462890625, -0.64697265625, -0.317626953125, -0.1839599609375, 0.428466796875, 0.361328125, -0.10089111328125, -0.95947265625, 0.7646484375, -0.230224609375, 0.94482421875, 0.63525390625, 0.008575439453125, -0.306884765625, -0.478271484375, 0.47021484375, 0.26513671875, 0.43359375, -0.259033203125, -0.054290771484375, 0.5107421875, -0.331787109375, -0.167724609375, 0.34814453125, 0.8525390625, -0.1483154296875, 0.124267578125, 0.6689453125, -0.1033935546875, 0.57763671875, 0.69287109375, -0.50634765625, 1.12890625, -0.447021484375, -0.009674072265625, 0.380126953125, -0.0626220703125, -0.0260467529296875, -0.5029296875, -0.192626953125, -0.473876953125, 0.66015625, 0.382568359375, -0.564453125, 0.876953125, 0.10308837890625, 0.413818359375, -0.61572265625, -0.002712249755859375, 0.72119140625, -0.029205322265625, 0.54931640625, -0.0478515625, 0.1151123046875, -0.276123046875, -0.6298828125, 1.001953125, -0.56494140625, -0.2529296875, 0.57421875, -0.064208984375, -0.25244140625, 0.362548828125, -0.2763671875, 0.75, -0.151611328125, 0.461669921875, 0.76953125, -0.62841796875, 0.9716796875, -0.0301666259765625, 0.2265625, 1.4716796875, 0.24951171875, -0.2176513671875, 0.3701171875, 0.5263671875, -0.85595703125, 0.3525390625, -1.05078125, 0.6015625, -0.045562744140625, 0.200927734375, -0.266357421875, -0.2261962890625, -0.333984375, 0.52392578125, 0.335205078125, -0.0050048828125, -0.14208984375, 0.5625, -0.54736328125, 0.72705078125, -0.328125, 0.6953125, -0.386962890625, -0.2027587890625, -0.005481719970703125, -0.266845703125, 0.06683349609375, -0.376708984375, 0.14501953125, 0.7578125, 0.5234375, 1.35546875, 1.2919921875, -0.226318359375, 0.364990234375, 0.423095703125, -0.52685546875, 0.3935546875, 0.38330078125, 1.0556640625, 0.416748046875, 0.461181640625, 0.0469970703125, 0.093017578125, -0.7236328125, -0.385009765625, 0.1390380859375, 0.67041015625, -0.475341796875, 0.3740234375, 0.248779296875, 0.1494140625, -0.91796875, -0.210693359375, 0.0303802490234375, -0.8173828125, -0.54638671875, 0.41015625, 0.03704833984375, 0.4140625, -0.65185546875, -0.638671875, 0.1275634765625, 1.146484375, -0.341796875, -0.109619140625, 0.4697265625, 0.30615234375, 0.0167999267578125, -0.22119140625, 0.00995635986328125, -0.014801025390625, -0.6767578125, 0.98046875, 0.039337158203125, -0.148681640625, 0.11639404296875, 0.70849609375, 0.1844482421875, 0.75146484375, -0.626953125, -0.384521484375, 0.4619140625, 1.0947265625, 0.09918212890625, 0.74462890625, 0.55419921875, 1.1552734375, 0.326904296875, 0.86474609375, 0.306884765625, 0.264892578125, 0.76708984375, 0.91015625, -0.2357177734375, -0.01302337646484375, 0.221435546875, 0.467529296875, 0.1466064453125, 0.638671875, 0.29638671875, 0.44775390625, -0.18115234375, 0.032867431640625, -0.6728515625, 0.1142578125, -0.2978515625, 0.50439453125, 0.2052001953125, 0.6064453125, -0.442626953125, -0.1087646484375, 0.3681640625, 0.978515625, -1.1103515625, -0.6884765625, 0.042022705078125, -0.03961181640625, -0.0960693359375, 0.051849365234375, 0.57666015625, 0.0285797119140625, 0.42529296875, 0.408203125, -0.366455078125, -0.63623046875, -0.7861328125, -0.740234375, -0.896484375, -0.40185546875, -0.5849609375, -0.234619140625, 0.1978759765625, -0.978515625, -0.07916259765625, -0.5234375, -0.047027587890625, 0.1627197265625, -0.5322265625, 1.03125, -0.5634765625, 0.5048828125, -0.81396484375, 0.235595703125, 0.427001953125, 1.072265625, -0.430908203125, -0.108642578125, -0.1849365234375, -0.31787109375, 0.196044921875, -0.17626953125, 0.4287109375, -0.0341796875, -0.43115234375, -0.7578125, -0.4189453125, -0.16748046875, -0.476318359375, 0.2705078125, -0.6591796875, 0.80517578125, 0.5, -0.52197265625, 0.673828125, 1.0166015625, -0.59716796875, 0.53466796875, 0.1663818359375, 0.1090087890625, -0.65869140625, 1.3125, 0.6787109375, 0.400390625, -0.42138671875, -0.533203125, -0.3681640625, -0.281005859375, 0.338623046875, -0.546875, -0.63623046875, 0.6552734375, 0.0238494873046875, -1.0849609375, 0.1781005859375, -1.0458984375, -0.619140625, -0.237060546875, -0.496826171875, 0.84423828125, 0.80908203125, 0.254638671875, -0.05657958984375, -0.400390625, 0.1473388671875, 0.42138671875, 0.40576171875, -0.8291015625, 0.263671875, 0.7724609375, 0.05462646484375, 0.34521484375, 0.343994140625, -0.3359375, -0.031402587890625, -0.01007080078125, -0.2374267578125, 0.65625, 0.108642578125, 0.2283935546875, 0.390625, 0.472900390625, -0.826171875, -0.1346435546875, -0.30712890625, 0.515625, 0.45068359375, 0.56982421875, 0.305419921875, -0.258544921875, -0.72216796875, -1.0166015625, 0.368896484375, 0.062347412109375, 0.7314453125, -0.5927734375, 0.89990234375, -0.059295654296875, -0.3046875, 0.488525390625, -0.66357421875, 0.0909423828125, 1.1416015625, -0.301513671875, 0.4501953125, -0.70166015625, 0.44921875, 0.12115478515625, 0.138671875, 0.49267578125, 0.23193359375, 0.77294921875, -0.27099609375, -0.54150390625, -0.485595703125, -0.1568603515625, -0.0576171875, -0.7685546875, 0.2191162109375, -0.57080078125, -0.412841796875, -0.7265625, 0.4306640625, 0.82275390625, 1.0576171875, -0.01462554931640625, 0.59326171875, -0.1046142578125, 0.29931640625, 0.56005859375, -0.52392578125, 0.16845703125, -0.5673828125, 0.70751953125, 0.48779296875, 0.171875, -0.62451171875, 0.061126708984375, -0.2076416015625, -0.23046875, 0.12109375, -0.319580078125, -1.0693359375, 0.25537109375, -0.171630859375, 0.59228515625, -0.59765625, -0.344970703125, -0.11004638671875, 0.467529296875, 0.5439453125, -0.73779296875, 0.2127685546875, -1.1064453125, 0.68310546875, 0.359619140625, -0.250732421875, -0.388916015625, -0.5078125, -0.79638671875, -1.095703125, -0.06903076171875, 1.0439453125, 0.11712646484375, 0.380615234375, -1.15625, 0.400634765625, -0.051910400390625, -0.54736328125, 0.1885986328125, -0.3291015625, 0.283935546875, -0.0477294921875, 0.728515625, -0.73974609375, -0.564453125, -0.0182342529296875, -0.95263671875, 0.57080078125, -0.443359375, 0.4169921875, -0.0197601318359375, -0.16552734375, -0.115234375, 0.378662109375, -0.187744140625, 0.28515625, -0.345703125, 0.30908203125, -0.89794921875, -0.4453125, 0.6748046875, -0.2196044921875, -0.179443359375, 0.7548828125, -0.2169189453125, -0.5322265625, 0.1552734375, 0.48486328125, -0.3779296875, 0.537109375, -0.39892578125, 0.408935546875, -0.172119140625, -0.404296875, -0.177001953125, -0.70849609375, 0.8623046875, 0.210205078125, -0.57373046875, -0.474853515625, -0.92138671875, -0.185546875, 0.00908660888671875, -0.196044921875, 0.60400390625, 0.1722412109375, 0.08056640625, -0.06256103515625, -0.221923828125, -0.5810546875, -0.0670166015625, -0.348388671875, 0.01152801513671875, 0.047821044921875, 0.4052734375, 0.404296875, -0.056060791015625, -0.5, -0.4111328125, -0.2340087890625, 0.1390380859375, -0.54345703125, -0.375, -0.235595703125, -0.2890625, -0.63916015625, 0.280517578125, -0.1246337890625, 0.51611328125, 1.0166015625, -0.01617431640625, 0.65869140625, 0.304931640625, -0.9775390625, 1.13671875, 0.203125, -1.2138671875, -0.69677734375, 0.299560546875, 0.10009765625, 0.68359375, 0.1942138671875, -0.481201171875, -0.8681640625, -0.9501953125, 0.2027587890625, -0.88720703125, -0.245849609375, -1.212890625, -0.5361328125, -0.378662109375, 0.4365234375, -0.0665283203125, -0.67724609375, 0.2626953125, -1.0625, 0.38134765625, -0.95947265625, 0.104248046875, -0.7236328125, -0.4853515625, -0.2052001953125, 1.060546875, 0.23876953125, 0.625, 0.0013666152954101562, -0.30126953125, 0.1019287109375, 0.1982421875, -0.5126953125, -0.475830078125, 0.201171875, -0.051849365234375, -0.277099609375, -0.291259765625, -0.5068359375, 0.61474609375, -0.72216796875, 0.42919921875, -0.051910400390625, -0.298583984375, -0.12005615234375, -0.41796875, 1.0888671875, -0.348876953125, 0.1973876953125, -0.4853515625, 0.226806640625, 0.6552734375, -0.2210693359375, -0.30322265625, -0.3466796875, -0.491455078125, -1.25390625, 0.490234375, -0.368408203125, 0.080810546875, -0.7939453125, -0.2174072265625, 1.3291015625, -0.564453125, 0.268310546875, 1.455078125, 0.1661376953125, 0.2191162109375, -0.498046875, 0.671875, 0.7080078125, -0.428955078125, -0.1109619140625, 0.12261962890625, -0.65869140625, -0.118896484375, -0.394775390625, -1.1728515625, -0.77197265625, 0.457275390625, 1.154296875, -0.45263671875, 0.88037109375, -0.24462890625, -1.107421875, -0.591796875, 0.78955078125, -0.1331787109375, 0.240234375, 0.86181640625, 0.28466796875, -0.254150390625, 0.285400390625, -0.107177734375, -0.38134765625, -0.59326171875, 1.177734375, -0.328125, -0.11663818359375, 1.2236328125, 0.87646484375, -1.130859375, -0.82861328125, -0.393310546875, -0.06707763671875, 0.26708984375, -0.8798828125, 0.146728515625, 0.420166015625, -0.56787109375, 0.126708984375, 0.48681640625, -0.3681640625, 0.40625, 0.037567138671875, 0.274169921875, -0.34228515625, 0.313720703125, 0.703125, -0.21435546875, -0.3544921875, -0.9794921875, -0.33642578125, -0.230224609375, -0.0576171875, 0.95654296875, -0.20947265625, 0.405029296875, 0.35205078125, -0.1539306640625, 0.66748046875, -0.609375, -0.28955078125, 0.26220703125, -0.72412109375, -0.310302734375, -0.322265625, 0.44140625, 0.1602783203125, 0.751953125, -0.58056640625, 0.0267333984375, 0.27490234375, 0.44384765625, -0.397705078125, -0.935546875, -0.273193359375, -1.1533203125, -0.55517578125, -0.50390625, -0.6923828125, -0.01372528076171875, 0.57275390625, 0.176513671875, -0.623046875, -0.041595458984375, 0.2249755859375, -0.311279296875, 0.6923828125, -0.59326171875, 0.22021484375, -0.64794921875, -0.344482421875, -0.59619140625, 0.06280517578125, -0.83984375, -0.142333984375, -0.414794921875, 0.394775390625, -0.431396484375, 0.341552734375, -0.4091796875, 0.396484375, -0.1715087890625, -0.63134765625, -0.1396484375, 0.1719970703125, -0.673828125, 1.046875, 0.57080078125, 0.1455078125, 0.34521484375, -0.4990234375, -0.296630859375, -0.31298828125, 0.6123046875, 0.14013671875, -0.0026798248291015625, -0.297607421875, -0.07452392578125, 0.026336669921875, -1.0908203125, 0.29443359375, -0.13232421875, 0.0850830078125, 0.0972900390625, -0.23876953125, 0.465576171875, 1.2509765625, -0.3701171875, 0.39599609375, -0.090087890625, 0.397705078125, 0.443359375, 0.2335205078125, -0.092041015625, 0.8212890625, -0.20361328125, -0.58154296875, 0.1402587890625, 0.1871337890625, 0.1578369140625, 0.04315185546875, -0.388916015625, -0.8583984375, -0.9638671875, -0.224609375, -0.11358642578125, 0.432373046875, 0.5634765625, -0.2274169921875, 0.0099639892578125, -0.3720703125, -0.32470703125, -0.32177734375, -1.3505859375, -0.86767578125, 0.66162109375, -0.126708984375, -0.84375, 0.0214385986328125, -0.202880859375, -0.0936279296875, 0.10711669921875, 0.283447265625, -0.3759765625, 0.48193359375, -0.392822265625, 0.49658203125, -0.2587890625, -0.2227783203125, 0.0252685546875, 0.435791015625, -0.67578125, -0.71240234375, 0.27685546875, 0.9208984375, 0.0303192138671875, -0.35888671875, -0.66796875, 0.4404296875, -0.1474609375, -0.08502197265625, -0.52197265625, 0.399658203125, 0.0001615285873413086, 0.5009765625, -0.69189453125, 0.006313323974609375, -0.56640625, 0.48974609375, 0.1572265625, -0.669921875, -0.57470703125, 0.83935546875, 0.49755859375, -0.3330078125, 0.35302734375, -0.130615234375, 0.419189453125, -0.12493896484375, 0.06219482421875, -0.28662109375, 0.84521484375, 0.81494140625, 0.95068359375, -0.067138671875, 0.395751953125, 0.5986328125, 0.376708984375, 0.0181427001953125, 0.446533203125, 0.039947509765625, 0.014404296875, 0.063720703125, -0.1151123046875, -0.1099853515625, -0.300048828125, -0.67578125, 0.326904296875, -0.33154296875, 0.1650390625, -0.09881591796875, -0.720703125, 0.98486328125, -0.24951171875, -0.0738525390625, 0.09588623046875, -0.6376953125, 0.2421875, 0.6767578125, -0.225341796875, -0.3984375, 0.7119140625, 0.8173828125, 0.54443359375, 0.4677734375, 0.2327880859375, 0.55322265625, -0.68310546875, 0.127197265625, 0.402587890625, -0.0428466796875, -0.3056640625, -0.5673828125, -1.072265625, 0.494873046875, -0.654296875, -0.35400390625, 0.401123046875, -0.8837890625, 0.162353515625, -0.1458740234375, 0.8740234375, -0.354736328125, 0.1397705078125, 0.447509765625, -0.11798095703125, -0.541015625, 0.9404296875, -0.0107269287109375, 0.26220703125, -0.1514892578125, 1.31640625, 0.01111602783203125, 1.44140625, 0.93310546875, 0.041229248046875, 0.08380126953125, 0.462158203125, -0.380126953125, -0.62451171875, -0.27001953125, -0.414794921875, -0.116455078125, -0.724609375, -0.56005859375, -0.2900390625, 0.91455078125, -0.009185791015625, -0.78271484375, -0.332763671875, 0.266845703125, -0.8154296875, 0.414794921875, 0.288818359375, 0.39453125, 0.142822265625, -0.0806884765625, -0.48193359375, -0.5888671875, 0.5947265625, -0.529296875, 0.29638671875, -0.64892578125, -0.2310791015625, -0.4580078125, -0.66845703125, -0.312255859375, -0.2247314453125, -0.2442626953125, -0.8076171875, 0.50048828125, 0.263916015625, 0.4189453125, 0.261474609375, -0.5830078125, 0.1409912109375, 0.82470703125, 1.0947265625, -0.03179931640625, 0.7392578125, 0.417236328125, -0.253173828125, 0.06463623046875, -0.38525390625, 0.42822265625, 0.12322998046875, 0.431884765625, -0.341796875, 0.147216796875, -0.76904296875, -1.0498046875, 0.1356201171875, 0.521484375, 0.057861328125, -0.5693359375, -1.109375, -0.57861328125, -0.90283203125, -0.18212890625, -0.884765625, 0.67529296875, -0.286865234375, 0.1175537109375, -0.08203125, -0.9853515625, 4.38671875, 0.80078125, 0.931640625, 0.1728515625, 0.385009765625, 0.89501953125, 0.265625, -0.8046875, 0.00147247314453125, -0.393798828125, 0.93017578125, -0.29248046875, 0.1124267578125, 0.67529296875, 0.3193359375, 0.5498046875, -0.7685546875, -0.0239715576171875, 0.062469482421875, -1.2998046875, -0.56103515625, 0.29638671875, -0.09124755859375, 0.68310546875, -0.03411865234375, 0.1568603515625, 0.91064453125, -1.205078125, -0.372802734375, -0.83349609375, 0.429443359375, -0.150146484375, 0.68408203125, 0.260986328125, 0.00945281982421875, 0.74169921875, -0.2462158203125, -0.411376953125, -0.28662109375, 0.08343505859375, -0.2210693359375, -0.197509765625, 0.32177734375, -0.541015625, -0.281005859375, 0.2353515625, -0.6220703125, 0.71435546875, 0.08123779296875, -1.0068359375, 0.57275390625, 0.126220703125, 0.78125, -0.78125, -0.6689453125, 0.07940673828125, 0.458740234375, -0.12890625, -0.12188720703125, 0.6162109375, 0.317626953125, 0.8671875, -0.373779296875, 0.85400390625, -1.03515625, 0.837890625, -0.2275390625, 0.266845703125, -0.7294921875, 0.258544921875, -0.273681640625, -0.564453125, -0.331787109375, -0.66455078125, 0.5625, 0.1656494140625, -0.39453125, 0.61669921875, 0.7998046875, -0.383056640625, -0.0288543701171875, -0.437255859375, -0.33544921875, -0.332763671875, 0.578125, 1.2470703125, -0.429443359375, -0.267333984375, -0.1485595703125, 0.625, 0.431640625, 0.63525390625, 0.10198974609375, -0.54150390625, -0.450927734375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Submitted Solution: ``` import sys input = sys.stdin.readline q=int(input()) for testcases in range(q): a,b=map(int,input().split()) S=input().strip() T=[] NOW=0 for s in S: if s==".": NOW+=1 else: if NOW!=0: T.append(NOW) NOW=0 T.sort() LA=[] LB=[] flag=0 SP=0 for t in T: LA.append(t//a) LB.append(t//b) SP+=t//b-t//a if sum(LA)%2==1 and SP<=1: print("YES") else: print("NO") ``` No
106,233
[ 0.44287109375, 0.240478515625, -0.087890625, 0.341552734375, -0.591796875, -0.5078125, -0.1556396484375, 0.25732421875, 0.2320556640625, 0.87841796875, 0.70458984375, 0.2056884765625, 0.13916015625, -0.640625, -0.50146484375, -0.04205322265625, -0.654296875, -0.849609375, -0.380859375, -0.224365234375, 0.0240325927734375, -0.1005859375, -1.3369140625, 0.0732421875, -0.2235107421875, 0.7412109375, 0.1297607421875, -0.041015625, 0.88623046875, 1.02734375, -0.01287841796875, -0.466796875, 0.5283203125, -0.65869140625, -0.421142578125, -0.397705078125, 0.76708984375, -0.69775390625, -0.2042236328125, -0.515625, 0.24169921875, -0.423828125, 0.45751953125, -0.60791015625, -1.3544921875, 0.0294342041015625, -0.193115234375, -0.50634765625, -0.216552734375, -0.48974609375, 0.10821533203125, -0.395263671875, 0.303955078125, -0.290283203125, 0.22119140625, 0.272216796875, 0.058868408203125, 0.0958251953125, -0.765625, 0.1998291015625, 0.338623046875, -0.24658203125, -0.019744873046875, -0.92822265625, 0.0936279296875, 0.044525146484375, 0.225830078125, -0.462890625, 0.2509765625, -0.5712890625, -0.205810546875, -0.1949462890625, -0.64697265625, -0.317626953125, -0.1839599609375, 0.428466796875, 0.361328125, -0.10089111328125, -0.95947265625, 0.7646484375, -0.230224609375, 0.94482421875, 0.63525390625, 0.008575439453125, -0.306884765625, -0.478271484375, 0.47021484375, 0.26513671875, 0.43359375, -0.259033203125, -0.054290771484375, 0.5107421875, -0.331787109375, -0.167724609375, 0.34814453125, 0.8525390625, -0.1483154296875, 0.124267578125, 0.6689453125, -0.1033935546875, 0.57763671875, 0.69287109375, -0.50634765625, 1.12890625, -0.447021484375, -0.009674072265625, 0.380126953125, -0.0626220703125, -0.0260467529296875, -0.5029296875, -0.192626953125, -0.473876953125, 0.66015625, 0.382568359375, -0.564453125, 0.876953125, 0.10308837890625, 0.413818359375, -0.61572265625, -0.002712249755859375, 0.72119140625, -0.029205322265625, 0.54931640625, -0.0478515625, 0.1151123046875, -0.276123046875, -0.6298828125, 1.001953125, -0.56494140625, -0.2529296875, 0.57421875, -0.064208984375, -0.25244140625, 0.362548828125, -0.2763671875, 0.75, -0.151611328125, 0.461669921875, 0.76953125, -0.62841796875, 0.9716796875, -0.0301666259765625, 0.2265625, 1.4716796875, 0.24951171875, -0.2176513671875, 0.3701171875, 0.5263671875, -0.85595703125, 0.3525390625, -1.05078125, 0.6015625, -0.045562744140625, 0.200927734375, -0.266357421875, -0.2261962890625, -0.333984375, 0.52392578125, 0.335205078125, -0.0050048828125, -0.14208984375, 0.5625, -0.54736328125, 0.72705078125, -0.328125, 0.6953125, -0.386962890625, -0.2027587890625, -0.005481719970703125, -0.266845703125, 0.06683349609375, -0.376708984375, 0.14501953125, 0.7578125, 0.5234375, 1.35546875, 1.2919921875, -0.226318359375, 0.364990234375, 0.423095703125, -0.52685546875, 0.3935546875, 0.38330078125, 1.0556640625, 0.416748046875, 0.461181640625, 0.0469970703125, 0.093017578125, -0.7236328125, -0.385009765625, 0.1390380859375, 0.67041015625, -0.475341796875, 0.3740234375, 0.248779296875, 0.1494140625, -0.91796875, -0.210693359375, 0.0303802490234375, -0.8173828125, -0.54638671875, 0.41015625, 0.03704833984375, 0.4140625, -0.65185546875, -0.638671875, 0.1275634765625, 1.146484375, -0.341796875, -0.109619140625, 0.4697265625, 0.30615234375, 0.0167999267578125, -0.22119140625, 0.00995635986328125, -0.014801025390625, -0.6767578125, 0.98046875, 0.039337158203125, -0.148681640625, 0.11639404296875, 0.70849609375, 0.1844482421875, 0.75146484375, -0.626953125, -0.384521484375, 0.4619140625, 1.0947265625, 0.09918212890625, 0.74462890625, 0.55419921875, 1.1552734375, 0.326904296875, 0.86474609375, 0.306884765625, 0.264892578125, 0.76708984375, 0.91015625, -0.2357177734375, -0.01302337646484375, 0.221435546875, 0.467529296875, 0.1466064453125, 0.638671875, 0.29638671875, 0.44775390625, -0.18115234375, 0.032867431640625, -0.6728515625, 0.1142578125, -0.2978515625, 0.50439453125, 0.2052001953125, 0.6064453125, -0.442626953125, -0.1087646484375, 0.3681640625, 0.978515625, -1.1103515625, -0.6884765625, 0.042022705078125, -0.03961181640625, -0.0960693359375, 0.051849365234375, 0.57666015625, 0.0285797119140625, 0.42529296875, 0.408203125, -0.366455078125, -0.63623046875, -0.7861328125, -0.740234375, -0.896484375, -0.40185546875, -0.5849609375, -0.234619140625, 0.1978759765625, -0.978515625, -0.07916259765625, -0.5234375, -0.047027587890625, 0.1627197265625, -0.5322265625, 1.03125, -0.5634765625, 0.5048828125, -0.81396484375, 0.235595703125, 0.427001953125, 1.072265625, -0.430908203125, -0.108642578125, -0.1849365234375, -0.31787109375, 0.196044921875, -0.17626953125, 0.4287109375, -0.0341796875, -0.43115234375, -0.7578125, -0.4189453125, -0.16748046875, -0.476318359375, 0.2705078125, -0.6591796875, 0.80517578125, 0.5, -0.52197265625, 0.673828125, 1.0166015625, -0.59716796875, 0.53466796875, 0.1663818359375, 0.1090087890625, -0.65869140625, 1.3125, 0.6787109375, 0.400390625, -0.42138671875, -0.533203125, -0.3681640625, -0.281005859375, 0.338623046875, -0.546875, -0.63623046875, 0.6552734375, 0.0238494873046875, -1.0849609375, 0.1781005859375, -1.0458984375, -0.619140625, -0.237060546875, -0.496826171875, 0.84423828125, 0.80908203125, 0.254638671875, -0.05657958984375, -0.400390625, 0.1473388671875, 0.42138671875, 0.40576171875, -0.8291015625, 0.263671875, 0.7724609375, 0.05462646484375, 0.34521484375, 0.343994140625, -0.3359375, -0.031402587890625, -0.01007080078125, -0.2374267578125, 0.65625, 0.108642578125, 0.2283935546875, 0.390625, 0.472900390625, -0.826171875, -0.1346435546875, -0.30712890625, 0.515625, 0.45068359375, 0.56982421875, 0.305419921875, -0.258544921875, -0.72216796875, -1.0166015625, 0.368896484375, 0.062347412109375, 0.7314453125, -0.5927734375, 0.89990234375, -0.059295654296875, -0.3046875, 0.488525390625, -0.66357421875, 0.0909423828125, 1.1416015625, -0.301513671875, 0.4501953125, -0.70166015625, 0.44921875, 0.12115478515625, 0.138671875, 0.49267578125, 0.23193359375, 0.77294921875, -0.27099609375, -0.54150390625, -0.485595703125, -0.1568603515625, -0.0576171875, -0.7685546875, 0.2191162109375, -0.57080078125, -0.412841796875, -0.7265625, 0.4306640625, 0.82275390625, 1.0576171875, -0.01462554931640625, 0.59326171875, -0.1046142578125, 0.29931640625, 0.56005859375, -0.52392578125, 0.16845703125, -0.5673828125, 0.70751953125, 0.48779296875, 0.171875, -0.62451171875, 0.061126708984375, -0.2076416015625, -0.23046875, 0.12109375, -0.319580078125, -1.0693359375, 0.25537109375, -0.171630859375, 0.59228515625, -0.59765625, -0.344970703125, -0.11004638671875, 0.467529296875, 0.5439453125, -0.73779296875, 0.2127685546875, -1.1064453125, 0.68310546875, 0.359619140625, -0.250732421875, -0.388916015625, -0.5078125, -0.79638671875, -1.095703125, -0.06903076171875, 1.0439453125, 0.11712646484375, 0.380615234375, -1.15625, 0.400634765625, -0.051910400390625, -0.54736328125, 0.1885986328125, -0.3291015625, 0.283935546875, -0.0477294921875, 0.728515625, -0.73974609375, -0.564453125, -0.0182342529296875, -0.95263671875, 0.57080078125, -0.443359375, 0.4169921875, -0.0197601318359375, -0.16552734375, -0.115234375, 0.378662109375, -0.187744140625, 0.28515625, -0.345703125, 0.30908203125, -0.89794921875, -0.4453125, 0.6748046875, -0.2196044921875, -0.179443359375, 0.7548828125, -0.2169189453125, -0.5322265625, 0.1552734375, 0.48486328125, -0.3779296875, 0.537109375, -0.39892578125, 0.408935546875, -0.172119140625, -0.404296875, -0.177001953125, -0.70849609375, 0.8623046875, 0.210205078125, -0.57373046875, -0.474853515625, -0.92138671875, -0.185546875, 0.00908660888671875, -0.196044921875, 0.60400390625, 0.1722412109375, 0.08056640625, -0.06256103515625, -0.221923828125, -0.5810546875, -0.0670166015625, -0.348388671875, 0.01152801513671875, 0.047821044921875, 0.4052734375, 0.404296875, -0.056060791015625, -0.5, -0.4111328125, -0.2340087890625, 0.1390380859375, -0.54345703125, -0.375, -0.235595703125, -0.2890625, -0.63916015625, 0.280517578125, -0.1246337890625, 0.51611328125, 1.0166015625, -0.01617431640625, 0.65869140625, 0.304931640625, -0.9775390625, 1.13671875, 0.203125, -1.2138671875, -0.69677734375, 0.299560546875, 0.10009765625, 0.68359375, 0.1942138671875, -0.481201171875, -0.8681640625, -0.9501953125, 0.2027587890625, -0.88720703125, -0.245849609375, -1.212890625, -0.5361328125, -0.378662109375, 0.4365234375, -0.0665283203125, -0.67724609375, 0.2626953125, -1.0625, 0.38134765625, -0.95947265625, 0.104248046875, -0.7236328125, -0.4853515625, -0.2052001953125, 1.060546875, 0.23876953125, 0.625, 0.0013666152954101562, -0.30126953125, 0.1019287109375, 0.1982421875, -0.5126953125, -0.475830078125, 0.201171875, -0.051849365234375, -0.277099609375, -0.291259765625, -0.5068359375, 0.61474609375, -0.72216796875, 0.42919921875, -0.051910400390625, -0.298583984375, -0.12005615234375, -0.41796875, 1.0888671875, -0.348876953125, 0.1973876953125, -0.4853515625, 0.226806640625, 0.6552734375, -0.2210693359375, -0.30322265625, -0.3466796875, -0.491455078125, -1.25390625, 0.490234375, -0.368408203125, 0.080810546875, -0.7939453125, -0.2174072265625, 1.3291015625, -0.564453125, 0.268310546875, 1.455078125, 0.1661376953125, 0.2191162109375, -0.498046875, 0.671875, 0.7080078125, -0.428955078125, -0.1109619140625, 0.12261962890625, -0.65869140625, -0.118896484375, -0.394775390625, -1.1728515625, -0.77197265625, 0.457275390625, 1.154296875, -0.45263671875, 0.88037109375, -0.24462890625, -1.107421875, -0.591796875, 0.78955078125, -0.1331787109375, 0.240234375, 0.86181640625, 0.28466796875, -0.254150390625, 0.285400390625, -0.107177734375, -0.38134765625, -0.59326171875, 1.177734375, -0.328125, -0.11663818359375, 1.2236328125, 0.87646484375, -1.130859375, -0.82861328125, -0.393310546875, -0.06707763671875, 0.26708984375, -0.8798828125, 0.146728515625, 0.420166015625, -0.56787109375, 0.126708984375, 0.48681640625, -0.3681640625, 0.40625, 0.037567138671875, 0.274169921875, -0.34228515625, 0.313720703125, 0.703125, -0.21435546875, -0.3544921875, -0.9794921875, -0.33642578125, -0.230224609375, -0.0576171875, 0.95654296875, -0.20947265625, 0.405029296875, 0.35205078125, -0.1539306640625, 0.66748046875, -0.609375, -0.28955078125, 0.26220703125, -0.72412109375, -0.310302734375, -0.322265625, 0.44140625, 0.1602783203125, 0.751953125, -0.58056640625, 0.0267333984375, 0.27490234375, 0.44384765625, -0.397705078125, -0.935546875, -0.273193359375, -1.1533203125, -0.55517578125, -0.50390625, -0.6923828125, -0.01372528076171875, 0.57275390625, 0.176513671875, -0.623046875, -0.041595458984375, 0.2249755859375, -0.311279296875, 0.6923828125, -0.59326171875, 0.22021484375, -0.64794921875, -0.344482421875, -0.59619140625, 0.06280517578125, -0.83984375, -0.142333984375, -0.414794921875, 0.394775390625, -0.431396484375, 0.341552734375, -0.4091796875, 0.396484375, -0.1715087890625, -0.63134765625, -0.1396484375, 0.1719970703125, -0.673828125, 1.046875, 0.57080078125, 0.1455078125, 0.34521484375, -0.4990234375, -0.296630859375, -0.31298828125, 0.6123046875, 0.14013671875, -0.0026798248291015625, -0.297607421875, -0.07452392578125, 0.026336669921875, -1.0908203125, 0.29443359375, -0.13232421875, 0.0850830078125, 0.0972900390625, -0.23876953125, 0.465576171875, 1.2509765625, -0.3701171875, 0.39599609375, -0.090087890625, 0.397705078125, 0.443359375, 0.2335205078125, -0.092041015625, 0.8212890625, -0.20361328125, -0.58154296875, 0.1402587890625, 0.1871337890625, 0.1578369140625, 0.04315185546875, -0.388916015625, -0.8583984375, -0.9638671875, -0.224609375, -0.11358642578125, 0.432373046875, 0.5634765625, -0.2274169921875, 0.0099639892578125, -0.3720703125, -0.32470703125, -0.32177734375, -1.3505859375, -0.86767578125, 0.66162109375, -0.126708984375, -0.84375, 0.0214385986328125, -0.202880859375, -0.0936279296875, 0.10711669921875, 0.283447265625, -0.3759765625, 0.48193359375, -0.392822265625, 0.49658203125, -0.2587890625, -0.2227783203125, 0.0252685546875, 0.435791015625, -0.67578125, -0.71240234375, 0.27685546875, 0.9208984375, 0.0303192138671875, -0.35888671875, -0.66796875, 0.4404296875, -0.1474609375, -0.08502197265625, -0.52197265625, 0.399658203125, 0.0001615285873413086, 0.5009765625, -0.69189453125, 0.006313323974609375, -0.56640625, 0.48974609375, 0.1572265625, -0.669921875, -0.57470703125, 0.83935546875, 0.49755859375, -0.3330078125, 0.35302734375, -0.130615234375, 0.419189453125, -0.12493896484375, 0.06219482421875, -0.28662109375, 0.84521484375, 0.81494140625, 0.95068359375, -0.067138671875, 0.395751953125, 0.5986328125, 0.376708984375, 0.0181427001953125, 0.446533203125, 0.039947509765625, 0.014404296875, 0.063720703125, -0.1151123046875, -0.1099853515625, -0.300048828125, -0.67578125, 0.326904296875, -0.33154296875, 0.1650390625, -0.09881591796875, -0.720703125, 0.98486328125, -0.24951171875, -0.0738525390625, 0.09588623046875, -0.6376953125, 0.2421875, 0.6767578125, -0.225341796875, -0.3984375, 0.7119140625, 0.8173828125, 0.54443359375, 0.4677734375, 0.2327880859375, 0.55322265625, -0.68310546875, 0.127197265625, 0.402587890625, -0.0428466796875, -0.3056640625, -0.5673828125, -1.072265625, 0.494873046875, -0.654296875, -0.35400390625, 0.401123046875, -0.8837890625, 0.162353515625, -0.1458740234375, 0.8740234375, -0.354736328125, 0.1397705078125, 0.447509765625, -0.11798095703125, -0.541015625, 0.9404296875, -0.0107269287109375, 0.26220703125, -0.1514892578125, 1.31640625, 0.01111602783203125, 1.44140625, 0.93310546875, 0.041229248046875, 0.08380126953125, 0.462158203125, -0.380126953125, -0.62451171875, -0.27001953125, -0.414794921875, -0.116455078125, -0.724609375, -0.56005859375, -0.2900390625, 0.91455078125, -0.009185791015625, -0.78271484375, -0.332763671875, 0.266845703125, -0.8154296875, 0.414794921875, 0.288818359375, 0.39453125, 0.142822265625, -0.0806884765625, -0.48193359375, -0.5888671875, 0.5947265625, -0.529296875, 0.29638671875, -0.64892578125, -0.2310791015625, -0.4580078125, -0.66845703125, -0.312255859375, -0.2247314453125, -0.2442626953125, -0.8076171875, 0.50048828125, 0.263916015625, 0.4189453125, 0.261474609375, -0.5830078125, 0.1409912109375, 0.82470703125, 1.0947265625, -0.03179931640625, 0.7392578125, 0.417236328125, -0.253173828125, 0.06463623046875, -0.38525390625, 0.42822265625, 0.12322998046875, 0.431884765625, -0.341796875, 0.147216796875, -0.76904296875, -1.0498046875, 0.1356201171875, 0.521484375, 0.057861328125, -0.5693359375, -1.109375, -0.57861328125, -0.90283203125, -0.18212890625, -0.884765625, 0.67529296875, -0.286865234375, 0.1175537109375, -0.08203125, -0.9853515625, 4.38671875, 0.80078125, 0.931640625, 0.1728515625, 0.385009765625, 0.89501953125, 0.265625, -0.8046875, 0.00147247314453125, -0.393798828125, 0.93017578125, -0.29248046875, 0.1124267578125, 0.67529296875, 0.3193359375, 0.5498046875, -0.7685546875, -0.0239715576171875, 0.062469482421875, -1.2998046875, -0.56103515625, 0.29638671875, -0.09124755859375, 0.68310546875, -0.03411865234375, 0.1568603515625, 0.91064453125, -1.205078125, -0.372802734375, -0.83349609375, 0.429443359375, -0.150146484375, 0.68408203125, 0.260986328125, 0.00945281982421875, 0.74169921875, -0.2462158203125, -0.411376953125, -0.28662109375, 0.08343505859375, -0.2210693359375, -0.197509765625, 0.32177734375, -0.541015625, -0.281005859375, 0.2353515625, -0.6220703125, 0.71435546875, 0.08123779296875, -1.0068359375, 0.57275390625, 0.126220703125, 0.78125, -0.78125, -0.6689453125, 0.07940673828125, 0.458740234375, -0.12890625, -0.12188720703125, 0.6162109375, 0.317626953125, 0.8671875, -0.373779296875, 0.85400390625, -1.03515625, 0.837890625, -0.2275390625, 0.266845703125, -0.7294921875, 0.258544921875, -0.273681640625, -0.564453125, -0.331787109375, -0.66455078125, 0.5625, 0.1656494140625, -0.39453125, 0.61669921875, 0.7998046875, -0.383056640625, -0.0288543701171875, -0.437255859375, -0.33544921875, -0.332763671875, 0.578125, 1.2470703125, -0.429443359375, -0.267333984375, -0.1485595703125, 0.625, 0.431640625, 0.63525390625, 0.10198974609375, -0.54150390625, -0.450927734375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Submitted Solution: ``` T = int(input()) for i in range(T): [a, b] = [int(i) for i in input().split()] game = input() length = 0 spaces = [] aspace = 0 bspace = 0 for g in game: if(g=='.'):length+=1 else: if(length>=b): spaces.append(length) length = 0 for s in spaces: if(s >= a): aspace+=s//a bspace+=int((s%a+1)//2 >= b) elif(s >= b): bspace+=1 if(bspace>1 or aspace%3==2): print("NO") else: print("YES") ``` No
106,234
[ 0.44287109375, 0.240478515625, -0.087890625, 0.341552734375, -0.591796875, -0.5078125, -0.1556396484375, 0.25732421875, 0.2320556640625, 0.87841796875, 0.70458984375, 0.2056884765625, 0.13916015625, -0.640625, -0.50146484375, -0.04205322265625, -0.654296875, -0.849609375, -0.380859375, -0.224365234375, 0.0240325927734375, -0.1005859375, -1.3369140625, 0.0732421875, -0.2235107421875, 0.7412109375, 0.1297607421875, -0.041015625, 0.88623046875, 1.02734375, -0.01287841796875, -0.466796875, 0.5283203125, -0.65869140625, -0.421142578125, -0.397705078125, 0.76708984375, -0.69775390625, -0.2042236328125, -0.515625, 0.24169921875, -0.423828125, 0.45751953125, -0.60791015625, -1.3544921875, 0.0294342041015625, -0.193115234375, -0.50634765625, -0.216552734375, -0.48974609375, 0.10821533203125, -0.395263671875, 0.303955078125, -0.290283203125, 0.22119140625, 0.272216796875, 0.058868408203125, 0.0958251953125, -0.765625, 0.1998291015625, 0.338623046875, -0.24658203125, -0.019744873046875, -0.92822265625, 0.0936279296875, 0.044525146484375, 0.225830078125, -0.462890625, 0.2509765625, -0.5712890625, -0.205810546875, -0.1949462890625, -0.64697265625, -0.317626953125, -0.1839599609375, 0.428466796875, 0.361328125, -0.10089111328125, -0.95947265625, 0.7646484375, -0.230224609375, 0.94482421875, 0.63525390625, 0.008575439453125, -0.306884765625, -0.478271484375, 0.47021484375, 0.26513671875, 0.43359375, -0.259033203125, -0.054290771484375, 0.5107421875, -0.331787109375, -0.167724609375, 0.34814453125, 0.8525390625, -0.1483154296875, 0.124267578125, 0.6689453125, -0.1033935546875, 0.57763671875, 0.69287109375, -0.50634765625, 1.12890625, -0.447021484375, -0.009674072265625, 0.380126953125, -0.0626220703125, -0.0260467529296875, -0.5029296875, -0.192626953125, -0.473876953125, 0.66015625, 0.382568359375, -0.564453125, 0.876953125, 0.10308837890625, 0.413818359375, -0.61572265625, -0.002712249755859375, 0.72119140625, -0.029205322265625, 0.54931640625, -0.0478515625, 0.1151123046875, -0.276123046875, -0.6298828125, 1.001953125, -0.56494140625, -0.2529296875, 0.57421875, -0.064208984375, -0.25244140625, 0.362548828125, -0.2763671875, 0.75, -0.151611328125, 0.461669921875, 0.76953125, -0.62841796875, 0.9716796875, -0.0301666259765625, 0.2265625, 1.4716796875, 0.24951171875, -0.2176513671875, 0.3701171875, 0.5263671875, -0.85595703125, 0.3525390625, -1.05078125, 0.6015625, -0.045562744140625, 0.200927734375, -0.266357421875, -0.2261962890625, -0.333984375, 0.52392578125, 0.335205078125, -0.0050048828125, -0.14208984375, 0.5625, -0.54736328125, 0.72705078125, -0.328125, 0.6953125, -0.386962890625, -0.2027587890625, -0.005481719970703125, -0.266845703125, 0.06683349609375, -0.376708984375, 0.14501953125, 0.7578125, 0.5234375, 1.35546875, 1.2919921875, -0.226318359375, 0.364990234375, 0.423095703125, -0.52685546875, 0.3935546875, 0.38330078125, 1.0556640625, 0.416748046875, 0.461181640625, 0.0469970703125, 0.093017578125, -0.7236328125, -0.385009765625, 0.1390380859375, 0.67041015625, -0.475341796875, 0.3740234375, 0.248779296875, 0.1494140625, -0.91796875, -0.210693359375, 0.0303802490234375, -0.8173828125, -0.54638671875, 0.41015625, 0.03704833984375, 0.4140625, -0.65185546875, -0.638671875, 0.1275634765625, 1.146484375, -0.341796875, -0.109619140625, 0.4697265625, 0.30615234375, 0.0167999267578125, -0.22119140625, 0.00995635986328125, -0.014801025390625, -0.6767578125, 0.98046875, 0.039337158203125, -0.148681640625, 0.11639404296875, 0.70849609375, 0.1844482421875, 0.75146484375, -0.626953125, -0.384521484375, 0.4619140625, 1.0947265625, 0.09918212890625, 0.74462890625, 0.55419921875, 1.1552734375, 0.326904296875, 0.86474609375, 0.306884765625, 0.264892578125, 0.76708984375, 0.91015625, -0.2357177734375, -0.01302337646484375, 0.221435546875, 0.467529296875, 0.1466064453125, 0.638671875, 0.29638671875, 0.44775390625, -0.18115234375, 0.032867431640625, -0.6728515625, 0.1142578125, -0.2978515625, 0.50439453125, 0.2052001953125, 0.6064453125, -0.442626953125, -0.1087646484375, 0.3681640625, 0.978515625, -1.1103515625, -0.6884765625, 0.042022705078125, -0.03961181640625, -0.0960693359375, 0.051849365234375, 0.57666015625, 0.0285797119140625, 0.42529296875, 0.408203125, -0.366455078125, -0.63623046875, -0.7861328125, -0.740234375, -0.896484375, -0.40185546875, -0.5849609375, -0.234619140625, 0.1978759765625, -0.978515625, -0.07916259765625, -0.5234375, -0.047027587890625, 0.1627197265625, -0.5322265625, 1.03125, -0.5634765625, 0.5048828125, -0.81396484375, 0.235595703125, 0.427001953125, 1.072265625, -0.430908203125, -0.108642578125, -0.1849365234375, -0.31787109375, 0.196044921875, -0.17626953125, 0.4287109375, -0.0341796875, -0.43115234375, -0.7578125, -0.4189453125, -0.16748046875, -0.476318359375, 0.2705078125, -0.6591796875, 0.80517578125, 0.5, -0.52197265625, 0.673828125, 1.0166015625, -0.59716796875, 0.53466796875, 0.1663818359375, 0.1090087890625, -0.65869140625, 1.3125, 0.6787109375, 0.400390625, -0.42138671875, -0.533203125, -0.3681640625, -0.281005859375, 0.338623046875, -0.546875, -0.63623046875, 0.6552734375, 0.0238494873046875, -1.0849609375, 0.1781005859375, -1.0458984375, -0.619140625, -0.237060546875, -0.496826171875, 0.84423828125, 0.80908203125, 0.254638671875, -0.05657958984375, -0.400390625, 0.1473388671875, 0.42138671875, 0.40576171875, -0.8291015625, 0.263671875, 0.7724609375, 0.05462646484375, 0.34521484375, 0.343994140625, -0.3359375, -0.031402587890625, -0.01007080078125, -0.2374267578125, 0.65625, 0.108642578125, 0.2283935546875, 0.390625, 0.472900390625, -0.826171875, -0.1346435546875, -0.30712890625, 0.515625, 0.45068359375, 0.56982421875, 0.305419921875, -0.258544921875, -0.72216796875, -1.0166015625, 0.368896484375, 0.062347412109375, 0.7314453125, -0.5927734375, 0.89990234375, -0.059295654296875, -0.3046875, 0.488525390625, -0.66357421875, 0.0909423828125, 1.1416015625, -0.301513671875, 0.4501953125, -0.70166015625, 0.44921875, 0.12115478515625, 0.138671875, 0.49267578125, 0.23193359375, 0.77294921875, -0.27099609375, -0.54150390625, -0.485595703125, -0.1568603515625, -0.0576171875, -0.7685546875, 0.2191162109375, -0.57080078125, -0.412841796875, -0.7265625, 0.4306640625, 0.82275390625, 1.0576171875, -0.01462554931640625, 0.59326171875, -0.1046142578125, 0.29931640625, 0.56005859375, -0.52392578125, 0.16845703125, -0.5673828125, 0.70751953125, 0.48779296875, 0.171875, -0.62451171875, 0.061126708984375, -0.2076416015625, -0.23046875, 0.12109375, -0.319580078125, -1.0693359375, 0.25537109375, -0.171630859375, 0.59228515625, -0.59765625, -0.344970703125, -0.11004638671875, 0.467529296875, 0.5439453125, -0.73779296875, 0.2127685546875, -1.1064453125, 0.68310546875, 0.359619140625, -0.250732421875, -0.388916015625, -0.5078125, -0.79638671875, -1.095703125, -0.06903076171875, 1.0439453125, 0.11712646484375, 0.380615234375, -1.15625, 0.400634765625, -0.051910400390625, -0.54736328125, 0.1885986328125, -0.3291015625, 0.283935546875, -0.0477294921875, 0.728515625, -0.73974609375, -0.564453125, -0.0182342529296875, -0.95263671875, 0.57080078125, -0.443359375, 0.4169921875, -0.0197601318359375, -0.16552734375, -0.115234375, 0.378662109375, -0.187744140625, 0.28515625, -0.345703125, 0.30908203125, -0.89794921875, -0.4453125, 0.6748046875, -0.2196044921875, -0.179443359375, 0.7548828125, -0.2169189453125, -0.5322265625, 0.1552734375, 0.48486328125, -0.3779296875, 0.537109375, -0.39892578125, 0.408935546875, -0.172119140625, -0.404296875, -0.177001953125, -0.70849609375, 0.8623046875, 0.210205078125, -0.57373046875, -0.474853515625, -0.92138671875, -0.185546875, 0.00908660888671875, -0.196044921875, 0.60400390625, 0.1722412109375, 0.08056640625, -0.06256103515625, -0.221923828125, -0.5810546875, -0.0670166015625, -0.348388671875, 0.01152801513671875, 0.047821044921875, 0.4052734375, 0.404296875, -0.056060791015625, -0.5, -0.4111328125, -0.2340087890625, 0.1390380859375, -0.54345703125, -0.375, -0.235595703125, -0.2890625, -0.63916015625, 0.280517578125, -0.1246337890625, 0.51611328125, 1.0166015625, -0.01617431640625, 0.65869140625, 0.304931640625, -0.9775390625, 1.13671875, 0.203125, -1.2138671875, -0.69677734375, 0.299560546875, 0.10009765625, 0.68359375, 0.1942138671875, -0.481201171875, -0.8681640625, -0.9501953125, 0.2027587890625, -0.88720703125, -0.245849609375, -1.212890625, -0.5361328125, -0.378662109375, 0.4365234375, -0.0665283203125, -0.67724609375, 0.2626953125, -1.0625, 0.38134765625, -0.95947265625, 0.104248046875, -0.7236328125, -0.4853515625, -0.2052001953125, 1.060546875, 0.23876953125, 0.625, 0.0013666152954101562, -0.30126953125, 0.1019287109375, 0.1982421875, -0.5126953125, -0.475830078125, 0.201171875, -0.051849365234375, -0.277099609375, -0.291259765625, -0.5068359375, 0.61474609375, -0.72216796875, 0.42919921875, -0.051910400390625, -0.298583984375, -0.12005615234375, -0.41796875, 1.0888671875, -0.348876953125, 0.1973876953125, -0.4853515625, 0.226806640625, 0.6552734375, -0.2210693359375, -0.30322265625, -0.3466796875, -0.491455078125, -1.25390625, 0.490234375, -0.368408203125, 0.080810546875, -0.7939453125, -0.2174072265625, 1.3291015625, -0.564453125, 0.268310546875, 1.455078125, 0.1661376953125, 0.2191162109375, -0.498046875, 0.671875, 0.7080078125, -0.428955078125, -0.1109619140625, 0.12261962890625, -0.65869140625, -0.118896484375, -0.394775390625, -1.1728515625, -0.77197265625, 0.457275390625, 1.154296875, -0.45263671875, 0.88037109375, -0.24462890625, -1.107421875, -0.591796875, 0.78955078125, -0.1331787109375, 0.240234375, 0.86181640625, 0.28466796875, -0.254150390625, 0.285400390625, -0.107177734375, -0.38134765625, -0.59326171875, 1.177734375, -0.328125, -0.11663818359375, 1.2236328125, 0.87646484375, -1.130859375, -0.82861328125, -0.393310546875, -0.06707763671875, 0.26708984375, -0.8798828125, 0.146728515625, 0.420166015625, -0.56787109375, 0.126708984375, 0.48681640625, -0.3681640625, 0.40625, 0.037567138671875, 0.274169921875, -0.34228515625, 0.313720703125, 0.703125, -0.21435546875, -0.3544921875, -0.9794921875, -0.33642578125, -0.230224609375, -0.0576171875, 0.95654296875, -0.20947265625, 0.405029296875, 0.35205078125, -0.1539306640625, 0.66748046875, -0.609375, -0.28955078125, 0.26220703125, -0.72412109375, -0.310302734375, -0.322265625, 0.44140625, 0.1602783203125, 0.751953125, -0.58056640625, 0.0267333984375, 0.27490234375, 0.44384765625, -0.397705078125, -0.935546875, -0.273193359375, -1.1533203125, -0.55517578125, -0.50390625, -0.6923828125, -0.01372528076171875, 0.57275390625, 0.176513671875, -0.623046875, -0.041595458984375, 0.2249755859375, -0.311279296875, 0.6923828125, -0.59326171875, 0.22021484375, -0.64794921875, -0.344482421875, -0.59619140625, 0.06280517578125, -0.83984375, -0.142333984375, -0.414794921875, 0.394775390625, -0.431396484375, 0.341552734375, -0.4091796875, 0.396484375, -0.1715087890625, -0.63134765625, -0.1396484375, 0.1719970703125, -0.673828125, 1.046875, 0.57080078125, 0.1455078125, 0.34521484375, -0.4990234375, -0.296630859375, -0.31298828125, 0.6123046875, 0.14013671875, -0.0026798248291015625, -0.297607421875, -0.07452392578125, 0.026336669921875, -1.0908203125, 0.29443359375, -0.13232421875, 0.0850830078125, 0.0972900390625, -0.23876953125, 0.465576171875, 1.2509765625, -0.3701171875, 0.39599609375, -0.090087890625, 0.397705078125, 0.443359375, 0.2335205078125, -0.092041015625, 0.8212890625, -0.20361328125, -0.58154296875, 0.1402587890625, 0.1871337890625, 0.1578369140625, 0.04315185546875, -0.388916015625, -0.8583984375, -0.9638671875, -0.224609375, -0.11358642578125, 0.432373046875, 0.5634765625, -0.2274169921875, 0.0099639892578125, -0.3720703125, -0.32470703125, -0.32177734375, -1.3505859375, -0.86767578125, 0.66162109375, -0.126708984375, -0.84375, 0.0214385986328125, -0.202880859375, -0.0936279296875, 0.10711669921875, 0.283447265625, -0.3759765625, 0.48193359375, -0.392822265625, 0.49658203125, -0.2587890625, -0.2227783203125, 0.0252685546875, 0.435791015625, -0.67578125, -0.71240234375, 0.27685546875, 0.9208984375, 0.0303192138671875, -0.35888671875, -0.66796875, 0.4404296875, -0.1474609375, -0.08502197265625, -0.52197265625, 0.399658203125, 0.0001615285873413086, 0.5009765625, -0.69189453125, 0.006313323974609375, -0.56640625, 0.48974609375, 0.1572265625, -0.669921875, -0.57470703125, 0.83935546875, 0.49755859375, -0.3330078125, 0.35302734375, -0.130615234375, 0.419189453125, -0.12493896484375, 0.06219482421875, -0.28662109375, 0.84521484375, 0.81494140625, 0.95068359375, -0.067138671875, 0.395751953125, 0.5986328125, 0.376708984375, 0.0181427001953125, 0.446533203125, 0.039947509765625, 0.014404296875, 0.063720703125, -0.1151123046875, -0.1099853515625, -0.300048828125, -0.67578125, 0.326904296875, -0.33154296875, 0.1650390625, -0.09881591796875, -0.720703125, 0.98486328125, -0.24951171875, -0.0738525390625, 0.09588623046875, -0.6376953125, 0.2421875, 0.6767578125, -0.225341796875, -0.3984375, 0.7119140625, 0.8173828125, 0.54443359375, 0.4677734375, 0.2327880859375, 0.55322265625, -0.68310546875, 0.127197265625, 0.402587890625, -0.0428466796875, -0.3056640625, -0.5673828125, -1.072265625, 0.494873046875, -0.654296875, -0.35400390625, 0.401123046875, -0.8837890625, 0.162353515625, -0.1458740234375, 0.8740234375, -0.354736328125, 0.1397705078125, 0.447509765625, -0.11798095703125, -0.541015625, 0.9404296875, -0.0107269287109375, 0.26220703125, -0.1514892578125, 1.31640625, 0.01111602783203125, 1.44140625, 0.93310546875, 0.041229248046875, 0.08380126953125, 0.462158203125, -0.380126953125, -0.62451171875, -0.27001953125, -0.414794921875, -0.116455078125, -0.724609375, -0.56005859375, -0.2900390625, 0.91455078125, -0.009185791015625, -0.78271484375, -0.332763671875, 0.266845703125, -0.8154296875, 0.414794921875, 0.288818359375, 0.39453125, 0.142822265625, -0.0806884765625, -0.48193359375, -0.5888671875, 0.5947265625, -0.529296875, 0.29638671875, -0.64892578125, -0.2310791015625, -0.4580078125, -0.66845703125, -0.312255859375, -0.2247314453125, -0.2442626953125, -0.8076171875, 0.50048828125, 0.263916015625, 0.4189453125, 0.261474609375, -0.5830078125, 0.1409912109375, 0.82470703125, 1.0947265625, -0.03179931640625, 0.7392578125, 0.417236328125, -0.253173828125, 0.06463623046875, -0.38525390625, 0.42822265625, 0.12322998046875, 0.431884765625, -0.341796875, 0.147216796875, -0.76904296875, -1.0498046875, 0.1356201171875, 0.521484375, 0.057861328125, -0.5693359375, -1.109375, -0.57861328125, -0.90283203125, -0.18212890625, -0.884765625, 0.67529296875, -0.286865234375, 0.1175537109375, -0.08203125, -0.9853515625, 4.38671875, 0.80078125, 0.931640625, 0.1728515625, 0.385009765625, 0.89501953125, 0.265625, -0.8046875, 0.00147247314453125, -0.393798828125, 0.93017578125, -0.29248046875, 0.1124267578125, 0.67529296875, 0.3193359375, 0.5498046875, -0.7685546875, -0.0239715576171875, 0.062469482421875, -1.2998046875, -0.56103515625, 0.29638671875, -0.09124755859375, 0.68310546875, -0.03411865234375, 0.1568603515625, 0.91064453125, -1.205078125, -0.372802734375, -0.83349609375, 0.429443359375, -0.150146484375, 0.68408203125, 0.260986328125, 0.00945281982421875, 0.74169921875, -0.2462158203125, -0.411376953125, -0.28662109375, 0.08343505859375, -0.2210693359375, -0.197509765625, 0.32177734375, -0.541015625, -0.281005859375, 0.2353515625, -0.6220703125, 0.71435546875, 0.08123779296875, -1.0068359375, 0.57275390625, 0.126220703125, 0.78125, -0.78125, -0.6689453125, 0.07940673828125, 0.458740234375, -0.12890625, -0.12188720703125, 0.6162109375, 0.317626953125, 0.8671875, -0.373779296875, 0.85400390625, -1.03515625, 0.837890625, -0.2275390625, 0.266845703125, -0.7294921875, 0.258544921875, -0.273681640625, -0.564453125, -0.331787109375, -0.66455078125, 0.5625, 0.1656494140625, -0.39453125, 0.61669921875, 0.7998046875, -0.383056640625, -0.0288543701171875, -0.437255859375, -0.33544921875, -0.332763671875, 0.578125, 1.2470703125, -0.429443359375, -0.267333984375, -0.1485595703125, 0.625, 0.431640625, 0.63525390625, 0.10198974609375, -0.54150390625, -0.450927734375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Submitted Solution: ``` def main(): import sys input = sys.stdin.readline q = int(input()) for _ in range(q): a, b = map(int, input().split()) S = input().rstrip('\n') S += '!' win = 1 cnt = 0 flg = 0 num = 0 for s in S: if s == '.': cnt += 1 else: if cnt: if b <= cnt < a: win = 0 break elif cnt < b: pass elif cnt < 2*b: num += 1 else: num += 1 if flg: flg = 2 win = 0 break else: flg = 1 tmp = cnt cnt = 0 if flg == 1: if num % 2 == 0: if a >= 2*b: win = 0 else: if not 2*a <= tmp <= a+3*b-2: win = 0 else: if tmp > a+2*b-2: win = 0 elif flg == 0: if num % 2 == 0: win = 0 if win: print('Yes') else: print('No') if __name__ == '__main__': main() ``` No
106,235
[ 0.44287109375, 0.240478515625, -0.087890625, 0.341552734375, -0.591796875, -0.5078125, -0.1556396484375, 0.25732421875, 0.2320556640625, 0.87841796875, 0.70458984375, 0.2056884765625, 0.13916015625, -0.640625, -0.50146484375, -0.04205322265625, -0.654296875, -0.849609375, -0.380859375, -0.224365234375, 0.0240325927734375, -0.1005859375, -1.3369140625, 0.0732421875, -0.2235107421875, 0.7412109375, 0.1297607421875, -0.041015625, 0.88623046875, 1.02734375, -0.01287841796875, -0.466796875, 0.5283203125, -0.65869140625, -0.421142578125, -0.397705078125, 0.76708984375, -0.69775390625, -0.2042236328125, -0.515625, 0.24169921875, -0.423828125, 0.45751953125, -0.60791015625, -1.3544921875, 0.0294342041015625, -0.193115234375, -0.50634765625, -0.216552734375, -0.48974609375, 0.10821533203125, -0.395263671875, 0.303955078125, -0.290283203125, 0.22119140625, 0.272216796875, 0.058868408203125, 0.0958251953125, -0.765625, 0.1998291015625, 0.338623046875, -0.24658203125, -0.019744873046875, -0.92822265625, 0.0936279296875, 0.044525146484375, 0.225830078125, -0.462890625, 0.2509765625, -0.5712890625, -0.205810546875, -0.1949462890625, -0.64697265625, -0.317626953125, -0.1839599609375, 0.428466796875, 0.361328125, -0.10089111328125, -0.95947265625, 0.7646484375, -0.230224609375, 0.94482421875, 0.63525390625, 0.008575439453125, -0.306884765625, -0.478271484375, 0.47021484375, 0.26513671875, 0.43359375, -0.259033203125, -0.054290771484375, 0.5107421875, -0.331787109375, -0.167724609375, 0.34814453125, 0.8525390625, -0.1483154296875, 0.124267578125, 0.6689453125, -0.1033935546875, 0.57763671875, 0.69287109375, -0.50634765625, 1.12890625, -0.447021484375, -0.009674072265625, 0.380126953125, -0.0626220703125, -0.0260467529296875, -0.5029296875, -0.192626953125, -0.473876953125, 0.66015625, 0.382568359375, -0.564453125, 0.876953125, 0.10308837890625, 0.413818359375, -0.61572265625, -0.002712249755859375, 0.72119140625, -0.029205322265625, 0.54931640625, -0.0478515625, 0.1151123046875, -0.276123046875, -0.6298828125, 1.001953125, -0.56494140625, -0.2529296875, 0.57421875, -0.064208984375, -0.25244140625, 0.362548828125, -0.2763671875, 0.75, -0.151611328125, 0.461669921875, 0.76953125, -0.62841796875, 0.9716796875, -0.0301666259765625, 0.2265625, 1.4716796875, 0.24951171875, -0.2176513671875, 0.3701171875, 0.5263671875, -0.85595703125, 0.3525390625, -1.05078125, 0.6015625, -0.045562744140625, 0.200927734375, -0.266357421875, -0.2261962890625, -0.333984375, 0.52392578125, 0.335205078125, -0.0050048828125, -0.14208984375, 0.5625, -0.54736328125, 0.72705078125, -0.328125, 0.6953125, -0.386962890625, -0.2027587890625, -0.005481719970703125, -0.266845703125, 0.06683349609375, -0.376708984375, 0.14501953125, 0.7578125, 0.5234375, 1.35546875, 1.2919921875, -0.226318359375, 0.364990234375, 0.423095703125, -0.52685546875, 0.3935546875, 0.38330078125, 1.0556640625, 0.416748046875, 0.461181640625, 0.0469970703125, 0.093017578125, -0.7236328125, -0.385009765625, 0.1390380859375, 0.67041015625, -0.475341796875, 0.3740234375, 0.248779296875, 0.1494140625, -0.91796875, -0.210693359375, 0.0303802490234375, -0.8173828125, -0.54638671875, 0.41015625, 0.03704833984375, 0.4140625, -0.65185546875, -0.638671875, 0.1275634765625, 1.146484375, -0.341796875, -0.109619140625, 0.4697265625, 0.30615234375, 0.0167999267578125, -0.22119140625, 0.00995635986328125, -0.014801025390625, -0.6767578125, 0.98046875, 0.039337158203125, -0.148681640625, 0.11639404296875, 0.70849609375, 0.1844482421875, 0.75146484375, -0.626953125, -0.384521484375, 0.4619140625, 1.0947265625, 0.09918212890625, 0.74462890625, 0.55419921875, 1.1552734375, 0.326904296875, 0.86474609375, 0.306884765625, 0.264892578125, 0.76708984375, 0.91015625, -0.2357177734375, -0.01302337646484375, 0.221435546875, 0.467529296875, 0.1466064453125, 0.638671875, 0.29638671875, 0.44775390625, -0.18115234375, 0.032867431640625, -0.6728515625, 0.1142578125, -0.2978515625, 0.50439453125, 0.2052001953125, 0.6064453125, -0.442626953125, -0.1087646484375, 0.3681640625, 0.978515625, -1.1103515625, -0.6884765625, 0.042022705078125, -0.03961181640625, -0.0960693359375, 0.051849365234375, 0.57666015625, 0.0285797119140625, 0.42529296875, 0.408203125, -0.366455078125, -0.63623046875, -0.7861328125, -0.740234375, -0.896484375, -0.40185546875, -0.5849609375, -0.234619140625, 0.1978759765625, -0.978515625, -0.07916259765625, -0.5234375, -0.047027587890625, 0.1627197265625, -0.5322265625, 1.03125, -0.5634765625, 0.5048828125, -0.81396484375, 0.235595703125, 0.427001953125, 1.072265625, -0.430908203125, -0.108642578125, -0.1849365234375, -0.31787109375, 0.196044921875, -0.17626953125, 0.4287109375, -0.0341796875, -0.43115234375, -0.7578125, -0.4189453125, -0.16748046875, -0.476318359375, 0.2705078125, -0.6591796875, 0.80517578125, 0.5, -0.52197265625, 0.673828125, 1.0166015625, -0.59716796875, 0.53466796875, 0.1663818359375, 0.1090087890625, -0.65869140625, 1.3125, 0.6787109375, 0.400390625, -0.42138671875, -0.533203125, -0.3681640625, -0.281005859375, 0.338623046875, -0.546875, -0.63623046875, 0.6552734375, 0.0238494873046875, -1.0849609375, 0.1781005859375, -1.0458984375, -0.619140625, -0.237060546875, -0.496826171875, 0.84423828125, 0.80908203125, 0.254638671875, -0.05657958984375, -0.400390625, 0.1473388671875, 0.42138671875, 0.40576171875, -0.8291015625, 0.263671875, 0.7724609375, 0.05462646484375, 0.34521484375, 0.343994140625, -0.3359375, -0.031402587890625, -0.01007080078125, -0.2374267578125, 0.65625, 0.108642578125, 0.2283935546875, 0.390625, 0.472900390625, -0.826171875, -0.1346435546875, -0.30712890625, 0.515625, 0.45068359375, 0.56982421875, 0.305419921875, -0.258544921875, -0.72216796875, -1.0166015625, 0.368896484375, 0.062347412109375, 0.7314453125, -0.5927734375, 0.89990234375, -0.059295654296875, -0.3046875, 0.488525390625, -0.66357421875, 0.0909423828125, 1.1416015625, -0.301513671875, 0.4501953125, -0.70166015625, 0.44921875, 0.12115478515625, 0.138671875, 0.49267578125, 0.23193359375, 0.77294921875, -0.27099609375, -0.54150390625, -0.485595703125, -0.1568603515625, -0.0576171875, -0.7685546875, 0.2191162109375, -0.57080078125, -0.412841796875, -0.7265625, 0.4306640625, 0.82275390625, 1.0576171875, -0.01462554931640625, 0.59326171875, -0.1046142578125, 0.29931640625, 0.56005859375, -0.52392578125, 0.16845703125, -0.5673828125, 0.70751953125, 0.48779296875, 0.171875, -0.62451171875, 0.061126708984375, -0.2076416015625, -0.23046875, 0.12109375, -0.319580078125, -1.0693359375, 0.25537109375, -0.171630859375, 0.59228515625, -0.59765625, -0.344970703125, -0.11004638671875, 0.467529296875, 0.5439453125, -0.73779296875, 0.2127685546875, -1.1064453125, 0.68310546875, 0.359619140625, -0.250732421875, -0.388916015625, -0.5078125, -0.79638671875, -1.095703125, -0.06903076171875, 1.0439453125, 0.11712646484375, 0.380615234375, -1.15625, 0.400634765625, -0.051910400390625, -0.54736328125, 0.1885986328125, -0.3291015625, 0.283935546875, -0.0477294921875, 0.728515625, -0.73974609375, -0.564453125, -0.0182342529296875, -0.95263671875, 0.57080078125, -0.443359375, 0.4169921875, -0.0197601318359375, -0.16552734375, -0.115234375, 0.378662109375, -0.187744140625, 0.28515625, -0.345703125, 0.30908203125, -0.89794921875, -0.4453125, 0.6748046875, -0.2196044921875, -0.179443359375, 0.7548828125, -0.2169189453125, -0.5322265625, 0.1552734375, 0.48486328125, -0.3779296875, 0.537109375, -0.39892578125, 0.408935546875, -0.172119140625, -0.404296875, -0.177001953125, -0.70849609375, 0.8623046875, 0.210205078125, -0.57373046875, -0.474853515625, -0.92138671875, -0.185546875, 0.00908660888671875, -0.196044921875, 0.60400390625, 0.1722412109375, 0.08056640625, -0.06256103515625, -0.221923828125, -0.5810546875, -0.0670166015625, -0.348388671875, 0.01152801513671875, 0.047821044921875, 0.4052734375, 0.404296875, -0.056060791015625, -0.5, -0.4111328125, -0.2340087890625, 0.1390380859375, -0.54345703125, -0.375, -0.235595703125, -0.2890625, -0.63916015625, 0.280517578125, -0.1246337890625, 0.51611328125, 1.0166015625, -0.01617431640625, 0.65869140625, 0.304931640625, -0.9775390625, 1.13671875, 0.203125, -1.2138671875, -0.69677734375, 0.299560546875, 0.10009765625, 0.68359375, 0.1942138671875, -0.481201171875, -0.8681640625, -0.9501953125, 0.2027587890625, -0.88720703125, -0.245849609375, -1.212890625, -0.5361328125, -0.378662109375, 0.4365234375, -0.0665283203125, -0.67724609375, 0.2626953125, -1.0625, 0.38134765625, -0.95947265625, 0.104248046875, -0.7236328125, -0.4853515625, -0.2052001953125, 1.060546875, 0.23876953125, 0.625, 0.0013666152954101562, -0.30126953125, 0.1019287109375, 0.1982421875, -0.5126953125, -0.475830078125, 0.201171875, -0.051849365234375, -0.277099609375, -0.291259765625, -0.5068359375, 0.61474609375, -0.72216796875, 0.42919921875, -0.051910400390625, -0.298583984375, -0.12005615234375, -0.41796875, 1.0888671875, -0.348876953125, 0.1973876953125, -0.4853515625, 0.226806640625, 0.6552734375, -0.2210693359375, -0.30322265625, -0.3466796875, -0.491455078125, -1.25390625, 0.490234375, -0.368408203125, 0.080810546875, -0.7939453125, -0.2174072265625, 1.3291015625, -0.564453125, 0.268310546875, 1.455078125, 0.1661376953125, 0.2191162109375, -0.498046875, 0.671875, 0.7080078125, -0.428955078125, -0.1109619140625, 0.12261962890625, -0.65869140625, -0.118896484375, -0.394775390625, -1.1728515625, -0.77197265625, 0.457275390625, 1.154296875, -0.45263671875, 0.88037109375, -0.24462890625, -1.107421875, -0.591796875, 0.78955078125, -0.1331787109375, 0.240234375, 0.86181640625, 0.28466796875, -0.254150390625, 0.285400390625, -0.107177734375, -0.38134765625, -0.59326171875, 1.177734375, -0.328125, -0.11663818359375, 1.2236328125, 0.87646484375, -1.130859375, -0.82861328125, -0.393310546875, -0.06707763671875, 0.26708984375, -0.8798828125, 0.146728515625, 0.420166015625, -0.56787109375, 0.126708984375, 0.48681640625, -0.3681640625, 0.40625, 0.037567138671875, 0.274169921875, -0.34228515625, 0.313720703125, 0.703125, -0.21435546875, -0.3544921875, -0.9794921875, -0.33642578125, -0.230224609375, -0.0576171875, 0.95654296875, -0.20947265625, 0.405029296875, 0.35205078125, -0.1539306640625, 0.66748046875, -0.609375, -0.28955078125, 0.26220703125, -0.72412109375, -0.310302734375, -0.322265625, 0.44140625, 0.1602783203125, 0.751953125, -0.58056640625, 0.0267333984375, 0.27490234375, 0.44384765625, -0.397705078125, -0.935546875, -0.273193359375, -1.1533203125, -0.55517578125, -0.50390625, -0.6923828125, -0.01372528076171875, 0.57275390625, 0.176513671875, -0.623046875, -0.041595458984375, 0.2249755859375, -0.311279296875, 0.6923828125, -0.59326171875, 0.22021484375, -0.64794921875, -0.344482421875, -0.59619140625, 0.06280517578125, -0.83984375, -0.142333984375, -0.414794921875, 0.394775390625, -0.431396484375, 0.341552734375, -0.4091796875, 0.396484375, -0.1715087890625, -0.63134765625, -0.1396484375, 0.1719970703125, -0.673828125, 1.046875, 0.57080078125, 0.1455078125, 0.34521484375, -0.4990234375, -0.296630859375, -0.31298828125, 0.6123046875, 0.14013671875, -0.0026798248291015625, -0.297607421875, -0.07452392578125, 0.026336669921875, -1.0908203125, 0.29443359375, -0.13232421875, 0.0850830078125, 0.0972900390625, -0.23876953125, 0.465576171875, 1.2509765625, -0.3701171875, 0.39599609375, -0.090087890625, 0.397705078125, 0.443359375, 0.2335205078125, -0.092041015625, 0.8212890625, -0.20361328125, -0.58154296875, 0.1402587890625, 0.1871337890625, 0.1578369140625, 0.04315185546875, -0.388916015625, -0.8583984375, -0.9638671875, -0.224609375, -0.11358642578125, 0.432373046875, 0.5634765625, -0.2274169921875, 0.0099639892578125, -0.3720703125, -0.32470703125, -0.32177734375, -1.3505859375, -0.86767578125, 0.66162109375, -0.126708984375, -0.84375, 0.0214385986328125, -0.202880859375, -0.0936279296875, 0.10711669921875, 0.283447265625, -0.3759765625, 0.48193359375, -0.392822265625, 0.49658203125, -0.2587890625, -0.2227783203125, 0.0252685546875, 0.435791015625, -0.67578125, -0.71240234375, 0.27685546875, 0.9208984375, 0.0303192138671875, -0.35888671875, -0.66796875, 0.4404296875, -0.1474609375, -0.08502197265625, -0.52197265625, 0.399658203125, 0.0001615285873413086, 0.5009765625, -0.69189453125, 0.006313323974609375, -0.56640625, 0.48974609375, 0.1572265625, -0.669921875, -0.57470703125, 0.83935546875, 0.49755859375, -0.3330078125, 0.35302734375, -0.130615234375, 0.419189453125, -0.12493896484375, 0.06219482421875, -0.28662109375, 0.84521484375, 0.81494140625, 0.95068359375, -0.067138671875, 0.395751953125, 0.5986328125, 0.376708984375, 0.0181427001953125, 0.446533203125, 0.039947509765625, 0.014404296875, 0.063720703125, -0.1151123046875, -0.1099853515625, -0.300048828125, -0.67578125, 0.326904296875, -0.33154296875, 0.1650390625, -0.09881591796875, -0.720703125, 0.98486328125, -0.24951171875, -0.0738525390625, 0.09588623046875, -0.6376953125, 0.2421875, 0.6767578125, -0.225341796875, -0.3984375, 0.7119140625, 0.8173828125, 0.54443359375, 0.4677734375, 0.2327880859375, 0.55322265625, -0.68310546875, 0.127197265625, 0.402587890625, -0.0428466796875, -0.3056640625, -0.5673828125, -1.072265625, 0.494873046875, -0.654296875, -0.35400390625, 0.401123046875, -0.8837890625, 0.162353515625, -0.1458740234375, 0.8740234375, -0.354736328125, 0.1397705078125, 0.447509765625, -0.11798095703125, -0.541015625, 0.9404296875, -0.0107269287109375, 0.26220703125, -0.1514892578125, 1.31640625, 0.01111602783203125, 1.44140625, 0.93310546875, 0.041229248046875, 0.08380126953125, 0.462158203125, -0.380126953125, -0.62451171875, -0.27001953125, -0.414794921875, -0.116455078125, -0.724609375, -0.56005859375, -0.2900390625, 0.91455078125, -0.009185791015625, -0.78271484375, -0.332763671875, 0.266845703125, -0.8154296875, 0.414794921875, 0.288818359375, 0.39453125, 0.142822265625, -0.0806884765625, -0.48193359375, -0.5888671875, 0.5947265625, -0.529296875, 0.29638671875, -0.64892578125, -0.2310791015625, -0.4580078125, -0.66845703125, -0.312255859375, -0.2247314453125, -0.2442626953125, -0.8076171875, 0.50048828125, 0.263916015625, 0.4189453125, 0.261474609375, -0.5830078125, 0.1409912109375, 0.82470703125, 1.0947265625, -0.03179931640625, 0.7392578125, 0.417236328125, -0.253173828125, 0.06463623046875, -0.38525390625, 0.42822265625, 0.12322998046875, 0.431884765625, -0.341796875, 0.147216796875, -0.76904296875, -1.0498046875, 0.1356201171875, 0.521484375, 0.057861328125, -0.5693359375, -1.109375, -0.57861328125, -0.90283203125, -0.18212890625, -0.884765625, 0.67529296875, -0.286865234375, 0.1175537109375, -0.08203125, -0.9853515625, 4.38671875, 0.80078125, 0.931640625, 0.1728515625, 0.385009765625, 0.89501953125, 0.265625, -0.8046875, 0.00147247314453125, -0.393798828125, 0.93017578125, -0.29248046875, 0.1124267578125, 0.67529296875, 0.3193359375, 0.5498046875, -0.7685546875, -0.0239715576171875, 0.062469482421875, -1.2998046875, -0.56103515625, 0.29638671875, -0.09124755859375, 0.68310546875, -0.03411865234375, 0.1568603515625, 0.91064453125, -1.205078125, -0.372802734375, -0.83349609375, 0.429443359375, -0.150146484375, 0.68408203125, 0.260986328125, 0.00945281982421875, 0.74169921875, -0.2462158203125, -0.411376953125, -0.28662109375, 0.08343505859375, -0.2210693359375, -0.197509765625, 0.32177734375, -0.541015625, -0.281005859375, 0.2353515625, -0.6220703125, 0.71435546875, 0.08123779296875, -1.0068359375, 0.57275390625, 0.126220703125, 0.78125, -0.78125, -0.6689453125, 0.07940673828125, 0.458740234375, -0.12890625, -0.12188720703125, 0.6162109375, 0.317626953125, 0.8671875, -0.373779296875, 0.85400390625, -1.03515625, 0.837890625, -0.2275390625, 0.266845703125, -0.7294921875, 0.258544921875, -0.273681640625, -0.564453125, -0.331787109375, -0.66455078125, 0.5625, 0.1656494140625, -0.39453125, 0.61669921875, 0.7998046875, -0.383056640625, -0.0288543701171875, -0.437255859375, -0.33544921875, -0.332763671875, 0.578125, 1.2470703125, -0.429443359375, -0.267333984375, -0.1485595703125, 0.625, 0.431640625, 0.63525390625, 0.10198974609375, -0.54150390625, -0.450927734375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b. For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX. Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally. You have to answer q independent queries. Input The first line contains one integer q (1 ≀ q ≀ 3 β‹… 10^5) β€” the number of queries. The first line of each query contains two integers a and b (1 ≀ b < a ≀ 3 β‹… 10^5). The second line of each query contains the string s (1 ≀ |s| ≀ 3 β‹… 10^5), consisting of only characters . and X. It is guaranteed that sum of all |s| over all queries not exceed 3 β‹… 10^5. Output For each test case print YES if Alice can win and NO otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer). Example Input 3 3 2 XX......XX...X 4 2 X...X.X..X 5 3 .......X..X Output YES NO YES Note In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move. In the second query Alice can not win because she cannot even make one move. In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that. Submitted Solution: ``` Q = int(input()) for q in range(Q): a, b = tuple(map(int, input().split())) s = input() ones = [] count = 0 flag = False for i in s: if i == "X": if a > count >= b: print('NO') flag = True break elif count >= b: ones.append(count) count = 0 else: count += 1 if count != 0: ones.append(count) if a > count >= b: print('NO') continue if flag: continue if len(ones) == 0: print('NO') continue count_more2b = 0 more2b = 0 for one in ones: if one >= 2 * b: count_more2b += 1 more2b = one if count_more2b >= 2: print('NO') flag = True break if flag: continue if count_more2b == 0: if len(ones) % 2 == 0: print('NO') else: print('YES') continue elif more2b - a >= 2 * b: print('NO') continue else: if a > more2b - a >= b: print('NO') continue if more2b - a < b: ones.pop() if len(ones) % 2 == 0: print('YES') else: print('NO') ``` No
106,236
[ 0.44287109375, 0.240478515625, -0.087890625, 0.341552734375, -0.591796875, -0.5078125, -0.1556396484375, 0.25732421875, 0.2320556640625, 0.87841796875, 0.70458984375, 0.2056884765625, 0.13916015625, -0.640625, -0.50146484375, -0.04205322265625, -0.654296875, -0.849609375, -0.380859375, -0.224365234375, 0.0240325927734375, -0.1005859375, -1.3369140625, 0.0732421875, -0.2235107421875, 0.7412109375, 0.1297607421875, -0.041015625, 0.88623046875, 1.02734375, -0.01287841796875, -0.466796875, 0.5283203125, -0.65869140625, -0.421142578125, -0.397705078125, 0.76708984375, -0.69775390625, -0.2042236328125, -0.515625, 0.24169921875, -0.423828125, 0.45751953125, -0.60791015625, -1.3544921875, 0.0294342041015625, -0.193115234375, -0.50634765625, -0.216552734375, -0.48974609375, 0.10821533203125, -0.395263671875, 0.303955078125, -0.290283203125, 0.22119140625, 0.272216796875, 0.058868408203125, 0.0958251953125, -0.765625, 0.1998291015625, 0.338623046875, -0.24658203125, -0.019744873046875, -0.92822265625, 0.0936279296875, 0.044525146484375, 0.225830078125, -0.462890625, 0.2509765625, -0.5712890625, -0.205810546875, -0.1949462890625, -0.64697265625, -0.317626953125, -0.1839599609375, 0.428466796875, 0.361328125, -0.10089111328125, -0.95947265625, 0.7646484375, -0.230224609375, 0.94482421875, 0.63525390625, 0.008575439453125, -0.306884765625, -0.478271484375, 0.47021484375, 0.26513671875, 0.43359375, -0.259033203125, -0.054290771484375, 0.5107421875, -0.331787109375, -0.167724609375, 0.34814453125, 0.8525390625, -0.1483154296875, 0.124267578125, 0.6689453125, -0.1033935546875, 0.57763671875, 0.69287109375, -0.50634765625, 1.12890625, -0.447021484375, -0.009674072265625, 0.380126953125, -0.0626220703125, -0.0260467529296875, -0.5029296875, -0.192626953125, -0.473876953125, 0.66015625, 0.382568359375, -0.564453125, 0.876953125, 0.10308837890625, 0.413818359375, -0.61572265625, -0.002712249755859375, 0.72119140625, -0.029205322265625, 0.54931640625, -0.0478515625, 0.1151123046875, -0.276123046875, -0.6298828125, 1.001953125, -0.56494140625, -0.2529296875, 0.57421875, -0.064208984375, -0.25244140625, 0.362548828125, -0.2763671875, 0.75, -0.151611328125, 0.461669921875, 0.76953125, -0.62841796875, 0.9716796875, -0.0301666259765625, 0.2265625, 1.4716796875, 0.24951171875, -0.2176513671875, 0.3701171875, 0.5263671875, -0.85595703125, 0.3525390625, -1.05078125, 0.6015625, -0.045562744140625, 0.200927734375, -0.266357421875, -0.2261962890625, -0.333984375, 0.52392578125, 0.335205078125, -0.0050048828125, -0.14208984375, 0.5625, -0.54736328125, 0.72705078125, -0.328125, 0.6953125, -0.386962890625, -0.2027587890625, -0.005481719970703125, -0.266845703125, 0.06683349609375, -0.376708984375, 0.14501953125, 0.7578125, 0.5234375, 1.35546875, 1.2919921875, -0.226318359375, 0.364990234375, 0.423095703125, -0.52685546875, 0.3935546875, 0.38330078125, 1.0556640625, 0.416748046875, 0.461181640625, 0.0469970703125, 0.093017578125, -0.7236328125, -0.385009765625, 0.1390380859375, 0.67041015625, -0.475341796875, 0.3740234375, 0.248779296875, 0.1494140625, -0.91796875, -0.210693359375, 0.0303802490234375, -0.8173828125, -0.54638671875, 0.41015625, 0.03704833984375, 0.4140625, -0.65185546875, -0.638671875, 0.1275634765625, 1.146484375, -0.341796875, -0.109619140625, 0.4697265625, 0.30615234375, 0.0167999267578125, -0.22119140625, 0.00995635986328125, -0.014801025390625, -0.6767578125, 0.98046875, 0.039337158203125, -0.148681640625, 0.11639404296875, 0.70849609375, 0.1844482421875, 0.75146484375, -0.626953125, -0.384521484375, 0.4619140625, 1.0947265625, 0.09918212890625, 0.74462890625, 0.55419921875, 1.1552734375, 0.326904296875, 0.86474609375, 0.306884765625, 0.264892578125, 0.76708984375, 0.91015625, -0.2357177734375, -0.01302337646484375, 0.221435546875, 0.467529296875, 0.1466064453125, 0.638671875, 0.29638671875, 0.44775390625, -0.18115234375, 0.032867431640625, -0.6728515625, 0.1142578125, -0.2978515625, 0.50439453125, 0.2052001953125, 0.6064453125, -0.442626953125, -0.1087646484375, 0.3681640625, 0.978515625, -1.1103515625, -0.6884765625, 0.042022705078125, -0.03961181640625, -0.0960693359375, 0.051849365234375, 0.57666015625, 0.0285797119140625, 0.42529296875, 0.408203125, -0.366455078125, -0.63623046875, -0.7861328125, -0.740234375, -0.896484375, -0.40185546875, -0.5849609375, -0.234619140625, 0.1978759765625, -0.978515625, -0.07916259765625, -0.5234375, -0.047027587890625, 0.1627197265625, -0.5322265625, 1.03125, -0.5634765625, 0.5048828125, -0.81396484375, 0.235595703125, 0.427001953125, 1.072265625, -0.430908203125, -0.108642578125, -0.1849365234375, -0.31787109375, 0.196044921875, -0.17626953125, 0.4287109375, -0.0341796875, -0.43115234375, -0.7578125, -0.4189453125, -0.16748046875, -0.476318359375, 0.2705078125, -0.6591796875, 0.80517578125, 0.5, -0.52197265625, 0.673828125, 1.0166015625, -0.59716796875, 0.53466796875, 0.1663818359375, 0.1090087890625, -0.65869140625, 1.3125, 0.6787109375, 0.400390625, -0.42138671875, -0.533203125, -0.3681640625, -0.281005859375, 0.338623046875, -0.546875, -0.63623046875, 0.6552734375, 0.0238494873046875, -1.0849609375, 0.1781005859375, -1.0458984375, -0.619140625, -0.237060546875, -0.496826171875, 0.84423828125, 0.80908203125, 0.254638671875, -0.05657958984375, -0.400390625, 0.1473388671875, 0.42138671875, 0.40576171875, -0.8291015625, 0.263671875, 0.7724609375, 0.05462646484375, 0.34521484375, 0.343994140625, -0.3359375, -0.031402587890625, -0.01007080078125, -0.2374267578125, 0.65625, 0.108642578125, 0.2283935546875, 0.390625, 0.472900390625, -0.826171875, -0.1346435546875, -0.30712890625, 0.515625, 0.45068359375, 0.56982421875, 0.305419921875, -0.258544921875, -0.72216796875, -1.0166015625, 0.368896484375, 0.062347412109375, 0.7314453125, -0.5927734375, 0.89990234375, -0.059295654296875, -0.3046875, 0.488525390625, -0.66357421875, 0.0909423828125, 1.1416015625, -0.301513671875, 0.4501953125, -0.70166015625, 0.44921875, 0.12115478515625, 0.138671875, 0.49267578125, 0.23193359375, 0.77294921875, -0.27099609375, -0.54150390625, -0.485595703125, -0.1568603515625, -0.0576171875, -0.7685546875, 0.2191162109375, -0.57080078125, -0.412841796875, -0.7265625, 0.4306640625, 0.82275390625, 1.0576171875, -0.01462554931640625, 0.59326171875, -0.1046142578125, 0.29931640625, 0.56005859375, -0.52392578125, 0.16845703125, -0.5673828125, 0.70751953125, 0.48779296875, 0.171875, -0.62451171875, 0.061126708984375, -0.2076416015625, -0.23046875, 0.12109375, -0.319580078125, -1.0693359375, 0.25537109375, -0.171630859375, 0.59228515625, -0.59765625, -0.344970703125, -0.11004638671875, 0.467529296875, 0.5439453125, -0.73779296875, 0.2127685546875, -1.1064453125, 0.68310546875, 0.359619140625, -0.250732421875, -0.388916015625, -0.5078125, -0.79638671875, -1.095703125, -0.06903076171875, 1.0439453125, 0.11712646484375, 0.380615234375, -1.15625, 0.400634765625, -0.051910400390625, -0.54736328125, 0.1885986328125, -0.3291015625, 0.283935546875, -0.0477294921875, 0.728515625, -0.73974609375, -0.564453125, -0.0182342529296875, -0.95263671875, 0.57080078125, -0.443359375, 0.4169921875, -0.0197601318359375, -0.16552734375, -0.115234375, 0.378662109375, -0.187744140625, 0.28515625, -0.345703125, 0.30908203125, -0.89794921875, -0.4453125, 0.6748046875, -0.2196044921875, -0.179443359375, 0.7548828125, -0.2169189453125, -0.5322265625, 0.1552734375, 0.48486328125, -0.3779296875, 0.537109375, -0.39892578125, 0.408935546875, -0.172119140625, -0.404296875, -0.177001953125, -0.70849609375, 0.8623046875, 0.210205078125, -0.57373046875, -0.474853515625, -0.92138671875, -0.185546875, 0.00908660888671875, -0.196044921875, 0.60400390625, 0.1722412109375, 0.08056640625, -0.06256103515625, -0.221923828125, -0.5810546875, -0.0670166015625, -0.348388671875, 0.01152801513671875, 0.047821044921875, 0.4052734375, 0.404296875, -0.056060791015625, -0.5, -0.4111328125, -0.2340087890625, 0.1390380859375, -0.54345703125, -0.375, -0.235595703125, -0.2890625, -0.63916015625, 0.280517578125, -0.1246337890625, 0.51611328125, 1.0166015625, -0.01617431640625, 0.65869140625, 0.304931640625, -0.9775390625, 1.13671875, 0.203125, -1.2138671875, -0.69677734375, 0.299560546875, 0.10009765625, 0.68359375, 0.1942138671875, -0.481201171875, -0.8681640625, -0.9501953125, 0.2027587890625, -0.88720703125, -0.245849609375, -1.212890625, -0.5361328125, -0.378662109375, 0.4365234375, -0.0665283203125, -0.67724609375, 0.2626953125, -1.0625, 0.38134765625, -0.95947265625, 0.104248046875, -0.7236328125, -0.4853515625, -0.2052001953125, 1.060546875, 0.23876953125, 0.625, 0.0013666152954101562, -0.30126953125, 0.1019287109375, 0.1982421875, -0.5126953125, -0.475830078125, 0.201171875, -0.051849365234375, -0.277099609375, -0.291259765625, -0.5068359375, 0.61474609375, -0.72216796875, 0.42919921875, -0.051910400390625, -0.298583984375, -0.12005615234375, -0.41796875, 1.0888671875, -0.348876953125, 0.1973876953125, -0.4853515625, 0.226806640625, 0.6552734375, -0.2210693359375, -0.30322265625, -0.3466796875, -0.491455078125, -1.25390625, 0.490234375, -0.368408203125, 0.080810546875, -0.7939453125, -0.2174072265625, 1.3291015625, -0.564453125, 0.268310546875, 1.455078125, 0.1661376953125, 0.2191162109375, -0.498046875, 0.671875, 0.7080078125, -0.428955078125, -0.1109619140625, 0.12261962890625, -0.65869140625, -0.118896484375, -0.394775390625, -1.1728515625, -0.77197265625, 0.457275390625, 1.154296875, -0.45263671875, 0.88037109375, -0.24462890625, -1.107421875, -0.591796875, 0.78955078125, -0.1331787109375, 0.240234375, 0.86181640625, 0.28466796875, -0.254150390625, 0.285400390625, -0.107177734375, -0.38134765625, -0.59326171875, 1.177734375, -0.328125, -0.11663818359375, 1.2236328125, 0.87646484375, -1.130859375, -0.82861328125, -0.393310546875, -0.06707763671875, 0.26708984375, -0.8798828125, 0.146728515625, 0.420166015625, -0.56787109375, 0.126708984375, 0.48681640625, -0.3681640625, 0.40625, 0.037567138671875, 0.274169921875, -0.34228515625, 0.313720703125, 0.703125, -0.21435546875, -0.3544921875, -0.9794921875, -0.33642578125, -0.230224609375, -0.0576171875, 0.95654296875, -0.20947265625, 0.405029296875, 0.35205078125, -0.1539306640625, 0.66748046875, -0.609375, -0.28955078125, 0.26220703125, -0.72412109375, -0.310302734375, -0.322265625, 0.44140625, 0.1602783203125, 0.751953125, -0.58056640625, 0.0267333984375, 0.27490234375, 0.44384765625, -0.397705078125, -0.935546875, -0.273193359375, -1.1533203125, -0.55517578125, -0.50390625, -0.6923828125, -0.01372528076171875, 0.57275390625, 0.176513671875, -0.623046875, -0.041595458984375, 0.2249755859375, -0.311279296875, 0.6923828125, -0.59326171875, 0.22021484375, -0.64794921875, -0.344482421875, -0.59619140625, 0.06280517578125, -0.83984375, -0.142333984375, -0.414794921875, 0.394775390625, -0.431396484375, 0.341552734375, -0.4091796875, 0.396484375, -0.1715087890625, -0.63134765625, -0.1396484375, 0.1719970703125, -0.673828125, 1.046875, 0.57080078125, 0.1455078125, 0.34521484375, -0.4990234375, -0.296630859375, -0.31298828125, 0.6123046875, 0.14013671875, -0.0026798248291015625, -0.297607421875, -0.07452392578125, 0.026336669921875, -1.0908203125, 0.29443359375, -0.13232421875, 0.0850830078125, 0.0972900390625, -0.23876953125, 0.465576171875, 1.2509765625, -0.3701171875, 0.39599609375, -0.090087890625, 0.397705078125, 0.443359375, 0.2335205078125, -0.092041015625, 0.8212890625, -0.20361328125, -0.58154296875, 0.1402587890625, 0.1871337890625, 0.1578369140625, 0.04315185546875, -0.388916015625, -0.8583984375, -0.9638671875, -0.224609375, -0.11358642578125, 0.432373046875, 0.5634765625, -0.2274169921875, 0.0099639892578125, -0.3720703125, -0.32470703125, -0.32177734375, -1.3505859375, -0.86767578125, 0.66162109375, -0.126708984375, -0.84375, 0.0214385986328125, -0.202880859375, -0.0936279296875, 0.10711669921875, 0.283447265625, -0.3759765625, 0.48193359375, -0.392822265625, 0.49658203125, -0.2587890625, -0.2227783203125, 0.0252685546875, 0.435791015625, -0.67578125, -0.71240234375, 0.27685546875, 0.9208984375, 0.0303192138671875, -0.35888671875, -0.66796875, 0.4404296875, -0.1474609375, -0.08502197265625, -0.52197265625, 0.399658203125, 0.0001615285873413086, 0.5009765625, -0.69189453125, 0.006313323974609375, -0.56640625, 0.48974609375, 0.1572265625, -0.669921875, -0.57470703125, 0.83935546875, 0.49755859375, -0.3330078125, 0.35302734375, -0.130615234375, 0.419189453125, -0.12493896484375, 0.06219482421875, -0.28662109375, 0.84521484375, 0.81494140625, 0.95068359375, -0.067138671875, 0.395751953125, 0.5986328125, 0.376708984375, 0.0181427001953125, 0.446533203125, 0.039947509765625, 0.014404296875, 0.063720703125, -0.1151123046875, -0.1099853515625, -0.300048828125, -0.67578125, 0.326904296875, -0.33154296875, 0.1650390625, -0.09881591796875, -0.720703125, 0.98486328125, -0.24951171875, -0.0738525390625, 0.09588623046875, -0.6376953125, 0.2421875, 0.6767578125, -0.225341796875, -0.3984375, 0.7119140625, 0.8173828125, 0.54443359375, 0.4677734375, 0.2327880859375, 0.55322265625, -0.68310546875, 0.127197265625, 0.402587890625, -0.0428466796875, -0.3056640625, -0.5673828125, -1.072265625, 0.494873046875, -0.654296875, -0.35400390625, 0.401123046875, -0.8837890625, 0.162353515625, -0.1458740234375, 0.8740234375, -0.354736328125, 0.1397705078125, 0.447509765625, -0.11798095703125, -0.541015625, 0.9404296875, -0.0107269287109375, 0.26220703125, -0.1514892578125, 1.31640625, 0.01111602783203125, 1.44140625, 0.93310546875, 0.041229248046875, 0.08380126953125, 0.462158203125, -0.380126953125, -0.62451171875, -0.27001953125, -0.414794921875, -0.116455078125, -0.724609375, -0.56005859375, -0.2900390625, 0.91455078125, -0.009185791015625, -0.78271484375, -0.332763671875, 0.266845703125, -0.8154296875, 0.414794921875, 0.288818359375, 0.39453125, 0.142822265625, -0.0806884765625, -0.48193359375, -0.5888671875, 0.5947265625, -0.529296875, 0.29638671875, -0.64892578125, -0.2310791015625, -0.4580078125, -0.66845703125, -0.312255859375, -0.2247314453125, -0.2442626953125, -0.8076171875, 0.50048828125, 0.263916015625, 0.4189453125, 0.261474609375, -0.5830078125, 0.1409912109375, 0.82470703125, 1.0947265625, -0.03179931640625, 0.7392578125, 0.417236328125, -0.253173828125, 0.06463623046875, -0.38525390625, 0.42822265625, 0.12322998046875, 0.431884765625, -0.341796875, 0.147216796875, -0.76904296875, -1.0498046875, 0.1356201171875, 0.521484375, 0.057861328125, -0.5693359375, -1.109375, -0.57861328125, -0.90283203125, -0.18212890625, -0.884765625, 0.67529296875, -0.286865234375, 0.1175537109375, -0.08203125, -0.9853515625, 4.38671875, 0.80078125, 0.931640625, 0.1728515625, 0.385009765625, 0.89501953125, 0.265625, -0.8046875, 0.00147247314453125, -0.393798828125, 0.93017578125, -0.29248046875, 0.1124267578125, 0.67529296875, 0.3193359375, 0.5498046875, -0.7685546875, -0.0239715576171875, 0.062469482421875, -1.2998046875, -0.56103515625, 0.29638671875, -0.09124755859375, 0.68310546875, -0.03411865234375, 0.1568603515625, 0.91064453125, -1.205078125, -0.372802734375, -0.83349609375, 0.429443359375, -0.150146484375, 0.68408203125, 0.260986328125, 0.00945281982421875, 0.74169921875, -0.2462158203125, -0.411376953125, -0.28662109375, 0.08343505859375, -0.2210693359375, -0.197509765625, 0.32177734375, -0.541015625, -0.281005859375, 0.2353515625, -0.6220703125, 0.71435546875, 0.08123779296875, -1.0068359375, 0.57275390625, 0.126220703125, 0.78125, -0.78125, -0.6689453125, 0.07940673828125, 0.458740234375, -0.12890625, -0.12188720703125, 0.6162109375, 0.317626953125, 0.8671875, -0.373779296875, 0.85400390625, -1.03515625, 0.837890625, -0.2275390625, 0.266845703125, -0.7294921875, 0.258544921875, -0.273681640625, -0.564453125, -0.331787109375, -0.66455078125, 0.5625, 0.1656494140625, -0.39453125, 0.61669921875, 0.7998046875, -0.383056640625, -0.0288543701171875, -0.437255859375, -0.33544921875, -0.332763671875, 0.578125, 1.2470703125, -0.429443359375, -0.267333984375, -0.1485595703125, 0.625, 0.431640625, 0.63525390625, 0.10198974609375, -0.54150390625, -0.450927734375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows: * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} = 1, then s_i = 1); * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≀ n and w_{i+x} = 1, then s_i = 1); * if both of the aforementioned conditions are false, then s_i is 0. You are given the integer x and the resulting string s. Reconstruct the original string w. Input The first line contains one integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Each test case consists of two lines. The first line contains the resulting string s (2 ≀ |s| ≀ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≀ x ≀ |s| - 1). The total length of all strings s in the input does not exceed 10^5. Output For each test case, print the answer on a separate line as follows: * if no string w can produce the string s at the end of the process, print -1; * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. Example Input 3 101110 2 01 1 110 1 Output 111011 10 -1 Tags: 2-sat, brute force, constructive algorithms, greedy Correct Solution: ``` #------------------------template--------------------------# import os import sys from math import * from collections import * from fractions import * from bisect import * from heapq import* from io import BytesIO, IOBase def vsInput(): sys.stdin = open('input.txt', 'r') sys.stdout = open('output.txt', 'w') BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") ALPHA='abcdefghijklmnopqrstuvwxyz' M=998244353 EPS=1e-6 def value():return tuple(map(int,input().split())) def array():return [int(i) for i in input().split()] def Int():return int(input()) def Str():return input() def arrayS():return [i for i in input().split()] #-------------------------code---------------------------# # vsInput() for _ in range(Int()): s=input() x=Int() n=len(s) w=[1]*n for i in range(n): if(s[i]=='0'): if(i+x<n): w[i+x]=0 if(i-x>=0): w[i-x]=0 ok=True for i in range(n): if(s[i]=='0'): if(i+x<n and w[i+x]==1): ok=False if(i-x>=0 and w[i-x]==1): ok=False else: if(i+x>=n or w[i+x]==0): if(i-x<0 or w[i-x]==0): ok=False if(ok): print(*w,sep="") else: print(-1) ```
107,217
[ 0.201416015625, 0.06231689453125, -0.035919189453125, 0.2349853515625, -0.365478515625, -0.341064453125, 0.058929443359375, -0.210693359375, 0.276123046875, 1.033203125, 0.69287109375, -0.280517578125, 0.140869140625, -1.130859375, -0.378173828125, 0.004566192626953125, -0.67822265625, -0.65625, -0.68310546875, -0.160400390625, -0.0247650146484375, -0.23046875, -1.41796875, -0.166259765625, -0.461669921875, 0.83251953125, 0.477783203125, 0.167236328125, 0.98388671875, 1.1103515625, -0.200439453125, -0.414306640625, 0.61865234375, -1.25, -0.43701171875, -0.370849609375, 0.89111328125, -0.744140625, -0.2288818359375, -0.216552734375, 0.325439453125, -0.41845703125, 0.301025390625, -0.88525390625, -1.2900390625, -0.264892578125, -0.69873046875, -0.39306640625, -0.087890625, -0.71533203125, 0.0181427001953125, -0.345458984375, 0.380615234375, -0.2529296875, 0.19873046875, 0.2001953125, 0.1038818359375, -0.3564453125, -0.888671875, 0.30126953125, -0.11944580078125, -0.031707763671875, 0.1746826171875, -0.5810546875, -0.32568359375, 0.06201171875, -0.220703125, -0.34765625, -0.11590576171875, -1.05859375, 0.1007080078125, 0.320556640625, -0.501953125, -0.2071533203125, -0.34375, 0.03521728515625, 0.35400390625, -0.140380859375, -0.7314453125, 0.96240234375, -0.01294708251953125, 0.91748046875, 0.1212158203125, 0.2415771484375, -0.40234375, -0.58349609375, -0.1483154296875, 0.3173828125, 0.270263671875, -0.25048828125, -0.038818359375, 0.61181640625, -0.5546875, 0.291015625, 0.356201171875, 0.58154296875, -0.233642578125, 0.299072265625, 0.2001953125, 0.0439453125, 0.72607421875, 1.1435546875, -0.54248046875, 0.98095703125, -0.64453125, 0.20556640625, 0.1949462890625, 0.050445556640625, -0.36474609375, -0.1981201171875, -0.0576171875, -0.446044921875, 0.7060546875, 0.3896484375, -0.4970703125, 0.79296875, -0.1483154296875, 0.09368896484375, -0.85498046875, 0.2064208984375, 0.38525390625, 0.100830078125, 0.5712890625, -0.10650634765625, -0.2666015625, -0.5380859375, -0.31201171875, 1.087890625, -0.41845703125, 0.058746337890625, 0.5283203125, -0.053924560546875, -0.11065673828125, 0.1798095703125, 0.139892578125, 0.8837890625, -0.3564453125, 0.3779296875, 0.7236328125, -0.31884765625, 1.0400390625, -0.55419921875, -0.2025146484375, 1.4296875, 0.462890625, 0.177001953125, 0.8544921875, 0.470947265625, -0.73291015625, 0.426513671875, -0.79296875, 0.5615234375, 0.11773681640625, 0.33642578125, -0.1546630859375, 0.183349609375, -0.31103515625, 0.42236328125, 0.06329345703125, 0.0833740234375, -0.59716796875, 0.433837890625, 0.0275726318359375, 0.9140625, -0.25439453125, 0.923828125, -0.277587890625, 0.00801849365234375, -0.4150390625, -0.810546875, 0.265380859375, -0.2161865234375, -0.458984375, 0.7802734375, 0.72607421875, 0.984375, 0.96142578125, -0.482666015625, 0.233642578125, 0.0296783447265625, -0.5302734375, -0.06597900390625, 0.0692138671875, 0.9814453125, 0.1666259765625, 0.447265625, 0.1058349609375, -0.217529296875, -0.84375, -0.5791015625, 0.208251953125, 1.03515625, -0.84033203125, 0.08087158203125, -0.04766845703125, 0.240478515625, -0.7275390625, -0.2236328125, -0.326416015625, -0.8564453125, -0.3564453125, 0.5517578125, 0.0926513671875, 0.1527099609375, -0.693359375, -0.5869140625, 0.578125, 1, -0.237548828125, -0.328369140625, 0.2021484375, -0.0296478271484375, -0.1719970703125, 0.49560546875, 0.0205841064453125, -0.33447265625, -0.697265625, 0.95703125, -0.05926513671875, 0.03485107421875, -0.059326171875, 0.9130859375, 0.27001953125, 0.87353515625, -0.289306640625, 0.05450439453125, 0.253173828125, 1.2119140625, 0.04638671875, 0.3466796875, 0.5263671875, 1.1259765625, 0.64599609375, 0.71240234375, 0.52978515625, 0.186767578125, 0.8544921875, 0.974609375, 0.034637451171875, 0.41015625, -0.0693359375, 0.33740234375, 0.10894775390625, 0.437255859375, 0.1685791015625, 0.275390625, 0.00762939453125, 0.1959228515625, -0.3955078125, 0.1904296875, -0.2366943359375, 0.78466796875, 0.11004638671875, 0.36669921875, -0.6806640625, -0.84228515625, -0.11236572265625, 0.7626953125, -0.99365234375, -0.453369140625, -0.16064453125, 0.362060546875, -0.0206451416015625, 0.047393798828125, 0.333740234375, 0.59375, 0.61181640625, 0.255126953125, -0.16357421875, -0.46240234375, -0.98583984375, -0.495361328125, -0.93798828125, -0.203125, -0.409423828125, 0.2171630859375, -0.108154296875, -0.72216796875, 0.044677734375, -0.1353759765625, -0.5107421875, 0.313720703125, -1.0966796875, 0.5078125, -0.32763671875, 0.358154296875, -0.83544921875, 0.5478515625, 0.2318115234375, 1.0546875, -0.57373046875, -0.0185089111328125, 0.247314453125, -0.734375, 0.1572265625, 0.1060791015625, 0.307861328125, 0.361328125, -0.1553955078125, -0.59375, -0.349609375, -0.243408203125, -0.298828125, 0.1748046875, -0.47412109375, 0.8837890625, 0.45361328125, -0.60791015625, 0.658203125, 0.83837890625, -0.978515625, 0.55029296875, 0.09930419921875, -0.15869140625, -0.75390625, 1.4443359375, 0.317626953125, 0.282470703125, -0.56201171875, -0.26416015625, -0.034942626953125, 0.018463134765625, 0.12432861328125, -0.603515625, -0.40478515625, 0.57958984375, 0.08416748046875, -1.11328125, 0.13037109375, -0.8515625, -0.53369140625, -0.2364501953125, -0.293212890625, 1.1376953125, 0.77392578125, 0.1729736328125, -0.0816650390625, -0.1826171875, -0.170654296875, 0.63623046875, 0.7353515625, -0.57373046875, -0.0008807182312011719, 0.7919921875, 0.0731201171875, -0.162109375, -0.0022411346435546875, -0.165283203125, 0.12066650390625, -0.01043701171875, 0.34228515625, 0.81884765625, 0.1944580078125, 0.20263671875, 0.54248046875, 0.7734375, -1.0927734375, -0.180419921875, 0.00707244873046875, 0.552734375, 0.60302734375, 0.01288604736328125, 0.3798828125, -0.11041259765625, -0.51025390625, -1.240234375, 0.2340087890625, 0.3173828125, 0.65087890625, -0.66748046875, 0.8759765625, 0.1671142578125, -0.288818359375, 0.13720703125, -0.5048828125, 0.245849609375, 0.96337890625, -0.003566741943359375, 0.529296875, -0.7802734375, 0.3125, 0.18701171875, -0.061553955078125, 0.6513671875, 0.280517578125, 0.73388671875, -0.4951171875, -0.451416015625, -0.603515625, -0.2294921875, -0.0242462158203125, -0.7001953125, 0.203857421875, -0.414306640625, -0.51025390625, -0.935546875, 0.23095703125, 0.73828125, 0.7626953125, -0.0377197265625, 0.5517578125, 0.1199951171875, 0.62646484375, 0.5322265625, -0.2386474609375, 0.309814453125, -0.75927734375, 0.67041015625, 0.213134765625, -0.220703125, -0.58642578125, -0.33740234375, -0.255126953125, -0.1365966796875, 0.1741943359375, -0.367919921875, -0.62451171875, 0.446533203125, -0.190185546875, 0.7236328125, -0.671875, -0.451171875, -0.3291015625, 0.46630859375, 0.252685546875, -0.95556640625, 0.386474609375, -0.76220703125, 0.8095703125, 0.419677734375, -0.165771484375, -0.63671875, -0.48291015625, -0.72802734375, -0.6787109375, 0.00405120849609375, 1.0537109375, -0.212158203125, 0.46875, -1.212890625, 0.143798828125, 0.466064453125, -0.37109375, -0.12396240234375, -0.0557861328125, 0.59814453125, 0.06640625, 0.99169921875, -0.8251953125, -0.5732421875, -0.1424560546875, -1.291015625, 0.4189453125, -0.8203125, 0.51318359375, 0.133056640625, 0.1446533203125, -0.302734375, 0.6396484375, -0.1243896484375, 0.2265625, -0.297119140625, 0.368408203125, -0.92626953125, -0.5400390625, 0.77880859375, -0.48193359375, -0.2242431640625, 1.0322265625, -0.130126953125, -0.552734375, 0.433349609375, 0.470458984375, -0.580078125, 0.45849609375, -0.4462890625, 0.58447265625, -0.2900390625, -0.456298828125, -0.0633544921875, -0.5888671875, 0.9130859375, 0.113525390625, -0.95703125, -0.325927734375, -0.86572265625, 0.114013671875, -0.1053466796875, -0.308837890625, 0.1390380859375, 0.0679931640625, 0.2257080078125, -0.26025390625, -0.184326171875, -0.3818359375, -0.51708984375, -0.290771484375, -0.035552978515625, 0.1566162109375, 0.60693359375, 0.35009765625, -0.01113128662109375, -0.32568359375, -0.349853515625, -0.0223236083984375, 0.0100555419921875, -0.5361328125, -0.08697509765625, -0.07177734375, -0.31103515625, -0.01397705078125, 0.345703125, -0.1331787109375, 0.03515625, 0.7880859375, 0.11279296875, 0.505859375, 0.1759033203125, -0.63720703125, 0.640625, 0.0517578125, -1.0849609375, -0.387939453125, 0.49462890625, 0.04278564453125, 0.56201171875, 0.26171875, -1.091796875, -0.6474609375, -0.626953125, 0.152587890625, -0.615234375, -0.0243682861328125, -0.9697265625, -0.5087890625, -0.39990234375, 0.67626953125, 0.135986328125, -0.78662109375, 0.2064208984375, -1.2109375, 0.037628173828125, -1.056640625, -0.1295166015625, -0.796875, -0.43701171875, -0.05194091796875, 0.712890625, 0.006317138671875, 0.427490234375, 0.0848388671875, -0.10076904296875, 0.329345703125, 0.30126953125, -0.7080078125, -0.2169189453125, -0.229736328125, -0.005157470703125, -0.1605224609375, 0.041717529296875, -0.481689453125, 0.70361328125, -0.6767578125, 0.349365234375, -0.10693359375, -0.409912109375, -0.0855712890625, 0.034271240234375, 0.9765625, -0.11541748046875, 0.259765625, -0.290771484375, 0.14111328125, 0.5771484375, -0.303466796875, -0.55029296875, -0.92919921875, -0.437744140625, -1.0615234375, 0.607421875, -0.14501953125, 0.1107177734375, -0.73388671875, -0.5341796875, 1.1015625, -0.58349609375, 0.4765625, 1.17578125, -0.1424560546875, 0.389892578125, -0.1539306640625, 0.54296875, 0.58642578125, -0.7333984375, 0.29736328125, 0.5537109375, -0.5419921875, 0.364501953125, -0.399658203125, -0.80859375, -0.56982421875, 0.1876220703125, 1.052734375, -0.1812744140625, 0.56787109375, -0.322509765625, -1.056640625, -0.5498046875, 0.72265625, 0.07781982421875, 0.322265625, 0.6669921875, 0.25, 0.1219482421875, 0.16064453125, -0.270751953125, 0.24560546875, -0.501953125, 1.3134765625, -0.1099853515625, -0.26513671875, 1.005859375, 0.80859375, -0.96630859375, -0.98388671875, 0.1669921875, 0.02734375, -0.411865234375, -0.63720703125, 0.090087890625, 0.5712890625, -0.69970703125, 0.060150146484375, 0.513671875, -0.1444091796875, 0.6181640625, -0.1964111328125, 0.54248046875, -0.58349609375, 0.93408203125, 0.67724609375, -0.525390625, -0.0277557373046875, -0.7607421875, -0.459228515625, -0.50341796875, 0.0469970703125, 0.51953125, -0.62890625, 0.3115234375, 0.63427734375, 0.1861572265625, 0.875, -0.548828125, -0.5283203125, 0.06805419921875, -0.419921875, -0.76220703125, 0.1455078125, -0.10589599609375, 0.0928955078125, 0.54345703125, -0.66064453125, 0.1146240234375, -0.081298828125, 0.09173583984375, -0.378662109375, -1.03515625, -0.306640625, -0.8701171875, -0.333984375, -0.91455078125, -0.87841796875, -0.04443359375, 0.1558837890625, 0.11541748046875, -0.56396484375, -0.154296875, 0.1923828125, -0.3818359375, 0.86767578125, -0.81787109375, 0.317626953125, -0.176025390625, -0.49560546875, -0.81689453125, -0.0000692605972290039, -0.38330078125, 0.15576171875, -0.82763671875, 0.285888671875, -0.31640625, 0.61181640625, -0.261962890625, 0.29443359375, -0.497314453125, -0.412353515625, 0.300537109375, -0.0172882080078125, -0.37890625, 0.90771484375, 0.315673828125, -0.043060302734375, 0.23095703125, -0.30078125, -0.053497314453125, -0.73876953125, 0.365234375, 0.79931640625, -0.2457275390625, -0.3134765625, 0.049560546875, 0.11907958984375, -1.0986328125, 0.5126953125, -0.4326171875, 0.01068115234375, 0.5712890625, -0.17626953125, 0.413330078125, 1.2431640625, -0.39990234375, 0.755859375, -0.007305145263671875, 0.1865234375, 0.2418212890625, 0.171875, -0.1624755859375, 0.54248046875, 0.053436279296875, 0.07244873046875, 0.2193603515625, 0.1734619140625, 0.12493896484375, 0.220947265625, -0.077880859375, -0.5595703125, -0.7939453125, -0.275390625, -0.265380859375, 0.24169921875, 0.44482421875, -0.175537109375, -0.146484375, -0.1859130859375, -0.329345703125, 0.460205078125, -1.142578125, -1.2626953125, 0.59375, -0.238525390625, -0.436767578125, -0.301513671875, -0.494140625, -0.3779296875, 0.0208282470703125, 0.253173828125, -0.368896484375, 0.35009765625, -0.349853515625, 0.46044921875, -0.238525390625, 0.0283660888671875, 0.09881591796875, 0.58837890625, -0.537109375, -0.6689453125, 0.08502197265625, 1.1005859375, 0.023895263671875, -0.330810546875, -0.1571044921875, 0.288330078125, -0.059478759765625, 0.46923828125, -0.284423828125, 0.271240234375, -0.472412109375, 0.53662109375, -0.88330078125, 0.328125, -0.392822265625, 0.38720703125, 0.29931640625, -0.364013671875, -0.50634765625, 0.74609375, 0.58056640625, 0.024383544921875, 0.91748046875, -0.182373046875, 0.5458984375, 0.045013427734375, 0.031524658203125, -0.117919921875, 0.89404296875, 0.70068359375, 0.65380859375, -0.2156982421875, 0.267822265625, 0.81982421875, 0.2247314453125, -0.464111328125, 0.328857421875, 0.07958984375, -0.09478759765625, 0.29638671875, -0.08563232421875, -0.1285400390625, 0.07598876953125, -0.499267578125, 0.57373046875, -0.27294921875, -0.1077880859375, -0.25, -0.94287109375, 1.0546875, -0.1336669921875, -0.04400634765625, 0.287109375, -0.3642578125, 0.258544921875, 0.7548828125, -0.2230224609375, -0.2626953125, 0.818359375, 0.677734375, 0.352783203125, 0.69140625, 0.19482421875, 0.408447265625, -0.7265625, 0.10821533203125, 0.048828125, 0.09979248046875, -0.441650390625, -0.338134765625, -0.55419921875, 0.469482421875, -0.63916015625, -0.1787109375, 0.54736328125, -0.8037109375, 0.07122802734375, -0.58203125, 1.0419921875, -0.73388671875, 0.138427734375, 0.320068359375, -0.047637939453125, -0.52685546875, 0.9638671875, -0.08404541015625, 0.181884765625, 0.06390380859375, 1.0478515625, -0.0987548828125, 1.3037109375, 0.75732421875, 0.0010318756103515625, -0.2509765625, 0.344970703125, -0.4599609375, -0.2049560546875, -0.57958984375, -0.4755859375, 0.2060546875, -0.990234375, -0.677734375, 0.0166168212890625, 0.7685546875, 0.2012939453125, -1.173828125, -0.218505859375, 0.10833740234375, -0.9677734375, 0.1448974609375, 0.293701171875, 0.4072265625, -0.006328582763671875, -0.376220703125, -0.158447265625, -0.5166015625, 0.5830078125, -0.88525390625, 0.352783203125, -0.6767578125, -0.419677734375, -0.779296875, -0.47216796875, -0.1234130859375, -0.440673828125, -0.39013671875, -0.60888671875, 0.32568359375, 0.477783203125, 0.50439453125, 0.0347900390625, -0.37353515625, 0.06524658203125, 0.76416015625, 0.91943359375, 0.24267578125, 0.86669921875, 0.386474609375, -0.29248046875, 0.53515625, -0.260009765625, 0.224365234375, -0.415771484375, 0.3076171875, -0.68310546875, 0.1162109375, -0.7705078125, -1.05078125, -0.10125732421875, 0.292236328125, 0.10272216796875, -0.6103515625, -0.90869140625, -0.5146484375, -1.01953125, -0.0133514404296875, -0.59521484375, 0.7587890625, -0.341552734375, -0.10699462890625, -0.1390380859375, -1.4140625, 4.390625, 0.8642578125, 0.61962890625, 0.3642578125, 0.42919921875, 0.7734375, 0.361083984375, -0.609375, -0.398681640625, -0.4921875, 0.69189453125, -0.2025146484375, -0.09515380859375, 0.71337890625, 0.5859375, 0.27978515625, -0.492919921875, 0.1259765625, 0.230224609375, -0.93115234375, -0.7255859375, 0.447021484375, -0.234130859375, 0.8046875, 0.12469482421875, 0.256591796875, 0.6298828125, -1.13671875, -0.093994140625, -0.60107421875, 0.08380126953125, -0.330322265625, 0.89794921875, -0.03961181640625, -0.23046875, 0.763671875, 0.39599609375, -0.1441650390625, -0.187255859375, -0.031036376953125, -0.005035400390625, -0.09674072265625, 0.74755859375, -0.8173828125, -0.275146484375, 0.373046875, -0.7353515625, 0.405029296875, 0.22412109375, -1.1591796875, 0.9521484375, -0.36181640625, 0.5400390625, -0.55810546875, -0.91064453125, 0.189453125, 0.04693603515625, 0.27734375, -0.389404296875, 0.27587890625, 0.52978515625, 0.5849609375, 0.1251220703125, 0.6328125, -1.0869140625, 0.457763671875, -0.359130859375, 0.6435546875, -0.69140625, -0.0823974609375, -0.06903076171875, -0.3232421875, -0.091796875, -0.54541015625, 0.70361328125, 0.1475830078125, -0.5966796875, 0.6650390625, 0.62939453125, -0.6884765625, 0.1556396484375, -0.1856689453125, -0.0928955078125, -0.394287109375, 0.490966796875, 1.3232421875, -0.46875, -0.3037109375, -0.497802734375, 0.38330078125, 0.42041015625, 1.0859375, 0.047088623046875, -0.167236328125, -0.2154541015625 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows: * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} = 1, then s_i = 1); * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≀ n and w_{i+x} = 1, then s_i = 1); * if both of the aforementioned conditions are false, then s_i is 0. You are given the integer x and the resulting string s. Reconstruct the original string w. Input The first line contains one integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Each test case consists of two lines. The first line contains the resulting string s (2 ≀ |s| ≀ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≀ x ≀ |s| - 1). The total length of all strings s in the input does not exceed 10^5. Output For each test case, print the answer on a separate line as follows: * if no string w can produce the string s at the end of the process, print -1; * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. Example Input 3 101110 2 01 1 110 1 Output 111011 10 -1 Tags: 2-sat, brute force, constructive algorithms, greedy Correct Solution: ``` t = int(input()) for i in range(t): s = input() m = len(s) x = int(input()) ANS = [1] * m for i in range(m): if s[i] == "0": if i-x >= 0: ANS[i-x] = 0 if i+x < m: ANS[i+x] = 0 ng = 0 for i in range(m): one = 0 if (i-x >= 0 and ANS[i-x] == 1) or (i+x < m and ANS[i+x] == 1): one = 1 if (one == 1 and s[i] == "0") or (one == 0 and s[i] == "1"): ng = 1 break if ng == 1: print(-1) else: print("".join([str(i) for i in ANS])) ```
107,218
[ 0.301513671875, 0.0816650390625, 0.0927734375, 0.11077880859375, -0.380859375, -0.446533203125, 0.051483154296875, -0.1529541015625, 0.2353515625, 0.904296875, 0.65673828125, -0.3623046875, 0.08343505859375, -1.134765625, -0.330322265625, -0.0777587890625, -0.59228515625, -0.580078125, -0.374267578125, -0.257080078125, -0.0236663818359375, -0.038116455078125, -1.517578125, -0.2108154296875, -0.442626953125, 0.81982421875, 0.43701171875, 0.145751953125, 0.96630859375, 1.2255859375, -0.245361328125, -0.463134765625, 0.65869140625, -1.28125, -0.3779296875, -0.443115234375, 0.7177734375, -0.81103515625, -0.2088623046875, -0.29638671875, 0.359619140625, -0.363525390625, 0.43115234375, -0.8359375, -1.3349609375, -0.259033203125, -0.6201171875, -0.274658203125, -0.12744140625, -0.73095703125, -0.07733154296875, -0.369873046875, 0.298828125, -0.28369140625, 0.224853515625, 0.05853271484375, 0.034027099609375, -0.348876953125, -0.88525390625, 0.402587890625, -0.10101318359375, -0.151123046875, 0.2568359375, -0.6748046875, -0.292724609375, -0.0328369140625, -0.11285400390625, -0.345947265625, -0.0364990234375, -0.939453125, 0.1290283203125, 0.36181640625, -0.4697265625, -0.2215576171875, -0.3583984375, 0.0181427001953125, 0.286376953125, 0.1661376953125, -0.72412109375, 0.9775390625, -0.095703125, 0.97607421875, 0.2301025390625, 0.278564453125, -0.319580078125, -0.58447265625, -0.10577392578125, 0.427001953125, 0.270751953125, -0.28857421875, -0.1844482421875, 0.5615234375, -0.66650390625, 0.34716796875, 0.2369384765625, 0.5224609375, -0.290771484375, 0.11346435546875, 0.331298828125, 0.034576416015625, 0.64990234375, 1.0615234375, -0.460205078125, 0.9248046875, -0.60693359375, 0.1474609375, 0.19921875, 0.145751953125, -0.411865234375, -0.0616455078125, -0.050506591796875, -0.2412109375, 0.69384765625, 0.2587890625, -0.5576171875, 0.7880859375, -0.04681396484375, 0.172607421875, -0.7890625, 0.298583984375, 0.44482421875, 0.1253662109375, 0.6337890625, 0.010162353515625, -0.3017578125, -0.359619140625, -0.3154296875, 1.0166015625, -0.397216796875, -0.09735107421875, 0.452880859375, 0.014190673828125, 0.045501708984375, 0.16796875, -0.0091705322265625, 0.92138671875, -0.365478515625, 0.484130859375, 0.7294921875, -0.42822265625, 1.0341796875, -0.6064453125, -0.12060546875, 1.3994140625, 0.376953125, 0.1807861328125, 0.96484375, 0.425537109375, -0.87060546875, 0.320556640625, -0.921875, 0.7041015625, 0.1009521484375, 0.235595703125, -0.109375, 0.1534423828125, -0.2327880859375, 0.3046875, -0.06048583984375, 0.11431884765625, -0.47314453125, 0.466064453125, -0.1795654296875, 0.96533203125, -0.2127685546875, 0.82373046875, -0.0941162109375, -0.0789794921875, -0.3984375, -0.76611328125, 0.243896484375, -0.277587890625, -0.341796875, 0.90771484375, 0.72802734375, 1.0166015625, 1.0986328125, -0.342529296875, 0.2142333984375, 0.088134765625, -0.58642578125, 0.10650634765625, 0.2261962890625, 0.95703125, 0.270751953125, 0.537109375, 0.0966796875, -0.2880859375, -0.86767578125, -0.433837890625, 0.0762939453125, 0.9775390625, -0.78125, 0.2255859375, 0.0977783203125, 0.222412109375, -0.7724609375, -0.1304931640625, -0.455322265625, -0.91650390625, -0.3173828125, 0.483154296875, 0.06768798828125, 0.1412353515625, -0.6767578125, -0.51708984375, 0.505859375, 1.025390625, -0.2491455078125, -0.31396484375, 0.1077880859375, 0.040802001953125, -0.038604736328125, 0.386474609375, -0.006748199462890625, -0.219482421875, -0.79833984375, 0.93017578125, -0.10174560546875, -0.03533935546875, 0.09307861328125, 0.78173828125, 0.31591796875, 0.98974609375, -0.177490234375, -0.10174560546875, 0.329833984375, 1.091796875, 0.08843994140625, 0.318603515625, 0.46826171875, 1.193359375, 0.671875, 0.7109375, 0.44775390625, 0.211669921875, 0.677734375, 1.00390625, 0.1346435546875, 0.423095703125, -0.1513671875, 0.272705078125, 0.21484375, 0.468505859375, 0.240478515625, 0.259765625, -0.054595947265625, 0.2222900390625, -0.340576171875, 0.130126953125, -0.2142333984375, 0.9306640625, 0.2435302734375, 0.323974609375, -0.64306640625, -0.78271484375, 0.10443115234375, 0.82373046875, -1.048828125, -0.4365234375, -0.187744140625, 0.29638671875, -0.0005512237548828125, 0.0027217864990234375, 0.284912109375, 0.495849609375, 0.5830078125, 0.28271484375, -0.3203125, -0.54833984375, -0.9892578125, -0.5576171875, -1.0458984375, -0.2315673828125, -0.34619140625, 0.10467529296875, -0.092041015625, -0.8564453125, 0.031768798828125, -0.501953125, -0.492431640625, 0.33544921875, -0.9990234375, 0.50146484375, -0.1881103515625, 0.378662109375, -0.93994140625, 0.432373046875, 0.301513671875, 1.099609375, -0.50341796875, 0.037200927734375, 0.10186767578125, -0.90869140625, 0.1317138671875, 0.019378662109375, 0.285888671875, 0.265869140625, -0.281494140625, -0.65478515625, -0.327880859375, -0.134765625, -0.432373046875, 0.232666015625, -0.50390625, 0.9638671875, 0.462890625, -0.59375, 0.5986328125, 0.87890625, -0.89208984375, 0.58740234375, 0.1624755859375, 0.0662841796875, -0.72509765625, 1.404296875, 0.342041015625, 0.388427734375, -0.591796875, -0.380859375, -0.21630859375, -0.061279296875, 0.23828125, -0.62255859375, -0.264892578125, 0.334228515625, 0.03924560546875, -1.01171875, 0.24853515625, -0.9794921875, -0.521484375, -0.369384765625, -0.2335205078125, 1.1494140625, 0.90869140625, 0.1661376953125, -0.06768798828125, -0.24072265625, -0.1912841796875, 0.6826171875, 0.71142578125, -0.50927734375, 0.188720703125, 0.98779296875, -0.042999267578125, -0.1619873046875, -0.047698974609375, -0.18017578125, 0.053741455078125, 0.0789794921875, 0.343017578125, 0.837890625, 0.282470703125, 0.1470947265625, 0.48974609375, 0.8251953125, -1.1123046875, -0.1572265625, -0.087646484375, 0.44677734375, 0.50146484375, 0.1326904296875, 0.39990234375, -0.0794677734375, -0.492919921875, -1.251953125, 0.311767578125, 0.2705078125, 0.79931640625, -0.7353515625, 0.83349609375, 0.16552734375, -0.279052734375, 0.1544189453125, -0.491943359375, 0.154052734375, 1.0107421875, 0.059539794921875, 0.6171875, -0.83349609375, 0.2529296875, 0.272705078125, -0.06011962890625, 0.59521484375, 0.26708984375, 0.66845703125, -0.32568359375, -0.375, -0.5029296875, -0.2452392578125, -0.055145263671875, -0.7099609375, 0.154052734375, -0.4375, -0.55419921875, -1.044921875, 0.2314453125, 0.69677734375, 0.73291015625, 0.05023193359375, 0.462158203125, -0.06732177734375, 0.70361328125, 0.56298828125, -0.26318359375, 0.219482421875, -0.8037109375, 0.78466796875, 0.17626953125, -0.314697265625, -0.529296875, -0.257568359375, -0.246826171875, -0.1566162109375, 0.0733642578125, -0.494384765625, -0.50048828125, 0.391357421875, -0.173583984375, 0.71044921875, -0.5673828125, -0.42724609375, -0.368408203125, 0.521484375, 0.1407470703125, -0.96337890625, 0.383056640625, -0.7119140625, 0.84814453125, 0.2666015625, -0.11614990234375, -0.6611328125, -0.59814453125, -0.666015625, -0.787109375, -0.06256103515625, 1.0439453125, -0.00493621826171875, 0.456787109375, -1.244140625, 0.09716796875, 0.289794921875, -0.46337890625, -0.059051513671875, -0.1474609375, 0.481689453125, 0.151123046875, 0.87451171875, -0.82080078125, -0.65234375, -0.225830078125, -1.4111328125, 0.5322265625, -0.89404296875, 0.4677734375, 0.260009765625, 0.1688232421875, -0.3076171875, 0.51220703125, -0.1549072265625, 0.2347412109375, -0.283203125, 0.412841796875, -0.8427734375, -0.4853515625, 0.73876953125, -0.415283203125, -0.317138671875, 0.87939453125, -0.24267578125, -0.45263671875, 0.377685546875, 0.40234375, -0.62646484375, 0.53564453125, -0.42578125, 0.703125, -0.225341796875, -0.421630859375, -0.170654296875, -0.55419921875, 0.89892578125, 0.087646484375, -1.0966796875, -0.1551513671875, -0.9541015625, 0.057830810546875, -0.137939453125, -0.23974609375, 0.26904296875, 0.2080078125, 0.1475830078125, -0.216064453125, -0.1778564453125, -0.442138671875, -0.42919921875, -0.4619140625, -0.17431640625, 0.1812744140625, 0.5244140625, 0.392822265625, -0.0279083251953125, -0.232421875, -0.32958984375, 0.1224365234375, 0.07110595703125, -0.42919921875, -0.06243896484375, -0.09356689453125, -0.255859375, -0.10711669921875, 0.4931640625, -0.267333984375, 0.11065673828125, 0.892578125, 0.0709228515625, 0.50244140625, 0.27783203125, -0.638671875, 0.6513671875, 0.21484375, -1.1435546875, -0.443603515625, 0.42822265625, -0.01390838623046875, 0.56201171875, 0.33251953125, -1.1728515625, -0.7685546875, -0.70751953125, 0.076171875, -0.7138671875, -0.06988525390625, -1.064453125, -0.51806640625, -0.443359375, 0.572265625, 0.05194091796875, -0.740234375, 0.173828125, -1.2158203125, 0.149169921875, -1.212890625, -0.12249755859375, -0.736328125, -0.6015625, -0.09759521484375, 0.73583984375, 0.02374267578125, 0.337646484375, 0.1336669921875, -0.244384765625, 0.305419921875, 0.323486328125, -0.76220703125, -0.176025390625, -0.21142578125, -0.00815582275390625, -0.1680908203125, 0.0059967041015625, -0.386474609375, 0.736328125, -0.646484375, 0.338623046875, -0.05718994140625, -0.454345703125, -0.136962890625, 0.0167694091796875, 1.115234375, -0.1768798828125, 0.250732421875, -0.40771484375, 0.01267242431640625, 0.58447265625, -0.31494140625, -0.6103515625, -0.947265625, -0.353515625, -1.01953125, 0.7138671875, -0.2479248046875, 0.1966552734375, -0.673828125, -0.494873046875, 1.0576171875, -0.654296875, 0.515625, 1.1728515625, -0.0911865234375, 0.423095703125, -0.039154052734375, 0.5126953125, 0.58984375, -0.8037109375, 0.22802734375, 0.4111328125, -0.56689453125, 0.38037109375, -0.219482421875, -0.85498046875, -0.59375, 0.1939697265625, 1.1533203125, -0.13232421875, 0.6240234375, -0.349609375, -1.083984375, -0.52099609375, 0.7021484375, 0.12420654296875, 0.3232421875, 0.74853515625, 0.1766357421875, -0.0006418228149414062, 0.1561279296875, -0.305419921875, 0.0899658203125, -0.395751953125, 1.14453125, -0.03619384765625, -0.1773681640625, 1.0859375, 0.90869140625, -0.96484375, -0.96044921875, 0.2200927734375, -0.23046875, -0.386962890625, -0.6552734375, 0.0648193359375, 0.459716796875, -0.728515625, 0.05963134765625, 0.480712890625, -0.066162109375, 0.630859375, -0.26025390625, 0.421142578125, -0.66259765625, 0.9091796875, 0.6904296875, -0.42529296875, -0.04193115234375, -0.90625, -0.3251953125, -0.49560546875, -0.03411865234375, 0.58203125, -0.56689453125, 0.250244140625, 0.791015625, -0.00345611572265625, 0.85986328125, -0.6142578125, -0.60986328125, 0.08160400390625, -0.45849609375, -0.69189453125, 0.033477783203125, 0.04119873046875, 0.01549530029296875, 0.46826171875, -0.74169921875, 0.06597900390625, -0.036224365234375, 0.145263671875, -0.309814453125, -1.013671875, -0.2193603515625, -0.853515625, -0.365234375, -0.8984375, -0.7294921875, -0.056060791015625, 0.136474609375, 0.01300048828125, -0.59716796875, -0.266845703125, 0.208740234375, -0.4775390625, 0.9541015625, -0.740234375, 0.3984375, -0.28564453125, -0.552734375, -0.68994140625, 0.041473388671875, -0.5869140625, 0.024749755859375, -0.72705078125, 0.436767578125, -0.3779296875, 0.60107421875, -0.353271484375, 0.4462890625, -0.35888671875, -0.57763671875, 0.306884765625, -0.080322265625, -0.399169921875, 0.96337890625, 0.329345703125, -0.061981201171875, 0.171142578125, -0.45849609375, 0.07867431640625, -0.58740234375, 0.3212890625, 0.7353515625, -0.268310546875, -0.2098388671875, 0.095458984375, 0.11749267578125, -1.15234375, 0.466064453125, -0.354248046875, -0.0540771484375, 0.5390625, -0.11517333984375, 0.450439453125, 1.19140625, -0.4111328125, 0.619140625, -0.0302581787109375, 0.24072265625, 0.33349609375, 0.28955078125, -0.198974609375, 0.53271484375, 0.046295166015625, -0.03277587890625, 0.1199951171875, 0.06463623046875, 0.189453125, 0.1756591796875, -0.0484619140625, -0.630859375, -0.7958984375, -0.2130126953125, -0.29052734375, 0.27490234375, 0.482666015625, -0.212890625, -0.267578125, -0.08306884765625, -0.418212890625, 0.276123046875, -1.1982421875, -1.033203125, 0.53369140625, -0.2529296875, -0.50146484375, -0.294189453125, -0.398681640625, -0.2386474609375, 0.1697998046875, 0.373291015625, -0.53466796875, 0.305419921875, -0.365234375, 0.41455078125, -0.3583984375, -0.191650390625, 0.12548828125, 0.499267578125, -0.40234375, -0.72802734375, 0.11083984375, 1.1953125, 0.1336669921875, -0.243896484375, -0.26953125, 0.281005859375, -0.1339111328125, 0.1961669921875, -0.330322265625, 0.4267578125, -0.48681640625, 0.380615234375, -0.880859375, 0.255859375, -0.455322265625, 0.338134765625, 0.4296875, -0.379150390625, -0.56982421875, 0.59765625, 0.463134765625, -0.029022216796875, 0.92333984375, -0.2763671875, 0.59130859375, 0.097900390625, 0.1673583984375, -0.1878662109375, 0.9609375, 0.69677734375, 0.68115234375, -0.11248779296875, 0.300048828125, 0.8203125, 0.08026123046875, -0.41796875, 0.417724609375, 0.2193603515625, -0.10650634765625, 0.404296875, -0.2413330078125, -0.171142578125, 0.0263671875, -0.5263671875, 0.6123046875, -0.298095703125, 0.058013916015625, -0.09918212890625, -0.97412109375, 1.1357421875, -0.265869140625, -0.00862884521484375, 0.205078125, -0.419921875, 0.2978515625, 0.6943359375, -0.338623046875, -0.09942626953125, 0.74609375, 0.72021484375, 0.52685546875, 0.6611328125, 0.2337646484375, 0.418212890625, -0.7861328125, 0.064453125, -0.09271240234375, 0.13818359375, -0.279052734375, -0.5390625, -0.54443359375, 0.43408203125, -0.6376953125, -0.27294921875, 0.66455078125, -0.7919921875, 0.25732421875, -0.3740234375, 1.07421875, -0.47607421875, 0.05633544921875, 0.2919921875, -0.20068359375, -0.61767578125, 0.89501953125, -0.1263427734375, 0.25341796875, -0.0018558502197265625, 1.19140625, -0.10546875, 1.4150390625, 0.6162109375, -0.020660400390625, -0.1279296875, 0.3271484375, -0.1798095703125, -0.2322998046875, -0.51123046875, -0.47216796875, 0.2022705078125, -0.92822265625, -0.681640625, -0.0131378173828125, 0.83984375, 0.1802978515625, -1.2177734375, -0.08966064453125, 0.12286376953125, -0.923828125, 0.239501953125, 0.1424560546875, 0.370849609375, 0.185791015625, -0.282958984375, -0.0936279296875, -0.340576171875, 0.60400390625, -0.8095703125, 0.45703125, -0.5830078125, -0.387939453125, -0.6953125, -0.61279296875, -0.10626220703125, -0.41943359375, -0.42822265625, -0.59619140625, 0.29052734375, 0.52099609375, 0.6064453125, 0.1549072265625, -0.30859375, 0.0205841064453125, 0.86181640625, 0.876953125, 0.1068115234375, 0.958984375, 0.1883544921875, -0.274169921875, 0.5517578125, -0.477294921875, 0.3037109375, -0.257080078125, 0.32763671875, -0.5849609375, 0.10223388671875, -0.79443359375, -1.03515625, -0.031768798828125, 0.3798828125, 0.1009521484375, -0.52734375, -0.89892578125, -0.415771484375, -1.1708984375, -0.1424560546875, -0.59521484375, 0.98876953125, -0.52978515625, -0.046905517578125, -0.1295166015625, -1.51171875, 4.36328125, 0.630859375, 0.61376953125, 0.362548828125, 0.50439453125, 0.76318359375, 0.3447265625, -0.497314453125, -0.5576171875, -0.406494140625, 0.63427734375, -0.34912109375, -0.046905517578125, 0.80615234375, 0.57470703125, 0.248046875, -0.476806640625, 0.09222412109375, 0.2484130859375, -0.955078125, -0.705078125, 0.3486328125, -0.1844482421875, 0.87451171875, 0.09405517578125, 0.1781005859375, 0.57568359375, -1.015625, -0.0231781005859375, -0.7294921875, 0.1448974609375, -0.35107421875, 0.83740234375, 0.021392822265625, -0.10833740234375, 0.74560546875, 0.280029296875, -0.1959228515625, -0.016326904296875, 0.08709716796875, -0.057525634765625, -0.2071533203125, 0.712890625, -0.85986328125, -0.37841796875, 0.41552734375, -0.69287109375, 0.44677734375, 0.19482421875, -1.029296875, 0.9931640625, -0.422607421875, 0.430419921875, -0.54052734375, -0.92236328125, 0.386962890625, 0.07696533203125, 0.251953125, -0.2880859375, 0.3271484375, 0.63720703125, 0.73046875, -0.046295166015625, 0.53076171875, -0.99853515625, 0.79736328125, -0.2293701171875, 0.748046875, -0.60009765625, -0.12890625, 0.00954437255859375, -0.317138671875, -0.1358642578125, -0.533203125, 0.68212890625, 0.10577392578125, -0.479736328125, 0.66845703125, 0.483154296875, -0.78173828125, 0.0284423828125, -0.176025390625, -0.11053466796875, -0.50390625, 0.52978515625, 1.333984375, -0.432861328125, -0.197998046875, -0.42626953125, 0.4541015625, 0.5546875, 1.037109375, 0.026519775390625, -0.2105712890625, -0.1405029296875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows: * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} = 1, then s_i = 1); * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≀ n and w_{i+x} = 1, then s_i = 1); * if both of the aforementioned conditions are false, then s_i is 0. You are given the integer x and the resulting string s. Reconstruct the original string w. Input The first line contains one integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Each test case consists of two lines. The first line contains the resulting string s (2 ≀ |s| ≀ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≀ x ≀ |s| - 1). The total length of all strings s in the input does not exceed 10^5. Output For each test case, print the answer on a separate line as follows: * if no string w can produce the string s at the end of the process, print -1; * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. Example Input 3 101110 2 01 1 110 1 Output 111011 10 -1 Tags: 2-sat, brute force, constructive algorithms, greedy Correct Solution: ``` import sys;input=sys.stdin.readline def process(): s = input().strip() x, = map(int, input().split()) n = len(s) t = [1] * n for i in range(n): if int(s[i]) == 0: if i-x >= 0: t[i-x] = 0 if i+x < n: t[i+x] = 0 for i in range(n): if int(s[i]) == 1: r = 0 if i-x >= 0: if t[i-x] == 1: r = 1 if i+x < n: if t[i+x] == 1: r = 1 if not r: print(-1) return print("".join(str(c) for c in t)) T, = map(int, input().split()) for _ in range(T): process() ```
107,219
[ 0.2138671875, 0.115478515625, 0.10040283203125, 0.1292724609375, -0.4638671875, -0.454345703125, -0.052764892578125, -0.1622314453125, 0.13525390625, 0.9375, 0.60693359375, -0.314697265625, 0.1307373046875, -1.109375, -0.357177734375, -0.09619140625, -0.59912109375, -0.6572265625, -0.3857421875, -0.263671875, -0.036529541015625, -0.035491943359375, -1.4765625, -0.12310791015625, -0.50146484375, 0.8154296875, 0.47021484375, 0.1116943359375, 1.0146484375, 1.1748046875, -0.36865234375, -0.48828125, 0.67724609375, -1.291015625, -0.396728515625, -0.46142578125, 0.74462890625, -0.81005859375, -0.229248046875, -0.342529296875, 0.33544921875, -0.369873046875, 0.445068359375, -0.84912109375, -1.357421875, -0.273681640625, -0.6103515625, -0.27978515625, -0.095703125, -0.65625, -0.016204833984375, -0.32666015625, 0.298828125, -0.3056640625, 0.2122802734375, 0.0970458984375, 0.0083770751953125, -0.30029296875, -0.83642578125, 0.39892578125, -0.10626220703125, -0.1728515625, 0.27734375, -0.6015625, -0.267333984375, 0.069580078125, -0.1510009765625, -0.37060546875, -0.08746337890625, -0.95068359375, 0.1300048828125, 0.353515625, -0.473388671875, -0.289306640625, -0.3388671875, 0.0618896484375, 0.34033203125, 0.1422119140625, -0.76806640625, 0.90478515625, -0.09234619140625, 1.041015625, 0.16015625, 0.267333984375, -0.32421875, -0.578125, -0.08111572265625, 0.41845703125, 0.2237548828125, -0.298828125, -0.1722412109375, 0.58984375, -0.65625, 0.300537109375, 0.1734619140625, 0.52880859375, -0.345947265625, 0.1387939453125, 0.27001953125, 0.11993408203125, 0.58349609375, 1.046875, -0.459716796875, 0.9462890625, -0.61474609375, 0.17626953125, 0.26953125, 0.23291015625, -0.452392578125, -0.030426025390625, -0.01995849609375, -0.283447265625, 0.7109375, 0.323974609375, -0.60205078125, 0.794921875, -0.0399169921875, 0.2259521484375, -0.84716796875, 0.336181640625, 0.428466796875, 0.097900390625, 0.57568359375, -0.07281494140625, -0.332763671875, -0.392822265625, -0.3154296875, 1.0966796875, -0.351318359375, -0.1282958984375, 0.426513671875, 0.0006718635559082031, 0.07611083984375, 0.14794921875, 0.052520751953125, 0.94287109375, -0.3515625, 0.431884765625, 0.69970703125, -0.3984375, 1.005859375, -0.61376953125, -0.137451171875, 1.458984375, 0.376708984375, 0.1995849609375, 1.0078125, 0.43212890625, -0.83203125, 0.349365234375, -0.89404296875, 0.70947265625, 0.0667724609375, 0.28564453125, -0.14111328125, 0.15234375, -0.28125, 0.374755859375, -0.0947265625, 0.151611328125, -0.56787109375, 0.5263671875, -0.091552734375, 0.9775390625, -0.175048828125, 0.8193359375, -0.105712890625, -0.12384033203125, -0.4541015625, -0.77001953125, 0.290771484375, -0.287109375, -0.35791015625, 0.80078125, 0.724609375, 0.98388671875, 1.1005859375, -0.34814453125, 0.2347412109375, 0.11590576171875, -0.73828125, 0.1478271484375, 0.285888671875, 0.94580078125, 0.3251953125, 0.57080078125, 0.1297607421875, -0.261962890625, -0.91162109375, -0.434326171875, 0.126220703125, 0.9873046875, -0.775390625, 0.179443359375, 0.07794189453125, 0.169677734375, -0.8115234375, -0.1959228515625, -0.43798828125, -0.9248046875, -0.35302734375, 0.47216796875, 0.08184814453125, 0.13330078125, -0.70556640625, -0.5146484375, 0.541015625, 1.07421875, -0.235107421875, -0.293701171875, 0.1368408203125, 0.041259765625, -0.07891845703125, 0.357421875, -0.0533447265625, -0.1802978515625, -0.779296875, 0.8662109375, -0.06744384765625, -0.0543212890625, 0.12396240234375, 0.83349609375, 0.32763671875, 0.916015625, -0.260498046875, -0.1312255859375, 0.323486328125, 1.115234375, 0.1556396484375, 0.28466796875, 0.44189453125, 1.1513671875, 0.65966796875, 0.66943359375, 0.402587890625, 0.19287109375, 0.7119140625, 1.0078125, 0.0208740234375, 0.443115234375, -0.17578125, 0.292724609375, 0.1290283203125, 0.42578125, 0.2130126953125, 0.26318359375, -0.058990478515625, 0.1785888671875, -0.413330078125, 0.09088134765625, -0.275146484375, 0.88134765625, 0.2008056640625, 0.2291259765625, -0.603515625, -0.8095703125, 0.159912109375, 0.80419921875, -1.0927734375, -0.40234375, -0.14453125, 0.34033203125, 0.00466156005859375, -0.004024505615234375, 0.299560546875, 0.472412109375, 0.5966796875, 0.30908203125, -0.295654296875, -0.5302734375, -0.9013671875, -0.58984375, -1.05078125, -0.2144775390625, -0.384521484375, 0.11199951171875, -0.07183837890625, -0.81396484375, -0.030517578125, -0.51318359375, -0.43212890625, 0.338134765625, -0.97314453125, 0.5087890625, -0.2327880859375, 0.335693359375, -0.94287109375, 0.484375, 0.28759765625, 1.16015625, -0.56298828125, 0.07476806640625, 0.0601806640625, -0.88525390625, 0.1358642578125, -0.044952392578125, 0.330078125, 0.2822265625, -0.2279052734375, -0.6748046875, -0.3291015625, -0.11627197265625, -0.424072265625, 0.212158203125, -0.54345703125, 0.97412109375, 0.45458984375, -0.63427734375, 0.591796875, 0.9072265625, -0.89501953125, 0.5244140625, 0.10791015625, -0.0167388916015625, -0.7490234375, 1.4482421875, 0.293701171875, 0.29443359375, -0.59814453125, -0.375732421875, -0.193359375, -0.0103607177734375, 0.2568359375, -0.6552734375, -0.2396240234375, 0.392333984375, 0.0531005859375, -0.90673828125, 0.260986328125, -1.0283203125, -0.434326171875, -0.298828125, -0.2332763671875, 1.216796875, 0.9228515625, 0.1917724609375, -0.1240234375, -0.19677734375, -0.2177734375, 0.734375, 0.72412109375, -0.54248046875, 0.1385498046875, 1.017578125, -0.0030269622802734375, -0.1776123046875, 0.00794219970703125, -0.252197265625, 0.0914306640625, 0.037200927734375, 0.3134765625, 0.81494140625, 0.352783203125, 0.17578125, 0.53369140625, 0.75830078125, -1.1474609375, -0.19287109375, -0.064697265625, 0.459228515625, 0.54150390625, 0.0171661376953125, 0.403564453125, 0.050628662109375, -0.53271484375, -1.2578125, 0.316650390625, 0.247314453125, 0.7734375, -0.69873046875, 0.8330078125, 0.1650390625, -0.32275390625, 0.21142578125, -0.53857421875, 0.158203125, 1.03515625, 0.016448974609375, 0.53125, -0.7880859375, 0.2303466796875, 0.26513671875, -0.05255126953125, 0.57421875, 0.1912841796875, 0.6875, -0.3173828125, -0.329345703125, -0.60888671875, -0.228759765625, 0.01512908935546875, -0.7255859375, 0.175048828125, -0.4482421875, -0.6142578125, -1.0400390625, 0.1536865234375, 0.76708984375, 0.7109375, 0.00033211708068847656, 0.5205078125, -0.0640869140625, 0.6982421875, 0.63232421875, -0.2283935546875, 0.2457275390625, -0.78515625, 0.8056640625, 0.140869140625, -0.2841796875, -0.55078125, -0.273681640625, -0.2193603515625, -0.1319580078125, 0.04461669921875, -0.45458984375, -0.465087890625, 0.354248046875, -0.1561279296875, 0.6337890625, -0.6826171875, -0.456787109375, -0.4130859375, 0.472900390625, 0.154296875, -0.900390625, 0.323486328125, -0.73486328125, 0.79638671875, 0.272705078125, -0.12420654296875, -0.7529296875, -0.60009765625, -0.697265625, -0.798828125, -0.09417724609375, 1.0888671875, -0.0008082389831542969, 0.445068359375, -1.2197265625, 0.11944580078125, 0.366455078125, -0.47412109375, -0.1187744140625, -0.1282958984375, 0.5126953125, 0.206298828125, 0.84619140625, -0.7890625, -0.69140625, -0.27099609375, -1.435546875, 0.56005859375, -0.90283203125, 0.4833984375, 0.351806640625, 0.152587890625, -0.341796875, 0.55859375, -0.1318359375, 0.216796875, -0.2257080078125, 0.374267578125, -0.84814453125, -0.58984375, 0.7734375, -0.415771484375, -0.30615234375, 0.8974609375, -0.18212890625, -0.436767578125, 0.398681640625, 0.412353515625, -0.5693359375, 0.57568359375, -0.48974609375, 0.68798828125, -0.1810302734375, -0.470458984375, -0.25634765625, -0.51123046875, 0.94921875, 0.255859375, -1.08984375, -0.15576171875, -0.92578125, 0.059661865234375, -0.11553955078125, -0.2298583984375, 0.1824951171875, 0.1441650390625, 0.1419677734375, -0.20751953125, -0.22314453125, -0.45654296875, -0.371337890625, -0.450439453125, -0.11041259765625, 0.1580810546875, 0.51416015625, 0.42041015625, -0.041839599609375, -0.30615234375, -0.365234375, 0.056488037109375, -0.0767822265625, -0.468017578125, 0.0014858245849609375, -0.037200927734375, -0.2509765625, -0.0982666015625, 0.46142578125, -0.249755859375, 0.116943359375, 0.89306640625, 0.038421630859375, 0.472412109375, 0.331787109375, -0.50439453125, 0.61083984375, 0.174072265625, -1.177734375, -0.369873046875, 0.431884765625, -0.0994873046875, 0.53759765625, 0.277587890625, -1.2421875, -0.74267578125, -0.74560546875, 0.187744140625, -0.73291015625, -0.019073486328125, -1.072265625, -0.4892578125, -0.4873046875, 0.59716796875, 0.00885009765625, -0.72412109375, 0.097412109375, -1.17578125, 0.10357666015625, -1.1962890625, -0.11212158203125, -0.66064453125, -0.6298828125, -0.1392822265625, 0.734375, 0.0489501953125, 0.369140625, 0.11505126953125, -0.1385498046875, 0.296630859375, 0.34033203125, -0.765625, -0.2093505859375, -0.2529296875, 0.030029296875, -0.1611328125, -0.00690460205078125, -0.444580078125, 0.67138671875, -0.63916015625, 0.427978515625, -0.13134765625, -0.47998046875, -0.10540771484375, 0.0765380859375, 1.0986328125, -0.21826171875, 0.263427734375, -0.377685546875, 0.1273193359375, 0.63623046875, -0.2069091796875, -0.59326171875, -0.91748046875, -0.3623046875, -1.0400390625, 0.69775390625, -0.260009765625, 0.1851806640625, -0.65185546875, -0.4814453125, 0.9375, -0.6787109375, 0.548828125, 1.2119140625, -0.1551513671875, 0.36767578125, -0.0256805419921875, 0.59375, 0.6142578125, -0.86083984375, 0.30712890625, 0.541015625, -0.5654296875, 0.365234375, -0.276611328125, -0.85205078125, -0.62939453125, 0.0517578125, 1.193359375, -0.1407470703125, 0.63671875, -0.379638671875, -1.0849609375, -0.476806640625, 0.8115234375, 0.11767578125, 0.287353515625, 0.7333984375, 0.1593017578125, -0.0046234130859375, 0.18017578125, -0.315673828125, 0.136962890625, -0.426513671875, 1.1337890625, -0.010650634765625, -0.24169921875, 1.1162109375, 0.86572265625, -0.9501953125, -1.015625, 0.2152099609375, -0.22802734375, -0.380126953125, -0.68017578125, 0.0445556640625, 0.463134765625, -0.783203125, -0.0182342529296875, 0.5244140625, -0.054962158203125, 0.67041015625, -0.254150390625, 0.421142578125, -0.65478515625, 0.82666015625, 0.638671875, -0.428955078125, 0.0127410888671875, -0.8720703125, -0.3076171875, -0.53955078125, -0.056793212890625, 0.64013671875, -0.60009765625, 0.274169921875, 0.7890625, -0.0182952880859375, 0.89794921875, -0.64111328125, -0.5791015625, 0.007648468017578125, -0.445556640625, -0.72265625, 0.03948974609375, -0.0008029937744140625, 0.05352783203125, 0.53125, -0.78564453125, 0.02166748046875, -0.10638427734375, 0.15087890625, -0.310302734375, -0.9814453125, -0.17529296875, -0.8837890625, -0.2919921875, -0.89013671875, -0.68896484375, -0.1568603515625, 0.10931396484375, -0.0174713134765625, -0.5634765625, -0.21630859375, 0.1837158203125, -0.4287109375, 0.986328125, -0.78857421875, 0.392822265625, -0.28173828125, -0.481201171875, -0.69580078125, 0.066650390625, -0.603515625, 0.034210205078125, -0.65673828125, 0.34716796875, -0.44873046875, 0.55517578125, -0.33544921875, 0.369384765625, -0.37646484375, -0.576171875, 0.2900390625, -0.040802001953125, -0.45654296875, 1.0166015625, 0.390380859375, -0.06463623046875, 0.228759765625, -0.456787109375, 0.12115478515625, -0.62548828125, 0.2939453125, 0.72265625, -0.279296875, -0.192626953125, 0.051055908203125, 0.1358642578125, -1.1435546875, 0.47314453125, -0.35498046875, -0.079345703125, 0.5107421875, -0.10955810546875, 0.4443359375, 1.154296875, -0.336181640625, 0.6064453125, 0.0171051025390625, 0.273193359375, 0.357421875, 0.1533203125, -0.2451171875, 0.49755859375, -0.036712646484375, 0.05419921875, 0.208984375, 0.08551025390625, 0.2452392578125, 0.217041015625, -0.082275390625, -0.6396484375, -0.78076171875, -0.2203369140625, -0.2449951171875, 0.26806640625, 0.478515625, -0.281005859375, -0.286376953125, -0.12420654296875, -0.468017578125, 0.3046875, -1.1455078125, -1.060546875, 0.50048828125, -0.26220703125, -0.5380859375, -0.281494140625, -0.383056640625, -0.261474609375, 0.130615234375, 0.38037109375, -0.41259765625, 0.283935546875, -0.324951171875, 0.47265625, -0.410400390625, -0.0838623046875, 0.1705322265625, 0.4482421875, -0.373291015625, -0.6884765625, 0.188720703125, 1.15234375, 0.16015625, -0.307861328125, -0.3115234375, 0.33203125, -0.068359375, 0.11322021484375, -0.325927734375, 0.48828125, -0.4599609375, 0.383056640625, -0.8427734375, 0.2291259765625, -0.444580078125, 0.33935546875, 0.34619140625, -0.38525390625, -0.59521484375, 0.62255859375, 0.52880859375, 0.03656005859375, 0.8828125, -0.293212890625, 0.62548828125, 0.0897216796875, 0.22021484375, -0.271240234375, 0.86572265625, 0.74560546875, 0.7001953125, -0.1719970703125, 0.34033203125, 0.82958984375, 0.09710693359375, -0.447998046875, 0.35009765625, 0.1676025390625, -0.117919921875, 0.397705078125, -0.2431640625, -0.175048828125, 0.0614013671875, -0.488037109375, 0.64111328125, -0.364501953125, 0.07489013671875, -0.13134765625, -0.99609375, 1.130859375, -0.2459716796875, 0.01468658447265625, 0.252197265625, -0.3671875, 0.277587890625, 0.76416015625, -0.2451171875, -0.13720703125, 0.703125, 0.7763671875, 0.564453125, 0.6279296875, 0.348388671875, 0.38818359375, -0.77734375, 0.073974609375, -0.02496337890625, 0.173583984375, -0.238037109375, -0.4541015625, -0.58642578125, 0.47802734375, -0.65185546875, -0.2257080078125, 0.5791015625, -0.7822265625, 0.2783203125, -0.35546875, 1.142578125, -0.433837890625, 0.0179443359375, 0.283203125, -0.2152099609375, -0.6474609375, 0.89697265625, -0.0965576171875, 0.2235107421875, 0.0506591796875, 1.1962890625, -0.1256103515625, 1.4501953125, 0.6943359375, -0.07464599609375, -0.1304931640625, 0.352783203125, -0.1663818359375, -0.25537109375, -0.51806640625, -0.36083984375, 0.244140625, -0.93505859375, -0.63330078125, 0.0289306640625, 0.83203125, 0.19091796875, -1.158203125, -0.078125, 0.06573486328125, -0.8486328125, 0.2548828125, 0.1851806640625, 0.43212890625, 0.1922607421875, -0.267578125, -0.11273193359375, -0.343994140625, 0.623046875, -0.7548828125, 0.49951171875, -0.578125, -0.39453125, -0.66259765625, -0.6015625, -0.10321044921875, -0.41064453125, -0.3701171875, -0.603515625, 0.30078125, 0.49560546875, 0.5791015625, 0.11798095703125, -0.243896484375, 0.05816650390625, 0.796875, 0.8955078125, 0.1324462890625, 0.9814453125, 0.184326171875, -0.33203125, 0.5048828125, -0.4189453125, 0.31298828125, -0.32275390625, 0.260986328125, -0.60693359375, 0.069091796875, -0.794921875, -1.095703125, -0.06390380859375, 0.373046875, 0.0914306640625, -0.51708984375, -0.9169921875, -0.4208984375, -1.1767578125, -0.1217041015625, -0.57470703125, 0.89794921875, -0.44091796875, -0.07061767578125, -0.0908203125, -1.5712890625, 4.34765625, 0.6728515625, 0.61279296875, 0.259765625, 0.521484375, 0.81982421875, 0.2568359375, -0.462158203125, -0.5546875, -0.441162109375, 0.63330078125, -0.329345703125, -0.060211181640625, 0.83154296875, 0.5888671875, 0.2454833984375, -0.461669921875, 0.08447265625, 0.2225341796875, -0.90380859375, -0.70361328125, 0.290771484375, -0.2386474609375, 0.85595703125, 0.057373046875, 0.2666015625, 0.583984375, -1.029296875, -0.00919342041015625, -0.70556640625, 0.2159423828125, -0.314697265625, 0.763671875, -0.040008544921875, -0.0933837890625, 0.76904296875, 0.267578125, -0.124267578125, -0.04833984375, 0.042510986328125, -0.0711669921875, -0.208984375, 0.69970703125, -0.91162109375, -0.37109375, 0.456298828125, -0.70068359375, 0.50048828125, 0.266845703125, -1.0439453125, 0.97998046875, -0.439453125, 0.45166015625, -0.5146484375, -0.84521484375, 0.388427734375, 0.09033203125, 0.312744140625, -0.332275390625, 0.339599609375, 0.66064453125, 0.67724609375, -0.02978515625, 0.5361328125, -0.98779296875, 0.75390625, -0.26416015625, 0.78515625, -0.6494140625, -0.1754150390625, 0.018341064453125, -0.298583984375, -0.06463623046875, -0.52783203125, 0.7060546875, 0.1343994140625, -0.478759765625, 0.65625, 0.59814453125, -0.744140625, 0.0814208984375, -0.1624755859375, -0.125732421875, -0.57275390625, 0.55126953125, 1.310546875, -0.4091796875, -0.2342529296875, -0.400634765625, 0.37890625, 0.595703125, 1.037109375, 0.07745361328125, -0.2169189453125, -0.1329345703125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows: * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} = 1, then s_i = 1); * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≀ n and w_{i+x} = 1, then s_i = 1); * if both of the aforementioned conditions are false, then s_i is 0. You are given the integer x and the resulting string s. Reconstruct the original string w. Input The first line contains one integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Each test case consists of two lines. The first line contains the resulting string s (2 ≀ |s| ≀ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≀ x ≀ |s| - 1). The total length of all strings s in the input does not exceed 10^5. Output For each test case, print the answer on a separate line as follows: * if no string w can produce the string s at the end of the process, print -1; * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. Example Input 3 101110 2 01 1 110 1 Output 111011 10 -1 Tags: 2-sat, brute force, constructive algorithms, greedy Correct Solution: ``` from sys import stdin inp = lambda : stdin.readline().strip() t = int(inp()) for _ in range(t): s = inp() x = int(inp()) w = ['1']*len(s) for i in range(len(s)): if s[i] == '0': if i - x > -1: w[i-x] = '0' if i + x < len(s): w[i+x] = '0' for i in range(len(s)): if s[i] == '1': if not ((i - x > -1 and w[i-x] == '1' ) or (i + x < len(s) and w[i+x] =='1')): print(-1) break else: print(''.join(map(str,w))) ```
107,220
[ 0.252197265625, 0.1009521484375, 0.0771484375, 0.10528564453125, -0.431884765625, -0.43896484375, -0.0716552734375, -0.1373291015625, 0.1207275390625, 0.89404296875, 0.703125, -0.3388671875, 0.1627197265625, -1.12890625, -0.383056640625, -0.182373046875, -0.6484375, -0.55859375, -0.36669921875, -0.2322998046875, 0.056915283203125, -0.06512451171875, -1.53125, -0.200439453125, -0.435546875, 0.87255859375, 0.421875, 0.151611328125, 1.05859375, 1.13671875, -0.2491455078125, -0.431884765625, 0.76806640625, -1.2578125, -0.4677734375, -0.42578125, 0.7412109375, -0.7666015625, -0.1385498046875, -0.365478515625, 0.4267578125, -0.330322265625, 0.349853515625, -0.85693359375, -1.4482421875, -0.2386474609375, -0.54833984375, -0.1622314453125, -0.1380615234375, -0.7080078125, -0.07220458984375, -0.2401123046875, 0.382080078125, -0.361328125, 0.128173828125, 0.045318603515625, -0.036285400390625, -0.25927734375, -0.8515625, 0.34765625, -0.2244873046875, -0.2091064453125, 0.374755859375, -0.634765625, -0.201904296875, 0.07537841796875, -0.1759033203125, -0.3232421875, 0.033447265625, -1.021484375, 0.1478271484375, 0.324951171875, -0.5927734375, -0.415283203125, -0.361083984375, 0.1317138671875, 0.305908203125, 0.27880859375, -0.75, 0.94189453125, -0.11627197265625, 1.046875, 0.154541015625, 0.1890869140625, -0.414794921875, -0.5078125, -0.040283203125, 0.318359375, 0.2822265625, -0.2103271484375, -0.1798095703125, 0.529296875, -0.5693359375, 0.302001953125, 0.1617431640625, 0.4296875, -0.299072265625, 0.07562255859375, 0.345458984375, 0.038482666015625, 0.6328125, 0.9873046875, -0.5322265625, 0.83642578125, -0.63037109375, 0.205810546875, 0.1312255859375, 0.2147216796875, -0.529296875, 0.08624267578125, -0.00771331787109375, -0.24072265625, 0.66162109375, 0.251708984375, -0.49462890625, 0.580078125, -0.1650390625, 0.1397705078125, -0.84814453125, 0.3291015625, 0.4599609375, 0.1575927734375, 0.66064453125, -0.03515625, -0.2283935546875, -0.370849609375, -0.328125, 1.0126953125, -0.34375, -0.1326904296875, 0.37109375, -0.03753662109375, 0.051605224609375, 0.1705322265625, 0.00839996337890625, 0.93896484375, -0.322021484375, 0.43115234375, 0.7119140625, -0.415283203125, 0.9462890625, -0.60107421875, -0.1739501953125, 1.4169921875, 0.39990234375, 0.2113037109375, 0.9306640625, 0.385986328125, -0.85791015625, 0.3115234375, -0.81201171875, 0.77099609375, 0.1556396484375, 0.24755859375, -0.057708740234375, 0.22216796875, -0.25244140625, 0.371826171875, 0.026092529296875, 0.119873046875, -0.5478515625, 0.51220703125, -0.1295166015625, 0.912109375, -0.0562744140625, 0.8125, -0.156005859375, -0.11798095703125, -0.415283203125, -0.71533203125, 0.2130126953125, -0.393798828125, -0.2174072265625, 0.759765625, 0.775390625, 1.01953125, 0.99755859375, -0.40478515625, 0.331298828125, 0.03515625, -0.78857421875, 0.2408447265625, 0.330078125, 0.90966796875, 0.299560546875, 0.4833984375, 0.1513671875, -0.2452392578125, -0.83935546875, -0.431884765625, 0.164794921875, 0.93408203125, -0.78759765625, 0.289306640625, 0.153076171875, 0.176513671875, -0.82421875, -0.1474609375, -0.329345703125, -0.93701171875, -0.3759765625, 0.43359375, 0.0645751953125, 0.090087890625, -0.7314453125, -0.54638671875, 0.453369140625, 1.1484375, -0.383056640625, -0.420654296875, 0.068603515625, 0.03863525390625, -0.11798095703125, 0.419189453125, -0.09075927734375, -0.035308837890625, -0.875, 0.966796875, -0.11669921875, -0.10565185546875, 0.1688232421875, 0.8740234375, 0.281494140625, 0.91357421875, -0.220947265625, -0.1395263671875, 0.31982421875, 1.1328125, 0.2099609375, 0.357421875, 0.424072265625, 1.134765625, 0.5810546875, 0.63232421875, 0.296875, 0.256103515625, 0.74462890625, 1.115234375, 0.0234375, 0.4912109375, -0.28369140625, 0.4599609375, 0.1812744140625, 0.3720703125, 0.25048828125, 0.1693115234375, -0.04034423828125, 0.1820068359375, -0.491455078125, 0.2222900390625, -0.330322265625, 0.96484375, 0.278564453125, 0.1983642578125, -0.677734375, -0.68115234375, 0.32568359375, 0.81689453125, -1.197265625, -0.370849609375, -0.050628662109375, 0.286865234375, -0.0095977783203125, -0.03717041015625, 0.345947265625, 0.5068359375, 0.76513671875, 0.2978515625, -0.32861328125, -0.52783203125, -0.861328125, -0.4326171875, -0.966796875, -0.2489013671875, -0.3994140625, 0.1380615234375, 0.0251922607421875, -0.837890625, 0.1041259765625, -0.44677734375, -0.489990234375, 0.38232421875, -0.95947265625, 0.4326171875, -0.1767578125, 0.264404296875, -0.98828125, 0.478271484375, 0.281494140625, 1.16796875, -0.53857421875, 0.07421875, 0.045623779296875, -0.87451171875, 0.13916015625, -0.1512451171875, 0.32763671875, 0.220703125, -0.26220703125, -0.6337890625, -0.27490234375, -0.126708984375, -0.355712890625, 0.2388916015625, -0.6708984375, 0.96044921875, 0.5859375, -0.65576171875, 0.50537109375, 0.89501953125, -0.8486328125, 0.6171875, 0.0760498046875, 0.1578369140625, -0.72607421875, 1.33984375, 0.30908203125, 0.2646484375, -0.609375, -0.432373046875, -0.10406494140625, -0.06707763671875, 0.2269287109375, -0.52880859375, -0.2445068359375, 0.381591796875, 0.0679931640625, -0.9638671875, 0.239013671875, -1.03125, -0.4560546875, -0.315185546875, -0.344970703125, 1.162109375, 0.96142578125, 0.259521484375, -0.0689697265625, -0.275146484375, -0.404541015625, 0.71484375, 0.66259765625, -0.40380859375, 0.1365966796875, 1.0732421875, -0.1124267578125, -0.0109405517578125, -0.1199951171875, -0.191162109375, 0.0809326171875, 0.0188140869140625, 0.1336669921875, 0.8046875, 0.28271484375, 0.1439208984375, 0.5224609375, 0.75830078125, -1.0966796875, -0.1644287109375, 0.00844573974609375, 0.384521484375, 0.53125, 0.146240234375, 0.433837890625, 0.08404541015625, -0.55615234375, -1.25390625, 0.31005859375, 0.372314453125, 0.6767578125, -0.73583984375, 0.794921875, 0.277587890625, -0.3271484375, 0.151611328125, -0.57763671875, 0.159423828125, 1.03515625, 0.03253173828125, 0.54150390625, -0.81884765625, 0.329345703125, 0.2406005859375, -0.183837890625, 0.58837890625, 0.3623046875, 0.58984375, -0.263427734375, -0.368408203125, -0.61669921875, -0.322021484375, -0.05804443359375, -0.681640625, 0.1395263671875, -0.40869140625, -0.52587890625, -1.0517578125, 0.1527099609375, 0.68505859375, 0.71337890625, 0.1346435546875, 0.4716796875, 0.0065155029296875, 0.6396484375, 0.67138671875, -0.175048828125, 0.34033203125, -0.72509765625, 0.89111328125, 0.07879638671875, -0.2135009765625, -0.44580078125, -0.259033203125, -0.3525390625, -0.05828857421875, 0.03173828125, -0.56396484375, -0.430419921875, 0.3427734375, -0.0235748291015625, 0.57275390625, -0.67822265625, -0.330322265625, -0.340087890625, 0.4697265625, 0.12322998046875, -0.94384765625, 0.39697265625, -0.8056640625, 0.77294921875, 0.294189453125, -0.171142578125, -0.79541015625, -0.546875, -0.7626953125, -0.83203125, -0.06365966796875, 1.123046875, -0.07452392578125, 0.434814453125, -1.279296875, 0.12548828125, 0.2861328125, -0.59033203125, -0.057861328125, -0.1341552734375, 0.5771484375, 0.1309814453125, 0.81103515625, -0.771484375, -0.6748046875, -0.396728515625, -1.4052734375, 0.5927734375, -0.88818359375, 0.385009765625, 0.37255859375, 0.2069091796875, -0.360595703125, 0.53515625, -0.1353759765625, 0.25732421875, -0.144287109375, 0.363525390625, -0.85595703125, -0.61865234375, 0.78857421875, -0.314697265625, -0.358154296875, 0.794921875, -0.1981201171875, -0.52392578125, 0.31884765625, 0.400390625, -0.5478515625, 0.54833984375, -0.410400390625, 0.72509765625, -0.10052490234375, -0.4794921875, -0.1961669921875, -0.53369140625, 0.86572265625, 0.2325439453125, -1.146484375, -0.192138671875, -0.8828125, 0.0887451171875, -0.1412353515625, -0.2470703125, 0.0765380859375, 0.1553955078125, 0.1341552734375, -0.05828857421875, -0.330810546875, -0.343505859375, -0.43017578125, -0.442138671875, -0.205078125, 0.2802734375, 0.484130859375, 0.51123046875, -0.04876708984375, -0.371826171875, -0.363525390625, 0.08349609375, -0.0789794921875, -0.48388671875, 0.0926513671875, -0.16552734375, -0.356689453125, -0.006839752197265625, 0.501953125, -0.267333984375, 0.09906005859375, 0.9580078125, 0.1856689453125, 0.5546875, 0.331298828125, -0.44775390625, 0.53857421875, 0.1546630859375, -1.1748046875, -0.3232421875, 0.52197265625, -0.0537109375, 0.69384765625, 0.273681640625, -1.046875, -0.8857421875, -0.822265625, 0.1514892578125, -0.78369140625, -0.052703857421875, -1.0712890625, -0.47314453125, -0.462158203125, 0.67578125, -0.0809326171875, -0.77880859375, 0.0833740234375, -1.2587890625, 0.1661376953125, -1.1845703125, -0.12274169921875, -0.6484375, -0.5712890625, -0.1461181640625, 0.82763671875, 0.093994140625, 0.278076171875, -0.00237274169921875, -0.13525390625, 0.42626953125, 0.39453125, -0.7529296875, -0.1591796875, -0.232177734375, -0.021820068359375, -0.1334228515625, -0.036651611328125, -0.54150390625, 0.69091796875, -0.4677734375, 0.381103515625, -0.058807373046875, -0.4892578125, -0.11688232421875, 0.07244873046875, 1.162109375, -0.1754150390625, 0.272705078125, -0.41552734375, 0.12322998046875, 0.60546875, -0.29296875, -0.546875, -0.88818359375, -0.461181640625, -1.05078125, 0.72314453125, -0.2149658203125, 0.1395263671875, -0.55615234375, -0.41650390625, 0.84716796875, -0.57861328125, 0.70703125, 1.216796875, -0.1474609375, 0.398193359375, -0.0244598388671875, 0.57666015625, 0.62744140625, -0.79541015625, 0.257568359375, 0.49658203125, -0.5048828125, 0.308837890625, -0.3720703125, -0.81640625, -0.576171875, -0.029754638671875, 1.2509765625, -0.226806640625, 0.673828125, -0.361328125, -0.99609375, -0.3916015625, 0.71484375, 0.1177978515625, 0.299072265625, 0.9033203125, 0.2841796875, 0.034820556640625, 0.322265625, -0.326416015625, 0.1658935546875, -0.4736328125, 1.123046875, -0.201904296875, -0.259521484375, 1.1689453125, 0.97119140625, -0.98681640625, -1.0078125, 0.23876953125, -0.1884765625, -0.294677734375, -0.77587890625, -0.040435791015625, 0.51220703125, -0.72216796875, -0.0706787109375, 0.48974609375, -0.05487060546875, 0.603515625, -0.292236328125, 0.484130859375, -0.685546875, 0.84521484375, 0.6640625, -0.367431640625, -0.1251220703125, -0.95166015625, -0.246337890625, -0.39013671875, -0.01004791259765625, 0.7177734375, -0.52978515625, 0.3134765625, 0.68505859375, -0.01459503173828125, 0.81591796875, -0.5263671875, -0.5966796875, 0.082763671875, -0.41552734375, -0.6806640625, 0.1114501953125, 0.040191650390625, 0.1444091796875, 0.58837890625, -0.7255859375, 0.09552001953125, -0.0926513671875, 0.258056640625, -0.283203125, -0.921875, -0.2047119140625, -0.97412109375, -0.33984375, -0.90966796875, -0.71240234375, -0.10150146484375, 0.0191497802734375, 0.0626220703125, -0.5771484375, -0.1566162109375, -0.0015916824340820312, -0.525390625, 1.0224609375, -0.79736328125, 0.436767578125, -0.295166015625, -0.486083984375, -0.654296875, 0.11572265625, -0.64892578125, -0.0653076171875, -0.68115234375, 0.366455078125, -0.4345703125, 0.50341796875, -0.367431640625, 0.40673828125, -0.341796875, -0.56103515625, 0.2880859375, -0.09783935546875, -0.426513671875, 1.0048828125, 0.376220703125, -0.03204345703125, 0.1669921875, -0.5146484375, 0.1710205078125, -0.546875, 0.19384765625, 0.75732421875, -0.2103271484375, -0.07781982421875, -0.109130859375, 0.0254974365234375, -1.201171875, 0.494140625, -0.416748046875, -0.020294189453125, 0.483154296875, -0.11590576171875, 0.499267578125, 1.2021484375, -0.5107421875, 0.59912109375, -0.036895751953125, 0.27880859375, 0.371826171875, 0.1766357421875, -0.1778564453125, 0.56494140625, 0.040130615234375, -0.07318115234375, 0.2763671875, 0.1380615234375, 0.218017578125, 0.28564453125, -0.030364990234375, -0.6630859375, -0.87158203125, -0.27392578125, -0.220947265625, 0.238525390625, 0.409423828125, -0.312255859375, -0.345703125, -0.1751708984375, -0.459716796875, 0.17822265625, -1.2333984375, -1.046875, 0.59619140625, -0.35986328125, -0.55908203125, -0.283935546875, -0.49560546875, -0.2406005859375, 0.195556640625, 0.44482421875, -0.385009765625, 0.30517578125, -0.36181640625, 0.423828125, -0.374267578125, -0.1259765625, 0.282958984375, 0.395263671875, -0.411865234375, -0.69482421875, 0.10137939453125, 1.109375, 0.11370849609375, -0.25732421875, -0.393798828125, 0.1649169921875, -0.08740234375, 0.11578369140625, -0.337158203125, 0.374755859375, -0.438720703125, 0.28125, -0.8427734375, 0.2186279296875, -0.37841796875, 0.334716796875, 0.470703125, -0.3779296875, -0.5634765625, 0.5244140625, 0.464599609375, 0.04437255859375, 0.9609375, -0.284912109375, 0.60986328125, 0.10357666015625, 0.1539306640625, -0.236083984375, 0.95458984375, 0.783203125, 0.6494140625, -0.1192626953125, 0.359619140625, 0.77685546875, -0.034912109375, -0.53759765625, 0.355712890625, 0.1795654296875, -0.059356689453125, 0.368408203125, -0.269287109375, -0.2320556640625, -0.0211944580078125, -0.388427734375, 0.615234375, -0.3896484375, -0.057586669921875, -0.143798828125, -1.03125, 1.06640625, -0.306884765625, 0.0648193359375, 0.251953125, -0.460205078125, 0.32861328125, 0.681640625, -0.428955078125, -0.073974609375, 0.7041015625, 0.7265625, 0.5234375, 0.591796875, 0.3310546875, 0.3671875, -0.767578125, -0.053985595703125, -0.120361328125, 0.138427734375, -0.25634765625, -0.45654296875, -0.576171875, 0.420166015625, -0.638671875, -0.2060546875, 0.513671875, -0.68505859375, 0.1767578125, -0.30712890625, 1.1923828125, -0.4375, 0.035003662109375, 0.311767578125, -0.046539306640625, -0.68994140625, 0.91650390625, -0.1268310546875, 0.1845703125, 0.1597900390625, 1.228515625, -0.213134765625, 1.458984375, 0.65283203125, -0.0888671875, -0.13671875, 0.340087890625, -0.1064453125, -0.183349609375, -0.487548828125, -0.49951171875, 0.191650390625, -0.9228515625, -0.67919921875, 0.032989501953125, 0.85595703125, 0.21728515625, -1.2197265625, -0.090087890625, 0.1114501953125, -0.81494140625, 0.291259765625, 0.17041015625, 0.5146484375, 0.12481689453125, -0.4453125, -0.1788330078125, -0.490478515625, 0.55810546875, -0.72705078125, 0.55322265625, -0.7041015625, -0.432861328125, -0.740234375, -0.703125, -0.09423828125, -0.46875, -0.366455078125, -0.5771484375, 0.2464599609375, 0.572265625, 0.60986328125, 0.03350830078125, -0.272705078125, -0.10626220703125, 0.69580078125, 0.837890625, 0.178466796875, 0.947265625, 0.2587890625, -0.302490234375, 0.495361328125, -0.43408203125, 0.401123046875, -0.220458984375, 0.28125, -0.64599609375, 0.1285400390625, -0.79296875, -0.92529296875, -0.00910186767578125, 0.3603515625, 0.026275634765625, -0.5654296875, -0.83349609375, -0.441162109375, -1.0859375, -0.143798828125, -0.491943359375, 0.89306640625, -0.45263671875, -0.00021350383758544922, -0.146728515625, -1.5244140625, 4.34375, 0.724609375, 0.61181640625, 0.37939453125, 0.52392578125, 0.8173828125, 0.456298828125, -0.468505859375, -0.490966796875, -0.53369140625, 0.72216796875, -0.294921875, -0.036895751953125, 0.83349609375, 0.71533203125, 0.322509765625, -0.384765625, 0.142822265625, 0.3291015625, -0.97607421875, -0.66748046875, 0.2327880859375, -0.2802734375, 0.8427734375, 0.1834716796875, 0.269775390625, 0.6494140625, -1.068359375, 0.012451171875, -0.79833984375, 0.09954833984375, -0.27734375, 0.81787109375, -0.09906005859375, -0.1513671875, 0.77734375, 0.268310546875, -0.2032470703125, -0.053924560546875, 0.01480865478515625, -0.004180908203125, -0.2568359375, 0.71923828125, -0.82666015625, -0.316650390625, 0.429443359375, -0.54345703125, 0.5849609375, 0.305908203125, -0.8583984375, 0.87841796875, -0.392578125, 0.4404296875, -0.497802734375, -0.8271484375, 0.50830078125, 0.0201416015625, 0.2568359375, -0.35595703125, 0.350830078125, 0.56396484375, 0.6240234375, 0.045654296875, 0.6015625, -1.048828125, 0.75537109375, -0.2724609375, 0.81884765625, -0.64697265625, -0.269287109375, 0.0007081031799316406, -0.439697265625, -0.1314697265625, -0.6044921875, 0.63916015625, 0.10797119140625, -0.409423828125, 0.671875, 0.5810546875, -0.74609375, 0.1240234375, -0.09759521484375, -0.06597900390625, -0.529296875, 0.4140625, 1.1669921875, -0.473388671875, -0.2374267578125, -0.4775390625, 0.33984375, 0.53759765625, 0.955078125, -0.0260162353515625, -0.22265625, -0.11248779296875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows: * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} = 1, then s_i = 1); * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≀ n and w_{i+x} = 1, then s_i = 1); * if both of the aforementioned conditions are false, then s_i is 0. You are given the integer x and the resulting string s. Reconstruct the original string w. Input The first line contains one integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Each test case consists of two lines. The first line contains the resulting string s (2 ≀ |s| ≀ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≀ x ≀ |s| - 1). The total length of all strings s in the input does not exceed 10^5. Output For each test case, print the answer on a separate line as follows: * if no string w can produce the string s at the end of the process, print -1; * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. Example Input 3 101110 2 01 1 110 1 Output 111011 10 -1 Tags: 2-sat, brute force, constructive algorithms, greedy Correct Solution: ``` def get(): n=len(s) w = [1] * n for i in range(n): if s[i] == 0: if i - x >= 0: w[i - x] = 0 if i + x < n: w[i + x] = 0 for i in range(n): if s[i]: if i-x>=0 and w[i-x]==1:continue elif i+x<n and w[i+x]==1:continue else:return [-1] return w for _ in range(int(input())): s=list(map(int,input())) x=int(input()) for i in get(): print(i,end='') print() ```
107,221
[ 0.2763671875, 0.096435546875, 0.026519775390625, 0.1956787109375, -0.434326171875, -0.472900390625, -0.01035308837890625, -0.1412353515625, 0.2427978515625, 0.92626953125, 0.73388671875, -0.3486328125, 0.151611328125, -1.103515625, -0.306884765625, -0.0845947265625, -0.60400390625, -0.634765625, -0.3916015625, -0.26611328125, 0.029632568359375, -0.053375244140625, -1.470703125, -0.201171875, -0.5009765625, 0.8544921875, 0.4873046875, 0.15966796875, 1.0322265625, 1.1943359375, -0.30908203125, -0.431884765625, 0.64990234375, -1.314453125, -0.392822265625, -0.3779296875, 0.73876953125, -0.82080078125, -0.192626953125, -0.330810546875, 0.3544921875, -0.39697265625, 0.48681640625, -0.82861328125, -1.31640625, -0.2314453125, -0.62646484375, -0.2271728515625, -0.043212890625, -0.72265625, -0.0426025390625, -0.286865234375, 0.28076171875, -0.302490234375, 0.257568359375, 0.063720703125, 0.0042572021484375, -0.287109375, -0.82958984375, 0.440185546875, -0.08258056640625, -0.24951171875, 0.25830078125, -0.63720703125, -0.33056640625, 0.05487060546875, -0.08160400390625, -0.34375, -0.09283447265625, -1.0224609375, 0.131591796875, 0.3818359375, -0.4873046875, -0.2364501953125, -0.326416015625, 0.036956787109375, 0.2410888671875, 0.13525390625, -0.7841796875, 1.005859375, -0.01264190673828125, 0.98681640625, 0.176513671875, 0.25537109375, -0.372802734375, -0.5595703125, -0.10174560546875, 0.3740234375, 0.31201171875, -0.303955078125, -0.17236328125, 0.61083984375, -0.6396484375, 0.2919921875, 0.1959228515625, 0.51025390625, -0.299072265625, 0.08245849609375, 0.285400390625, 0.0621337890625, 0.65380859375, 1.115234375, -0.45654296875, 0.9169921875, -0.53662109375, 0.1510009765625, 0.257080078125, 0.1650390625, -0.37939453125, -0.064208984375, -0.0709228515625, -0.3095703125, 0.736328125, 0.226318359375, -0.5107421875, 0.79833984375, -0.103515625, 0.2041015625, -0.80517578125, 0.41796875, 0.459228515625, 0.136474609375, 0.5390625, 0.026611328125, -0.28369140625, -0.3818359375, -0.2880859375, 1.091796875, -0.3291015625, -0.10858154296875, 0.39208984375, -0.0175628662109375, 0.0167236328125, 0.12548828125, 0.0233612060546875, 0.92529296875, -0.366943359375, 0.50537109375, 0.7255859375, -0.450439453125, 1.033203125, -0.66015625, -0.2236328125, 1.365234375, 0.370361328125, 0.2110595703125, 0.99462890625, 0.350341796875, -0.88134765625, 0.393310546875, -0.9033203125, 0.7646484375, 0.10797119140625, 0.322509765625, -0.15185546875, 0.1705322265625, -0.283447265625, 0.35791015625, -0.06060791015625, 0.14794921875, -0.4560546875, 0.446533203125, -0.141845703125, 0.97509765625, -0.28271484375, 0.83203125, -0.11944580078125, -0.125, -0.362060546875, -0.77734375, 0.222900390625, -0.2685546875, -0.361083984375, 0.81201171875, 0.75146484375, 1.029296875, 1.0927734375, -0.33154296875, 0.2205810546875, 0.1234130859375, -0.57861328125, 0.1568603515625, 0.2159423828125, 0.90283203125, 0.2164306640625, 0.494873046875, 0.10296630859375, -0.26806640625, -0.9140625, -0.446533203125, 0.06396484375, 0.9765625, -0.8115234375, 0.16845703125, 0.1407470703125, 0.26025390625, -0.77001953125, -0.10198974609375, -0.4677734375, -0.92529296875, -0.282958984375, 0.495361328125, 0.1163330078125, 0.152099609375, -0.7119140625, -0.5439453125, 0.55419921875, 0.95947265625, -0.254150390625, -0.352783203125, 0.1231689453125, 0.0841064453125, 0.01812744140625, 0.29541015625, -0.00806427001953125, -0.1336669921875, -0.7802734375, 0.98193359375, -0.1441650390625, -0.058013916015625, 0.1492919921875, 0.80419921875, 0.328125, 0.9638671875, -0.1707763671875, -0.1099853515625, 0.31591796875, 1.1240234375, 0.1090087890625, 0.30810546875, 0.427734375, 1.203125, 0.67626953125, 0.677734375, 0.393798828125, 0.311279296875, 0.6962890625, 1.046875, 0.1859130859375, 0.359130859375, -0.186279296875, 0.264404296875, 0.158447265625, 0.42041015625, 0.1971435546875, 0.25244140625, -0.099609375, 0.24755859375, -0.3603515625, 0.11175537109375, -0.2315673828125, 0.88330078125, 0.2198486328125, 0.33154296875, -0.583984375, -0.7685546875, 0.12225341796875, 0.82470703125, -1.0302734375, -0.431884765625, -0.180908203125, 0.393310546875, -0.0016431808471679688, -0.0276336669921875, 0.34033203125, 0.51171875, 0.611328125, 0.294677734375, -0.326416015625, -0.587890625, -0.95703125, -0.55517578125, -1.0478515625, -0.23876953125, -0.390625, 0.1007080078125, -0.026031494140625, -0.85791015625, -0.027679443359375, -0.463623046875, -0.4189453125, 0.317138671875, -1.0498046875, 0.4873046875, -0.21142578125, 0.37646484375, -0.93408203125, 0.482421875, 0.36572265625, 1.14453125, -0.53271484375, 0.0535888671875, 0.06732177734375, -0.939453125, 0.1358642578125, 0.05059814453125, 0.2802734375, 0.262451171875, -0.281005859375, -0.6337890625, -0.348388671875, -0.1533203125, -0.390869140625, 0.188232421875, -0.525390625, 0.96435546875, 0.5146484375, -0.60546875, 0.568359375, 0.99365234375, -0.935546875, 0.59228515625, 0.166748046875, 0.0278472900390625, -0.79736328125, 1.4267578125, 0.341552734375, 0.34033203125, -0.6630859375, -0.35009765625, -0.2386474609375, -0.046417236328125, 0.344970703125, -0.693359375, -0.299560546875, 0.390869140625, -0.0252838134765625, -0.99853515625, 0.314453125, -0.96728515625, -0.61083984375, -0.3603515625, -0.26513671875, 1.08203125, 0.90478515625, 0.19140625, -0.06439208984375, -0.2247314453125, -0.151123046875, 0.7587890625, 0.7783203125, -0.461669921875, 0.16845703125, 0.96728515625, -0.024566650390625, -0.1300048828125, -0.0206756591796875, -0.1907958984375, 0.1533203125, 0.167236328125, 0.360107421875, 0.8896484375, 0.3466796875, 0.16796875, 0.5, 0.79638671875, -1.046875, -0.1346435546875, -0.08544921875, 0.5068359375, 0.58056640625, 0.141357421875, 0.4072265625, -0.0706787109375, -0.529296875, -1.2646484375, 0.3466796875, 0.2587890625, 0.80810546875, -0.7705078125, 0.8193359375, 0.1546630859375, -0.291748046875, 0.149658203125, -0.5341796875, 0.08233642578125, 0.98974609375, -0.0029582977294921875, 0.57568359375, -0.7744140625, 0.304443359375, 0.2086181640625, 0.017120361328125, 0.58447265625, 0.2568359375, 0.65478515625, -0.3232421875, -0.31591796875, -0.5634765625, -0.270263671875, -0.0296783447265625, -0.72705078125, 0.2139892578125, -0.451416015625, -0.53466796875, -1.0703125, 0.1639404296875, 0.7119140625, 0.751953125, -0.02203369140625, 0.499755859375, 0.022705078125, 0.72412109375, 0.580078125, -0.2724609375, 0.174072265625, -0.81201171875, 0.81689453125, 0.12335205078125, -0.2578125, -0.5458984375, -0.1944580078125, -0.246337890625, -0.14892578125, 0.11761474609375, -0.5107421875, -0.471923828125, 0.404052734375, -0.153076171875, 0.708984375, -0.607421875, -0.455810546875, -0.402587890625, 0.5703125, 0.1697998046875, -0.90673828125, 0.333251953125, -0.77978515625, 0.798828125, 0.320556640625, -0.0562744140625, -0.7119140625, -0.595703125, -0.68798828125, -0.7890625, -0.07672119140625, 1.0888671875, 0.005397796630859375, 0.371826171875, -1.23046875, 0.1337890625, 0.27978515625, -0.427978515625, -0.050994873046875, -0.17822265625, 0.5166015625, 0.153076171875, 0.86962890625, -0.85888671875, -0.68896484375, -0.25927734375, -1.3935546875, 0.5478515625, -0.8818359375, 0.425537109375, 0.3046875, 0.2060546875, -0.33544921875, 0.52197265625, -0.1182861328125, 0.2509765625, -0.2303466796875, 0.2958984375, -0.87060546875, -0.488525390625, 0.71728515625, -0.360595703125, -0.301513671875, 0.88232421875, -0.23046875, -0.43017578125, 0.437255859375, 0.47802734375, -0.63427734375, 0.51025390625, -0.4287109375, 0.70654296875, -0.288330078125, -0.445068359375, -0.2138671875, -0.499267578125, 0.8798828125, 0.1826171875, -1.0791015625, -0.189453125, -0.912109375, 0.0386962890625, -0.07965087890625, -0.2344970703125, 0.2474365234375, 0.116455078125, 0.1358642578125, -0.2117919921875, -0.2587890625, -0.438720703125, -0.401611328125, -0.3701171875, -0.1124267578125, 0.2159423828125, 0.603515625, 0.366943359375, -0.03631591796875, -0.230712890625, -0.27783203125, 0.1907958984375, 0.100341796875, -0.448974609375, -0.045257568359375, -0.02069091796875, -0.212890625, -0.087158203125, 0.5, -0.3291015625, 0.09100341796875, 0.89501953125, 0.038055419921875, 0.54638671875, 0.326904296875, -0.568359375, 0.56396484375, 0.176513671875, -1.2138671875, -0.492919921875, 0.419921875, -0.0230255126953125, 0.5517578125, 0.35888671875, -1.197265625, -0.76806640625, -0.74072265625, 0.0303497314453125, -0.7158203125, -0.033966064453125, -1.0244140625, -0.3974609375, -0.450439453125, 0.63232421875, 0.0275115966796875, -0.77099609375, 0.105712890625, -1.177734375, 0.1068115234375, -1.162109375, -0.1954345703125, -0.7177734375, -0.611328125, -0.09393310546875, 0.69677734375, 0.14208984375, 0.330810546875, 0.05657958984375, -0.2208251953125, 0.2822265625, 0.295654296875, -0.7109375, -0.16552734375, -0.2276611328125, -0.046966552734375, -0.1802978515625, -0.0254364013671875, -0.43359375, 0.71484375, -0.65771484375, 0.38134765625, -0.133056640625, -0.3466796875, -0.1358642578125, 0.03472900390625, 1.046875, -0.11358642578125, 0.23828125, -0.385498046875, 0.11053466796875, 0.55615234375, -0.29296875, -0.66357421875, -0.955078125, -0.4052734375, -1.0595703125, 0.66552734375, -0.197998046875, 0.1795654296875, -0.6552734375, -0.568359375, 1.03515625, -0.5576171875, 0.5146484375, 1.208984375, -0.11669921875, 0.398681640625, -0.09930419921875, 0.4814453125, 0.65576171875, -0.794921875, 0.214111328125, 0.4384765625, -0.5576171875, 0.360107421875, -0.1865234375, -0.7939453125, -0.61572265625, 0.154296875, 1.11328125, -0.1929931640625, 0.67578125, -0.323974609375, -1.0478515625, -0.501953125, 0.71826171875, 0.1688232421875, 0.30224609375, 0.71923828125, 0.157958984375, -0.055511474609375, 0.1273193359375, -0.318115234375, 0.08642578125, -0.44140625, 1.166015625, -0.0271453857421875, -0.160888671875, 1.091796875, 0.953125, -0.955078125, -0.9716796875, 0.282958984375, -0.232421875, -0.39501953125, -0.65869140625, 0.07147216796875, 0.424072265625, -0.6982421875, 0.0753173828125, 0.51220703125, -0.053619384765625, 0.578125, -0.2181396484375, 0.3623046875, -0.673828125, 0.92236328125, 0.5927734375, -0.39453125, -0.08563232421875, -0.91259765625, -0.33251953125, -0.560546875, -0.024200439453125, 0.6435546875, -0.64111328125, 0.1983642578125, 0.744140625, -0.040313720703125, 0.86767578125, -0.59716796875, -0.58349609375, 0.03973388671875, -0.4208984375, -0.73828125, 0.0635986328125, 0.0814208984375, -0.0114288330078125, 0.429443359375, -0.75048828125, 0.07781982421875, -0.07861328125, 0.052947998046875, -0.318603515625, -1.07421875, -0.196044921875, -0.92529296875, -0.312744140625, -0.935546875, -0.7060546875, -0.07232666015625, 0.09674072265625, 0.0007557868957519531, -0.5927734375, -0.1910400390625, 0.2197265625, -0.416259765625, 0.9541015625, -0.7666015625, 0.420654296875, -0.27783203125, -0.6181640625, -0.61767578125, 0.083984375, -0.55712890625, 0.046173095703125, -0.802734375, 0.383056640625, -0.428466796875, 0.63134765625, -0.351806640625, 0.401123046875, -0.43017578125, -0.6650390625, 0.274658203125, -0.104736328125, -0.403564453125, 0.98046875, 0.37939453125, -0.085205078125, 0.1802978515625, -0.51123046875, 0.08782958984375, -0.64501953125, 0.33154296875, 0.7392578125, -0.2802734375, -0.156982421875, 0.0889892578125, 0.1009521484375, -1.19921875, 0.47216796875, -0.342041015625, -0.07373046875, 0.50634765625, -0.06536865234375, 0.49072265625, 1.16796875, -0.38916015625, 0.619140625, -0.06243896484375, 0.26025390625, 0.373291015625, 0.205078125, -0.1934814453125, 0.46533203125, 0.06134033203125, -0.032135009765625, 0.1439208984375, 0.1195068359375, 0.12200927734375, 0.1387939453125, -0.128662109375, -0.708984375, -0.7490234375, -0.26171875, -0.302978515625, 0.2802734375, 0.484619140625, -0.15966796875, -0.258056640625, -0.1507568359375, -0.369384765625, 0.327880859375, -1.279296875, -1.0205078125, 0.583984375, -0.2220458984375, -0.552734375, -0.25341796875, -0.40283203125, -0.296630859375, 0.1490478515625, 0.373046875, -0.5166015625, 0.30908203125, -0.42578125, 0.458740234375, -0.431396484375, -0.118896484375, 0.1312255859375, 0.488037109375, -0.4599609375, -0.7421875, 0.069580078125, 1.115234375, 0.1478271484375, -0.322265625, -0.260986328125, 0.351806640625, -0.073486328125, 0.133056640625, -0.384765625, 0.456787109375, -0.54833984375, 0.39111328125, -0.85205078125, 0.2298583984375, -0.474609375, 0.34033203125, 0.44677734375, -0.39453125, -0.57958984375, 0.64013671875, 0.486572265625, -0.098388671875, 0.85791015625, -0.2181396484375, 0.60546875, 0.06195068359375, 0.10076904296875, -0.1968994140625, 0.96337890625, 0.6923828125, 0.6298828125, -0.1497802734375, 0.225341796875, 0.74169921875, 0.125244140625, -0.45654296875, 0.40234375, 0.2447509765625, -0.111328125, 0.406494140625, -0.2271728515625, -0.1597900390625, 0.048370361328125, -0.5537109375, 0.61669921875, -0.328125, 0.01326751708984375, -0.1842041015625, -0.98876953125, 1.1005859375, -0.181640625, 0.054046630859375, 0.21630859375, -0.419677734375, 0.21875, 0.72705078125, -0.280029296875, -0.1119384765625, 0.73193359375, 0.7685546875, 0.49658203125, 0.65625, 0.2490234375, 0.393798828125, -0.7529296875, 0.058441162109375, -0.06622314453125, 0.1324462890625, -0.300048828125, -0.5556640625, -0.5009765625, 0.406494140625, -0.61572265625, -0.265380859375, 0.62353515625, -0.81298828125, 0.312744140625, -0.302978515625, 0.99365234375, -0.4755859375, 0.03399658203125, 0.28125, -0.151123046875, -0.64404296875, 0.84326171875, -0.0972900390625, 0.243896484375, 0.00667572021484375, 1.1806640625, -0.1357421875, 1.3818359375, 0.6513671875, -0.0369873046875, -0.12115478515625, 0.359619140625, -0.123046875, -0.2315673828125, -0.53271484375, -0.439453125, 0.181396484375, -0.970703125, -0.64453125, -0.0242462158203125, 0.81591796875, 0.21484375, -1.25, -0.05322265625, 0.12060546875, -0.900390625, 0.250732421875, 0.2412109375, 0.406494140625, 0.1279296875, -0.255615234375, -0.11688232421875, -0.3349609375, 0.5654296875, -0.84912109375, 0.474365234375, -0.62744140625, -0.42431640625, -0.64599609375, -0.6376953125, -0.11041259765625, -0.390625, -0.42529296875, -0.6142578125, 0.33837890625, 0.496826171875, 0.6240234375, 0.09246826171875, -0.263427734375, 0.004283905029296875, 0.86376953125, 0.90087890625, 0.1875, 0.96923828125, 0.2294921875, -0.22900390625, 0.544921875, -0.5029296875, 0.270751953125, -0.27587890625, 0.29345703125, -0.6201171875, 0.072998046875, -0.79833984375, -1.1357421875, -0.0594482421875, 0.451904296875, 0.0777587890625, -0.45166015625, -0.9189453125, -0.406494140625, -1.1904296875, -0.1932373046875, -0.5595703125, 0.9599609375, -0.5, -0.0287933349609375, -0.191650390625, -1.5556640625, 4.34375, 0.69970703125, 0.609375, 0.359130859375, 0.56494140625, 0.8154296875, 0.3388671875, -0.413818359375, -0.55615234375, -0.317626953125, 0.63037109375, -0.337646484375, -0.0989990234375, 0.8056640625, 0.5634765625, 0.25439453125, -0.40771484375, 0.12420654296875, 0.16650390625, -0.88818359375, -0.6923828125, 0.3994140625, -0.2286376953125, 0.95556640625, 0.11376953125, 0.1787109375, 0.6669921875, -0.9892578125, -0.02880859375, -0.7119140625, 0.15771484375, -0.36376953125, 0.81591796875, 0.018768310546875, -0.1453857421875, 0.740234375, 0.280029296875, -0.151611328125, -0.025054931640625, 0.043426513671875, -0.0753173828125, -0.28369140625, 0.62451171875, -0.8515625, -0.386962890625, 0.453857421875, -0.7470703125, 0.424072265625, 0.2166748046875, -0.958984375, 0.96875, -0.431396484375, 0.470947265625, -0.6669921875, -0.8544921875, 0.36865234375, 0.11785888671875, 0.239013671875, -0.29833984375, 0.283447265625, 0.61474609375, 0.77783203125, -0.06793212890625, 0.51806640625, -1.015625, 0.7998046875, -0.27685546875, 0.7197265625, -0.57470703125, -0.06683349609375, 0.0170745849609375, -0.295166015625, -0.128662109375, -0.54150390625, 0.6328125, 0.1348876953125, -0.494384765625, 0.7060546875, 0.495849609375, -0.78173828125, -0.0008831024169921875, -0.1961669921875, -0.107666015625, -0.50732421875, 0.52490234375, 1.3193359375, -0.46484375, -0.2191162109375, -0.461669921875, 0.51220703125, 0.595703125, 1.013671875, 0.0288238525390625, -0.1500244140625, -0.07177734375 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows: * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} = 1, then s_i = 1); * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≀ n and w_{i+x} = 1, then s_i = 1); * if both of the aforementioned conditions are false, then s_i is 0. You are given the integer x and the resulting string s. Reconstruct the original string w. Input The first line contains one integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Each test case consists of two lines. The first line contains the resulting string s (2 ≀ |s| ≀ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≀ x ≀ |s| - 1). The total length of all strings s in the input does not exceed 10^5. Output For each test case, print the answer on a separate line as follows: * if no string w can produce the string s at the end of the process, print -1; * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. Example Input 3 101110 2 01 1 110 1 Output 111011 10 -1 Tags: 2-sat, brute force, constructive algorithms, greedy Correct Solution: ``` def process(n, x): l = [0 for i in range(len(n))] for i in range(len(l)): if i-x >= 0 and n[i-x] == 1: l[i] = 1 if i+x < len(l) and n[i+x] == 1: l[i] = 1 return l for t in range(int(input())): l = list(map(int, list(input()))) x = int(input()) n = [1 for i in range(len(l))] #print(l, x) for i in range(len(n)): if l[i] == 0: if i+x < len(n): n[i+x] = 0 if i-x > -1: n[i-x] = 0 #print(n) if process(n, x) != l: print(-1) else: print(''.join(map(str, n))) ```
107,222
[ 0.2161865234375, 0.061767578125, 0.10308837890625, 0.22412109375, -0.406005859375, -0.43017578125, -0.0299835205078125, -0.2152099609375, 0.1671142578125, 0.99853515625, 0.6201171875, -0.26025390625, 0.1654052734375, -1.0537109375, -0.30908203125, -0.017364501953125, -0.63720703125, -0.7080078125, -0.379150390625, -0.26416015625, -0.02178955078125, -0.055419921875, -1.5625, -0.1646728515625, -0.491943359375, 0.8173828125, 0.46142578125, 0.11474609375, 1.015625, 1.162109375, -0.34130859375, -0.463623046875, 0.72802734375, -1.259765625, -0.4541015625, -0.494140625, 0.693359375, -0.75, -0.25634765625, -0.30859375, 0.405517578125, -0.415283203125, 0.496337890625, -0.78564453125, -1.4111328125, -0.20654296875, -0.63623046875, -0.245849609375, -0.12255859375, -0.72607421875, -0.0484619140625, -0.31640625, 0.287353515625, -0.2685546875, 0.279052734375, 0.087646484375, 0.003780364990234375, -0.310546875, -0.8193359375, 0.429443359375, -0.08184814453125, -0.1785888671875, 0.287841796875, -0.65185546875, -0.3740234375, 0.052337646484375, -0.10516357421875, -0.407470703125, -0.027496337890625, -1.001953125, 0.19482421875, 0.3623046875, -0.53662109375, -0.258056640625, -0.323486328125, 0.0543212890625, 0.297607421875, -0.00263214111328125, -0.74267578125, 0.8916015625, -0.00159454345703125, 0.98291015625, 0.162841796875, 0.20947265625, -0.304443359375, -0.6298828125, -0.09979248046875, 0.4638671875, 0.3408203125, -0.31689453125, -0.1417236328125, 0.65625, -0.64599609375, 0.29638671875, 0.15673828125, 0.529296875, -0.360595703125, 0.163818359375, 0.307373046875, 0.1666259765625, 0.599609375, 1.091796875, -0.402587890625, 0.8857421875, -0.62109375, 0.1412353515625, 0.193115234375, 0.252685546875, -0.416259765625, -0.026458740234375, -0.01322174072265625, -0.3203125, 0.62060546875, 0.21142578125, -0.5693359375, 0.77685546875, 0.01293182373046875, 0.2373046875, -0.81298828125, 0.39892578125, 0.459716796875, 0.09014892578125, 0.580078125, 0.00772857666015625, -0.2401123046875, -0.360107421875, -0.330078125, 1.0859375, -0.391357421875, 0.03045654296875, 0.4521484375, 0.000007748603820800781, 0.10101318359375, 0.1466064453125, 0.04620361328125, 0.93896484375, -0.330810546875, 0.4873046875, 0.71533203125, -0.36083984375, 1.00390625, -0.63671875, -0.153076171875, 1.3857421875, 0.35546875, 0.2242431640625, 1.0888671875, 0.3896484375, -0.85546875, 0.343017578125, -0.94580078125, 0.73193359375, 0.131591796875, 0.3017578125, -0.171630859375, 0.1466064453125, -0.2685546875, 0.324951171875, -0.134765625, 0.11083984375, -0.56396484375, 0.435546875, -0.09234619140625, 1.0107421875, -0.17333984375, 0.77490234375, -0.158203125, -0.058013916015625, -0.3818359375, -0.83056640625, 0.2568359375, -0.2626953125, -0.35498046875, 0.86962890625, 0.6650390625, 0.994140625, 1.14453125, -0.332275390625, 0.2470703125, 0.0946044921875, -0.583984375, 0.10394287109375, 0.234130859375, 0.97509765625, 0.252197265625, 0.5576171875, 0.0194091796875, -0.244873046875, -0.83349609375, -0.3828125, 0.095458984375, 0.94873046875, -0.7998046875, 0.18603515625, 0.173828125, 0.23779296875, -0.69287109375, -0.1995849609375, -0.5244140625, -0.93798828125, -0.247314453125, 0.430419921875, 0.076171875, 0.1883544921875, -0.7138671875, -0.4609375, 0.48681640625, 0.96826171875, -0.32470703125, -0.3173828125, 0.1180419921875, 0.049102783203125, -0.0784912109375, 0.345703125, -0.004322052001953125, -0.1580810546875, -0.716796875, 0.943359375, -0.11761474609375, -0.0087127685546875, 0.1331787109375, 0.80615234375, 0.424072265625, 0.8583984375, -0.212646484375, -0.1417236328125, 0.26220703125, 1.1552734375, 0.12127685546875, 0.27490234375, 0.332275390625, 1.1611328125, 0.716796875, 0.69189453125, 0.47412109375, 0.22998046875, 0.62451171875, 1.0478515625, 0.11328125, 0.423828125, -0.1572265625, 0.2685546875, 0.220458984375, 0.318603515625, 0.224365234375, 0.32421875, -0.09033203125, 0.1785888671875, -0.38037109375, 0.10894775390625, -0.226806640625, 0.88037109375, 0.2200927734375, 0.28515625, -0.5771484375, -0.78125, 0.1082763671875, 0.8583984375, -0.99609375, -0.388916015625, -0.16455078125, 0.35205078125, 0.06817626953125, -0.0266876220703125, 0.318603515625, 0.50146484375, 0.64111328125, 0.353759765625, -0.380615234375, -0.57861328125, -0.97314453125, -0.66748046875, -0.97021484375, -0.1611328125, -0.347412109375, 0.1357421875, -0.006755828857421875, -0.8154296875, 0.02410888671875, -0.497802734375, -0.440673828125, 0.330810546875, -0.96435546875, 0.54296875, -0.179443359375, 0.447021484375, -0.8642578125, 0.445556640625, 0.320068359375, 1.1259765625, -0.56298828125, 0.07208251953125, 0.09307861328125, -0.95166015625, 0.123291015625, 0.05841064453125, 0.325927734375, 0.2310791015625, -0.318115234375, -0.64697265625, -0.250732421875, -0.10693359375, -0.4345703125, 0.208740234375, -0.6298828125, 0.990234375, 0.5087890625, -0.6103515625, 0.56982421875, 0.9013671875, -0.94384765625, 0.56396484375, 0.08837890625, 0.04327392578125, -0.7265625, 1.412109375, 0.3583984375, 0.358154296875, -0.65234375, -0.347900390625, -0.3095703125, -0.07061767578125, 0.310791015625, -0.6865234375, -0.219970703125, 0.408203125, 0.0163726806640625, -0.9248046875, 0.294921875, -1.0185546875, -0.496826171875, -0.341552734375, -0.173828125, 1.1923828125, 0.966796875, 0.1544189453125, -0.138916015625, -0.128173828125, -0.168701171875, 0.84326171875, 0.6796875, -0.4921875, 0.19970703125, 1.0009765625, 0.0196685791015625, -0.14990234375, 0.036376953125, -0.268310546875, 0.1007080078125, 0.1214599609375, 0.28515625, 0.85791015625, 0.369873046875, 0.156005859375, 0.49365234375, 0.79736328125, -1.0751953125, -0.175537109375, -0.1246337890625, 0.51708984375, 0.529296875, 0.1619873046875, 0.339599609375, -0.01514434814453125, -0.5888671875, -1.2802734375, 0.3330078125, 0.23828125, 0.7578125, -0.7890625, 0.74267578125, 0.2236328125, -0.32958984375, 0.1527099609375, -0.5400390625, 0.053741455078125, 1.044921875, -0.0201263427734375, 0.5986328125, -0.81201171875, 0.248291015625, 0.26123046875, -0.0025310516357421875, 0.5703125, 0.266357421875, 0.701171875, -0.330810546875, -0.32177734375, -0.5390625, -0.2098388671875, 0.0019292831420898438, -0.68896484375, 0.160888671875, -0.445068359375, -0.57666015625, -0.98046875, 0.1826171875, 0.712890625, 0.69921875, -0.054107666015625, 0.498291015625, -0.03125, 0.68408203125, 0.6259765625, -0.224853515625, 0.19921875, -0.7578125, 0.734375, 0.11834716796875, -0.307861328125, -0.52392578125, -0.2291259765625, -0.2685546875, -0.195068359375, 0.04150390625, -0.4453125, -0.572265625, 0.37548828125, -0.1722412109375, 0.69873046875, -0.60009765625, -0.54541015625, -0.332275390625, 0.52294921875, 0.1524658203125, -0.91650390625, 0.396728515625, -0.66015625, 0.8427734375, 0.323974609375, -0.07501220703125, -0.72314453125, -0.6376953125, -0.69921875, -0.693359375, -0.09564208984375, 1.03515625, -0.057373046875, 0.392822265625, -1.181640625, 0.053802490234375, 0.285400390625, -0.4091796875, -0.0467529296875, -0.10333251953125, 0.52880859375, 0.1805419921875, 0.87060546875, -0.81298828125, -0.666015625, -0.185546875, -1.4326171875, 0.4833984375, -0.90966796875, 0.374755859375, 0.301025390625, 0.1578369140625, -0.307373046875, 0.50341796875, -0.0960693359375, 0.231689453125, -0.2469482421875, 0.40771484375, -0.8330078125, -0.497802734375, 0.685546875, -0.3466796875, -0.327392578125, 0.82958984375, -0.2138671875, -0.42138671875, 0.3916015625, 0.404541015625, -0.57666015625, 0.5224609375, -0.4140625, 0.7900390625, -0.2440185546875, -0.46533203125, -0.169189453125, -0.51123046875, 0.8974609375, 0.1708984375, -1.1259765625, -0.15478515625, -0.93408203125, 0.045074462890625, -0.06768798828125, -0.227783203125, 0.2012939453125, 0.21044921875, 0.1187744140625, -0.1981201171875, -0.236328125, -0.468505859375, -0.4189453125, -0.492431640625, -0.09356689453125, 0.238525390625, 0.57373046875, 0.403564453125, -0.0026912689208984375, -0.2421875, -0.330078125, 0.10052490234375, 0.07440185546875, -0.52880859375, 0.007434844970703125, -0.035308837890625, -0.175537109375, -0.09869384765625, 0.428466796875, -0.2325439453125, 0.09564208984375, 0.93505859375, -0.0169830322265625, 0.45849609375, 0.2310791015625, -0.47900390625, 0.568359375, 0.148193359375, -1.138671875, -0.55029296875, 0.463623046875, -0.0770263671875, 0.52685546875, 0.34521484375, -1.193359375, -0.78125, -0.77392578125, 0.11676025390625, -0.72705078125, -0.01226806640625, -0.9892578125, -0.447021484375, -0.5126953125, 0.5830078125, 0.13525390625, -0.775390625, 0.06524658203125, -1.1669921875, 0.1585693359375, -1.1044921875, -0.11004638671875, -0.6171875, -0.58251953125, -0.1644287109375, 0.67724609375, 0.12841796875, 0.33837890625, 0.03680419921875, -0.2210693359375, 0.345458984375, 0.266357421875, -0.73828125, -0.2496337890625, -0.244384765625, -0.0170135498046875, -0.17724609375, -0.0184326171875, -0.39697265625, 0.7099609375, -0.6396484375, 0.444091796875, -0.173095703125, -0.52734375, -0.1900634765625, -0.019012451171875, 1.158203125, -0.1790771484375, 0.259765625, -0.347900390625, 0.1390380859375, 0.58740234375, -0.257568359375, -0.58740234375, -0.9580078125, -0.438720703125, -1.080078125, 0.73486328125, -0.27099609375, 0.1600341796875, -0.64208984375, -0.50927734375, 0.962890625, -0.66162109375, 0.51123046875, 1.2021484375, -0.118896484375, 0.343994140625, -0.0631103515625, 0.51123046875, 0.5478515625, -0.82421875, 0.232666015625, 0.47314453125, -0.51416015625, 0.324462890625, -0.195068359375, -0.83251953125, -0.6484375, 0.07086181640625, 1.19140625, -0.130859375, 0.62451171875, -0.361572265625, -1.080078125, -0.54736328125, 0.6787109375, 0.11993408203125, 0.267578125, 0.68408203125, 0.1475830078125, -0.01125335693359375, 0.061859130859375, -0.283935546875, -0.004505157470703125, -0.37939453125, 1.0859375, 0.036529541015625, -0.25244140625, 1.08984375, 0.86962890625, -0.87939453125, -0.94140625, 0.284912109375, -0.24853515625, -0.41259765625, -0.60009765625, 0.0987548828125, 0.49267578125, -0.76416015625, -0.0235443115234375, 0.5517578125, -0.14013671875, 0.626953125, -0.2427978515625, 0.403564453125, -0.60107421875, 0.82666015625, 0.65673828125, -0.4580078125, -0.011566162109375, -0.880859375, -0.385986328125, -0.556640625, -0.05328369140625, 0.615234375, -0.57275390625, 0.1690673828125, 0.76318359375, 0.0215301513671875, 0.77685546875, -0.59765625, -0.537109375, -0.038665771484375, -0.416748046875, -0.70068359375, 0.0182952880859375, 0.057464599609375, 0.08282470703125, 0.47265625, -0.74609375, 0.127197265625, -0.1337890625, 0.10272216796875, -0.327392578125, -1.11328125, -0.1468505859375, -0.91455078125, -0.303955078125, -0.91064453125, -0.66796875, -0.201171875, 0.12420654296875, -0.057037353515625, -0.6171875, -0.2093505859375, 0.2218017578125, -0.393310546875, 0.89892578125, -0.67431640625, 0.3984375, -0.2587890625, -0.5166015625, -0.58984375, 0.017608642578125, -0.5419921875, 0.080078125, -0.69677734375, 0.38671875, -0.407958984375, 0.5634765625, -0.39501953125, 0.330078125, -0.3486328125, -0.615234375, 0.2291259765625, -0.06854248046875, -0.383056640625, 0.986328125, 0.3876953125, -0.1253662109375, 0.1844482421875, -0.43212890625, 0.07684326171875, -0.662109375, 0.302978515625, 0.71240234375, -0.33447265625, -0.1644287109375, 0.09954833984375, 0.1568603515625, -1.1572265625, 0.43994140625, -0.366455078125, -0.10467529296875, 0.5205078125, -0.06402587890625, 0.459716796875, 1.16796875, -0.288330078125, 0.63330078125, -0.01971435546875, 0.2200927734375, 0.40087890625, 0.1903076171875, -0.161376953125, 0.41748046875, -0.025146484375, 0.003749847412109375, 0.1490478515625, 0.06964111328125, 0.1502685546875, 0.22216796875, -0.0810546875, -0.61279296875, -0.72998046875, -0.238525390625, -0.22509765625, 0.3310546875, 0.44970703125, -0.2490234375, -0.306396484375, -0.1273193359375, -0.41650390625, 0.296630859375, -1.2451171875, -1.015625, 0.58056640625, -0.2548828125, -0.480224609375, -0.317626953125, -0.3701171875, -0.35205078125, 0.1607666015625, 0.46875, -0.52783203125, 0.295166015625, -0.345458984375, 0.450439453125, -0.42138671875, -0.182373046875, 0.1507568359375, 0.46630859375, -0.393310546875, -0.64208984375, 0.1627197265625, 1.2138671875, 0.290771484375, -0.22021484375, -0.3017578125, 0.34619140625, -0.1336669921875, 0.081787109375, -0.353759765625, 0.477294921875, -0.4990234375, 0.43359375, -0.83837890625, 0.189453125, -0.42529296875, 0.341064453125, 0.361572265625, -0.3876953125, -0.6298828125, 0.626953125, 0.490966796875, -0.10211181640625, 0.86328125, -0.293701171875, 0.56298828125, 0.04693603515625, 0.271240234375, -0.2059326171875, 0.916015625, 0.72509765625, 0.67822265625, -0.1710205078125, 0.29150390625, 0.748046875, 0.18603515625, -0.41748046875, 0.34814453125, 0.20166015625, -0.0943603515625, 0.335205078125, -0.207763671875, -0.2103271484375, 0.01312255859375, -0.48046875, 0.62451171875, -0.33056640625, 0.04083251953125, -0.102783203125, -1.0380859375, 1.080078125, -0.226318359375, -0.0033168792724609375, 0.212890625, -0.35595703125, 0.2198486328125, 0.7705078125, -0.27880859375, -0.1904296875, 0.744140625, 0.7763671875, 0.5458984375, 0.76123046875, 0.261962890625, 0.293701171875, -0.65625, 0.075927734375, -0.0328369140625, 0.1451416015625, -0.2587890625, -0.50927734375, -0.493896484375, 0.428955078125, -0.71435546875, -0.271240234375, 0.64306640625, -0.72265625, 0.1824951171875, -0.37158203125, 1.08984375, -0.49267578125, 0.1273193359375, 0.35009765625, -0.239013671875, -0.69873046875, 0.853515625, -0.1083984375, 0.28515625, 0.00623321533203125, 1.2041015625, -0.1527099609375, 1.40625, 0.66015625, -0.05059814453125, -0.142333984375, 0.328125, -0.103271484375, -0.29443359375, -0.5712890625, -0.392822265625, 0.19091796875, -0.94921875, -0.5859375, -0.051239013671875, 0.8037109375, 0.1307373046875, -1.259765625, -0.03759765625, 0.1124267578125, -0.900390625, 0.15576171875, 0.269287109375, 0.33447265625, 0.213623046875, -0.158203125, -0.1219482421875, -0.26708984375, 0.5732421875, -0.8349609375, 0.488525390625, -0.6181640625, -0.39990234375, -0.611328125, -0.64892578125, -0.1461181640625, -0.447021484375, -0.375, -0.6337890625, 0.271240234375, 0.5205078125, 0.6328125, 0.1558837890625, -0.271484375, 0.051971435546875, 0.86865234375, 0.90869140625, 0.2071533203125, 0.94482421875, 0.247802734375, -0.279296875, 0.442626953125, -0.51318359375, 0.278076171875, -0.28076171875, 0.32421875, -0.56689453125, 0.060028076171875, -0.7900390625, -1.15234375, 0.00218963623046875, 0.430908203125, 0.1480712890625, -0.54931640625, -0.921875, -0.354736328125, -1.1904296875, -0.174560546875, -0.494873046875, 0.97021484375, -0.427490234375, -0.08489990234375, -0.10528564453125, -1.58203125, 4.3828125, 0.69775390625, 0.5791015625, 0.391357421875, 0.45166015625, 0.79296875, 0.30810546875, -0.46630859375, -0.60107421875, -0.35791015625, 0.59716796875, -0.299072265625, -0.01080322265625, 0.76806640625, 0.51806640625, 0.2176513671875, -0.44189453125, 0.2362060546875, 0.150390625, -0.837890625, -0.6806640625, 0.346435546875, -0.2027587890625, 0.8525390625, 0.027435302734375, 0.1785888671875, 0.5947265625, -0.95458984375, -0.06280517578125, -0.6640625, 0.249755859375, -0.42333984375, 0.84375, -0.04547119140625, -0.035858154296875, 0.67724609375, 0.29150390625, -0.1859130859375, -0.0516357421875, -0.020172119140625, -0.08465576171875, -0.2200927734375, 0.6787109375, -0.8798828125, -0.363037109375, 0.427978515625, -0.728515625, 0.45849609375, 0.25146484375, -0.94140625, 0.96044921875, -0.440185546875, 0.4521484375, -0.58154296875, -0.900390625, 0.279541015625, 0.08367919921875, 0.293701171875, -0.30712890625, 0.342041015625, 0.65966796875, 0.630859375, -0.041351318359375, 0.4482421875, -0.984375, 0.7451171875, -0.28125, 0.64111328125, -0.5966796875, -0.1558837890625, 0.02117919921875, -0.237060546875, -0.0390625, -0.537109375, 0.6650390625, 0.09991455078125, -0.5078125, 0.7060546875, 0.54248046875, -0.798828125, 0.058502197265625, -0.2127685546875, -0.0982666015625, -0.5341796875, 0.55224609375, 1.287109375, -0.4345703125, -0.26416015625, -0.46728515625, 0.416015625, 0.580078125, 0.94580078125, 0.037139892578125, -0.255615234375, -0.0703125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows: * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} = 1, then s_i = 1); * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≀ n and w_{i+x} = 1, then s_i = 1); * if both of the aforementioned conditions are false, then s_i is 0. You are given the integer x and the resulting string s. Reconstruct the original string w. Input The first line contains one integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Each test case consists of two lines. The first line contains the resulting string s (2 ≀ |s| ≀ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≀ x ≀ |s| - 1). The total length of all strings s in the input does not exceed 10^5. Output For each test case, print the answer on a separate line as follows: * if no string w can produce the string s at the end of the process, print -1; * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. Example Input 3 101110 2 01 1 110 1 Output 111011 10 -1 Tags: 2-sat, brute force, constructive algorithms, greedy Correct Solution: ``` import sys input = sys.stdin.readline def const(S): n=len(S) ANS=["0"]*n for i in range(n): if i-x>=0 and S[i-x]=="1": ANS[i]="1" if i+x<n and S[i+x]=="1": ANS[i]="1" return "".join(ANS) t=int(input()) for tests in range(t): S=input().strip() x=int(input()) n=len(S) ANS=["1"]*n for i in range(n): if S[i]=="0": if i-x>=0: ANS[i-x]="0" if i+x<n: ANS[i+x]="0" A="".join(ANS) if const(A)==S: print(A) else: print(-1) ```
107,223
[ 0.275146484375, 0.102783203125, 0.1611328125, 0.09100341796875, -0.418212890625, -0.44580078125, 0.0396728515625, -0.1488037109375, 0.2200927734375, 0.8642578125, 0.66650390625, -0.368896484375, 0.1649169921875, -1.0849609375, -0.3779296875, -0.10650634765625, -0.62109375, -0.5419921875, -0.39404296875, -0.2318115234375, 0.0172576904296875, -0.051361083984375, -1.4951171875, -0.1639404296875, -0.53662109375, 0.82080078125, 0.463134765625, 0.10101318359375, 1.044921875, 1.2158203125, -0.2498779296875, -0.46240234375, 0.63623046875, -1.326171875, -0.38037109375, -0.43505859375, 0.79296875, -0.873046875, -0.229736328125, -0.325439453125, 0.40087890625, -0.319091796875, 0.432373046875, -0.93310546875, -1.3310546875, -0.272705078125, -0.63037109375, -0.2646484375, -0.1416015625, -0.6416015625, -0.025909423828125, -0.28369140625, 0.298828125, -0.31494140625, 0.219970703125, 0.09942626953125, 0.01285552978515625, -0.356201171875, -0.8515625, 0.379150390625, -0.05450439453125, -0.1690673828125, 0.221923828125, -0.57373046875, -0.277587890625, 0.0141754150390625, -0.08197021484375, -0.353759765625, -0.080322265625, -0.9072265625, 0.15576171875, 0.34765625, -0.439697265625, -0.316650390625, -0.343994140625, 0.04913330078125, 0.331787109375, 0.2286376953125, -0.6923828125, 0.9140625, -0.1439208984375, 0.99658203125, 0.1976318359375, 0.231689453125, -0.372802734375, -0.55322265625, -0.1593017578125, 0.38916015625, 0.205078125, -0.272216796875, -0.15966796875, 0.60498046875, -0.6435546875, 0.3173828125, 0.23388671875, 0.60205078125, -0.277099609375, 0.09014892578125, 0.276611328125, 0.045684814453125, 0.59130859375, 1.056640625, -0.460693359375, 0.98046875, -0.57470703125, 0.1923828125, 0.1512451171875, 0.1929931640625, -0.412353515625, 0.02069091796875, -0.038604736328125, -0.2347412109375, 0.759765625, 0.310546875, -0.625, 0.84033203125, -0.04901123046875, 0.1480712890625, -0.81298828125, 0.32275390625, 0.4521484375, 0.141845703125, 0.62646484375, -0.0253753662109375, -0.376953125, -0.35595703125, -0.2978515625, 1.0791015625, -0.365966796875, -0.21044921875, 0.476806640625, 0.023223876953125, 0.10394287109375, 0.21630859375, -0.0187835693359375, 0.982421875, -0.38720703125, 0.451416015625, 0.654296875, -0.5185546875, 0.9990234375, -0.5830078125, -0.126953125, 1.44921875, 0.4150390625, 0.25048828125, 1, 0.466064453125, -0.80078125, 0.31884765625, -0.90673828125, 0.71875, 0.10107421875, 0.2587890625, -0.09417724609375, 0.07708740234375, -0.282958984375, 0.35302734375, -0.0341796875, 0.145751953125, -0.470947265625, 0.521484375, -0.1864013671875, 0.94091796875, -0.262939453125, 0.83447265625, -0.09576416015625, -0.12225341796875, -0.427978515625, -0.7119140625, 0.3525390625, -0.2744140625, -0.359375, 0.8232421875, 0.74072265625, 0.9560546875, 1.125, -0.3447265625, 0.19970703125, 0.1395263671875, -0.68212890625, 0.1239013671875, 0.29638671875, 0.96337890625, 0.357666015625, 0.51806640625, 0.129150390625, -0.30859375, -0.99755859375, -0.515625, 0.101318359375, 0.9384765625, -0.74951171875, 0.2406005859375, 0.045623779296875, 0.2305908203125, -0.85205078125, -0.1492919921875, -0.412841796875, -0.88427734375, -0.3310546875, 0.45751953125, 0.00786590576171875, 0.1051025390625, -0.712890625, -0.4833984375, 0.58837890625, 1.1015625, -0.21826171875, -0.332763671875, 0.12493896484375, -0.005397796630859375, -0.1304931640625, 0.360107421875, -0.004573822021484375, -0.240234375, -0.82958984375, 0.92626953125, -0.11651611328125, -0.07391357421875, 0.080810546875, 0.8388671875, 0.32373046875, 0.9482421875, -0.162841796875, -0.083251953125, 0.364013671875, 1.0859375, 0.11676025390625, 0.333984375, 0.48046875, 1.1591796875, 0.638671875, 0.67724609375, 0.33837890625, 0.283935546875, 0.7607421875, 0.99853515625, 0.0806884765625, 0.468017578125, -0.2154541015625, 0.248779296875, 0.1207275390625, 0.488037109375, 0.22802734375, 0.20849609375, 0.032257080078125, 0.205078125, -0.4296875, 0.038116455078125, -0.2288818359375, 0.9111328125, 0.20361328125, 0.30078125, -0.64697265625, -0.7919921875, 0.145263671875, 0.8583984375, -1.0849609375, -0.435302734375, -0.153076171875, 0.273681640625, -0.034393310546875, -0.0028591156005859375, 0.256103515625, 0.4619140625, 0.5712890625, 0.307861328125, -0.353759765625, -0.51171875, -0.9765625, -0.57568359375, -1.017578125, -0.2330322265625, -0.417724609375, 0.0823974609375, -0.09149169921875, -0.85693359375, 0.0118560791015625, -0.49267578125, -0.452392578125, 0.354736328125, -0.92529296875, 0.4931640625, -0.2108154296875, 0.364990234375, -0.9267578125, 0.455322265625, 0.261962890625, 1.205078125, -0.51025390625, 0.039642333984375, 0.0523681640625, -0.90625, 0.130126953125, -0.01169586181640625, 0.25439453125, 0.2861328125, -0.2369384765625, -0.7060546875, -0.351318359375, -0.122802734375, -0.451416015625, 0.294921875, -0.4609375, 0.91162109375, 0.424072265625, -0.556640625, 0.615234375, 0.97021484375, -0.89404296875, 0.55908203125, 0.1474609375, -0.05865478515625, -0.7626953125, 1.4013671875, 0.314208984375, 0.312255859375, -0.603515625, -0.42529296875, -0.154541015625, -0.0115814208984375, 0.2401123046875, -0.67724609375, -0.27734375, 0.43994140625, 0.07769775390625, -0.98046875, 0.2142333984375, -1.0087890625, -0.505859375, -0.3583984375, -0.265869140625, 1.1708984375, 0.84228515625, 0.2337646484375, -0.0679931640625, -0.2056884765625, -0.255126953125, 0.73828125, 0.744140625, -0.59130859375, 0.160888671875, 1.0126953125, -0.0297698974609375, -0.1553955078125, -0.033050537109375, -0.23974609375, 0.1004638671875, 0.005901336669921875, 0.339599609375, 0.8076171875, 0.312255859375, 0.18603515625, 0.5283203125, 0.74462890625, -1.1474609375, -0.14501953125, -0.0007882118225097656, 0.476318359375, 0.52685546875, 0.12176513671875, 0.42578125, 0.0008602142333984375, -0.5068359375, -1.203125, 0.25048828125, 0.2347412109375, 0.82666015625, -0.68115234375, 0.8515625, 0.105224609375, -0.254638671875, 0.1539306640625, -0.52734375, 0.1854248046875, 1.05859375, -0.02142333984375, 0.5625, -0.810546875, 0.247314453125, 0.320556640625, -0.0850830078125, 0.55224609375, 0.2491455078125, 0.654296875, -0.286376953125, -0.33740234375, -0.64892578125, -0.26611328125, -0.03277587890625, -0.80517578125, 0.15185546875, -0.376708984375, -0.607421875, -1.029296875, 0.2047119140625, 0.72802734375, 0.73681640625, -0.00788116455078125, 0.49072265625, -0.1162109375, 0.81201171875, 0.60107421875, -0.2437744140625, 0.1983642578125, -0.806640625, 0.84033203125, 0.191162109375, -0.2327880859375, -0.58837890625, -0.234130859375, -0.2237548828125, -0.14306640625, 0.09576416015625, -0.51171875, -0.494873046875, 0.34326171875, -0.1292724609375, 0.63720703125, -0.6416015625, -0.455078125, -0.432373046875, 0.463134765625, 0.186767578125, -0.9775390625, 0.37353515625, -0.80078125, 0.7685546875, 0.292724609375, -0.15576171875, -0.6875, -0.6181640625, -0.5693359375, -0.8271484375, -0.11474609375, 1.1240234375, 0.09210205078125, 0.496337890625, -1.2451171875, 0.177490234375, 0.32666015625, -0.49267578125, -0.1468505859375, -0.11737060546875, 0.47216796875, 0.156982421875, 0.8623046875, -0.7666015625, -0.6875, -0.2235107421875, -1.4228515625, 0.6259765625, -0.91015625, 0.5068359375, 0.301513671875, 0.1923828125, -0.366455078125, 0.64111328125, -0.148193359375, 0.1876220703125, -0.263916015625, 0.367431640625, -0.85498046875, -0.55908203125, 0.80224609375, -0.465576171875, -0.36767578125, 0.94921875, -0.2259521484375, -0.481689453125, 0.379150390625, 0.48291015625, -0.6123046875, 0.56103515625, -0.52587890625, 0.70556640625, -0.2044677734375, -0.51318359375, -0.2275390625, -0.58154296875, 0.94775390625, 0.1817626953125, -1.14453125, -0.1463623046875, -0.9287109375, 0.0218658447265625, -0.15673828125, -0.2449951171875, 0.28955078125, 0.1614990234375, 0.1302490234375, -0.2403564453125, -0.1953125, -0.414306640625, -0.397705078125, -0.5048828125, -0.13134765625, 0.121826171875, 0.505859375, 0.433837890625, -0.0987548828125, -0.305419921875, -0.365234375, 0.1549072265625, -0.030792236328125, -0.440185546875, -0.08245849609375, -0.07781982421875, -0.296875, -0.1573486328125, 0.451171875, -0.211669921875, 0.1541748046875, 0.8486328125, 0.04443359375, 0.462158203125, 0.31298828125, -0.603515625, 0.65869140625, 0.2939453125, -1.130859375, -0.324462890625, 0.424560546875, -0.06805419921875, 0.61962890625, 0.27978515625, -1.171875, -0.6787109375, -0.7021484375, 0.1431884765625, -0.71240234375, -0.0792236328125, -1.0869140625, -0.464111328125, -0.5205078125, 0.61328125, 0.01373291015625, -0.72265625, 0.10040283203125, -1.20703125, 0.0772705078125, -1.2578125, -0.1715087890625, -0.72509765625, -0.693359375, -0.1080322265625, 0.76611328125, 0.036865234375, 0.36669921875, 0.094482421875, -0.2369384765625, 0.323486328125, 0.35595703125, -0.77978515625, -0.1497802734375, -0.22265625, 0.06561279296875, -0.181884765625, -0.0180206298828125, -0.426025390625, 0.708984375, -0.72802734375, 0.3369140625, -0.1064453125, -0.452880859375, -0.0762939453125, 0.08673095703125, 1.0986328125, -0.2464599609375, 0.24267578125, -0.4404296875, 0.142333984375, 0.62353515625, -0.295654296875, -0.60546875, -0.927734375, -0.40380859375, -1.0361328125, 0.65185546875, -0.293701171875, 0.2120361328125, -0.72314453125, -0.468505859375, 0.9580078125, -0.69677734375, 0.53125, 1.2001953125, -0.07086181640625, 0.36083984375, -0.004734039306640625, 0.61767578125, 0.62646484375, -0.88671875, 0.23291015625, 0.53955078125, -0.499755859375, 0.3974609375, -0.2685546875, -0.87890625, -0.6171875, 0.1358642578125, 1.2197265625, -0.10345458984375, 0.68017578125, -0.336181640625, -1.0517578125, -0.49267578125, 0.82763671875, 0.07037353515625, 0.39306640625, 0.75439453125, 0.1729736328125, -0.0098419189453125, 0.2015380859375, -0.331298828125, 0.1446533203125, -0.422607421875, 1.158203125, 0.004611968994140625, -0.163818359375, 1.09375, 0.9248046875, -0.947265625, -1.044921875, 0.2100830078125, -0.218505859375, -0.3740234375, -0.70556640625, 0.09405517578125, 0.428955078125, -0.69873046875, -0.0232086181640625, 0.41748046875, -0.041656494140625, 0.6796875, -0.298095703125, 0.391357421875, -0.70068359375, 0.88916015625, 0.71533203125, -0.41650390625, -0.0291595458984375, -0.892578125, -0.27587890625, -0.54931640625, -0.07037353515625, 0.6533203125, -0.56640625, 0.279052734375, 0.802734375, 0.01076507568359375, 0.96533203125, -0.5908203125, -0.62158203125, 0.05645751953125, -0.48974609375, -0.74951171875, 0.053436279296875, 0.00885009765625, -0.0031833648681640625, 0.51611328125, -0.783203125, -0.0298004150390625, -0.056304931640625, 0.153564453125, -0.306884765625, -0.92333984375, -0.16552734375, -0.8447265625, -0.33203125, -0.91552734375, -0.7705078125, -0.09710693359375, 0.1845703125, -0.0276947021484375, -0.60986328125, -0.2958984375, 0.264404296875, -0.438232421875, 1.0009765625, -0.76171875, 0.388427734375, -0.314208984375, -0.53857421875, -0.7080078125, 0.0765380859375, -0.6162109375, 0.01436614990234375, -0.6962890625, 0.38916015625, -0.385498046875, 0.60888671875, -0.3115234375, 0.371337890625, -0.441650390625, -0.63330078125, 0.322021484375, -0.053741455078125, -0.4326171875, 0.97216796875, 0.374267578125, -0.0131988525390625, 0.187255859375, -0.53125, 0.07879638671875, -0.58740234375, 0.297607421875, 0.7353515625, -0.255615234375, -0.1373291015625, 0.03509521484375, 0.10443115234375, -1.1376953125, 0.46240234375, -0.371826171875, -0.05224609375, 0.5009765625, -0.1661376953125, 0.5078125, 1.171875, -0.356201171875, 0.55078125, -0.023162841796875, 0.29931640625, 0.38134765625, 0.134033203125, -0.2462158203125, 0.583984375, -0.00009632110595703125, 0.009765625, 0.1710205078125, 0.1627197265625, 0.2216796875, 0.219970703125, -0.07867431640625, -0.619140625, -0.85546875, -0.1923828125, -0.357421875, 0.278076171875, 0.441162109375, -0.187744140625, -0.285888671875, -0.1497802734375, -0.441650390625, 0.332275390625, -1.0517578125, -1.072265625, 0.51416015625, -0.28125, -0.61669921875, -0.318115234375, -0.431640625, -0.1744384765625, 0.172119140625, 0.35693359375, -0.465087890625, 0.318359375, -0.380126953125, 0.411376953125, -0.381591796875, -0.189697265625, 0.1685791015625, 0.449462890625, -0.40234375, -0.70751953125, 0.1571044921875, 1.166015625, 0.1834716796875, -0.330810546875, -0.318359375, 0.382568359375, -0.1170654296875, 0.1939697265625, -0.326171875, 0.49169921875, -0.517578125, 0.36083984375, -0.8603515625, 0.2388916015625, -0.43896484375, 0.40966796875, 0.359619140625, -0.384033203125, -0.5966796875, 0.619140625, 0.4921875, -0.0232391357421875, 0.95068359375, -0.269287109375, 0.60595703125, 0.1507568359375, 0.147705078125, -0.2373046875, 0.93994140625, 0.72900390625, 0.7861328125, -0.1607666015625, 0.304443359375, 0.86474609375, 0.10992431640625, -0.465087890625, 0.28125, 0.2161865234375, -0.0672607421875, 0.400146484375, -0.2001953125, -0.228271484375, 0.0286102294921875, -0.56787109375, 0.60595703125, -0.334228515625, 0.08880615234375, -0.1004638671875, -1.041015625, 1.15234375, -0.264892578125, 0.059234619140625, 0.207275390625, -0.37255859375, 0.340087890625, 0.736328125, -0.3603515625, -0.073486328125, 0.736328125, 0.759765625, 0.5048828125, 0.58984375, 0.266357421875, 0.48046875, -0.8017578125, 0.0673828125, -0.0877685546875, 0.1787109375, -0.29150390625, -0.51318359375, -0.56396484375, 0.467041015625, -0.642578125, -0.1976318359375, 0.64306640625, -0.82421875, 0.35546875, -0.34130859375, 1.0986328125, -0.47119140625, -0.0162811279296875, 0.30810546875, -0.206298828125, -0.63330078125, 0.884765625, -0.1365966796875, 0.2366943359375, 0.01629638671875, 1.1943359375, -0.10479736328125, 1.4091796875, 0.64208984375, -0.0203399658203125, -0.11993408203125, 0.3466796875, -0.1806640625, -0.1971435546875, -0.5244140625, -0.42236328125, 0.25341796875, -0.91943359375, -0.69775390625, 0.04052734375, 0.89453125, 0.170654296875, -1.1796875, -0.0738525390625, 0.10791015625, -0.93701171875, 0.1878662109375, 0.1748046875, 0.447509765625, 0.165771484375, -0.3369140625, -0.08587646484375, -0.402587890625, 0.6083984375, -0.78955078125, 0.45166015625, -0.5625, -0.39794921875, -0.7294921875, -0.62890625, -0.070068359375, -0.380126953125, -0.352783203125, -0.59033203125, 0.271728515625, 0.458740234375, 0.591796875, 0.1536865234375, -0.279296875, 0.0264434814453125, 0.751953125, 0.916015625, 0.06982421875, 0.9853515625, 0.153564453125, -0.401123046875, 0.54638671875, -0.3662109375, 0.318603515625, -0.29833984375, 0.2529296875, -0.62353515625, 0.08978271484375, -0.73828125, -1.072265625, -0.00545501708984375, 0.40234375, 0.06329345703125, -0.466064453125, -0.87744140625, -0.432373046875, -1.169921875, -0.12457275390625, -0.67138671875, 0.8935546875, -0.44873046875, -0.052581787109375, -0.07537841796875, -1.5625, 4.296875, 0.63818359375, 0.75, 0.240966796875, 0.5439453125, 0.77294921875, 0.29296875, -0.392578125, -0.4921875, -0.44677734375, 0.66845703125, -0.350341796875, -0.1036376953125, 0.80322265625, 0.642578125, 0.207275390625, -0.4912109375, 0.07537841796875, 0.234375, -1.0048828125, -0.69775390625, 0.24365234375, -0.2003173828125, 0.87841796875, 0.0911865234375, 0.234619140625, 0.57958984375, -1.08203125, -0.01177978515625, -0.7802734375, 0.2105712890625, -0.305908203125, 0.78369140625, -0.058685302734375, -0.0927734375, 0.75634765625, 0.1767578125, -0.169921875, -0.0892333984375, 0.08795166015625, -0.04803466796875, -0.281494140625, 0.732421875, -0.86279296875, -0.36865234375, 0.494140625, -0.70361328125, 0.498291015625, 0.1737060546875, -1.04296875, 1.0078125, -0.39990234375, 0.435546875, -0.58837890625, -0.79638671875, 0.4619140625, 0.139404296875, 0.231201171875, -0.28466796875, 0.343994140625, 0.6357421875, 0.73828125, 0.04022216796875, 0.50048828125, -0.96533203125, 0.7734375, -0.250244140625, 0.7890625, -0.60595703125, -0.207275390625, -0.01241302490234375, -0.29736328125, -0.1417236328125, -0.55517578125, 0.703125, 0.0645751953125, -0.483154296875, 0.71484375, 0.5615234375, -0.7451171875, 0.050628662109375, -0.1131591796875, -0.1373291015625, -0.54345703125, 0.5927734375, 1.337890625, -0.472900390625, -0.1829833984375, -0.328369140625, 0.460205078125, 0.61328125, 1.103515625, 0.07769775390625, -0.197021484375, -0.1802978515625 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows: * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} = 1, then s_i = 1); * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≀ n and w_{i+x} = 1, then s_i = 1); * if both of the aforementioned conditions are false, then s_i is 0. You are given the integer x and the resulting string s. Reconstruct the original string w. Input The first line contains one integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Each test case consists of two lines. The first line contains the resulting string s (2 ≀ |s| ≀ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≀ x ≀ |s| - 1). The total length of all strings s in the input does not exceed 10^5. Output For each test case, print the answer on a separate line as follows: * if no string w can produce the string s at the end of the process, print -1; * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. Example Input 3 101110 2 01 1 110 1 Output 111011 10 -1 Tags: 2-sat, brute force, constructive algorithms, greedy Correct Solution: ``` res = '' for _ in range(int(input())): s = input() x = int(input()) ls = len(s) a = ['1'] * ls for i, k in enumerate(s): if k == '0': if i-x>=0: a[i-x] = '0' if i + x < ls: a[i+x] = '0' for i, k in enumerate(s): if k == '1': f = 0 if i-x>=0: f |= int(a[i-x]) if i + x < ls: f |= int(a[i+x]) if not f: res += '-1\n' break else: res += ''.join(a) + '\n' print(res) ```
107,224
[ 0.25439453125, 0.07244873046875, 0.110595703125, 0.0836181640625, -0.40087890625, -0.47900390625, 0.03375244140625, -0.1444091796875, 0.205322265625, 0.90283203125, 0.67138671875, -0.3486328125, 0.188232421875, -1.1162109375, -0.381591796875, -0.08245849609375, -0.6669921875, -0.58984375, -0.404052734375, -0.216064453125, 0.0006017684936523438, -0.036163330078125, -1.501953125, -0.1993408203125, -0.465576171875, 0.89697265625, 0.464599609375, 0.1566162109375, 1.033203125, 1.23828125, -0.270263671875, -0.471435546875, 0.7236328125, -1.28125, -0.409912109375, -0.46533203125, 0.73779296875, -0.8232421875, -0.2117919921875, -0.33056640625, 0.414306640625, -0.39306640625, 0.446533203125, -0.8642578125, -1.3701171875, -0.2421875, -0.65283203125, -0.2249755859375, -0.12646484375, -0.697265625, -0.017608642578125, -0.327880859375, 0.34423828125, -0.3056640625, 0.2587890625, 0.022125244140625, 0.04681396484375, -0.283447265625, -0.8486328125, 0.364990234375, -0.1707763671875, -0.1934814453125, 0.2861328125, -0.6337890625, -0.28076171875, -0.0186920166015625, -0.11285400390625, -0.36279296875, -0.049957275390625, -0.986328125, 0.11865234375, 0.33544921875, -0.50439453125, -0.2578125, -0.34765625, 0.0238189697265625, 0.254638671875, 0.1302490234375, -0.75341796875, 1.0078125, -0.09881591796875, 0.9599609375, 0.23388671875, 0.228515625, -0.37939453125, -0.533203125, -0.12139892578125, 0.365966796875, 0.2247314453125, -0.29833984375, -0.133056640625, 0.59375, -0.61474609375, 0.31494140625, 0.222900390625, 0.459716796875, -0.258544921875, 0.11737060546875, 0.250732421875, 0.038787841796875, 0.654296875, 1.0634765625, -0.4423828125, 0.90478515625, -0.6064453125, 0.1505126953125, 0.1763916015625, 0.1817626953125, -0.390380859375, -0.07952880859375, -0.08880615234375, -0.24951171875, 0.7216796875, 0.220947265625, -0.55029296875, 0.7939453125, -0.05487060546875, 0.1883544921875, -0.77294921875, 0.30419921875, 0.402587890625, 0.160888671875, 0.64892578125, 0.0250244140625, -0.30908203125, -0.358642578125, -0.3525390625, 1.0087890625, -0.380615234375, -0.1014404296875, 0.4619140625, 0.0218353271484375, 0.04815673828125, 0.180908203125, -0.0006804466247558594, 0.8974609375, -0.374755859375, 0.52197265625, 0.71337890625, -0.38720703125, 1.0361328125, -0.609375, -0.1414794921875, 1.37890625, 0.33447265625, 0.1541748046875, 1.0029296875, 0.4189453125, -0.86376953125, 0.345947265625, -0.88720703125, 0.70751953125, 0.09796142578125, 0.25048828125, -0.0833740234375, 0.1842041015625, -0.2919921875, 0.293212890625, -0.036529541015625, 0.12017822265625, -0.4697265625, 0.4658203125, -0.1534423828125, 0.92431640625, -0.1951904296875, 0.79638671875, -0.1517333984375, -0.068115234375, -0.45947265625, -0.7939453125, 0.2578125, -0.306396484375, -0.3408203125, 0.85107421875, 0.71630859375, 0.98388671875, 1.0810546875, -0.36376953125, 0.210205078125, 0.092041015625, -0.53662109375, 0.1751708984375, 0.2286376953125, 0.9345703125, 0.2286376953125, 0.576171875, 0.09429931640625, -0.259765625, -0.9384765625, -0.4287109375, 0.11297607421875, 0.97314453125, -0.78466796875, 0.251953125, 0.08685302734375, 0.24560546875, -0.80029296875, -0.07342529296875, -0.433837890625, -0.951171875, -0.258056640625, 0.4775390625, 0.04229736328125, 0.120849609375, -0.68017578125, -0.50439453125, 0.50341796875, 1.0361328125, -0.2044677734375, -0.298828125, 0.08575439453125, 0.0745849609375, -0.055389404296875, 0.42138671875, -0.038482666015625, -0.2213134765625, -0.81103515625, 0.92822265625, -0.1544189453125, -0.051483154296875, 0.08721923828125, 0.810546875, 0.367431640625, 0.96728515625, -0.1826171875, -0.1409912109375, 0.327392578125, 1.125, 0.049530029296875, 0.34912109375, 0.4619140625, 1.19140625, 0.69677734375, 0.62890625, 0.383544921875, 0.245849609375, 0.6865234375, 1.0595703125, 0.200927734375, 0.410888671875, -0.1968994140625, 0.258056640625, 0.1995849609375, 0.432373046875, 0.282958984375, 0.24462890625, -0.07159423828125, 0.1929931640625, -0.37890625, 0.1522216796875, -0.251220703125, 0.9130859375, 0.25146484375, 0.269775390625, -0.64697265625, -0.833984375, 0.0965576171875, 0.83740234375, -1.0888671875, -0.43310546875, -0.1385498046875, 0.3759765625, 0.038818359375, -0.01532745361328125, 0.2548828125, 0.4931640625, 0.61083984375, 0.322509765625, -0.343017578125, -0.5986328125, -0.95166015625, -0.56591796875, -1.0166015625, -0.247802734375, -0.376953125, 0.128662109375, -0.059478759765625, -0.84326171875, 0.04522705078125, -0.436767578125, -0.456787109375, 0.319091796875, -0.99560546875, 0.44970703125, -0.2120361328125, 0.364990234375, -0.943359375, 0.4306640625, 0.35546875, 1.1083984375, -0.52587890625, 0.0300750732421875, 0.0885009765625, -0.88525390625, 0.13037109375, 0.02947998046875, 0.289306640625, 0.31103515625, -0.25244140625, -0.6474609375, -0.294189453125, -0.1314697265625, -0.458251953125, 0.1929931640625, -0.5029296875, 0.978515625, 0.49658203125, -0.60302734375, 0.5478515625, 0.8876953125, -0.92919921875, 0.5458984375, 0.20556640625, 0.05352783203125, -0.7236328125, 1.4033203125, 0.3388671875, 0.348388671875, -0.64208984375, -0.35546875, -0.2340087890625, -0.05560302734375, 0.26171875, -0.587890625, -0.218505859375, 0.350341796875, 0.0258026123046875, -1.015625, 0.2373046875, -0.95556640625, -0.5673828125, -0.356689453125, -0.2021484375, 1.1064453125, 0.9052734375, 0.1676025390625, -0.038543701171875, -0.214599609375, -0.2022705078125, 0.666015625, 0.70703125, -0.468505859375, 0.1806640625, 0.9814453125, -0.044189453125, -0.136962890625, -0.041015625, -0.195556640625, 0.06884765625, 0.1072998046875, 0.36474609375, 0.78466796875, 0.3291015625, 0.1712646484375, 0.48583984375, 0.82568359375, -1.0537109375, -0.1326904296875, -0.074951171875, 0.49169921875, 0.54150390625, 0.1484375, 0.401611328125, -0.05926513671875, -0.4755859375, -1.34765625, 0.339599609375, 0.287841796875, 0.72607421875, -0.6669921875, 0.8251953125, 0.178466796875, -0.302490234375, 0.1497802734375, -0.53125, 0.1317138671875, 1.0263671875, 0.04425048828125, 0.6259765625, -0.8046875, 0.260009765625, 0.2666015625, -0.093994140625, 0.55322265625, 0.25341796875, 0.65673828125, -0.308837890625, -0.352783203125, -0.5244140625, -0.2369384765625, -0.025665283203125, -0.72412109375, 0.2091064453125, -0.49072265625, -0.56591796875, -1.00390625, 0.17822265625, 0.71044921875, 0.708984375, -0.00693511962890625, 0.51904296875, -0.059051513671875, 0.72021484375, 0.57080078125, -0.246337890625, 0.2296142578125, -0.81005859375, 0.80419921875, 0.1363525390625, -0.296630859375, -0.50634765625, -0.252197265625, -0.198974609375, -0.1627197265625, 0.07476806640625, -0.50244140625, -0.42822265625, 0.35546875, -0.1087646484375, 0.705078125, -0.56787109375, -0.414306640625, -0.345947265625, 0.533203125, 0.0997314453125, -0.978515625, 0.36572265625, -0.75927734375, 0.78271484375, 0.2362060546875, -0.07281494140625, -0.677734375, -0.6396484375, -0.7041015625, -0.76171875, -0.114990234375, 1.041015625, -0.037139892578125, 0.435302734375, -1.2412109375, 0.06793212890625, 0.298095703125, -0.480224609375, -0.0145416259765625, -0.14697265625, 0.5048828125, 0.18359375, 0.88916015625, -0.8349609375, -0.7041015625, -0.24365234375, -1.408203125, 0.5185546875, -0.89013671875, 0.51171875, 0.29736328125, 0.177490234375, -0.3232421875, 0.5166015625, -0.13232421875, 0.252685546875, -0.25244140625, 0.361083984375, -0.88916015625, -0.49169921875, 0.76220703125, -0.357421875, -0.303466796875, 0.86376953125, -0.2218017578125, -0.447509765625, 0.368896484375, 0.396240234375, -0.61376953125, 0.51953125, -0.44287109375, 0.6982421875, -0.191650390625, -0.441650390625, -0.1513671875, -0.58251953125, 0.94482421875, 0.1114501953125, -1.08984375, -0.154296875, -0.91650390625, 0.096923828125, -0.11309814453125, -0.278076171875, 0.22607421875, 0.165283203125, 0.1650390625, -0.1953125, -0.2366943359375, -0.458740234375, -0.4208984375, -0.435302734375, -0.1463623046875, 0.189697265625, 0.552734375, 0.400390625, -0.007472991943359375, -0.16015625, -0.286376953125, 0.06292724609375, 0.06878662109375, -0.415283203125, -0.0146484375, -0.0548095703125, -0.2296142578125, -0.07794189453125, 0.5263671875, -0.25390625, 0.10791015625, 0.87890625, 0.048248291015625, 0.48681640625, 0.319091796875, -0.5732421875, 0.6328125, 0.1932373046875, -1.1396484375, -0.486083984375, 0.4736328125, -0.06854248046875, 0.5771484375, 0.3447265625, -1.18359375, -0.75634765625, -0.7412109375, 0.086669921875, -0.72802734375, -0.01435089111328125, -1.04296875, -0.4453125, -0.47314453125, 0.57958984375, 0.036712646484375, -0.732421875, 0.1566162109375, -1.205078125, 0.12298583984375, -1.1845703125, -0.1783447265625, -0.6611328125, -0.58642578125, -0.08782958984375, 0.7275390625, 0.035125732421875, 0.322509765625, 0.1365966796875, -0.21728515625, 0.278076171875, 0.30419921875, -0.75439453125, -0.2230224609375, -0.2347412109375, -0.034149169921875, -0.177978515625, -0.03460693359375, -0.413818359375, 0.7138671875, -0.6025390625, 0.3447265625, -0.102783203125, -0.42578125, -0.1480712890625, 0.04962158203125, 1.091796875, -0.1768798828125, 0.261962890625, -0.33203125, 0.03997802734375, 0.5625, -0.3076171875, -0.572265625, -0.91845703125, -0.318115234375, -1.05078125, 0.6806640625, -0.2381591796875, 0.1343994140625, -0.6484375, -0.55126953125, 1.0751953125, -0.65380859375, 0.5244140625, 1.13671875, -0.11102294921875, 0.4130859375, -0.060791015625, 0.440673828125, 0.6240234375, -0.79345703125, 0.273193359375, 0.47607421875, -0.57861328125, 0.406982421875, -0.214599609375, -0.81884765625, -0.5986328125, 0.163818359375, 1.1923828125, -0.18603515625, 0.62841796875, -0.3876953125, -1.076171875, -0.457275390625, 0.72607421875, 0.093505859375, 0.337890625, 0.796875, 0.19189453125, 0.01155853271484375, 0.21875, -0.302001953125, 0.11041259765625, -0.3828125, 1.14453125, 0.005664825439453125, -0.1573486328125, 1.09375, 0.91552734375, -0.95458984375, -0.986328125, 0.257568359375, -0.2098388671875, -0.35302734375, -0.66162109375, 0.0487060546875, 0.45703125, -0.73486328125, 0.0318603515625, 0.467041015625, -0.031494140625, 0.681640625, -0.260498046875, 0.392822265625, -0.630859375, 0.8486328125, 0.6953125, -0.4443359375, -0.044891357421875, -0.86962890625, -0.349609375, -0.533203125, -0.0416259765625, 0.587890625, -0.59228515625, 0.2294921875, 0.75146484375, 0.00814056396484375, 0.828125, -0.6337890625, -0.58740234375, 0.05963134765625, -0.412841796875, -0.712890625, 0.0263519287109375, 0.0814208984375, 0.00960540771484375, 0.45361328125, -0.7685546875, 0.05804443359375, -0.08038330078125, 0.1094970703125, -0.309326171875, -1.01953125, -0.2181396484375, -0.88232421875, -0.271240234375, -0.8857421875, -0.76123046875, -0.07208251953125, 0.145263671875, 0.00469207763671875, -0.5546875, -0.25634765625, 0.232421875, -0.4755859375, 0.9794921875, -0.75146484375, 0.412841796875, -0.2978515625, -0.50537109375, -0.6708984375, 0.0799560546875, -0.57763671875, -0.00888824462890625, -0.75146484375, 0.3759765625, -0.401123046875, 0.5537109375, -0.34619140625, 0.40185546875, -0.3251953125, -0.55859375, 0.305908203125, -0.1412353515625, -0.468017578125, 0.97802734375, 0.35205078125, -0.01617431640625, 0.210205078125, -0.49267578125, 0.05828857421875, -0.58984375, 0.280517578125, 0.7216796875, -0.273193359375, -0.18310546875, 0.08154296875, 0.1558837890625, -1.185546875, 0.4755859375, -0.363525390625, -0.055328369140625, 0.5068359375, -0.060272216796875, 0.457275390625, 1.1787109375, -0.373291015625, 0.595703125, -0.0125885009765625, 0.2379150390625, 0.317626953125, 0.2310791015625, -0.2408447265625, 0.50732421875, 0.0096282958984375, -0.020233154296875, 0.1290283203125, 0.10040283203125, 0.1689453125, 0.169921875, -0.045013427734375, -0.623046875, -0.732421875, -0.2396240234375, -0.306396484375, 0.316162109375, 0.455322265625, -0.2003173828125, -0.2445068359375, -0.0980224609375, -0.449462890625, 0.297119140625, -1.25390625, -1, 0.5126953125, -0.28564453125, -0.4814453125, -0.2802734375, -0.453369140625, -0.236572265625, 0.1248779296875, 0.41845703125, -0.552734375, 0.284912109375, -0.3837890625, 0.413818359375, -0.35791015625, -0.187255859375, 0.1826171875, 0.479248046875, -0.402099609375, -0.74169921875, 0.138916015625, 1.20703125, 0.1064453125, -0.23779296875, -0.2442626953125, 0.260498046875, -0.1004638671875, 0.1697998046875, -0.33544921875, 0.462158203125, -0.54443359375, 0.361328125, -0.8603515625, 0.25634765625, -0.409423828125, 0.390380859375, 0.372314453125, -0.409912109375, -0.56005859375, 0.5712890625, 0.4384765625, -0.01464080810546875, 0.8779296875, -0.248046875, 0.6064453125, 0.10101318359375, 0.149658203125, -0.26708984375, 0.93310546875, 0.67431640625, 0.595703125, -0.1094970703125, 0.30322265625, 0.818359375, 0.08245849609375, -0.44384765625, 0.450927734375, 0.231689453125, -0.05133056640625, 0.388671875, -0.205322265625, -0.195068359375, 0.0623779296875, -0.4833984375, 0.623046875, -0.334228515625, 0.07763671875, -0.09979248046875, -0.9794921875, 1.1650390625, -0.279052734375, -0.049285888671875, 0.181884765625, -0.414794921875, 0.28076171875, 0.771484375, -0.3642578125, -0.11895751953125, 0.74169921875, 0.7490234375, 0.464111328125, 0.63671875, 0.2568359375, 0.349853515625, -0.7744140625, 0.058349609375, -0.09197998046875, 0.2000732421875, -0.277587890625, -0.529296875, -0.52587890625, 0.40380859375, -0.58447265625, -0.2177734375, 0.6171875, -0.7236328125, 0.2303466796875, -0.36279296875, 1.05078125, -0.498291015625, 0.007289886474609375, 0.302001953125, -0.167724609375, -0.6181640625, 0.90234375, -0.103271484375, 0.1866455078125, 0.056915283203125, 1.1845703125, -0.1375732421875, 1.3583984375, 0.62548828125, -0.0223388671875, -0.17041015625, 0.360595703125, -0.1343994140625, -0.270263671875, -0.53271484375, -0.52197265625, 0.1656494140625, -0.9599609375, -0.62548828125, -0.046966552734375, 0.81298828125, 0.203857421875, -1.263671875, -0.06256103515625, 0.10540771484375, -0.921875, 0.23583984375, 0.1326904296875, 0.364013671875, 0.1856689453125, -0.236083984375, -0.10308837890625, -0.341796875, 0.587890625, -0.84765625, 0.443115234375, -0.62060546875, -0.357421875, -0.6611328125, -0.6025390625, -0.1376953125, -0.310546875, -0.376953125, -0.603515625, 0.3056640625, 0.49072265625, 0.5966796875, 0.12890625, -0.289306640625, 0.033599853515625, 0.85693359375, 0.9140625, 0.11590576171875, 0.87939453125, 0.1656494140625, -0.2138671875, 0.5517578125, -0.445068359375, 0.34326171875, -0.267578125, 0.296142578125, -0.59375, 0.10284423828125, -0.76025390625, -1.0302734375, -0.01280975341796875, 0.313232421875, 0.047821044921875, -0.50927734375, -0.84326171875, -0.41552734375, -1.1533203125, -0.1339111328125, -0.58642578125, 0.98095703125, -0.5078125, 0.0032978057861328125, -0.1524658203125, -1.5556640625, 4.37890625, 0.63720703125, 0.60693359375, 0.359619140625, 0.4765625, 0.736328125, 0.348876953125, -0.51953125, -0.515625, -0.387451171875, 0.59375, -0.3427734375, -0.056121826171875, 0.7734375, 0.546875, 0.2998046875, -0.433837890625, 0.12152099609375, 0.2227783203125, -0.91552734375, -0.73095703125, 0.375244140625, -0.2081298828125, 0.89794921875, 0.035400390625, 0.1396484375, 0.5810546875, -0.97802734375, 0.0252685546875, -0.68408203125, 0.1409912109375, -0.328125, 0.84521484375, 0.0027561187744140625, -0.0933837890625, 0.7099609375, 0.27734375, -0.1085205078125, -0.029937744140625, 0.0966796875, -0.08526611328125, -0.24267578125, 0.7294921875, -0.8701171875, -0.370361328125, 0.437255859375, -0.70703125, 0.3935546875, 0.209228515625, -1.0107421875, 0.955078125, -0.44287109375, 0.430419921875, -0.52880859375, -0.919921875, 0.3759765625, 0.08795166015625, 0.2432861328125, -0.36328125, 0.3046875, 0.6044921875, 0.66259765625, -0.0841064453125, 0.57470703125, -1.0048828125, 0.7646484375, -0.2344970703125, 0.76513671875, -0.61474609375, -0.156982421875, 0.00507354736328125, -0.2467041015625, -0.1229248046875, -0.50732421875, 0.66552734375, 0.11431884765625, -0.48876953125, 0.67626953125, 0.54248046875, -0.82666015625, 0.06842041015625, -0.1920166015625, -0.1351318359375, -0.451416015625, 0.51611328125, 1.275390625, -0.452392578125, -0.19677734375, -0.42041015625, 0.4169921875, 0.57080078125, 1.0537109375, 0.04840087890625, -0.18408203125, -0.061431884765625 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Tags: bitmasks, brute force, hashing, string suffix structures, strings, two pointers Correct Solution: ``` from itertools import accumulate, chain BITS = 20 for _ in range(int(input())): n, k = map(int, input().split());s = input();antis = [1 - int(si) for si in s];antis_s = ''.join(map(str, antis));antis_sums = tuple(chain((0,), accumulate(antis)));fbd = set();ans = 0 for i in range(n + 1 - k): if k < BITS or antis_sums[i] == antis_sums[i + k - BITS]:fbd.add(int(antis_s[max(i, i + k - BITS):i + k], base=2)) while ans in fbd:ans += 1 t = bin(ans)[2:] if len(t) > k:print("NO") else:print("YES");print(t.rjust(k, '0')) ```
107,235
[ 0.29541015625, -0.2432861328125, 0.1929931640625, 0.10858154296875, -0.342041015625, -0.495849609375, 0.12274169921875, 0.053955078125, -0.11297607421875, 0.537109375, 0.52392578125, -0.2119140625, -0.274169921875, -1.0546875, -0.6845703125, 0.0264739990234375, -0.351318359375, -0.38916015625, -0.364013671875, -0.297607421875, -0.09588623046875, -0.08154296875, -1.142578125, 0.05133056640625, -0.201904296875, 1.1103515625, 0.55859375, 0.04052734375, 1.197265625, 0.966796875, -0.5751953125, -0.49951171875, 0.54443359375, -1.142578125, -0.46044921875, -0.59228515625, 0.8232421875, -0.95458984375, -0.253173828125, -0.2783203125, 0.465576171875, -0.318359375, 0.5, -0.732421875, -1.365234375, 0.099609375, -0.058013916015625, -0.3017578125, -0.20166015625, -0.7890625, 0.0141143798828125, -0.316650390625, 0.2471923828125, -0.2000732421875, 0.03302001953125, 0.3076171875, 0.28173828125, -0.396484375, -0.31787109375, 0.60546875, -0.1971435546875, 0.353515625, 0.1466064453125, -0.6796875, -0.08258056640625, 0.1776123046875, -0.2247314453125, -0.44482421875, -0.1412353515625, -1.083984375, 0.066162109375, 0.0863037109375, -0.384033203125, -0.5771484375, -0.044036865234375, -0.0215911865234375, 0.09722900390625, -0.1658935546875, -0.444580078125, 0.62060546875, -0.1370849609375, 1.0322265625, 0.42919921875, 0.43505859375, -0.412841796875, -0.6904296875, 0.04266357421875, 0.221435546875, 0.35986328125, 0.076416015625, -0.20166015625, 0.460205078125, -0.6103515625, -0.1248779296875, 0.56396484375, 0.363037109375, 0.091552734375, 0.09161376953125, 0.27978515625, 0.289794921875, 0.62646484375, 1.037109375, -0.12274169921875, 1.328125, -0.9541015625, -0.106201171875, -0.26806640625, -0.0022869110107421875, -0.287841796875, -0.0228271484375, -0.12115478515625, -0.163818359375, 0.60107421875, 0.5146484375, -0.269287109375, 0.7646484375, -0.0189208984375, 0.5859375, -1.181640625, 0.318359375, 0.54736328125, 0.294677734375, 0.77099609375, -0.1480712890625, -0.0010004043579101562, -0.1942138671875, -0.51171875, 1.1337890625, -0.2919921875, -0.163818359375, 0.396240234375, -0.078369140625, -0.05316162109375, 0.058380126953125, 0.06353759765625, 0.4970703125, -0.0699462890625, 0.1951904296875, 0.81298828125, -0.50537109375, 0.6767578125, -0.46337890625, -0.265625, 1.5283203125, 0.414794921875, -0.13232421875, 1.09375, 0.217041015625, -0.8212890625, 0.66357421875, -0.994140625, 0.381591796875, -0.170654296875, 0.2239990234375, 0.1256103515625, -0.0239105224609375, -0.37841796875, 0.164306640625, 0.20263671875, -0.2890625, -0.427490234375, 0.1480712890625, -0.0565185546875, 0.9443359375, -0.332763671875, 0.88623046875, -0.494873046875, -0.56640625, -0.07647705078125, -0.348388671875, 0.0095062255859375, -0.326416015625, -0.2890625, 0.7900390625, 0.58251953125, 1.2177734375, 1.01171875, -0.30859375, 0.488037109375, 0.3271484375, -0.388671875, 0.302978515625, 0.24755859375, 0.7841796875, -0.259765625, 0.2117919921875, 0.0574951171875, -0.332275390625, -0.95849609375, -0.6884765625, 0.07781982421875, 0.68310546875, -0.42138671875, 0.0243377685546875, 0.2587890625, 0.1312255859375, -0.78857421875, -0.29296875, -0.19873046875, -1.037109375, -0.71240234375, 0.6123046875, -0.22021484375, 0.47509765625, -0.5244140625, -0.51318359375, 0.353515625, 1.0546875, -0.023681640625, 0.265869140625, 0.367431640625, -0.1817626953125, -0.07452392578125, 0.22021484375, -0.0762939453125, -0.216796875, -0.5703125, 0.9970703125, -0.183837890625, -0.05364990234375, 0.039794921875, 1.0126953125, 0.54248046875, 0.63720703125, -0.35205078125, -0.2418212890625, 0.22216796875, 1.2421875, 0.11151123046875, 0.378173828125, 0.340576171875, 1.0107421875, 0.78173828125, 0.5888671875, 0.424560546875, 0.73046875, 0.740234375, 0.74951171875, 0.193359375, 0.160888671875, -0.09515380859375, 0.3701171875, 0.1937255859375, 0.61572265625, 0.417236328125, 0.283935546875, -0.09515380859375, 0.141845703125, -0.463134765625, 0.5517578125, -0.1357421875, 0.849609375, 0.104736328125, 0.65771484375, -0.59130859375, -0.55810546875, 0.110107421875, 0.71533203125, -1.021484375, -0.337890625, -0.1627197265625, -0.048736572265625, -0.0894775390625, 0.025482177734375, 0.348876953125, 0.453125, 0.310791015625, 0.65185546875, -0.1015625, -0.2431640625, -0.982421875, -0.68798828125, -1.0859375, -0.0877685546875, -0.5888671875, 0.11090087890625, 0.290771484375, -0.884765625, 0.1962890625, -0.623046875, -0.384765625, 0.376708984375, -0.55908203125, 0.4521484375, -0.064208984375, 0.335205078125, -0.83203125, 0.480712890625, 0.1065673828125, 1.2861328125, -0.58935546875, -0.13037109375, -0.1368408203125, -0.6279296875, 0.3154296875, -0.143310546875, 0.0264434814453125, -0.037078857421875, -0.6982421875, -0.94970703125, -0.460693359375, -0.04254150390625, -0.264404296875, -0.08319091796875, -0.51953125, 0.93212890625, 0.5751953125, -0.658203125, 0.6162109375, 0.763671875, -0.970703125, 0.3193359375, 0.411865234375, -0.0784912109375, -0.93212890625, 1.3671875, 0.492431640625, 0.207763671875, -0.407958984375, -0.476806640625, -0.312744140625, -0.0296783447265625, 0.0623779296875, -0.422607421875, -0.064697265625, 0.74462890625, -0.0322265625, -1.150390625, 0.27978515625, -0.6171875, -0.2279052734375, -0.238037109375, -0.2320556640625, 0.8154296875, 0.80029296875, 0.2958984375, 0.12274169921875, -0.0802001953125, 0.0051727294921875, 0.494140625, 0.3271484375, -0.290283203125, -0.204345703125, 0.89892578125, 0.19970703125, 0.218994140625, -0.03912353515625, -0.10382080078125, -0.07049560546875, 0.240234375, 0.0819091796875, 0.9306640625, 0.177978515625, 0.54638671875, 0.15234375, 0.8271484375, -0.837890625, -0.384033203125, 0.006099700927734375, 0.55029296875, 0.66748046875, 0.3603515625, 0.60888671875, -0.1573486328125, -0.293212890625, -1.4248046875, 0.34375, 0.006900787353515625, 0.91064453125, -0.6298828125, 1.1259765625, 0.169921875, -0.339111328125, 0.85595703125, -0.68408203125, -0.1468505859375, 0.91357421875, -0.0772705078125, 0.681640625, -0.3974609375, 0.14453125, -0.1826171875, -0.11712646484375, 0.54345703125, 0.70849609375, 0.89697265625, -0.46875, -0.5625, -0.33740234375, -0.2071533203125, -0.00873565673828125, -0.289794921875, 0.146240234375, -0.23095703125, -0.11016845703125, -0.8369140625, 0.08660888671875, 0.6650390625, 0.90771484375, -0.03424072265625, 0.2115478515625, 0.52880859375, 0.44482421875, 1.064453125, -0.4970703125, 0.264404296875, -0.72314453125, 0.7216796875, 0.0182037353515625, -0.2196044921875, -0.8369140625, -0.3642578125, -0.200439453125, 0.120849609375, -0.047760009765625, -0.377197265625, -1.2216796875, 0.353759765625, -0.5625, 0.58447265625, -0.72265625, 0.1162109375, -0.6103515625, 0.302734375, 0.150390625, -0.93798828125, -0.0765380859375, -0.491455078125, 0.45166015625, 0.216552734375, -0.2296142578125, -0.42138671875, -0.7607421875, -0.449462890625, -0.8779296875, 0.6005859375, 1.0185546875, 0.031463623046875, 0.218505859375, -1.431640625, 0.5263671875, 0.48095703125, -0.57275390625, 0.099365234375, -0.1356201171875, 0.6689453125, 0.3388671875, 0.8291015625, -0.313232421875, -0.69287109375, -0.12298583984375, -1.291015625, 0.252197265625, -0.40576171875, 0.69091796875, 0.034912109375, -0.125732421875, -0.086669921875, 0.1697998046875, 0.131103515625, 0.409912109375, -0.379638671875, 0.254638671875, -0.8330078125, -0.85498046875, 0.6767578125, -0.405029296875, -0.41064453125, 1.236328125, -0.09515380859375, -0.176513671875, 0.3349609375, 0.66552734375, -0.3310546875, 0.57470703125, -0.488525390625, 0.2247314453125, -0.52734375, -0.320556640625, -0.425048828125, -0.3759765625, 0.8916015625, 0.1551513671875, -0.60546875, -0.08331298828125, -1.009765625, -0.327880859375, 0.14404296875, -0.3505859375, 0.23828125, -0.2183837890625, -0.06781005859375, -0.283203125, -0.12078857421875, -0.63818359375, -0.223388671875, -0.546875, -0.5263671875, 0.319580078125, 0.33056640625, 0.796875, 0.357666015625, -0.392822265625, -0.0333251953125, -0.032806396484375, 0.159423828125, -0.38525390625, -0.284423828125, -0.44970703125, -0.257568359375, -0.369384765625, 0.01800537109375, 0.4140625, 0.11773681640625, 0.4296875, 0.34716796875, 0.5390625, 0.466552734375, -0.70068359375, 0.890625, 0.242919921875, -0.87109375, -0.061981201171875, 0.5693359375, -0.0858154296875, 0.6728515625, -0.0105133056640625, -0.90625, -0.7451171875, -0.78369140625, 0.38623046875, -0.54931640625, -0.1771240234375, -1.0908203125, -0.263671875, -0.5166015625, 0.67041015625, -0.04522705078125, -0.345703125, 0.16748046875, -1.380859375, -0.31884765625, -0.69287109375, -0.286865234375, -0.9189453125, -0.281982421875, -0.352783203125, 0.73193359375, -0.1893310546875, 0.39990234375, -0.16796875, 0.099365234375, 0.29150390625, 0.3466796875, -0.466796875, -0.37890625, -0.307861328125, 0.2318115234375, -0.1715087890625, -0.07537841796875, -0.7890625, 0.72705078125, -0.89501953125, 0.269775390625, -0.2376708984375, 0.09637451171875, -0.32275390625, -0.302001953125, 1.1162109375, -0.36083984375, -0.3974609375, -0.1685791015625, 0.191650390625, 0.67138671875, -0.483642578125, -0.272216796875, -1.17578125, -0.48193359375, -0.89599609375, 0.56298828125, -0.2352294921875, -0.1217041015625, -0.49169921875, -0.60498046875, 1.08984375, -0.490478515625, 0.2216796875, 1.09765625, -0.0033664703369140625, 0.1920166015625, -0.75146484375, 0.6630859375, 0.7099609375, -0.64892578125, 0.104736328125, 0.1851806640625, -0.76220703125, 0.1785888671875, -0.371826171875, -1.0478515625, -0.431396484375, 0.51611328125, 1.0830078125, -0.353759765625, 0.60498046875, 0.1273193359375, -1.212890625, -0.5361328125, 1.255859375, 0.43310546875, 0.08447265625, 0.79150390625, -0.022796630859375, 0.023681640625, -0.3037109375, -0.7490234375, -0.2177734375, -0.54833984375, 1.400390625, -0.669921875, -0.470703125, 1.1025390625, 0.89990234375, -1.55078125, -0.87890625, 0.001617431640625, 0.2041015625, 0.08905029296875, -0.80810546875, -0.036468505859375, 0.492919921875, -0.5107421875, -0.1708984375, 0.173095703125, -0.034637451171875, 0.37255859375, 0.1270751953125, 0.67724609375, -0.66064453125, 0.52001953125, 0.93603515625, -0.435302734375, -0.239013671875, -0.7880859375, -0.35302734375, -0.4482421875, 0.06890869140625, 0.92626953125, -0.30322265625, -0.0751953125, 0.55029296875, -0.146484375, 0.99951171875, -0.501953125, 0.0233154296875, 0.400146484375, -0.65576171875, -0.51904296875, -0.07794189453125, 0.1239013671875, 0.0216217041015625, 0.63134765625, -0.927734375, 0.026458740234375, -0.061492919921875, 0.169677734375, -0.537109375, -0.65625, -0.3359375, -1.0595703125, -0.480224609375, -0.85986328125, -0.93603515625, -0.3720703125, 0.2685546875, 0.251220703125, -0.529296875, 0.030609130859375, 0.62890625, -0.57958984375, 1.1484375, -0.755859375, 0.332763671875, -0.1290283203125, -0.08819580078125, -0.54345703125, 0.0877685546875, -0.59619140625, 0.24072265625, -0.9853515625, 0.10003662109375, 0.11767578125, 0.68310546875, -0.12420654296875, 0.86572265625, -0.289306640625, -0.42236328125, 0.41748046875, -0.1845703125, -0.128173828125, 1.05859375, 0.458740234375, -0.052093505859375, 0.153564453125, -0.2420654296875, -0.317138671875, -0.5361328125, 0.09454345703125, 0.37451171875, -0.2249755859375, -0.11468505859375, -0.26318359375, 0.448974609375, -1.19140625, 0.35791015625, -0.335693359375, -0.09747314453125, -0.12353515625, -0.08770751953125, 0.57763671875, 1.15625, -0.428955078125, 0.190673828125, -0.2095947265625, 0.1287841796875, 0.291748046875, 0.1778564453125, -0.431884765625, 0.7255859375, 0.36474609375, -0.72314453125, -0.0867919921875, 0.15576171875, 0.25341796875, 0.436767578125, -0.3193359375, -0.85107421875, -1.0126953125, -0.26318359375, 0.123291015625, 0.2320556640625, 0.53125, -0.44140625, -0.38330078125, -0.322998046875, -0.697265625, 0.419677734375, -1.0283203125, -1.1669921875, 0.4970703125, 0.040283203125, -0.5625, -0.00664520263671875, -0.43896484375, -0.3349609375, -0.045166015625, 0.2236328125, -0.6572265625, 0.66845703125, -0.2374267578125, 0.35107421875, 0.02777099609375, -0.25, -0.04473876953125, 0.837890625, -0.734375, -0.45361328125, -0.28662109375, 0.8232421875, 0.1490478515625, -0.280517578125, -0.58544921875, 0.1707763671875, 0.424560546875, 0.083251953125, -0.53125, -0.047210693359375, -0.345947265625, 0.79345703125, -1.109375, 0.08123779296875, 0.10418701171875, 0.55810546875, 0.24951171875, -0.07257080078125, -0.367431640625, 0.87890625, 0.87060546875, 0.1217041015625, 0.86865234375, 0.1444091796875, 0.580078125, 0.2166748046875, 0.005584716796875, -0.365966796875, 0.75244140625, 0.75830078125, 0.8740234375, -0.194091796875, 0.14404296875, 0.7509765625, 0.335205078125, -0.44921875, 0.666015625, -0.0601806640625, -0.01453399658203125, -0.1422119140625, -0.202880859375, 0.007274627685546875, 0.0743408203125, -0.49267578125, 0.58642578125, -0.98291015625, -0.268798828125, -0.344482421875, -0.51611328125, 0.79443359375, -0.08917236328125, 0.0299835205078125, -0.10174560546875, -0.35595703125, 0.409423828125, 0.25732421875, -0.357421875, -0.02886962890625, 1.1357421875, 0.480712890625, 0.1873779296875, 0.79248046875, 0.14306640625, 0.5390625, -0.56884765625, 0.115234375, 0.006275177001953125, -0.33642578125, -0.424560546875, -0.68505859375, -0.96630859375, 0.7451171875, -0.262939453125, -0.2115478515625, 0.81640625, -0.96044921875, 0.03619384765625, -0.3955078125, 0.66796875, -0.46923828125, 0.356201171875, 0.384521484375, -0.44189453125, -1.044921875, 0.9091796875, -0.19287109375, 0.3974609375, 0.190673828125, 0.82275390625, 0.1466064453125, 1.4306640625, 0.72705078125, -0.0009636878967285156, 0.2403564453125, 0.3935546875, -0.3505859375, -0.60400390625, -0.466796875, -0.1690673828125, 0.1466064453125, -0.59033203125, -0.39794921875, 0.0770263671875, 0.478271484375, 0.32763671875, -1.0380859375, -0.29931640625, 0.40087890625, -1.0234375, 0.65283203125, 0.375, 0.307861328125, 0.3134765625, -0.2822265625, -0.329833984375, -0.515625, 0.27734375, -0.80029296875, 0.4580078125, -0.76220703125, -0.56298828125, -0.471435546875, -0.55126953125, -0.1785888671875, -0.10223388671875, -0.281982421875, -0.83251953125, 0.671875, 0.35107421875, 0.303466796875, 0.328369140625, -0.440185546875, 0.316650390625, 0.8662109375, 0.77685546875, 0.023345947265625, 0.84716796875, 0.365478515625, 0.04595947265625, 0.2030029296875, -0.1290283203125, 0.4580078125, -0.414306640625, 0.3818359375, -0.56005859375, 0.341796875, -0.9052734375, -1.166015625, 0.0938720703125, 0.290771484375, 0.2313232421875, -0.463623046875, -1.048828125, -0.3203125, -0.8525390625, -0.198486328125, -0.7958984375, 0.79931640625, -0.403076171875, 0.070068359375, -0.00281524658203125, -1.283203125, 4.2421875, 1.0029296875, 0.806640625, 0.299072265625, 0.1961669921875, 0.7861328125, 0.1798095703125, -0.7490234375, -0.1011962890625, -0.2880859375, 0.5654296875, -0.52734375, -0.0955810546875, 0.828125, 0.69287109375, 0.61474609375, -0.55419921875, -0.15771484375, 0.080810546875, -0.8681640625, -0.84326171875, 0.42431640625, 0.007404327392578125, 0.285400390625, 0.0712890625, 0.1668701171875, 0.57421875, -0.76611328125, -0.063232421875, -0.7939453125, 0.2230224609375, -0.56982421875, 0.96923828125, 0.1729736328125, -0.2137451171875, 0.66259765625, 0.1268310546875, -0.11468505859375, 0.07000732421875, 0.2177734375, -0.3173828125, -0.18359375, 0.496337890625, -0.7236328125, -0.300537109375, 0.3310546875, -0.63037109375, 0.3681640625, -0.01377105712890625, -0.9853515625, 1.0087890625, -0.2685546875, 0.1612548828125, -0.671875, -0.81982421875, -0.138671875, -0.044097900390625, -0.398193359375, -0.09259033203125, 0.423583984375, 0.59423828125, 0.630859375, 0.1700439453125, 0.6923828125, -1.5341796875, 0.63818359375, -0.058502197265625, 0.58935546875, -0.65185546875, 0.020965576171875, -0.5146484375, -0.374755859375, -0.260009765625, -0.383544921875, 0.84521484375, 0.1268310546875, -0.1971435546875, 1.029296875, 0.8369140625, -0.424560546875, 0.3046875, -0.137451171875, -0.288818359375, -0.51513671875, 1.123046875, 1.484375, -0.86962890625, -0.290283203125, -0.1295166015625, 0.47998046875, 0.255126953125, 0.77783203125, 0.310791015625, -0.473876953125, -0.4423828125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Tags: bitmasks, brute force, hashing, string suffix structures, strings, two pointers Correct Solution: ``` from collections import deque T = int(input()) r = 1 maxdigit = 20 def fastfrac(a,b,M): numb = pow(b,M-2,M) return ((a%M)*(numb%M))%M def getnum(k,s): n = len(s) dic = {} prefixnum = max(0,k-maxdigit) real = k - prefixnum maxreal = (1<<real) - 1 front = 0 pres = deque() for i in range(prefixnum): if s[i]=='1': pres.append(i) num = int(s[prefixnum:prefixnum+real],2) if len(pres)==prefixnum: dic[maxreal-num] = 1 if maxreal-num==front: front += 1 # print(pres) for i in range(n-k): if prefixnum>0: if pres and pres[0]==i: pres.popleft() if s[i+prefixnum] =='1': pres.append(i+prefixnum) # print(pres) num = num % ((maxreal+1)//2) num = 2*num + int(s[i+k]) if len(pres)<prefixnum: continue dic[maxreal-num] = 1 while front in dic: front += 1 # print(dic) if front>maxreal: return -1 else: return front while r<=T: n,k = map(int,input().split()) s = input() ans = getnum(k,s) if ans>=0: print("YES") subs = bin(ans)[2:] subs = '0'*(k-len(subs)) + subs print(subs) else: print("NO") r += 1 ```
107,236
[ 0.29541015625, -0.2432861328125, 0.1929931640625, 0.10858154296875, -0.342041015625, -0.495849609375, 0.12274169921875, 0.053955078125, -0.11297607421875, 0.537109375, 0.52392578125, -0.2119140625, -0.274169921875, -1.0546875, -0.6845703125, 0.0264739990234375, -0.351318359375, -0.38916015625, -0.364013671875, -0.297607421875, -0.09588623046875, -0.08154296875, -1.142578125, 0.05133056640625, -0.201904296875, 1.1103515625, 0.55859375, 0.04052734375, 1.197265625, 0.966796875, -0.5751953125, -0.49951171875, 0.54443359375, -1.142578125, -0.46044921875, -0.59228515625, 0.8232421875, -0.95458984375, -0.253173828125, -0.2783203125, 0.465576171875, -0.318359375, 0.5, -0.732421875, -1.365234375, 0.099609375, -0.058013916015625, -0.3017578125, -0.20166015625, -0.7890625, 0.0141143798828125, -0.316650390625, 0.2471923828125, -0.2000732421875, 0.03302001953125, 0.3076171875, 0.28173828125, -0.396484375, -0.31787109375, 0.60546875, -0.1971435546875, 0.353515625, 0.1466064453125, -0.6796875, -0.08258056640625, 0.1776123046875, -0.2247314453125, -0.44482421875, -0.1412353515625, -1.083984375, 0.066162109375, 0.0863037109375, -0.384033203125, -0.5771484375, -0.044036865234375, -0.0215911865234375, 0.09722900390625, -0.1658935546875, -0.444580078125, 0.62060546875, -0.1370849609375, 1.0322265625, 0.42919921875, 0.43505859375, -0.412841796875, -0.6904296875, 0.04266357421875, 0.221435546875, 0.35986328125, 0.076416015625, -0.20166015625, 0.460205078125, -0.6103515625, -0.1248779296875, 0.56396484375, 0.363037109375, 0.091552734375, 0.09161376953125, 0.27978515625, 0.289794921875, 0.62646484375, 1.037109375, -0.12274169921875, 1.328125, -0.9541015625, -0.106201171875, -0.26806640625, -0.0022869110107421875, -0.287841796875, -0.0228271484375, -0.12115478515625, -0.163818359375, 0.60107421875, 0.5146484375, -0.269287109375, 0.7646484375, -0.0189208984375, 0.5859375, -1.181640625, 0.318359375, 0.54736328125, 0.294677734375, 0.77099609375, -0.1480712890625, -0.0010004043579101562, -0.1942138671875, -0.51171875, 1.1337890625, -0.2919921875, -0.163818359375, 0.396240234375, -0.078369140625, -0.05316162109375, 0.058380126953125, 0.06353759765625, 0.4970703125, -0.0699462890625, 0.1951904296875, 0.81298828125, -0.50537109375, 0.6767578125, -0.46337890625, -0.265625, 1.5283203125, 0.414794921875, -0.13232421875, 1.09375, 0.217041015625, -0.8212890625, 0.66357421875, -0.994140625, 0.381591796875, -0.170654296875, 0.2239990234375, 0.1256103515625, -0.0239105224609375, -0.37841796875, 0.164306640625, 0.20263671875, -0.2890625, -0.427490234375, 0.1480712890625, -0.0565185546875, 0.9443359375, -0.332763671875, 0.88623046875, -0.494873046875, -0.56640625, -0.07647705078125, -0.348388671875, 0.0095062255859375, -0.326416015625, -0.2890625, 0.7900390625, 0.58251953125, 1.2177734375, 1.01171875, -0.30859375, 0.488037109375, 0.3271484375, -0.388671875, 0.302978515625, 0.24755859375, 0.7841796875, -0.259765625, 0.2117919921875, 0.0574951171875, -0.332275390625, -0.95849609375, -0.6884765625, 0.07781982421875, 0.68310546875, -0.42138671875, 0.0243377685546875, 0.2587890625, 0.1312255859375, -0.78857421875, -0.29296875, -0.19873046875, -1.037109375, -0.71240234375, 0.6123046875, -0.22021484375, 0.47509765625, -0.5244140625, -0.51318359375, 0.353515625, 1.0546875, -0.023681640625, 0.265869140625, 0.367431640625, -0.1817626953125, -0.07452392578125, 0.22021484375, -0.0762939453125, -0.216796875, -0.5703125, 0.9970703125, -0.183837890625, -0.05364990234375, 0.039794921875, 1.0126953125, 0.54248046875, 0.63720703125, -0.35205078125, -0.2418212890625, 0.22216796875, 1.2421875, 0.11151123046875, 0.378173828125, 0.340576171875, 1.0107421875, 0.78173828125, 0.5888671875, 0.424560546875, 0.73046875, 0.740234375, 0.74951171875, 0.193359375, 0.160888671875, -0.09515380859375, 0.3701171875, 0.1937255859375, 0.61572265625, 0.417236328125, 0.283935546875, -0.09515380859375, 0.141845703125, -0.463134765625, 0.5517578125, -0.1357421875, 0.849609375, 0.104736328125, 0.65771484375, -0.59130859375, -0.55810546875, 0.110107421875, 0.71533203125, -1.021484375, -0.337890625, -0.1627197265625, -0.048736572265625, -0.0894775390625, 0.025482177734375, 0.348876953125, 0.453125, 0.310791015625, 0.65185546875, -0.1015625, -0.2431640625, -0.982421875, -0.68798828125, -1.0859375, -0.0877685546875, -0.5888671875, 0.11090087890625, 0.290771484375, -0.884765625, 0.1962890625, -0.623046875, -0.384765625, 0.376708984375, -0.55908203125, 0.4521484375, -0.064208984375, 0.335205078125, -0.83203125, 0.480712890625, 0.1065673828125, 1.2861328125, -0.58935546875, -0.13037109375, -0.1368408203125, -0.6279296875, 0.3154296875, -0.143310546875, 0.0264434814453125, -0.037078857421875, -0.6982421875, -0.94970703125, -0.460693359375, -0.04254150390625, -0.264404296875, -0.08319091796875, -0.51953125, 0.93212890625, 0.5751953125, -0.658203125, 0.6162109375, 0.763671875, -0.970703125, 0.3193359375, 0.411865234375, -0.0784912109375, -0.93212890625, 1.3671875, 0.492431640625, 0.207763671875, -0.407958984375, -0.476806640625, -0.312744140625, -0.0296783447265625, 0.0623779296875, -0.422607421875, -0.064697265625, 0.74462890625, -0.0322265625, -1.150390625, 0.27978515625, -0.6171875, -0.2279052734375, -0.238037109375, -0.2320556640625, 0.8154296875, 0.80029296875, 0.2958984375, 0.12274169921875, -0.0802001953125, 0.0051727294921875, 0.494140625, 0.3271484375, -0.290283203125, -0.204345703125, 0.89892578125, 0.19970703125, 0.218994140625, -0.03912353515625, -0.10382080078125, -0.07049560546875, 0.240234375, 0.0819091796875, 0.9306640625, 0.177978515625, 0.54638671875, 0.15234375, 0.8271484375, -0.837890625, -0.384033203125, 0.006099700927734375, 0.55029296875, 0.66748046875, 0.3603515625, 0.60888671875, -0.1573486328125, -0.293212890625, -1.4248046875, 0.34375, 0.006900787353515625, 0.91064453125, -0.6298828125, 1.1259765625, 0.169921875, -0.339111328125, 0.85595703125, -0.68408203125, -0.1468505859375, 0.91357421875, -0.0772705078125, 0.681640625, -0.3974609375, 0.14453125, -0.1826171875, -0.11712646484375, 0.54345703125, 0.70849609375, 0.89697265625, -0.46875, -0.5625, -0.33740234375, -0.2071533203125, -0.00873565673828125, -0.289794921875, 0.146240234375, -0.23095703125, -0.11016845703125, -0.8369140625, 0.08660888671875, 0.6650390625, 0.90771484375, -0.03424072265625, 0.2115478515625, 0.52880859375, 0.44482421875, 1.064453125, -0.4970703125, 0.264404296875, -0.72314453125, 0.7216796875, 0.0182037353515625, -0.2196044921875, -0.8369140625, -0.3642578125, -0.200439453125, 0.120849609375, -0.047760009765625, -0.377197265625, -1.2216796875, 0.353759765625, -0.5625, 0.58447265625, -0.72265625, 0.1162109375, -0.6103515625, 0.302734375, 0.150390625, -0.93798828125, -0.0765380859375, -0.491455078125, 0.45166015625, 0.216552734375, -0.2296142578125, -0.42138671875, -0.7607421875, -0.449462890625, -0.8779296875, 0.6005859375, 1.0185546875, 0.031463623046875, 0.218505859375, -1.431640625, 0.5263671875, 0.48095703125, -0.57275390625, 0.099365234375, -0.1356201171875, 0.6689453125, 0.3388671875, 0.8291015625, -0.313232421875, -0.69287109375, -0.12298583984375, -1.291015625, 0.252197265625, -0.40576171875, 0.69091796875, 0.034912109375, -0.125732421875, -0.086669921875, 0.1697998046875, 0.131103515625, 0.409912109375, -0.379638671875, 0.254638671875, -0.8330078125, -0.85498046875, 0.6767578125, -0.405029296875, -0.41064453125, 1.236328125, -0.09515380859375, -0.176513671875, 0.3349609375, 0.66552734375, -0.3310546875, 0.57470703125, -0.488525390625, 0.2247314453125, -0.52734375, -0.320556640625, -0.425048828125, -0.3759765625, 0.8916015625, 0.1551513671875, -0.60546875, -0.08331298828125, -1.009765625, -0.327880859375, 0.14404296875, -0.3505859375, 0.23828125, -0.2183837890625, -0.06781005859375, -0.283203125, -0.12078857421875, -0.63818359375, -0.223388671875, -0.546875, -0.5263671875, 0.319580078125, 0.33056640625, 0.796875, 0.357666015625, -0.392822265625, -0.0333251953125, -0.032806396484375, 0.159423828125, -0.38525390625, -0.284423828125, -0.44970703125, -0.257568359375, -0.369384765625, 0.01800537109375, 0.4140625, 0.11773681640625, 0.4296875, 0.34716796875, 0.5390625, 0.466552734375, -0.70068359375, 0.890625, 0.242919921875, -0.87109375, -0.061981201171875, 0.5693359375, -0.0858154296875, 0.6728515625, -0.0105133056640625, -0.90625, -0.7451171875, -0.78369140625, 0.38623046875, -0.54931640625, -0.1771240234375, -1.0908203125, -0.263671875, -0.5166015625, 0.67041015625, -0.04522705078125, -0.345703125, 0.16748046875, -1.380859375, -0.31884765625, -0.69287109375, -0.286865234375, -0.9189453125, -0.281982421875, -0.352783203125, 0.73193359375, -0.1893310546875, 0.39990234375, -0.16796875, 0.099365234375, 0.29150390625, 0.3466796875, -0.466796875, -0.37890625, -0.307861328125, 0.2318115234375, -0.1715087890625, -0.07537841796875, -0.7890625, 0.72705078125, -0.89501953125, 0.269775390625, -0.2376708984375, 0.09637451171875, -0.32275390625, -0.302001953125, 1.1162109375, -0.36083984375, -0.3974609375, -0.1685791015625, 0.191650390625, 0.67138671875, -0.483642578125, -0.272216796875, -1.17578125, -0.48193359375, -0.89599609375, 0.56298828125, -0.2352294921875, -0.1217041015625, -0.49169921875, -0.60498046875, 1.08984375, -0.490478515625, 0.2216796875, 1.09765625, -0.0033664703369140625, 0.1920166015625, -0.75146484375, 0.6630859375, 0.7099609375, -0.64892578125, 0.104736328125, 0.1851806640625, -0.76220703125, 0.1785888671875, -0.371826171875, -1.0478515625, -0.431396484375, 0.51611328125, 1.0830078125, -0.353759765625, 0.60498046875, 0.1273193359375, -1.212890625, -0.5361328125, 1.255859375, 0.43310546875, 0.08447265625, 0.79150390625, -0.022796630859375, 0.023681640625, -0.3037109375, -0.7490234375, -0.2177734375, -0.54833984375, 1.400390625, -0.669921875, -0.470703125, 1.1025390625, 0.89990234375, -1.55078125, -0.87890625, 0.001617431640625, 0.2041015625, 0.08905029296875, -0.80810546875, -0.036468505859375, 0.492919921875, -0.5107421875, -0.1708984375, 0.173095703125, -0.034637451171875, 0.37255859375, 0.1270751953125, 0.67724609375, -0.66064453125, 0.52001953125, 0.93603515625, -0.435302734375, -0.239013671875, -0.7880859375, -0.35302734375, -0.4482421875, 0.06890869140625, 0.92626953125, -0.30322265625, -0.0751953125, 0.55029296875, -0.146484375, 0.99951171875, -0.501953125, 0.0233154296875, 0.400146484375, -0.65576171875, -0.51904296875, -0.07794189453125, 0.1239013671875, 0.0216217041015625, 0.63134765625, -0.927734375, 0.026458740234375, -0.061492919921875, 0.169677734375, -0.537109375, -0.65625, -0.3359375, -1.0595703125, -0.480224609375, -0.85986328125, -0.93603515625, -0.3720703125, 0.2685546875, 0.251220703125, -0.529296875, 0.030609130859375, 0.62890625, -0.57958984375, 1.1484375, -0.755859375, 0.332763671875, -0.1290283203125, -0.08819580078125, -0.54345703125, 0.0877685546875, -0.59619140625, 0.24072265625, -0.9853515625, 0.10003662109375, 0.11767578125, 0.68310546875, -0.12420654296875, 0.86572265625, -0.289306640625, -0.42236328125, 0.41748046875, -0.1845703125, -0.128173828125, 1.05859375, 0.458740234375, -0.052093505859375, 0.153564453125, -0.2420654296875, -0.317138671875, -0.5361328125, 0.09454345703125, 0.37451171875, -0.2249755859375, -0.11468505859375, -0.26318359375, 0.448974609375, -1.19140625, 0.35791015625, -0.335693359375, -0.09747314453125, -0.12353515625, -0.08770751953125, 0.57763671875, 1.15625, -0.428955078125, 0.190673828125, -0.2095947265625, 0.1287841796875, 0.291748046875, 0.1778564453125, -0.431884765625, 0.7255859375, 0.36474609375, -0.72314453125, -0.0867919921875, 0.15576171875, 0.25341796875, 0.436767578125, -0.3193359375, -0.85107421875, -1.0126953125, -0.26318359375, 0.123291015625, 0.2320556640625, 0.53125, -0.44140625, -0.38330078125, -0.322998046875, -0.697265625, 0.419677734375, -1.0283203125, -1.1669921875, 0.4970703125, 0.040283203125, -0.5625, -0.00664520263671875, -0.43896484375, -0.3349609375, -0.045166015625, 0.2236328125, -0.6572265625, 0.66845703125, -0.2374267578125, 0.35107421875, 0.02777099609375, -0.25, -0.04473876953125, 0.837890625, -0.734375, -0.45361328125, -0.28662109375, 0.8232421875, 0.1490478515625, -0.280517578125, -0.58544921875, 0.1707763671875, 0.424560546875, 0.083251953125, -0.53125, -0.047210693359375, -0.345947265625, 0.79345703125, -1.109375, 0.08123779296875, 0.10418701171875, 0.55810546875, 0.24951171875, -0.07257080078125, -0.367431640625, 0.87890625, 0.87060546875, 0.1217041015625, 0.86865234375, 0.1444091796875, 0.580078125, 0.2166748046875, 0.005584716796875, -0.365966796875, 0.75244140625, 0.75830078125, 0.8740234375, -0.194091796875, 0.14404296875, 0.7509765625, 0.335205078125, -0.44921875, 0.666015625, -0.0601806640625, -0.01453399658203125, -0.1422119140625, -0.202880859375, 0.007274627685546875, 0.0743408203125, -0.49267578125, 0.58642578125, -0.98291015625, -0.268798828125, -0.344482421875, -0.51611328125, 0.79443359375, -0.08917236328125, 0.0299835205078125, -0.10174560546875, -0.35595703125, 0.409423828125, 0.25732421875, -0.357421875, -0.02886962890625, 1.1357421875, 0.480712890625, 0.1873779296875, 0.79248046875, 0.14306640625, 0.5390625, -0.56884765625, 0.115234375, 0.006275177001953125, -0.33642578125, -0.424560546875, -0.68505859375, -0.96630859375, 0.7451171875, -0.262939453125, -0.2115478515625, 0.81640625, -0.96044921875, 0.03619384765625, -0.3955078125, 0.66796875, -0.46923828125, 0.356201171875, 0.384521484375, -0.44189453125, -1.044921875, 0.9091796875, -0.19287109375, 0.3974609375, 0.190673828125, 0.82275390625, 0.1466064453125, 1.4306640625, 0.72705078125, -0.0009636878967285156, 0.2403564453125, 0.3935546875, -0.3505859375, -0.60400390625, -0.466796875, -0.1690673828125, 0.1466064453125, -0.59033203125, -0.39794921875, 0.0770263671875, 0.478271484375, 0.32763671875, -1.0380859375, -0.29931640625, 0.40087890625, -1.0234375, 0.65283203125, 0.375, 0.307861328125, 0.3134765625, -0.2822265625, -0.329833984375, -0.515625, 0.27734375, -0.80029296875, 0.4580078125, -0.76220703125, -0.56298828125, -0.471435546875, -0.55126953125, -0.1785888671875, -0.10223388671875, -0.281982421875, -0.83251953125, 0.671875, 0.35107421875, 0.303466796875, 0.328369140625, -0.440185546875, 0.316650390625, 0.8662109375, 0.77685546875, 0.023345947265625, 0.84716796875, 0.365478515625, 0.04595947265625, 0.2030029296875, -0.1290283203125, 0.4580078125, -0.414306640625, 0.3818359375, -0.56005859375, 0.341796875, -0.9052734375, -1.166015625, 0.0938720703125, 0.290771484375, 0.2313232421875, -0.463623046875, -1.048828125, -0.3203125, -0.8525390625, -0.198486328125, -0.7958984375, 0.79931640625, -0.403076171875, 0.070068359375, -0.00281524658203125, -1.283203125, 4.2421875, 1.0029296875, 0.806640625, 0.299072265625, 0.1961669921875, 0.7861328125, 0.1798095703125, -0.7490234375, -0.1011962890625, -0.2880859375, 0.5654296875, -0.52734375, -0.0955810546875, 0.828125, 0.69287109375, 0.61474609375, -0.55419921875, -0.15771484375, 0.080810546875, -0.8681640625, -0.84326171875, 0.42431640625, 0.007404327392578125, 0.285400390625, 0.0712890625, 0.1668701171875, 0.57421875, -0.76611328125, -0.063232421875, -0.7939453125, 0.2230224609375, -0.56982421875, 0.96923828125, 0.1729736328125, -0.2137451171875, 0.66259765625, 0.1268310546875, -0.11468505859375, 0.07000732421875, 0.2177734375, -0.3173828125, -0.18359375, 0.496337890625, -0.7236328125, -0.300537109375, 0.3310546875, -0.63037109375, 0.3681640625, -0.01377105712890625, -0.9853515625, 1.0087890625, -0.2685546875, 0.1612548828125, -0.671875, -0.81982421875, -0.138671875, -0.044097900390625, -0.398193359375, -0.09259033203125, 0.423583984375, 0.59423828125, 0.630859375, 0.1700439453125, 0.6923828125, -1.5341796875, 0.63818359375, -0.058502197265625, 0.58935546875, -0.65185546875, 0.020965576171875, -0.5146484375, -0.374755859375, -0.260009765625, -0.383544921875, 0.84521484375, 0.1268310546875, -0.1971435546875, 1.029296875, 0.8369140625, -0.424560546875, 0.3046875, -0.137451171875, -0.288818359375, -0.51513671875, 1.123046875, 1.484375, -0.86962890625, -0.290283203125, -0.1295166015625, 0.47998046875, 0.255126953125, 0.77783203125, 0.310791015625, -0.473876953125, -0.4423828125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Tags: bitmasks, brute force, hashing, string suffix structures, strings, two pointers Correct Solution: ``` import sys input = sys.stdin.readline from collections import Counter import math t = int(input()) for _ in range(t): n,m = list(map(int,input().split())) k = min(32,m) s = input().rstrip() D = set() v = 2**k - 1 for i in range(m-k, len(s)-k+1): temp = s[i:i+k] #print(temp) D.add(v - int(temp,2)) ok = 0 cc = s[:m].count('0') if cc>0: on = 1 else: on = 0 for i in range(len(s)-m): if cc==0: on = 0 if s[i]=='0': cc -= 1 if s[i+m]=='0': cc += 1 if cc==0: on = 0 if on==1: print('YES') print(m*'0') ok = 1 else: for i in range(v+1): if i not in D: ans = (bin(i))[2:] ans = (m - len(ans)) * '0' + ans print('YES') print(ans) ok = 1 break if ok==0: print('NO') ```
107,237
[ 0.29541015625, -0.2432861328125, 0.1929931640625, 0.10858154296875, -0.342041015625, -0.495849609375, 0.12274169921875, 0.053955078125, -0.11297607421875, 0.537109375, 0.52392578125, -0.2119140625, -0.274169921875, -1.0546875, -0.6845703125, 0.0264739990234375, -0.351318359375, -0.38916015625, -0.364013671875, -0.297607421875, -0.09588623046875, -0.08154296875, -1.142578125, 0.05133056640625, -0.201904296875, 1.1103515625, 0.55859375, 0.04052734375, 1.197265625, 0.966796875, -0.5751953125, -0.49951171875, 0.54443359375, -1.142578125, -0.46044921875, -0.59228515625, 0.8232421875, -0.95458984375, -0.253173828125, -0.2783203125, 0.465576171875, -0.318359375, 0.5, -0.732421875, -1.365234375, 0.099609375, -0.058013916015625, -0.3017578125, -0.20166015625, -0.7890625, 0.0141143798828125, -0.316650390625, 0.2471923828125, -0.2000732421875, 0.03302001953125, 0.3076171875, 0.28173828125, -0.396484375, -0.31787109375, 0.60546875, -0.1971435546875, 0.353515625, 0.1466064453125, -0.6796875, -0.08258056640625, 0.1776123046875, -0.2247314453125, -0.44482421875, -0.1412353515625, -1.083984375, 0.066162109375, 0.0863037109375, -0.384033203125, -0.5771484375, -0.044036865234375, -0.0215911865234375, 0.09722900390625, -0.1658935546875, -0.444580078125, 0.62060546875, -0.1370849609375, 1.0322265625, 0.42919921875, 0.43505859375, -0.412841796875, -0.6904296875, 0.04266357421875, 0.221435546875, 0.35986328125, 0.076416015625, -0.20166015625, 0.460205078125, -0.6103515625, -0.1248779296875, 0.56396484375, 0.363037109375, 0.091552734375, 0.09161376953125, 0.27978515625, 0.289794921875, 0.62646484375, 1.037109375, -0.12274169921875, 1.328125, -0.9541015625, -0.106201171875, -0.26806640625, -0.0022869110107421875, -0.287841796875, -0.0228271484375, -0.12115478515625, -0.163818359375, 0.60107421875, 0.5146484375, -0.269287109375, 0.7646484375, -0.0189208984375, 0.5859375, -1.181640625, 0.318359375, 0.54736328125, 0.294677734375, 0.77099609375, -0.1480712890625, -0.0010004043579101562, -0.1942138671875, -0.51171875, 1.1337890625, -0.2919921875, -0.163818359375, 0.396240234375, -0.078369140625, -0.05316162109375, 0.058380126953125, 0.06353759765625, 0.4970703125, -0.0699462890625, 0.1951904296875, 0.81298828125, -0.50537109375, 0.6767578125, -0.46337890625, -0.265625, 1.5283203125, 0.414794921875, -0.13232421875, 1.09375, 0.217041015625, -0.8212890625, 0.66357421875, -0.994140625, 0.381591796875, -0.170654296875, 0.2239990234375, 0.1256103515625, -0.0239105224609375, -0.37841796875, 0.164306640625, 0.20263671875, -0.2890625, -0.427490234375, 0.1480712890625, -0.0565185546875, 0.9443359375, -0.332763671875, 0.88623046875, -0.494873046875, -0.56640625, -0.07647705078125, -0.348388671875, 0.0095062255859375, -0.326416015625, -0.2890625, 0.7900390625, 0.58251953125, 1.2177734375, 1.01171875, -0.30859375, 0.488037109375, 0.3271484375, -0.388671875, 0.302978515625, 0.24755859375, 0.7841796875, -0.259765625, 0.2117919921875, 0.0574951171875, -0.332275390625, -0.95849609375, -0.6884765625, 0.07781982421875, 0.68310546875, -0.42138671875, 0.0243377685546875, 0.2587890625, 0.1312255859375, -0.78857421875, -0.29296875, -0.19873046875, -1.037109375, -0.71240234375, 0.6123046875, -0.22021484375, 0.47509765625, -0.5244140625, -0.51318359375, 0.353515625, 1.0546875, -0.023681640625, 0.265869140625, 0.367431640625, -0.1817626953125, -0.07452392578125, 0.22021484375, -0.0762939453125, -0.216796875, -0.5703125, 0.9970703125, -0.183837890625, -0.05364990234375, 0.039794921875, 1.0126953125, 0.54248046875, 0.63720703125, -0.35205078125, -0.2418212890625, 0.22216796875, 1.2421875, 0.11151123046875, 0.378173828125, 0.340576171875, 1.0107421875, 0.78173828125, 0.5888671875, 0.424560546875, 0.73046875, 0.740234375, 0.74951171875, 0.193359375, 0.160888671875, -0.09515380859375, 0.3701171875, 0.1937255859375, 0.61572265625, 0.417236328125, 0.283935546875, -0.09515380859375, 0.141845703125, -0.463134765625, 0.5517578125, -0.1357421875, 0.849609375, 0.104736328125, 0.65771484375, -0.59130859375, -0.55810546875, 0.110107421875, 0.71533203125, -1.021484375, -0.337890625, -0.1627197265625, -0.048736572265625, -0.0894775390625, 0.025482177734375, 0.348876953125, 0.453125, 0.310791015625, 0.65185546875, -0.1015625, -0.2431640625, -0.982421875, -0.68798828125, -1.0859375, -0.0877685546875, -0.5888671875, 0.11090087890625, 0.290771484375, -0.884765625, 0.1962890625, -0.623046875, -0.384765625, 0.376708984375, -0.55908203125, 0.4521484375, -0.064208984375, 0.335205078125, -0.83203125, 0.480712890625, 0.1065673828125, 1.2861328125, -0.58935546875, -0.13037109375, -0.1368408203125, -0.6279296875, 0.3154296875, -0.143310546875, 0.0264434814453125, -0.037078857421875, -0.6982421875, -0.94970703125, -0.460693359375, -0.04254150390625, -0.264404296875, -0.08319091796875, -0.51953125, 0.93212890625, 0.5751953125, -0.658203125, 0.6162109375, 0.763671875, -0.970703125, 0.3193359375, 0.411865234375, -0.0784912109375, -0.93212890625, 1.3671875, 0.492431640625, 0.207763671875, -0.407958984375, -0.476806640625, -0.312744140625, -0.0296783447265625, 0.0623779296875, -0.422607421875, -0.064697265625, 0.74462890625, -0.0322265625, -1.150390625, 0.27978515625, -0.6171875, -0.2279052734375, -0.238037109375, -0.2320556640625, 0.8154296875, 0.80029296875, 0.2958984375, 0.12274169921875, -0.0802001953125, 0.0051727294921875, 0.494140625, 0.3271484375, -0.290283203125, -0.204345703125, 0.89892578125, 0.19970703125, 0.218994140625, -0.03912353515625, -0.10382080078125, -0.07049560546875, 0.240234375, 0.0819091796875, 0.9306640625, 0.177978515625, 0.54638671875, 0.15234375, 0.8271484375, -0.837890625, -0.384033203125, 0.006099700927734375, 0.55029296875, 0.66748046875, 0.3603515625, 0.60888671875, -0.1573486328125, -0.293212890625, -1.4248046875, 0.34375, 0.006900787353515625, 0.91064453125, -0.6298828125, 1.1259765625, 0.169921875, -0.339111328125, 0.85595703125, -0.68408203125, -0.1468505859375, 0.91357421875, -0.0772705078125, 0.681640625, -0.3974609375, 0.14453125, -0.1826171875, -0.11712646484375, 0.54345703125, 0.70849609375, 0.89697265625, -0.46875, -0.5625, -0.33740234375, -0.2071533203125, -0.00873565673828125, -0.289794921875, 0.146240234375, -0.23095703125, -0.11016845703125, -0.8369140625, 0.08660888671875, 0.6650390625, 0.90771484375, -0.03424072265625, 0.2115478515625, 0.52880859375, 0.44482421875, 1.064453125, -0.4970703125, 0.264404296875, -0.72314453125, 0.7216796875, 0.0182037353515625, -0.2196044921875, -0.8369140625, -0.3642578125, -0.200439453125, 0.120849609375, -0.047760009765625, -0.377197265625, -1.2216796875, 0.353759765625, -0.5625, 0.58447265625, -0.72265625, 0.1162109375, -0.6103515625, 0.302734375, 0.150390625, -0.93798828125, -0.0765380859375, -0.491455078125, 0.45166015625, 0.216552734375, -0.2296142578125, -0.42138671875, -0.7607421875, -0.449462890625, -0.8779296875, 0.6005859375, 1.0185546875, 0.031463623046875, 0.218505859375, -1.431640625, 0.5263671875, 0.48095703125, -0.57275390625, 0.099365234375, -0.1356201171875, 0.6689453125, 0.3388671875, 0.8291015625, -0.313232421875, -0.69287109375, -0.12298583984375, -1.291015625, 0.252197265625, -0.40576171875, 0.69091796875, 0.034912109375, -0.125732421875, -0.086669921875, 0.1697998046875, 0.131103515625, 0.409912109375, -0.379638671875, 0.254638671875, -0.8330078125, -0.85498046875, 0.6767578125, -0.405029296875, -0.41064453125, 1.236328125, -0.09515380859375, -0.176513671875, 0.3349609375, 0.66552734375, -0.3310546875, 0.57470703125, -0.488525390625, 0.2247314453125, -0.52734375, -0.320556640625, -0.425048828125, -0.3759765625, 0.8916015625, 0.1551513671875, -0.60546875, -0.08331298828125, -1.009765625, -0.327880859375, 0.14404296875, -0.3505859375, 0.23828125, -0.2183837890625, -0.06781005859375, -0.283203125, -0.12078857421875, -0.63818359375, -0.223388671875, -0.546875, -0.5263671875, 0.319580078125, 0.33056640625, 0.796875, 0.357666015625, -0.392822265625, -0.0333251953125, -0.032806396484375, 0.159423828125, -0.38525390625, -0.284423828125, -0.44970703125, -0.257568359375, -0.369384765625, 0.01800537109375, 0.4140625, 0.11773681640625, 0.4296875, 0.34716796875, 0.5390625, 0.466552734375, -0.70068359375, 0.890625, 0.242919921875, -0.87109375, -0.061981201171875, 0.5693359375, -0.0858154296875, 0.6728515625, -0.0105133056640625, -0.90625, -0.7451171875, -0.78369140625, 0.38623046875, -0.54931640625, -0.1771240234375, -1.0908203125, -0.263671875, -0.5166015625, 0.67041015625, -0.04522705078125, -0.345703125, 0.16748046875, -1.380859375, -0.31884765625, -0.69287109375, -0.286865234375, -0.9189453125, -0.281982421875, -0.352783203125, 0.73193359375, -0.1893310546875, 0.39990234375, -0.16796875, 0.099365234375, 0.29150390625, 0.3466796875, -0.466796875, -0.37890625, -0.307861328125, 0.2318115234375, -0.1715087890625, -0.07537841796875, -0.7890625, 0.72705078125, -0.89501953125, 0.269775390625, -0.2376708984375, 0.09637451171875, -0.32275390625, -0.302001953125, 1.1162109375, -0.36083984375, -0.3974609375, -0.1685791015625, 0.191650390625, 0.67138671875, -0.483642578125, -0.272216796875, -1.17578125, -0.48193359375, -0.89599609375, 0.56298828125, -0.2352294921875, -0.1217041015625, -0.49169921875, -0.60498046875, 1.08984375, -0.490478515625, 0.2216796875, 1.09765625, -0.0033664703369140625, 0.1920166015625, -0.75146484375, 0.6630859375, 0.7099609375, -0.64892578125, 0.104736328125, 0.1851806640625, -0.76220703125, 0.1785888671875, -0.371826171875, -1.0478515625, -0.431396484375, 0.51611328125, 1.0830078125, -0.353759765625, 0.60498046875, 0.1273193359375, -1.212890625, -0.5361328125, 1.255859375, 0.43310546875, 0.08447265625, 0.79150390625, -0.022796630859375, 0.023681640625, -0.3037109375, -0.7490234375, -0.2177734375, -0.54833984375, 1.400390625, -0.669921875, -0.470703125, 1.1025390625, 0.89990234375, -1.55078125, -0.87890625, 0.001617431640625, 0.2041015625, 0.08905029296875, -0.80810546875, -0.036468505859375, 0.492919921875, -0.5107421875, -0.1708984375, 0.173095703125, -0.034637451171875, 0.37255859375, 0.1270751953125, 0.67724609375, -0.66064453125, 0.52001953125, 0.93603515625, -0.435302734375, -0.239013671875, -0.7880859375, -0.35302734375, -0.4482421875, 0.06890869140625, 0.92626953125, -0.30322265625, -0.0751953125, 0.55029296875, -0.146484375, 0.99951171875, -0.501953125, 0.0233154296875, 0.400146484375, -0.65576171875, -0.51904296875, -0.07794189453125, 0.1239013671875, 0.0216217041015625, 0.63134765625, -0.927734375, 0.026458740234375, -0.061492919921875, 0.169677734375, -0.537109375, -0.65625, -0.3359375, -1.0595703125, -0.480224609375, -0.85986328125, -0.93603515625, -0.3720703125, 0.2685546875, 0.251220703125, -0.529296875, 0.030609130859375, 0.62890625, -0.57958984375, 1.1484375, -0.755859375, 0.332763671875, -0.1290283203125, -0.08819580078125, -0.54345703125, 0.0877685546875, -0.59619140625, 0.24072265625, -0.9853515625, 0.10003662109375, 0.11767578125, 0.68310546875, -0.12420654296875, 0.86572265625, -0.289306640625, -0.42236328125, 0.41748046875, -0.1845703125, -0.128173828125, 1.05859375, 0.458740234375, -0.052093505859375, 0.153564453125, -0.2420654296875, -0.317138671875, -0.5361328125, 0.09454345703125, 0.37451171875, -0.2249755859375, -0.11468505859375, -0.26318359375, 0.448974609375, -1.19140625, 0.35791015625, -0.335693359375, -0.09747314453125, -0.12353515625, -0.08770751953125, 0.57763671875, 1.15625, -0.428955078125, 0.190673828125, -0.2095947265625, 0.1287841796875, 0.291748046875, 0.1778564453125, -0.431884765625, 0.7255859375, 0.36474609375, -0.72314453125, -0.0867919921875, 0.15576171875, 0.25341796875, 0.436767578125, -0.3193359375, -0.85107421875, -1.0126953125, -0.26318359375, 0.123291015625, 0.2320556640625, 0.53125, -0.44140625, -0.38330078125, -0.322998046875, -0.697265625, 0.419677734375, -1.0283203125, -1.1669921875, 0.4970703125, 0.040283203125, -0.5625, -0.00664520263671875, -0.43896484375, -0.3349609375, -0.045166015625, 0.2236328125, -0.6572265625, 0.66845703125, -0.2374267578125, 0.35107421875, 0.02777099609375, -0.25, -0.04473876953125, 0.837890625, -0.734375, -0.45361328125, -0.28662109375, 0.8232421875, 0.1490478515625, -0.280517578125, -0.58544921875, 0.1707763671875, 0.424560546875, 0.083251953125, -0.53125, -0.047210693359375, -0.345947265625, 0.79345703125, -1.109375, 0.08123779296875, 0.10418701171875, 0.55810546875, 0.24951171875, -0.07257080078125, -0.367431640625, 0.87890625, 0.87060546875, 0.1217041015625, 0.86865234375, 0.1444091796875, 0.580078125, 0.2166748046875, 0.005584716796875, -0.365966796875, 0.75244140625, 0.75830078125, 0.8740234375, -0.194091796875, 0.14404296875, 0.7509765625, 0.335205078125, -0.44921875, 0.666015625, -0.0601806640625, -0.01453399658203125, -0.1422119140625, -0.202880859375, 0.007274627685546875, 0.0743408203125, -0.49267578125, 0.58642578125, -0.98291015625, -0.268798828125, -0.344482421875, -0.51611328125, 0.79443359375, -0.08917236328125, 0.0299835205078125, -0.10174560546875, -0.35595703125, 0.409423828125, 0.25732421875, -0.357421875, -0.02886962890625, 1.1357421875, 0.480712890625, 0.1873779296875, 0.79248046875, 0.14306640625, 0.5390625, -0.56884765625, 0.115234375, 0.006275177001953125, -0.33642578125, -0.424560546875, -0.68505859375, -0.96630859375, 0.7451171875, -0.262939453125, -0.2115478515625, 0.81640625, -0.96044921875, 0.03619384765625, -0.3955078125, 0.66796875, -0.46923828125, 0.356201171875, 0.384521484375, -0.44189453125, -1.044921875, 0.9091796875, -0.19287109375, 0.3974609375, 0.190673828125, 0.82275390625, 0.1466064453125, 1.4306640625, 0.72705078125, -0.0009636878967285156, 0.2403564453125, 0.3935546875, -0.3505859375, -0.60400390625, -0.466796875, -0.1690673828125, 0.1466064453125, -0.59033203125, -0.39794921875, 0.0770263671875, 0.478271484375, 0.32763671875, -1.0380859375, -0.29931640625, 0.40087890625, -1.0234375, 0.65283203125, 0.375, 0.307861328125, 0.3134765625, -0.2822265625, -0.329833984375, -0.515625, 0.27734375, -0.80029296875, 0.4580078125, -0.76220703125, -0.56298828125, -0.471435546875, -0.55126953125, -0.1785888671875, -0.10223388671875, -0.281982421875, -0.83251953125, 0.671875, 0.35107421875, 0.303466796875, 0.328369140625, -0.440185546875, 0.316650390625, 0.8662109375, 0.77685546875, 0.023345947265625, 0.84716796875, 0.365478515625, 0.04595947265625, 0.2030029296875, -0.1290283203125, 0.4580078125, -0.414306640625, 0.3818359375, -0.56005859375, 0.341796875, -0.9052734375, -1.166015625, 0.0938720703125, 0.290771484375, 0.2313232421875, -0.463623046875, -1.048828125, -0.3203125, -0.8525390625, -0.198486328125, -0.7958984375, 0.79931640625, -0.403076171875, 0.070068359375, -0.00281524658203125, -1.283203125, 4.2421875, 1.0029296875, 0.806640625, 0.299072265625, 0.1961669921875, 0.7861328125, 0.1798095703125, -0.7490234375, -0.1011962890625, -0.2880859375, 0.5654296875, -0.52734375, -0.0955810546875, 0.828125, 0.69287109375, 0.61474609375, -0.55419921875, -0.15771484375, 0.080810546875, -0.8681640625, -0.84326171875, 0.42431640625, 0.007404327392578125, 0.285400390625, 0.0712890625, 0.1668701171875, 0.57421875, -0.76611328125, -0.063232421875, -0.7939453125, 0.2230224609375, -0.56982421875, 0.96923828125, 0.1729736328125, -0.2137451171875, 0.66259765625, 0.1268310546875, -0.11468505859375, 0.07000732421875, 0.2177734375, -0.3173828125, -0.18359375, 0.496337890625, -0.7236328125, -0.300537109375, 0.3310546875, -0.63037109375, 0.3681640625, -0.01377105712890625, -0.9853515625, 1.0087890625, -0.2685546875, 0.1612548828125, -0.671875, -0.81982421875, -0.138671875, -0.044097900390625, -0.398193359375, -0.09259033203125, 0.423583984375, 0.59423828125, 0.630859375, 0.1700439453125, 0.6923828125, -1.5341796875, 0.63818359375, -0.058502197265625, 0.58935546875, -0.65185546875, 0.020965576171875, -0.5146484375, -0.374755859375, -0.260009765625, -0.383544921875, 0.84521484375, 0.1268310546875, -0.1971435546875, 1.029296875, 0.8369140625, -0.424560546875, 0.3046875, -0.137451171875, -0.288818359375, -0.51513671875, 1.123046875, 1.484375, -0.86962890625, -0.290283203125, -0.1295166015625, 0.47998046875, 0.255126953125, 0.77783203125, 0.310791015625, -0.473876953125, -0.4423828125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Tags: bitmasks, brute force, hashing, string suffix structures, strings, two pointers Correct Solution: ``` """ #If FastIO not needed, use this and don't forget to strip #import sys, math #input = sys.stdin.readline """ import os import sys from io import BytesIO, IOBase import heapq as h from bisect import bisect_left, bisect_right import time from types import GeneratorType BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): import os self.os = os self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: self.os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") """ recursively make the set smaller I need to remove from consideration anything with a 0 in its first K-20 digits """ out = [] for _ in range(int(input())): N, K = [int(s) for s in input().split()] S = input() K2 = min(K,20) start_str = -1 curr = 0 max_bit = pow(2,K2) - 1 no = set() for i in range(N): curr *= 2 if S[i] == '0': curr += 1 if curr > max_bit: curr &= max_bit start_str = i if i >= K-1 and (i - start_str) >= (K-K2): no.add(curr) flag = False for i in range(pow(2,K2)): if i not in no: out.append("YES") out.append('0'*(K-len(bin(i)[2:])) + bin(i)[2:]) flag = True break if not flag: out.append("NO") print('\n'.join(out)) #print(time.time()-start_time) ```
107,238
[ 0.29541015625, -0.2432861328125, 0.1929931640625, 0.10858154296875, -0.342041015625, -0.495849609375, 0.12274169921875, 0.053955078125, -0.11297607421875, 0.537109375, 0.52392578125, -0.2119140625, -0.274169921875, -1.0546875, -0.6845703125, 0.0264739990234375, -0.351318359375, -0.38916015625, -0.364013671875, -0.297607421875, -0.09588623046875, -0.08154296875, -1.142578125, 0.05133056640625, -0.201904296875, 1.1103515625, 0.55859375, 0.04052734375, 1.197265625, 0.966796875, -0.5751953125, -0.49951171875, 0.54443359375, -1.142578125, -0.46044921875, -0.59228515625, 0.8232421875, -0.95458984375, -0.253173828125, -0.2783203125, 0.465576171875, -0.318359375, 0.5, -0.732421875, -1.365234375, 0.099609375, -0.058013916015625, -0.3017578125, -0.20166015625, -0.7890625, 0.0141143798828125, -0.316650390625, 0.2471923828125, -0.2000732421875, 0.03302001953125, 0.3076171875, 0.28173828125, -0.396484375, -0.31787109375, 0.60546875, -0.1971435546875, 0.353515625, 0.1466064453125, -0.6796875, -0.08258056640625, 0.1776123046875, -0.2247314453125, -0.44482421875, -0.1412353515625, -1.083984375, 0.066162109375, 0.0863037109375, -0.384033203125, -0.5771484375, -0.044036865234375, -0.0215911865234375, 0.09722900390625, -0.1658935546875, -0.444580078125, 0.62060546875, -0.1370849609375, 1.0322265625, 0.42919921875, 0.43505859375, -0.412841796875, -0.6904296875, 0.04266357421875, 0.221435546875, 0.35986328125, 0.076416015625, -0.20166015625, 0.460205078125, -0.6103515625, -0.1248779296875, 0.56396484375, 0.363037109375, 0.091552734375, 0.09161376953125, 0.27978515625, 0.289794921875, 0.62646484375, 1.037109375, -0.12274169921875, 1.328125, -0.9541015625, -0.106201171875, -0.26806640625, -0.0022869110107421875, -0.287841796875, -0.0228271484375, -0.12115478515625, -0.163818359375, 0.60107421875, 0.5146484375, -0.269287109375, 0.7646484375, -0.0189208984375, 0.5859375, -1.181640625, 0.318359375, 0.54736328125, 0.294677734375, 0.77099609375, -0.1480712890625, -0.0010004043579101562, -0.1942138671875, -0.51171875, 1.1337890625, -0.2919921875, -0.163818359375, 0.396240234375, -0.078369140625, -0.05316162109375, 0.058380126953125, 0.06353759765625, 0.4970703125, -0.0699462890625, 0.1951904296875, 0.81298828125, -0.50537109375, 0.6767578125, -0.46337890625, -0.265625, 1.5283203125, 0.414794921875, -0.13232421875, 1.09375, 0.217041015625, -0.8212890625, 0.66357421875, -0.994140625, 0.381591796875, -0.170654296875, 0.2239990234375, 0.1256103515625, -0.0239105224609375, -0.37841796875, 0.164306640625, 0.20263671875, -0.2890625, -0.427490234375, 0.1480712890625, -0.0565185546875, 0.9443359375, -0.332763671875, 0.88623046875, -0.494873046875, -0.56640625, -0.07647705078125, -0.348388671875, 0.0095062255859375, -0.326416015625, -0.2890625, 0.7900390625, 0.58251953125, 1.2177734375, 1.01171875, -0.30859375, 0.488037109375, 0.3271484375, -0.388671875, 0.302978515625, 0.24755859375, 0.7841796875, -0.259765625, 0.2117919921875, 0.0574951171875, -0.332275390625, -0.95849609375, -0.6884765625, 0.07781982421875, 0.68310546875, -0.42138671875, 0.0243377685546875, 0.2587890625, 0.1312255859375, -0.78857421875, -0.29296875, -0.19873046875, -1.037109375, -0.71240234375, 0.6123046875, -0.22021484375, 0.47509765625, -0.5244140625, -0.51318359375, 0.353515625, 1.0546875, -0.023681640625, 0.265869140625, 0.367431640625, -0.1817626953125, -0.07452392578125, 0.22021484375, -0.0762939453125, -0.216796875, -0.5703125, 0.9970703125, -0.183837890625, -0.05364990234375, 0.039794921875, 1.0126953125, 0.54248046875, 0.63720703125, -0.35205078125, -0.2418212890625, 0.22216796875, 1.2421875, 0.11151123046875, 0.378173828125, 0.340576171875, 1.0107421875, 0.78173828125, 0.5888671875, 0.424560546875, 0.73046875, 0.740234375, 0.74951171875, 0.193359375, 0.160888671875, -0.09515380859375, 0.3701171875, 0.1937255859375, 0.61572265625, 0.417236328125, 0.283935546875, -0.09515380859375, 0.141845703125, -0.463134765625, 0.5517578125, -0.1357421875, 0.849609375, 0.104736328125, 0.65771484375, -0.59130859375, -0.55810546875, 0.110107421875, 0.71533203125, -1.021484375, -0.337890625, -0.1627197265625, -0.048736572265625, -0.0894775390625, 0.025482177734375, 0.348876953125, 0.453125, 0.310791015625, 0.65185546875, -0.1015625, -0.2431640625, -0.982421875, -0.68798828125, -1.0859375, -0.0877685546875, -0.5888671875, 0.11090087890625, 0.290771484375, -0.884765625, 0.1962890625, -0.623046875, -0.384765625, 0.376708984375, -0.55908203125, 0.4521484375, -0.064208984375, 0.335205078125, -0.83203125, 0.480712890625, 0.1065673828125, 1.2861328125, -0.58935546875, -0.13037109375, -0.1368408203125, -0.6279296875, 0.3154296875, -0.143310546875, 0.0264434814453125, -0.037078857421875, -0.6982421875, -0.94970703125, -0.460693359375, -0.04254150390625, -0.264404296875, -0.08319091796875, -0.51953125, 0.93212890625, 0.5751953125, -0.658203125, 0.6162109375, 0.763671875, -0.970703125, 0.3193359375, 0.411865234375, -0.0784912109375, -0.93212890625, 1.3671875, 0.492431640625, 0.207763671875, -0.407958984375, -0.476806640625, -0.312744140625, -0.0296783447265625, 0.0623779296875, -0.422607421875, -0.064697265625, 0.74462890625, -0.0322265625, -1.150390625, 0.27978515625, -0.6171875, -0.2279052734375, -0.238037109375, -0.2320556640625, 0.8154296875, 0.80029296875, 0.2958984375, 0.12274169921875, -0.0802001953125, 0.0051727294921875, 0.494140625, 0.3271484375, -0.290283203125, -0.204345703125, 0.89892578125, 0.19970703125, 0.218994140625, -0.03912353515625, -0.10382080078125, -0.07049560546875, 0.240234375, 0.0819091796875, 0.9306640625, 0.177978515625, 0.54638671875, 0.15234375, 0.8271484375, -0.837890625, -0.384033203125, 0.006099700927734375, 0.55029296875, 0.66748046875, 0.3603515625, 0.60888671875, -0.1573486328125, -0.293212890625, -1.4248046875, 0.34375, 0.006900787353515625, 0.91064453125, -0.6298828125, 1.1259765625, 0.169921875, -0.339111328125, 0.85595703125, -0.68408203125, -0.1468505859375, 0.91357421875, -0.0772705078125, 0.681640625, -0.3974609375, 0.14453125, -0.1826171875, -0.11712646484375, 0.54345703125, 0.70849609375, 0.89697265625, -0.46875, -0.5625, -0.33740234375, -0.2071533203125, -0.00873565673828125, -0.289794921875, 0.146240234375, -0.23095703125, -0.11016845703125, -0.8369140625, 0.08660888671875, 0.6650390625, 0.90771484375, -0.03424072265625, 0.2115478515625, 0.52880859375, 0.44482421875, 1.064453125, -0.4970703125, 0.264404296875, -0.72314453125, 0.7216796875, 0.0182037353515625, -0.2196044921875, -0.8369140625, -0.3642578125, -0.200439453125, 0.120849609375, -0.047760009765625, -0.377197265625, -1.2216796875, 0.353759765625, -0.5625, 0.58447265625, -0.72265625, 0.1162109375, -0.6103515625, 0.302734375, 0.150390625, -0.93798828125, -0.0765380859375, -0.491455078125, 0.45166015625, 0.216552734375, -0.2296142578125, -0.42138671875, -0.7607421875, -0.449462890625, -0.8779296875, 0.6005859375, 1.0185546875, 0.031463623046875, 0.218505859375, -1.431640625, 0.5263671875, 0.48095703125, -0.57275390625, 0.099365234375, -0.1356201171875, 0.6689453125, 0.3388671875, 0.8291015625, -0.313232421875, -0.69287109375, -0.12298583984375, -1.291015625, 0.252197265625, -0.40576171875, 0.69091796875, 0.034912109375, -0.125732421875, -0.086669921875, 0.1697998046875, 0.131103515625, 0.409912109375, -0.379638671875, 0.254638671875, -0.8330078125, -0.85498046875, 0.6767578125, -0.405029296875, -0.41064453125, 1.236328125, -0.09515380859375, -0.176513671875, 0.3349609375, 0.66552734375, -0.3310546875, 0.57470703125, -0.488525390625, 0.2247314453125, -0.52734375, -0.320556640625, -0.425048828125, -0.3759765625, 0.8916015625, 0.1551513671875, -0.60546875, -0.08331298828125, -1.009765625, -0.327880859375, 0.14404296875, -0.3505859375, 0.23828125, -0.2183837890625, -0.06781005859375, -0.283203125, -0.12078857421875, -0.63818359375, -0.223388671875, -0.546875, -0.5263671875, 0.319580078125, 0.33056640625, 0.796875, 0.357666015625, -0.392822265625, -0.0333251953125, -0.032806396484375, 0.159423828125, -0.38525390625, -0.284423828125, -0.44970703125, -0.257568359375, -0.369384765625, 0.01800537109375, 0.4140625, 0.11773681640625, 0.4296875, 0.34716796875, 0.5390625, 0.466552734375, -0.70068359375, 0.890625, 0.242919921875, -0.87109375, -0.061981201171875, 0.5693359375, -0.0858154296875, 0.6728515625, -0.0105133056640625, -0.90625, -0.7451171875, -0.78369140625, 0.38623046875, -0.54931640625, -0.1771240234375, -1.0908203125, -0.263671875, -0.5166015625, 0.67041015625, -0.04522705078125, -0.345703125, 0.16748046875, -1.380859375, -0.31884765625, -0.69287109375, -0.286865234375, -0.9189453125, -0.281982421875, -0.352783203125, 0.73193359375, -0.1893310546875, 0.39990234375, -0.16796875, 0.099365234375, 0.29150390625, 0.3466796875, -0.466796875, -0.37890625, -0.307861328125, 0.2318115234375, -0.1715087890625, -0.07537841796875, -0.7890625, 0.72705078125, -0.89501953125, 0.269775390625, -0.2376708984375, 0.09637451171875, -0.32275390625, -0.302001953125, 1.1162109375, -0.36083984375, -0.3974609375, -0.1685791015625, 0.191650390625, 0.67138671875, -0.483642578125, -0.272216796875, -1.17578125, -0.48193359375, -0.89599609375, 0.56298828125, -0.2352294921875, -0.1217041015625, -0.49169921875, -0.60498046875, 1.08984375, -0.490478515625, 0.2216796875, 1.09765625, -0.0033664703369140625, 0.1920166015625, -0.75146484375, 0.6630859375, 0.7099609375, -0.64892578125, 0.104736328125, 0.1851806640625, -0.76220703125, 0.1785888671875, -0.371826171875, -1.0478515625, -0.431396484375, 0.51611328125, 1.0830078125, -0.353759765625, 0.60498046875, 0.1273193359375, -1.212890625, -0.5361328125, 1.255859375, 0.43310546875, 0.08447265625, 0.79150390625, -0.022796630859375, 0.023681640625, -0.3037109375, -0.7490234375, -0.2177734375, -0.54833984375, 1.400390625, -0.669921875, -0.470703125, 1.1025390625, 0.89990234375, -1.55078125, -0.87890625, 0.001617431640625, 0.2041015625, 0.08905029296875, -0.80810546875, -0.036468505859375, 0.492919921875, -0.5107421875, -0.1708984375, 0.173095703125, -0.034637451171875, 0.37255859375, 0.1270751953125, 0.67724609375, -0.66064453125, 0.52001953125, 0.93603515625, -0.435302734375, -0.239013671875, -0.7880859375, -0.35302734375, -0.4482421875, 0.06890869140625, 0.92626953125, -0.30322265625, -0.0751953125, 0.55029296875, -0.146484375, 0.99951171875, -0.501953125, 0.0233154296875, 0.400146484375, -0.65576171875, -0.51904296875, -0.07794189453125, 0.1239013671875, 0.0216217041015625, 0.63134765625, -0.927734375, 0.026458740234375, -0.061492919921875, 0.169677734375, -0.537109375, -0.65625, -0.3359375, -1.0595703125, -0.480224609375, -0.85986328125, -0.93603515625, -0.3720703125, 0.2685546875, 0.251220703125, -0.529296875, 0.030609130859375, 0.62890625, -0.57958984375, 1.1484375, -0.755859375, 0.332763671875, -0.1290283203125, -0.08819580078125, -0.54345703125, 0.0877685546875, -0.59619140625, 0.24072265625, -0.9853515625, 0.10003662109375, 0.11767578125, 0.68310546875, -0.12420654296875, 0.86572265625, -0.289306640625, -0.42236328125, 0.41748046875, -0.1845703125, -0.128173828125, 1.05859375, 0.458740234375, -0.052093505859375, 0.153564453125, -0.2420654296875, -0.317138671875, -0.5361328125, 0.09454345703125, 0.37451171875, -0.2249755859375, -0.11468505859375, -0.26318359375, 0.448974609375, -1.19140625, 0.35791015625, -0.335693359375, -0.09747314453125, -0.12353515625, -0.08770751953125, 0.57763671875, 1.15625, -0.428955078125, 0.190673828125, -0.2095947265625, 0.1287841796875, 0.291748046875, 0.1778564453125, -0.431884765625, 0.7255859375, 0.36474609375, -0.72314453125, -0.0867919921875, 0.15576171875, 0.25341796875, 0.436767578125, -0.3193359375, -0.85107421875, -1.0126953125, -0.26318359375, 0.123291015625, 0.2320556640625, 0.53125, -0.44140625, -0.38330078125, -0.322998046875, -0.697265625, 0.419677734375, -1.0283203125, -1.1669921875, 0.4970703125, 0.040283203125, -0.5625, -0.00664520263671875, -0.43896484375, -0.3349609375, -0.045166015625, 0.2236328125, -0.6572265625, 0.66845703125, -0.2374267578125, 0.35107421875, 0.02777099609375, -0.25, -0.04473876953125, 0.837890625, -0.734375, -0.45361328125, -0.28662109375, 0.8232421875, 0.1490478515625, -0.280517578125, -0.58544921875, 0.1707763671875, 0.424560546875, 0.083251953125, -0.53125, -0.047210693359375, -0.345947265625, 0.79345703125, -1.109375, 0.08123779296875, 0.10418701171875, 0.55810546875, 0.24951171875, -0.07257080078125, -0.367431640625, 0.87890625, 0.87060546875, 0.1217041015625, 0.86865234375, 0.1444091796875, 0.580078125, 0.2166748046875, 0.005584716796875, -0.365966796875, 0.75244140625, 0.75830078125, 0.8740234375, -0.194091796875, 0.14404296875, 0.7509765625, 0.335205078125, -0.44921875, 0.666015625, -0.0601806640625, -0.01453399658203125, -0.1422119140625, -0.202880859375, 0.007274627685546875, 0.0743408203125, -0.49267578125, 0.58642578125, -0.98291015625, -0.268798828125, -0.344482421875, -0.51611328125, 0.79443359375, -0.08917236328125, 0.0299835205078125, -0.10174560546875, -0.35595703125, 0.409423828125, 0.25732421875, -0.357421875, -0.02886962890625, 1.1357421875, 0.480712890625, 0.1873779296875, 0.79248046875, 0.14306640625, 0.5390625, -0.56884765625, 0.115234375, 0.006275177001953125, -0.33642578125, -0.424560546875, -0.68505859375, -0.96630859375, 0.7451171875, -0.262939453125, -0.2115478515625, 0.81640625, -0.96044921875, 0.03619384765625, -0.3955078125, 0.66796875, -0.46923828125, 0.356201171875, 0.384521484375, -0.44189453125, -1.044921875, 0.9091796875, -0.19287109375, 0.3974609375, 0.190673828125, 0.82275390625, 0.1466064453125, 1.4306640625, 0.72705078125, -0.0009636878967285156, 0.2403564453125, 0.3935546875, -0.3505859375, -0.60400390625, -0.466796875, -0.1690673828125, 0.1466064453125, -0.59033203125, -0.39794921875, 0.0770263671875, 0.478271484375, 0.32763671875, -1.0380859375, -0.29931640625, 0.40087890625, -1.0234375, 0.65283203125, 0.375, 0.307861328125, 0.3134765625, -0.2822265625, -0.329833984375, -0.515625, 0.27734375, -0.80029296875, 0.4580078125, -0.76220703125, -0.56298828125, -0.471435546875, -0.55126953125, -0.1785888671875, -0.10223388671875, -0.281982421875, -0.83251953125, 0.671875, 0.35107421875, 0.303466796875, 0.328369140625, -0.440185546875, 0.316650390625, 0.8662109375, 0.77685546875, 0.023345947265625, 0.84716796875, 0.365478515625, 0.04595947265625, 0.2030029296875, -0.1290283203125, 0.4580078125, -0.414306640625, 0.3818359375, -0.56005859375, 0.341796875, -0.9052734375, -1.166015625, 0.0938720703125, 0.290771484375, 0.2313232421875, -0.463623046875, -1.048828125, -0.3203125, -0.8525390625, -0.198486328125, -0.7958984375, 0.79931640625, -0.403076171875, 0.070068359375, -0.00281524658203125, -1.283203125, 4.2421875, 1.0029296875, 0.806640625, 0.299072265625, 0.1961669921875, 0.7861328125, 0.1798095703125, -0.7490234375, -0.1011962890625, -0.2880859375, 0.5654296875, -0.52734375, -0.0955810546875, 0.828125, 0.69287109375, 0.61474609375, -0.55419921875, -0.15771484375, 0.080810546875, -0.8681640625, -0.84326171875, 0.42431640625, 0.007404327392578125, 0.285400390625, 0.0712890625, 0.1668701171875, 0.57421875, -0.76611328125, -0.063232421875, -0.7939453125, 0.2230224609375, -0.56982421875, 0.96923828125, 0.1729736328125, -0.2137451171875, 0.66259765625, 0.1268310546875, -0.11468505859375, 0.07000732421875, 0.2177734375, -0.3173828125, -0.18359375, 0.496337890625, -0.7236328125, -0.300537109375, 0.3310546875, -0.63037109375, 0.3681640625, -0.01377105712890625, -0.9853515625, 1.0087890625, -0.2685546875, 0.1612548828125, -0.671875, -0.81982421875, -0.138671875, -0.044097900390625, -0.398193359375, -0.09259033203125, 0.423583984375, 0.59423828125, 0.630859375, 0.1700439453125, 0.6923828125, -1.5341796875, 0.63818359375, -0.058502197265625, 0.58935546875, -0.65185546875, 0.020965576171875, -0.5146484375, -0.374755859375, -0.260009765625, -0.383544921875, 0.84521484375, 0.1268310546875, -0.1971435546875, 1.029296875, 0.8369140625, -0.424560546875, 0.3046875, -0.137451171875, -0.288818359375, -0.51513671875, 1.123046875, 1.484375, -0.86962890625, -0.290283203125, -0.1295166015625, 0.47998046875, 0.255126953125, 0.77783203125, 0.310791015625, -0.473876953125, -0.4423828125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Tags: bitmasks, brute force, hashing, string suffix structures, strings, two pointers Correct Solution: ``` import sys input = sys.stdin.readline t = int(input()) outL = [] for _ in range(t): n, k = map(int, input().split()) s = input().strip() bad = set() k2 = min(k, 20) last = -1 curr = 0 mask = (1 << k2) - 1 for i in range(n): curr *= 2 if s[i] == '0': curr += 1 if curr > mask: curr &= mask last = i if i >= k-1 and (i - last) >= (k-k2): bad.add(curr) for i in range(1 << k2): if i not in bad: outL.append('YES') out = bin(i)[2:] outL.append('0'*(k-len(out))+out) break else: outL.append('NO') print('\n'.join(outL)) ```
107,239
[ 0.29541015625, -0.2432861328125, 0.1929931640625, 0.10858154296875, -0.342041015625, -0.495849609375, 0.12274169921875, 0.053955078125, -0.11297607421875, 0.537109375, 0.52392578125, -0.2119140625, -0.274169921875, -1.0546875, -0.6845703125, 0.0264739990234375, -0.351318359375, -0.38916015625, -0.364013671875, -0.297607421875, -0.09588623046875, -0.08154296875, -1.142578125, 0.05133056640625, -0.201904296875, 1.1103515625, 0.55859375, 0.04052734375, 1.197265625, 0.966796875, -0.5751953125, -0.49951171875, 0.54443359375, -1.142578125, -0.46044921875, -0.59228515625, 0.8232421875, -0.95458984375, -0.253173828125, -0.2783203125, 0.465576171875, -0.318359375, 0.5, -0.732421875, -1.365234375, 0.099609375, -0.058013916015625, -0.3017578125, -0.20166015625, -0.7890625, 0.0141143798828125, -0.316650390625, 0.2471923828125, -0.2000732421875, 0.03302001953125, 0.3076171875, 0.28173828125, -0.396484375, -0.31787109375, 0.60546875, -0.1971435546875, 0.353515625, 0.1466064453125, -0.6796875, -0.08258056640625, 0.1776123046875, -0.2247314453125, -0.44482421875, -0.1412353515625, -1.083984375, 0.066162109375, 0.0863037109375, -0.384033203125, -0.5771484375, -0.044036865234375, -0.0215911865234375, 0.09722900390625, -0.1658935546875, -0.444580078125, 0.62060546875, -0.1370849609375, 1.0322265625, 0.42919921875, 0.43505859375, -0.412841796875, -0.6904296875, 0.04266357421875, 0.221435546875, 0.35986328125, 0.076416015625, -0.20166015625, 0.460205078125, -0.6103515625, -0.1248779296875, 0.56396484375, 0.363037109375, 0.091552734375, 0.09161376953125, 0.27978515625, 0.289794921875, 0.62646484375, 1.037109375, -0.12274169921875, 1.328125, -0.9541015625, -0.106201171875, -0.26806640625, -0.0022869110107421875, -0.287841796875, -0.0228271484375, -0.12115478515625, -0.163818359375, 0.60107421875, 0.5146484375, -0.269287109375, 0.7646484375, -0.0189208984375, 0.5859375, -1.181640625, 0.318359375, 0.54736328125, 0.294677734375, 0.77099609375, -0.1480712890625, -0.0010004043579101562, -0.1942138671875, -0.51171875, 1.1337890625, -0.2919921875, -0.163818359375, 0.396240234375, -0.078369140625, -0.05316162109375, 0.058380126953125, 0.06353759765625, 0.4970703125, -0.0699462890625, 0.1951904296875, 0.81298828125, -0.50537109375, 0.6767578125, -0.46337890625, -0.265625, 1.5283203125, 0.414794921875, -0.13232421875, 1.09375, 0.217041015625, -0.8212890625, 0.66357421875, -0.994140625, 0.381591796875, -0.170654296875, 0.2239990234375, 0.1256103515625, -0.0239105224609375, -0.37841796875, 0.164306640625, 0.20263671875, -0.2890625, -0.427490234375, 0.1480712890625, -0.0565185546875, 0.9443359375, -0.332763671875, 0.88623046875, -0.494873046875, -0.56640625, -0.07647705078125, -0.348388671875, 0.0095062255859375, -0.326416015625, -0.2890625, 0.7900390625, 0.58251953125, 1.2177734375, 1.01171875, -0.30859375, 0.488037109375, 0.3271484375, -0.388671875, 0.302978515625, 0.24755859375, 0.7841796875, -0.259765625, 0.2117919921875, 0.0574951171875, -0.332275390625, -0.95849609375, -0.6884765625, 0.07781982421875, 0.68310546875, -0.42138671875, 0.0243377685546875, 0.2587890625, 0.1312255859375, -0.78857421875, -0.29296875, -0.19873046875, -1.037109375, -0.71240234375, 0.6123046875, -0.22021484375, 0.47509765625, -0.5244140625, -0.51318359375, 0.353515625, 1.0546875, -0.023681640625, 0.265869140625, 0.367431640625, -0.1817626953125, -0.07452392578125, 0.22021484375, -0.0762939453125, -0.216796875, -0.5703125, 0.9970703125, -0.183837890625, -0.05364990234375, 0.039794921875, 1.0126953125, 0.54248046875, 0.63720703125, -0.35205078125, -0.2418212890625, 0.22216796875, 1.2421875, 0.11151123046875, 0.378173828125, 0.340576171875, 1.0107421875, 0.78173828125, 0.5888671875, 0.424560546875, 0.73046875, 0.740234375, 0.74951171875, 0.193359375, 0.160888671875, -0.09515380859375, 0.3701171875, 0.1937255859375, 0.61572265625, 0.417236328125, 0.283935546875, -0.09515380859375, 0.141845703125, -0.463134765625, 0.5517578125, -0.1357421875, 0.849609375, 0.104736328125, 0.65771484375, -0.59130859375, -0.55810546875, 0.110107421875, 0.71533203125, -1.021484375, -0.337890625, -0.1627197265625, -0.048736572265625, -0.0894775390625, 0.025482177734375, 0.348876953125, 0.453125, 0.310791015625, 0.65185546875, -0.1015625, -0.2431640625, -0.982421875, -0.68798828125, -1.0859375, -0.0877685546875, -0.5888671875, 0.11090087890625, 0.290771484375, -0.884765625, 0.1962890625, -0.623046875, -0.384765625, 0.376708984375, -0.55908203125, 0.4521484375, -0.064208984375, 0.335205078125, -0.83203125, 0.480712890625, 0.1065673828125, 1.2861328125, -0.58935546875, -0.13037109375, -0.1368408203125, -0.6279296875, 0.3154296875, -0.143310546875, 0.0264434814453125, -0.037078857421875, -0.6982421875, -0.94970703125, -0.460693359375, -0.04254150390625, -0.264404296875, -0.08319091796875, -0.51953125, 0.93212890625, 0.5751953125, -0.658203125, 0.6162109375, 0.763671875, -0.970703125, 0.3193359375, 0.411865234375, -0.0784912109375, -0.93212890625, 1.3671875, 0.492431640625, 0.207763671875, -0.407958984375, -0.476806640625, -0.312744140625, -0.0296783447265625, 0.0623779296875, -0.422607421875, -0.064697265625, 0.74462890625, -0.0322265625, -1.150390625, 0.27978515625, -0.6171875, -0.2279052734375, -0.238037109375, -0.2320556640625, 0.8154296875, 0.80029296875, 0.2958984375, 0.12274169921875, -0.0802001953125, 0.0051727294921875, 0.494140625, 0.3271484375, -0.290283203125, -0.204345703125, 0.89892578125, 0.19970703125, 0.218994140625, -0.03912353515625, -0.10382080078125, -0.07049560546875, 0.240234375, 0.0819091796875, 0.9306640625, 0.177978515625, 0.54638671875, 0.15234375, 0.8271484375, -0.837890625, -0.384033203125, 0.006099700927734375, 0.55029296875, 0.66748046875, 0.3603515625, 0.60888671875, -0.1573486328125, -0.293212890625, -1.4248046875, 0.34375, 0.006900787353515625, 0.91064453125, -0.6298828125, 1.1259765625, 0.169921875, -0.339111328125, 0.85595703125, -0.68408203125, -0.1468505859375, 0.91357421875, -0.0772705078125, 0.681640625, -0.3974609375, 0.14453125, -0.1826171875, -0.11712646484375, 0.54345703125, 0.70849609375, 0.89697265625, -0.46875, -0.5625, -0.33740234375, -0.2071533203125, -0.00873565673828125, -0.289794921875, 0.146240234375, -0.23095703125, -0.11016845703125, -0.8369140625, 0.08660888671875, 0.6650390625, 0.90771484375, -0.03424072265625, 0.2115478515625, 0.52880859375, 0.44482421875, 1.064453125, -0.4970703125, 0.264404296875, -0.72314453125, 0.7216796875, 0.0182037353515625, -0.2196044921875, -0.8369140625, -0.3642578125, -0.200439453125, 0.120849609375, -0.047760009765625, -0.377197265625, -1.2216796875, 0.353759765625, -0.5625, 0.58447265625, -0.72265625, 0.1162109375, -0.6103515625, 0.302734375, 0.150390625, -0.93798828125, -0.0765380859375, -0.491455078125, 0.45166015625, 0.216552734375, -0.2296142578125, -0.42138671875, -0.7607421875, -0.449462890625, -0.8779296875, 0.6005859375, 1.0185546875, 0.031463623046875, 0.218505859375, -1.431640625, 0.5263671875, 0.48095703125, -0.57275390625, 0.099365234375, -0.1356201171875, 0.6689453125, 0.3388671875, 0.8291015625, -0.313232421875, -0.69287109375, -0.12298583984375, -1.291015625, 0.252197265625, -0.40576171875, 0.69091796875, 0.034912109375, -0.125732421875, -0.086669921875, 0.1697998046875, 0.131103515625, 0.409912109375, -0.379638671875, 0.254638671875, -0.8330078125, -0.85498046875, 0.6767578125, -0.405029296875, -0.41064453125, 1.236328125, -0.09515380859375, -0.176513671875, 0.3349609375, 0.66552734375, -0.3310546875, 0.57470703125, -0.488525390625, 0.2247314453125, -0.52734375, -0.320556640625, -0.425048828125, -0.3759765625, 0.8916015625, 0.1551513671875, -0.60546875, -0.08331298828125, -1.009765625, -0.327880859375, 0.14404296875, -0.3505859375, 0.23828125, -0.2183837890625, -0.06781005859375, -0.283203125, -0.12078857421875, -0.63818359375, -0.223388671875, -0.546875, -0.5263671875, 0.319580078125, 0.33056640625, 0.796875, 0.357666015625, -0.392822265625, -0.0333251953125, -0.032806396484375, 0.159423828125, -0.38525390625, -0.284423828125, -0.44970703125, -0.257568359375, -0.369384765625, 0.01800537109375, 0.4140625, 0.11773681640625, 0.4296875, 0.34716796875, 0.5390625, 0.466552734375, -0.70068359375, 0.890625, 0.242919921875, -0.87109375, -0.061981201171875, 0.5693359375, -0.0858154296875, 0.6728515625, -0.0105133056640625, -0.90625, -0.7451171875, -0.78369140625, 0.38623046875, -0.54931640625, -0.1771240234375, -1.0908203125, -0.263671875, -0.5166015625, 0.67041015625, -0.04522705078125, -0.345703125, 0.16748046875, -1.380859375, -0.31884765625, -0.69287109375, -0.286865234375, -0.9189453125, -0.281982421875, -0.352783203125, 0.73193359375, -0.1893310546875, 0.39990234375, -0.16796875, 0.099365234375, 0.29150390625, 0.3466796875, -0.466796875, -0.37890625, -0.307861328125, 0.2318115234375, -0.1715087890625, -0.07537841796875, -0.7890625, 0.72705078125, -0.89501953125, 0.269775390625, -0.2376708984375, 0.09637451171875, -0.32275390625, -0.302001953125, 1.1162109375, -0.36083984375, -0.3974609375, -0.1685791015625, 0.191650390625, 0.67138671875, -0.483642578125, -0.272216796875, -1.17578125, -0.48193359375, -0.89599609375, 0.56298828125, -0.2352294921875, -0.1217041015625, -0.49169921875, -0.60498046875, 1.08984375, -0.490478515625, 0.2216796875, 1.09765625, -0.0033664703369140625, 0.1920166015625, -0.75146484375, 0.6630859375, 0.7099609375, -0.64892578125, 0.104736328125, 0.1851806640625, -0.76220703125, 0.1785888671875, -0.371826171875, -1.0478515625, -0.431396484375, 0.51611328125, 1.0830078125, -0.353759765625, 0.60498046875, 0.1273193359375, -1.212890625, -0.5361328125, 1.255859375, 0.43310546875, 0.08447265625, 0.79150390625, -0.022796630859375, 0.023681640625, -0.3037109375, -0.7490234375, -0.2177734375, -0.54833984375, 1.400390625, -0.669921875, -0.470703125, 1.1025390625, 0.89990234375, -1.55078125, -0.87890625, 0.001617431640625, 0.2041015625, 0.08905029296875, -0.80810546875, -0.036468505859375, 0.492919921875, -0.5107421875, -0.1708984375, 0.173095703125, -0.034637451171875, 0.37255859375, 0.1270751953125, 0.67724609375, -0.66064453125, 0.52001953125, 0.93603515625, -0.435302734375, -0.239013671875, -0.7880859375, -0.35302734375, -0.4482421875, 0.06890869140625, 0.92626953125, -0.30322265625, -0.0751953125, 0.55029296875, -0.146484375, 0.99951171875, -0.501953125, 0.0233154296875, 0.400146484375, -0.65576171875, -0.51904296875, -0.07794189453125, 0.1239013671875, 0.0216217041015625, 0.63134765625, -0.927734375, 0.026458740234375, -0.061492919921875, 0.169677734375, -0.537109375, -0.65625, -0.3359375, -1.0595703125, -0.480224609375, -0.85986328125, -0.93603515625, -0.3720703125, 0.2685546875, 0.251220703125, -0.529296875, 0.030609130859375, 0.62890625, -0.57958984375, 1.1484375, -0.755859375, 0.332763671875, -0.1290283203125, -0.08819580078125, -0.54345703125, 0.0877685546875, -0.59619140625, 0.24072265625, -0.9853515625, 0.10003662109375, 0.11767578125, 0.68310546875, -0.12420654296875, 0.86572265625, -0.289306640625, -0.42236328125, 0.41748046875, -0.1845703125, -0.128173828125, 1.05859375, 0.458740234375, -0.052093505859375, 0.153564453125, -0.2420654296875, -0.317138671875, -0.5361328125, 0.09454345703125, 0.37451171875, -0.2249755859375, -0.11468505859375, -0.26318359375, 0.448974609375, -1.19140625, 0.35791015625, -0.335693359375, -0.09747314453125, -0.12353515625, -0.08770751953125, 0.57763671875, 1.15625, -0.428955078125, 0.190673828125, -0.2095947265625, 0.1287841796875, 0.291748046875, 0.1778564453125, -0.431884765625, 0.7255859375, 0.36474609375, -0.72314453125, -0.0867919921875, 0.15576171875, 0.25341796875, 0.436767578125, -0.3193359375, -0.85107421875, -1.0126953125, -0.26318359375, 0.123291015625, 0.2320556640625, 0.53125, -0.44140625, -0.38330078125, -0.322998046875, -0.697265625, 0.419677734375, -1.0283203125, -1.1669921875, 0.4970703125, 0.040283203125, -0.5625, -0.00664520263671875, -0.43896484375, -0.3349609375, -0.045166015625, 0.2236328125, -0.6572265625, 0.66845703125, -0.2374267578125, 0.35107421875, 0.02777099609375, -0.25, -0.04473876953125, 0.837890625, -0.734375, -0.45361328125, -0.28662109375, 0.8232421875, 0.1490478515625, -0.280517578125, -0.58544921875, 0.1707763671875, 0.424560546875, 0.083251953125, -0.53125, -0.047210693359375, -0.345947265625, 0.79345703125, -1.109375, 0.08123779296875, 0.10418701171875, 0.55810546875, 0.24951171875, -0.07257080078125, -0.367431640625, 0.87890625, 0.87060546875, 0.1217041015625, 0.86865234375, 0.1444091796875, 0.580078125, 0.2166748046875, 0.005584716796875, -0.365966796875, 0.75244140625, 0.75830078125, 0.8740234375, -0.194091796875, 0.14404296875, 0.7509765625, 0.335205078125, -0.44921875, 0.666015625, -0.0601806640625, -0.01453399658203125, -0.1422119140625, -0.202880859375, 0.007274627685546875, 0.0743408203125, -0.49267578125, 0.58642578125, -0.98291015625, -0.268798828125, -0.344482421875, -0.51611328125, 0.79443359375, -0.08917236328125, 0.0299835205078125, -0.10174560546875, -0.35595703125, 0.409423828125, 0.25732421875, -0.357421875, -0.02886962890625, 1.1357421875, 0.480712890625, 0.1873779296875, 0.79248046875, 0.14306640625, 0.5390625, -0.56884765625, 0.115234375, 0.006275177001953125, -0.33642578125, -0.424560546875, -0.68505859375, -0.96630859375, 0.7451171875, -0.262939453125, -0.2115478515625, 0.81640625, -0.96044921875, 0.03619384765625, -0.3955078125, 0.66796875, -0.46923828125, 0.356201171875, 0.384521484375, -0.44189453125, -1.044921875, 0.9091796875, -0.19287109375, 0.3974609375, 0.190673828125, 0.82275390625, 0.1466064453125, 1.4306640625, 0.72705078125, -0.0009636878967285156, 0.2403564453125, 0.3935546875, -0.3505859375, -0.60400390625, -0.466796875, -0.1690673828125, 0.1466064453125, -0.59033203125, -0.39794921875, 0.0770263671875, 0.478271484375, 0.32763671875, -1.0380859375, -0.29931640625, 0.40087890625, -1.0234375, 0.65283203125, 0.375, 0.307861328125, 0.3134765625, -0.2822265625, -0.329833984375, -0.515625, 0.27734375, -0.80029296875, 0.4580078125, -0.76220703125, -0.56298828125, -0.471435546875, -0.55126953125, -0.1785888671875, -0.10223388671875, -0.281982421875, -0.83251953125, 0.671875, 0.35107421875, 0.303466796875, 0.328369140625, -0.440185546875, 0.316650390625, 0.8662109375, 0.77685546875, 0.023345947265625, 0.84716796875, 0.365478515625, 0.04595947265625, 0.2030029296875, -0.1290283203125, 0.4580078125, -0.414306640625, 0.3818359375, -0.56005859375, 0.341796875, -0.9052734375, -1.166015625, 0.0938720703125, 0.290771484375, 0.2313232421875, -0.463623046875, -1.048828125, -0.3203125, -0.8525390625, -0.198486328125, -0.7958984375, 0.79931640625, -0.403076171875, 0.070068359375, -0.00281524658203125, -1.283203125, 4.2421875, 1.0029296875, 0.806640625, 0.299072265625, 0.1961669921875, 0.7861328125, 0.1798095703125, -0.7490234375, -0.1011962890625, -0.2880859375, 0.5654296875, -0.52734375, -0.0955810546875, 0.828125, 0.69287109375, 0.61474609375, -0.55419921875, -0.15771484375, 0.080810546875, -0.8681640625, -0.84326171875, 0.42431640625, 0.007404327392578125, 0.285400390625, 0.0712890625, 0.1668701171875, 0.57421875, -0.76611328125, -0.063232421875, -0.7939453125, 0.2230224609375, -0.56982421875, 0.96923828125, 0.1729736328125, -0.2137451171875, 0.66259765625, 0.1268310546875, -0.11468505859375, 0.07000732421875, 0.2177734375, -0.3173828125, -0.18359375, 0.496337890625, -0.7236328125, -0.300537109375, 0.3310546875, -0.63037109375, 0.3681640625, -0.01377105712890625, -0.9853515625, 1.0087890625, -0.2685546875, 0.1612548828125, -0.671875, -0.81982421875, -0.138671875, -0.044097900390625, -0.398193359375, -0.09259033203125, 0.423583984375, 0.59423828125, 0.630859375, 0.1700439453125, 0.6923828125, -1.5341796875, 0.63818359375, -0.058502197265625, 0.58935546875, -0.65185546875, 0.020965576171875, -0.5146484375, -0.374755859375, -0.260009765625, -0.383544921875, 0.84521484375, 0.1268310546875, -0.1971435546875, 1.029296875, 0.8369140625, -0.424560546875, 0.3046875, -0.137451171875, -0.288818359375, -0.51513671875, 1.123046875, 1.484375, -0.86962890625, -0.290283203125, -0.1295166015625, 0.47998046875, 0.255126953125, 0.77783203125, 0.310791015625, -0.473876953125, -0.4423828125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Tags: bitmasks, brute force, hashing, string suffix structures, strings, two pointers Correct Solution: ``` import sys input = sys.stdin.readline a = int(input()) for case in range(a): n, k0 = [int(x) for x in input().split(' ')] start_inds = set([i for i in range(n-k0+1)]) s = input() k = min(20, k0) if k < k0: next_0 = [] curr_0 = n for i in range(n-1,-1,-1): if s[i] == '0': curr_0 = i next_0.append(curr_0) next_0.reverse() for i in range(n-k0+1): if next_0[i] < i + k0 - 20: start_inds.remove(i) Z = 1 << k avoid = set() for i in start_inds: r = int(s[i + k0 - k:i + k0], 2) avoid.add(Z - 1 - r) j = 0 while j in avoid and j < Z: j += 1 ans = bin(j)[2:] if j == Z: print("NO") else: print("YES") ans = '0' * (k0 - len(ans)) + ans print(ans) ```
107,240
[ 0.29541015625, -0.2432861328125, 0.1929931640625, 0.10858154296875, -0.342041015625, -0.495849609375, 0.12274169921875, 0.053955078125, -0.11297607421875, 0.537109375, 0.52392578125, -0.2119140625, -0.274169921875, -1.0546875, -0.6845703125, 0.0264739990234375, -0.351318359375, -0.38916015625, -0.364013671875, -0.297607421875, -0.09588623046875, -0.08154296875, -1.142578125, 0.05133056640625, -0.201904296875, 1.1103515625, 0.55859375, 0.04052734375, 1.197265625, 0.966796875, -0.5751953125, -0.49951171875, 0.54443359375, -1.142578125, -0.46044921875, -0.59228515625, 0.8232421875, -0.95458984375, -0.253173828125, -0.2783203125, 0.465576171875, -0.318359375, 0.5, -0.732421875, -1.365234375, 0.099609375, -0.058013916015625, -0.3017578125, -0.20166015625, -0.7890625, 0.0141143798828125, -0.316650390625, 0.2471923828125, -0.2000732421875, 0.03302001953125, 0.3076171875, 0.28173828125, -0.396484375, -0.31787109375, 0.60546875, -0.1971435546875, 0.353515625, 0.1466064453125, -0.6796875, -0.08258056640625, 0.1776123046875, -0.2247314453125, -0.44482421875, -0.1412353515625, -1.083984375, 0.066162109375, 0.0863037109375, -0.384033203125, -0.5771484375, -0.044036865234375, -0.0215911865234375, 0.09722900390625, -0.1658935546875, -0.444580078125, 0.62060546875, -0.1370849609375, 1.0322265625, 0.42919921875, 0.43505859375, -0.412841796875, -0.6904296875, 0.04266357421875, 0.221435546875, 0.35986328125, 0.076416015625, -0.20166015625, 0.460205078125, -0.6103515625, -0.1248779296875, 0.56396484375, 0.363037109375, 0.091552734375, 0.09161376953125, 0.27978515625, 0.289794921875, 0.62646484375, 1.037109375, -0.12274169921875, 1.328125, -0.9541015625, -0.106201171875, -0.26806640625, -0.0022869110107421875, -0.287841796875, -0.0228271484375, -0.12115478515625, -0.163818359375, 0.60107421875, 0.5146484375, -0.269287109375, 0.7646484375, -0.0189208984375, 0.5859375, -1.181640625, 0.318359375, 0.54736328125, 0.294677734375, 0.77099609375, -0.1480712890625, -0.0010004043579101562, -0.1942138671875, -0.51171875, 1.1337890625, -0.2919921875, -0.163818359375, 0.396240234375, -0.078369140625, -0.05316162109375, 0.058380126953125, 0.06353759765625, 0.4970703125, -0.0699462890625, 0.1951904296875, 0.81298828125, -0.50537109375, 0.6767578125, -0.46337890625, -0.265625, 1.5283203125, 0.414794921875, -0.13232421875, 1.09375, 0.217041015625, -0.8212890625, 0.66357421875, -0.994140625, 0.381591796875, -0.170654296875, 0.2239990234375, 0.1256103515625, -0.0239105224609375, -0.37841796875, 0.164306640625, 0.20263671875, -0.2890625, -0.427490234375, 0.1480712890625, -0.0565185546875, 0.9443359375, -0.332763671875, 0.88623046875, -0.494873046875, -0.56640625, -0.07647705078125, -0.348388671875, 0.0095062255859375, -0.326416015625, -0.2890625, 0.7900390625, 0.58251953125, 1.2177734375, 1.01171875, -0.30859375, 0.488037109375, 0.3271484375, -0.388671875, 0.302978515625, 0.24755859375, 0.7841796875, -0.259765625, 0.2117919921875, 0.0574951171875, -0.332275390625, -0.95849609375, -0.6884765625, 0.07781982421875, 0.68310546875, -0.42138671875, 0.0243377685546875, 0.2587890625, 0.1312255859375, -0.78857421875, -0.29296875, -0.19873046875, -1.037109375, -0.71240234375, 0.6123046875, -0.22021484375, 0.47509765625, -0.5244140625, -0.51318359375, 0.353515625, 1.0546875, -0.023681640625, 0.265869140625, 0.367431640625, -0.1817626953125, -0.07452392578125, 0.22021484375, -0.0762939453125, -0.216796875, -0.5703125, 0.9970703125, -0.183837890625, -0.05364990234375, 0.039794921875, 1.0126953125, 0.54248046875, 0.63720703125, -0.35205078125, -0.2418212890625, 0.22216796875, 1.2421875, 0.11151123046875, 0.378173828125, 0.340576171875, 1.0107421875, 0.78173828125, 0.5888671875, 0.424560546875, 0.73046875, 0.740234375, 0.74951171875, 0.193359375, 0.160888671875, -0.09515380859375, 0.3701171875, 0.1937255859375, 0.61572265625, 0.417236328125, 0.283935546875, -0.09515380859375, 0.141845703125, -0.463134765625, 0.5517578125, -0.1357421875, 0.849609375, 0.104736328125, 0.65771484375, -0.59130859375, -0.55810546875, 0.110107421875, 0.71533203125, -1.021484375, -0.337890625, -0.1627197265625, -0.048736572265625, -0.0894775390625, 0.025482177734375, 0.348876953125, 0.453125, 0.310791015625, 0.65185546875, -0.1015625, -0.2431640625, -0.982421875, -0.68798828125, -1.0859375, -0.0877685546875, -0.5888671875, 0.11090087890625, 0.290771484375, -0.884765625, 0.1962890625, -0.623046875, -0.384765625, 0.376708984375, -0.55908203125, 0.4521484375, -0.064208984375, 0.335205078125, -0.83203125, 0.480712890625, 0.1065673828125, 1.2861328125, -0.58935546875, -0.13037109375, -0.1368408203125, -0.6279296875, 0.3154296875, -0.143310546875, 0.0264434814453125, -0.037078857421875, -0.6982421875, -0.94970703125, -0.460693359375, -0.04254150390625, -0.264404296875, -0.08319091796875, -0.51953125, 0.93212890625, 0.5751953125, -0.658203125, 0.6162109375, 0.763671875, -0.970703125, 0.3193359375, 0.411865234375, -0.0784912109375, -0.93212890625, 1.3671875, 0.492431640625, 0.207763671875, -0.407958984375, -0.476806640625, -0.312744140625, -0.0296783447265625, 0.0623779296875, -0.422607421875, -0.064697265625, 0.74462890625, -0.0322265625, -1.150390625, 0.27978515625, -0.6171875, -0.2279052734375, -0.238037109375, -0.2320556640625, 0.8154296875, 0.80029296875, 0.2958984375, 0.12274169921875, -0.0802001953125, 0.0051727294921875, 0.494140625, 0.3271484375, -0.290283203125, -0.204345703125, 0.89892578125, 0.19970703125, 0.218994140625, -0.03912353515625, -0.10382080078125, -0.07049560546875, 0.240234375, 0.0819091796875, 0.9306640625, 0.177978515625, 0.54638671875, 0.15234375, 0.8271484375, -0.837890625, -0.384033203125, 0.006099700927734375, 0.55029296875, 0.66748046875, 0.3603515625, 0.60888671875, -0.1573486328125, -0.293212890625, -1.4248046875, 0.34375, 0.006900787353515625, 0.91064453125, -0.6298828125, 1.1259765625, 0.169921875, -0.339111328125, 0.85595703125, -0.68408203125, -0.1468505859375, 0.91357421875, -0.0772705078125, 0.681640625, -0.3974609375, 0.14453125, -0.1826171875, -0.11712646484375, 0.54345703125, 0.70849609375, 0.89697265625, -0.46875, -0.5625, -0.33740234375, -0.2071533203125, -0.00873565673828125, -0.289794921875, 0.146240234375, -0.23095703125, -0.11016845703125, -0.8369140625, 0.08660888671875, 0.6650390625, 0.90771484375, -0.03424072265625, 0.2115478515625, 0.52880859375, 0.44482421875, 1.064453125, -0.4970703125, 0.264404296875, -0.72314453125, 0.7216796875, 0.0182037353515625, -0.2196044921875, -0.8369140625, -0.3642578125, -0.200439453125, 0.120849609375, -0.047760009765625, -0.377197265625, -1.2216796875, 0.353759765625, -0.5625, 0.58447265625, -0.72265625, 0.1162109375, -0.6103515625, 0.302734375, 0.150390625, -0.93798828125, -0.0765380859375, -0.491455078125, 0.45166015625, 0.216552734375, -0.2296142578125, -0.42138671875, -0.7607421875, -0.449462890625, -0.8779296875, 0.6005859375, 1.0185546875, 0.031463623046875, 0.218505859375, -1.431640625, 0.5263671875, 0.48095703125, -0.57275390625, 0.099365234375, -0.1356201171875, 0.6689453125, 0.3388671875, 0.8291015625, -0.313232421875, -0.69287109375, -0.12298583984375, -1.291015625, 0.252197265625, -0.40576171875, 0.69091796875, 0.034912109375, -0.125732421875, -0.086669921875, 0.1697998046875, 0.131103515625, 0.409912109375, -0.379638671875, 0.254638671875, -0.8330078125, -0.85498046875, 0.6767578125, -0.405029296875, -0.41064453125, 1.236328125, -0.09515380859375, -0.176513671875, 0.3349609375, 0.66552734375, -0.3310546875, 0.57470703125, -0.488525390625, 0.2247314453125, -0.52734375, -0.320556640625, -0.425048828125, -0.3759765625, 0.8916015625, 0.1551513671875, -0.60546875, -0.08331298828125, -1.009765625, -0.327880859375, 0.14404296875, -0.3505859375, 0.23828125, -0.2183837890625, -0.06781005859375, -0.283203125, -0.12078857421875, -0.63818359375, -0.223388671875, -0.546875, -0.5263671875, 0.319580078125, 0.33056640625, 0.796875, 0.357666015625, -0.392822265625, -0.0333251953125, -0.032806396484375, 0.159423828125, -0.38525390625, -0.284423828125, -0.44970703125, -0.257568359375, -0.369384765625, 0.01800537109375, 0.4140625, 0.11773681640625, 0.4296875, 0.34716796875, 0.5390625, 0.466552734375, -0.70068359375, 0.890625, 0.242919921875, -0.87109375, -0.061981201171875, 0.5693359375, -0.0858154296875, 0.6728515625, -0.0105133056640625, -0.90625, -0.7451171875, -0.78369140625, 0.38623046875, -0.54931640625, -0.1771240234375, -1.0908203125, -0.263671875, -0.5166015625, 0.67041015625, -0.04522705078125, -0.345703125, 0.16748046875, -1.380859375, -0.31884765625, -0.69287109375, -0.286865234375, -0.9189453125, -0.281982421875, -0.352783203125, 0.73193359375, -0.1893310546875, 0.39990234375, -0.16796875, 0.099365234375, 0.29150390625, 0.3466796875, -0.466796875, -0.37890625, -0.307861328125, 0.2318115234375, -0.1715087890625, -0.07537841796875, -0.7890625, 0.72705078125, -0.89501953125, 0.269775390625, -0.2376708984375, 0.09637451171875, -0.32275390625, -0.302001953125, 1.1162109375, -0.36083984375, -0.3974609375, -0.1685791015625, 0.191650390625, 0.67138671875, -0.483642578125, -0.272216796875, -1.17578125, -0.48193359375, -0.89599609375, 0.56298828125, -0.2352294921875, -0.1217041015625, -0.49169921875, -0.60498046875, 1.08984375, -0.490478515625, 0.2216796875, 1.09765625, -0.0033664703369140625, 0.1920166015625, -0.75146484375, 0.6630859375, 0.7099609375, -0.64892578125, 0.104736328125, 0.1851806640625, -0.76220703125, 0.1785888671875, -0.371826171875, -1.0478515625, -0.431396484375, 0.51611328125, 1.0830078125, -0.353759765625, 0.60498046875, 0.1273193359375, -1.212890625, -0.5361328125, 1.255859375, 0.43310546875, 0.08447265625, 0.79150390625, -0.022796630859375, 0.023681640625, -0.3037109375, -0.7490234375, -0.2177734375, -0.54833984375, 1.400390625, -0.669921875, -0.470703125, 1.1025390625, 0.89990234375, -1.55078125, -0.87890625, 0.001617431640625, 0.2041015625, 0.08905029296875, -0.80810546875, -0.036468505859375, 0.492919921875, -0.5107421875, -0.1708984375, 0.173095703125, -0.034637451171875, 0.37255859375, 0.1270751953125, 0.67724609375, -0.66064453125, 0.52001953125, 0.93603515625, -0.435302734375, -0.239013671875, -0.7880859375, -0.35302734375, -0.4482421875, 0.06890869140625, 0.92626953125, -0.30322265625, -0.0751953125, 0.55029296875, -0.146484375, 0.99951171875, -0.501953125, 0.0233154296875, 0.400146484375, -0.65576171875, -0.51904296875, -0.07794189453125, 0.1239013671875, 0.0216217041015625, 0.63134765625, -0.927734375, 0.026458740234375, -0.061492919921875, 0.169677734375, -0.537109375, -0.65625, -0.3359375, -1.0595703125, -0.480224609375, -0.85986328125, -0.93603515625, -0.3720703125, 0.2685546875, 0.251220703125, -0.529296875, 0.030609130859375, 0.62890625, -0.57958984375, 1.1484375, -0.755859375, 0.332763671875, -0.1290283203125, -0.08819580078125, -0.54345703125, 0.0877685546875, -0.59619140625, 0.24072265625, -0.9853515625, 0.10003662109375, 0.11767578125, 0.68310546875, -0.12420654296875, 0.86572265625, -0.289306640625, -0.42236328125, 0.41748046875, -0.1845703125, -0.128173828125, 1.05859375, 0.458740234375, -0.052093505859375, 0.153564453125, -0.2420654296875, -0.317138671875, -0.5361328125, 0.09454345703125, 0.37451171875, -0.2249755859375, -0.11468505859375, -0.26318359375, 0.448974609375, -1.19140625, 0.35791015625, -0.335693359375, -0.09747314453125, -0.12353515625, -0.08770751953125, 0.57763671875, 1.15625, -0.428955078125, 0.190673828125, -0.2095947265625, 0.1287841796875, 0.291748046875, 0.1778564453125, -0.431884765625, 0.7255859375, 0.36474609375, -0.72314453125, -0.0867919921875, 0.15576171875, 0.25341796875, 0.436767578125, -0.3193359375, -0.85107421875, -1.0126953125, -0.26318359375, 0.123291015625, 0.2320556640625, 0.53125, -0.44140625, -0.38330078125, -0.322998046875, -0.697265625, 0.419677734375, -1.0283203125, -1.1669921875, 0.4970703125, 0.040283203125, -0.5625, -0.00664520263671875, -0.43896484375, -0.3349609375, -0.045166015625, 0.2236328125, -0.6572265625, 0.66845703125, -0.2374267578125, 0.35107421875, 0.02777099609375, -0.25, -0.04473876953125, 0.837890625, -0.734375, -0.45361328125, -0.28662109375, 0.8232421875, 0.1490478515625, -0.280517578125, -0.58544921875, 0.1707763671875, 0.424560546875, 0.083251953125, -0.53125, -0.047210693359375, -0.345947265625, 0.79345703125, -1.109375, 0.08123779296875, 0.10418701171875, 0.55810546875, 0.24951171875, -0.07257080078125, -0.367431640625, 0.87890625, 0.87060546875, 0.1217041015625, 0.86865234375, 0.1444091796875, 0.580078125, 0.2166748046875, 0.005584716796875, -0.365966796875, 0.75244140625, 0.75830078125, 0.8740234375, -0.194091796875, 0.14404296875, 0.7509765625, 0.335205078125, -0.44921875, 0.666015625, -0.0601806640625, -0.01453399658203125, -0.1422119140625, -0.202880859375, 0.007274627685546875, 0.0743408203125, -0.49267578125, 0.58642578125, -0.98291015625, -0.268798828125, -0.344482421875, -0.51611328125, 0.79443359375, -0.08917236328125, 0.0299835205078125, -0.10174560546875, -0.35595703125, 0.409423828125, 0.25732421875, -0.357421875, -0.02886962890625, 1.1357421875, 0.480712890625, 0.1873779296875, 0.79248046875, 0.14306640625, 0.5390625, -0.56884765625, 0.115234375, 0.006275177001953125, -0.33642578125, -0.424560546875, -0.68505859375, -0.96630859375, 0.7451171875, -0.262939453125, -0.2115478515625, 0.81640625, -0.96044921875, 0.03619384765625, -0.3955078125, 0.66796875, -0.46923828125, 0.356201171875, 0.384521484375, -0.44189453125, -1.044921875, 0.9091796875, -0.19287109375, 0.3974609375, 0.190673828125, 0.82275390625, 0.1466064453125, 1.4306640625, 0.72705078125, -0.0009636878967285156, 0.2403564453125, 0.3935546875, -0.3505859375, -0.60400390625, -0.466796875, -0.1690673828125, 0.1466064453125, -0.59033203125, -0.39794921875, 0.0770263671875, 0.478271484375, 0.32763671875, -1.0380859375, -0.29931640625, 0.40087890625, -1.0234375, 0.65283203125, 0.375, 0.307861328125, 0.3134765625, -0.2822265625, -0.329833984375, -0.515625, 0.27734375, -0.80029296875, 0.4580078125, -0.76220703125, -0.56298828125, -0.471435546875, -0.55126953125, -0.1785888671875, -0.10223388671875, -0.281982421875, -0.83251953125, 0.671875, 0.35107421875, 0.303466796875, 0.328369140625, -0.440185546875, 0.316650390625, 0.8662109375, 0.77685546875, 0.023345947265625, 0.84716796875, 0.365478515625, 0.04595947265625, 0.2030029296875, -0.1290283203125, 0.4580078125, -0.414306640625, 0.3818359375, -0.56005859375, 0.341796875, -0.9052734375, -1.166015625, 0.0938720703125, 0.290771484375, 0.2313232421875, -0.463623046875, -1.048828125, -0.3203125, -0.8525390625, -0.198486328125, -0.7958984375, 0.79931640625, -0.403076171875, 0.070068359375, -0.00281524658203125, -1.283203125, 4.2421875, 1.0029296875, 0.806640625, 0.299072265625, 0.1961669921875, 0.7861328125, 0.1798095703125, -0.7490234375, -0.1011962890625, -0.2880859375, 0.5654296875, -0.52734375, -0.0955810546875, 0.828125, 0.69287109375, 0.61474609375, -0.55419921875, -0.15771484375, 0.080810546875, -0.8681640625, -0.84326171875, 0.42431640625, 0.007404327392578125, 0.285400390625, 0.0712890625, 0.1668701171875, 0.57421875, -0.76611328125, -0.063232421875, -0.7939453125, 0.2230224609375, -0.56982421875, 0.96923828125, 0.1729736328125, -0.2137451171875, 0.66259765625, 0.1268310546875, -0.11468505859375, 0.07000732421875, 0.2177734375, -0.3173828125, -0.18359375, 0.496337890625, -0.7236328125, -0.300537109375, 0.3310546875, -0.63037109375, 0.3681640625, -0.01377105712890625, -0.9853515625, 1.0087890625, -0.2685546875, 0.1612548828125, -0.671875, -0.81982421875, -0.138671875, -0.044097900390625, -0.398193359375, -0.09259033203125, 0.423583984375, 0.59423828125, 0.630859375, 0.1700439453125, 0.6923828125, -1.5341796875, 0.63818359375, -0.058502197265625, 0.58935546875, -0.65185546875, 0.020965576171875, -0.5146484375, -0.374755859375, -0.260009765625, -0.383544921875, 0.84521484375, 0.1268310546875, -0.1971435546875, 1.029296875, 0.8369140625, -0.424560546875, 0.3046875, -0.137451171875, -0.288818359375, -0.51513671875, 1.123046875, 1.484375, -0.86962890625, -0.290283203125, -0.1295166015625, 0.47998046875, 0.255126953125, 0.77783203125, 0.310791015625, -0.473876953125, -0.4423828125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Tags: bitmasks, brute force, hashing, string suffix structures, strings, two pointers Correct Solution: ``` import sys input = sys.stdin.readline t = int(input()) for case in range(t): n, k0 = [int(x) for x in input().split(' ')] starts = set([i for i in range(n - k0 + 1)]) s = input() k = min(20, k0) if k < k0: nz = [] cz = n for i in range(n - 1, -1, -1): if s[i] == '0': cz = i nz.append(cz) nz.reverse() for i in range(n - k0 + 1): if nz[i] < i + k0 - 20: starts.remove(i) Z = 1 << k avoid = set() for i in starts: r = int(s[i + k0 - k:i + k0], 2) avoid.add(Z - 1 - r) j = 0 while j in avoid and j < Z: j += 1 ans = bin(j)[2:] if j == Z: print("NO") else: print("YES") ans = '0' * (k0 - len(ans)) + ans print(ans) ```
107,241
[ 0.29541015625, -0.2432861328125, 0.1929931640625, 0.10858154296875, -0.342041015625, -0.495849609375, 0.12274169921875, 0.053955078125, -0.11297607421875, 0.537109375, 0.52392578125, -0.2119140625, -0.274169921875, -1.0546875, -0.6845703125, 0.0264739990234375, -0.351318359375, -0.38916015625, -0.364013671875, -0.297607421875, -0.09588623046875, -0.08154296875, -1.142578125, 0.05133056640625, -0.201904296875, 1.1103515625, 0.55859375, 0.04052734375, 1.197265625, 0.966796875, -0.5751953125, -0.49951171875, 0.54443359375, -1.142578125, -0.46044921875, -0.59228515625, 0.8232421875, -0.95458984375, -0.253173828125, -0.2783203125, 0.465576171875, -0.318359375, 0.5, -0.732421875, -1.365234375, 0.099609375, -0.058013916015625, -0.3017578125, -0.20166015625, -0.7890625, 0.0141143798828125, -0.316650390625, 0.2471923828125, -0.2000732421875, 0.03302001953125, 0.3076171875, 0.28173828125, -0.396484375, -0.31787109375, 0.60546875, -0.1971435546875, 0.353515625, 0.1466064453125, -0.6796875, -0.08258056640625, 0.1776123046875, -0.2247314453125, -0.44482421875, -0.1412353515625, -1.083984375, 0.066162109375, 0.0863037109375, -0.384033203125, -0.5771484375, -0.044036865234375, -0.0215911865234375, 0.09722900390625, -0.1658935546875, -0.444580078125, 0.62060546875, -0.1370849609375, 1.0322265625, 0.42919921875, 0.43505859375, -0.412841796875, -0.6904296875, 0.04266357421875, 0.221435546875, 0.35986328125, 0.076416015625, -0.20166015625, 0.460205078125, -0.6103515625, -0.1248779296875, 0.56396484375, 0.363037109375, 0.091552734375, 0.09161376953125, 0.27978515625, 0.289794921875, 0.62646484375, 1.037109375, -0.12274169921875, 1.328125, -0.9541015625, -0.106201171875, -0.26806640625, -0.0022869110107421875, -0.287841796875, -0.0228271484375, -0.12115478515625, -0.163818359375, 0.60107421875, 0.5146484375, -0.269287109375, 0.7646484375, -0.0189208984375, 0.5859375, -1.181640625, 0.318359375, 0.54736328125, 0.294677734375, 0.77099609375, -0.1480712890625, -0.0010004043579101562, -0.1942138671875, -0.51171875, 1.1337890625, -0.2919921875, -0.163818359375, 0.396240234375, -0.078369140625, -0.05316162109375, 0.058380126953125, 0.06353759765625, 0.4970703125, -0.0699462890625, 0.1951904296875, 0.81298828125, -0.50537109375, 0.6767578125, -0.46337890625, -0.265625, 1.5283203125, 0.414794921875, -0.13232421875, 1.09375, 0.217041015625, -0.8212890625, 0.66357421875, -0.994140625, 0.381591796875, -0.170654296875, 0.2239990234375, 0.1256103515625, -0.0239105224609375, -0.37841796875, 0.164306640625, 0.20263671875, -0.2890625, -0.427490234375, 0.1480712890625, -0.0565185546875, 0.9443359375, -0.332763671875, 0.88623046875, -0.494873046875, -0.56640625, -0.07647705078125, -0.348388671875, 0.0095062255859375, -0.326416015625, -0.2890625, 0.7900390625, 0.58251953125, 1.2177734375, 1.01171875, -0.30859375, 0.488037109375, 0.3271484375, -0.388671875, 0.302978515625, 0.24755859375, 0.7841796875, -0.259765625, 0.2117919921875, 0.0574951171875, -0.332275390625, -0.95849609375, -0.6884765625, 0.07781982421875, 0.68310546875, -0.42138671875, 0.0243377685546875, 0.2587890625, 0.1312255859375, -0.78857421875, -0.29296875, -0.19873046875, -1.037109375, -0.71240234375, 0.6123046875, -0.22021484375, 0.47509765625, -0.5244140625, -0.51318359375, 0.353515625, 1.0546875, -0.023681640625, 0.265869140625, 0.367431640625, -0.1817626953125, -0.07452392578125, 0.22021484375, -0.0762939453125, -0.216796875, -0.5703125, 0.9970703125, -0.183837890625, -0.05364990234375, 0.039794921875, 1.0126953125, 0.54248046875, 0.63720703125, -0.35205078125, -0.2418212890625, 0.22216796875, 1.2421875, 0.11151123046875, 0.378173828125, 0.340576171875, 1.0107421875, 0.78173828125, 0.5888671875, 0.424560546875, 0.73046875, 0.740234375, 0.74951171875, 0.193359375, 0.160888671875, -0.09515380859375, 0.3701171875, 0.1937255859375, 0.61572265625, 0.417236328125, 0.283935546875, -0.09515380859375, 0.141845703125, -0.463134765625, 0.5517578125, -0.1357421875, 0.849609375, 0.104736328125, 0.65771484375, -0.59130859375, -0.55810546875, 0.110107421875, 0.71533203125, -1.021484375, -0.337890625, -0.1627197265625, -0.048736572265625, -0.0894775390625, 0.025482177734375, 0.348876953125, 0.453125, 0.310791015625, 0.65185546875, -0.1015625, -0.2431640625, -0.982421875, -0.68798828125, -1.0859375, -0.0877685546875, -0.5888671875, 0.11090087890625, 0.290771484375, -0.884765625, 0.1962890625, -0.623046875, -0.384765625, 0.376708984375, -0.55908203125, 0.4521484375, -0.064208984375, 0.335205078125, -0.83203125, 0.480712890625, 0.1065673828125, 1.2861328125, -0.58935546875, -0.13037109375, -0.1368408203125, -0.6279296875, 0.3154296875, -0.143310546875, 0.0264434814453125, -0.037078857421875, -0.6982421875, -0.94970703125, -0.460693359375, -0.04254150390625, -0.264404296875, -0.08319091796875, -0.51953125, 0.93212890625, 0.5751953125, -0.658203125, 0.6162109375, 0.763671875, -0.970703125, 0.3193359375, 0.411865234375, -0.0784912109375, -0.93212890625, 1.3671875, 0.492431640625, 0.207763671875, -0.407958984375, -0.476806640625, -0.312744140625, -0.0296783447265625, 0.0623779296875, -0.422607421875, -0.064697265625, 0.74462890625, -0.0322265625, -1.150390625, 0.27978515625, -0.6171875, -0.2279052734375, -0.238037109375, -0.2320556640625, 0.8154296875, 0.80029296875, 0.2958984375, 0.12274169921875, -0.0802001953125, 0.0051727294921875, 0.494140625, 0.3271484375, -0.290283203125, -0.204345703125, 0.89892578125, 0.19970703125, 0.218994140625, -0.03912353515625, -0.10382080078125, -0.07049560546875, 0.240234375, 0.0819091796875, 0.9306640625, 0.177978515625, 0.54638671875, 0.15234375, 0.8271484375, -0.837890625, -0.384033203125, 0.006099700927734375, 0.55029296875, 0.66748046875, 0.3603515625, 0.60888671875, -0.1573486328125, -0.293212890625, -1.4248046875, 0.34375, 0.006900787353515625, 0.91064453125, -0.6298828125, 1.1259765625, 0.169921875, -0.339111328125, 0.85595703125, -0.68408203125, -0.1468505859375, 0.91357421875, -0.0772705078125, 0.681640625, -0.3974609375, 0.14453125, -0.1826171875, -0.11712646484375, 0.54345703125, 0.70849609375, 0.89697265625, -0.46875, -0.5625, -0.33740234375, -0.2071533203125, -0.00873565673828125, -0.289794921875, 0.146240234375, -0.23095703125, -0.11016845703125, -0.8369140625, 0.08660888671875, 0.6650390625, 0.90771484375, -0.03424072265625, 0.2115478515625, 0.52880859375, 0.44482421875, 1.064453125, -0.4970703125, 0.264404296875, -0.72314453125, 0.7216796875, 0.0182037353515625, -0.2196044921875, -0.8369140625, -0.3642578125, -0.200439453125, 0.120849609375, -0.047760009765625, -0.377197265625, -1.2216796875, 0.353759765625, -0.5625, 0.58447265625, -0.72265625, 0.1162109375, -0.6103515625, 0.302734375, 0.150390625, -0.93798828125, -0.0765380859375, -0.491455078125, 0.45166015625, 0.216552734375, -0.2296142578125, -0.42138671875, -0.7607421875, -0.449462890625, -0.8779296875, 0.6005859375, 1.0185546875, 0.031463623046875, 0.218505859375, -1.431640625, 0.5263671875, 0.48095703125, -0.57275390625, 0.099365234375, -0.1356201171875, 0.6689453125, 0.3388671875, 0.8291015625, -0.313232421875, -0.69287109375, -0.12298583984375, -1.291015625, 0.252197265625, -0.40576171875, 0.69091796875, 0.034912109375, -0.125732421875, -0.086669921875, 0.1697998046875, 0.131103515625, 0.409912109375, -0.379638671875, 0.254638671875, -0.8330078125, -0.85498046875, 0.6767578125, -0.405029296875, -0.41064453125, 1.236328125, -0.09515380859375, -0.176513671875, 0.3349609375, 0.66552734375, -0.3310546875, 0.57470703125, -0.488525390625, 0.2247314453125, -0.52734375, -0.320556640625, -0.425048828125, -0.3759765625, 0.8916015625, 0.1551513671875, -0.60546875, -0.08331298828125, -1.009765625, -0.327880859375, 0.14404296875, -0.3505859375, 0.23828125, -0.2183837890625, -0.06781005859375, -0.283203125, -0.12078857421875, -0.63818359375, -0.223388671875, -0.546875, -0.5263671875, 0.319580078125, 0.33056640625, 0.796875, 0.357666015625, -0.392822265625, -0.0333251953125, -0.032806396484375, 0.159423828125, -0.38525390625, -0.284423828125, -0.44970703125, -0.257568359375, -0.369384765625, 0.01800537109375, 0.4140625, 0.11773681640625, 0.4296875, 0.34716796875, 0.5390625, 0.466552734375, -0.70068359375, 0.890625, 0.242919921875, -0.87109375, -0.061981201171875, 0.5693359375, -0.0858154296875, 0.6728515625, -0.0105133056640625, -0.90625, -0.7451171875, -0.78369140625, 0.38623046875, -0.54931640625, -0.1771240234375, -1.0908203125, -0.263671875, -0.5166015625, 0.67041015625, -0.04522705078125, -0.345703125, 0.16748046875, -1.380859375, -0.31884765625, -0.69287109375, -0.286865234375, -0.9189453125, -0.281982421875, -0.352783203125, 0.73193359375, -0.1893310546875, 0.39990234375, -0.16796875, 0.099365234375, 0.29150390625, 0.3466796875, -0.466796875, -0.37890625, -0.307861328125, 0.2318115234375, -0.1715087890625, -0.07537841796875, -0.7890625, 0.72705078125, -0.89501953125, 0.269775390625, -0.2376708984375, 0.09637451171875, -0.32275390625, -0.302001953125, 1.1162109375, -0.36083984375, -0.3974609375, -0.1685791015625, 0.191650390625, 0.67138671875, -0.483642578125, -0.272216796875, -1.17578125, -0.48193359375, -0.89599609375, 0.56298828125, -0.2352294921875, -0.1217041015625, -0.49169921875, -0.60498046875, 1.08984375, -0.490478515625, 0.2216796875, 1.09765625, -0.0033664703369140625, 0.1920166015625, -0.75146484375, 0.6630859375, 0.7099609375, -0.64892578125, 0.104736328125, 0.1851806640625, -0.76220703125, 0.1785888671875, -0.371826171875, -1.0478515625, -0.431396484375, 0.51611328125, 1.0830078125, -0.353759765625, 0.60498046875, 0.1273193359375, -1.212890625, -0.5361328125, 1.255859375, 0.43310546875, 0.08447265625, 0.79150390625, -0.022796630859375, 0.023681640625, -0.3037109375, -0.7490234375, -0.2177734375, -0.54833984375, 1.400390625, -0.669921875, -0.470703125, 1.1025390625, 0.89990234375, -1.55078125, -0.87890625, 0.001617431640625, 0.2041015625, 0.08905029296875, -0.80810546875, -0.036468505859375, 0.492919921875, -0.5107421875, -0.1708984375, 0.173095703125, -0.034637451171875, 0.37255859375, 0.1270751953125, 0.67724609375, -0.66064453125, 0.52001953125, 0.93603515625, -0.435302734375, -0.239013671875, -0.7880859375, -0.35302734375, -0.4482421875, 0.06890869140625, 0.92626953125, -0.30322265625, -0.0751953125, 0.55029296875, -0.146484375, 0.99951171875, -0.501953125, 0.0233154296875, 0.400146484375, -0.65576171875, -0.51904296875, -0.07794189453125, 0.1239013671875, 0.0216217041015625, 0.63134765625, -0.927734375, 0.026458740234375, -0.061492919921875, 0.169677734375, -0.537109375, -0.65625, -0.3359375, -1.0595703125, -0.480224609375, -0.85986328125, -0.93603515625, -0.3720703125, 0.2685546875, 0.251220703125, -0.529296875, 0.030609130859375, 0.62890625, -0.57958984375, 1.1484375, -0.755859375, 0.332763671875, -0.1290283203125, -0.08819580078125, -0.54345703125, 0.0877685546875, -0.59619140625, 0.24072265625, -0.9853515625, 0.10003662109375, 0.11767578125, 0.68310546875, -0.12420654296875, 0.86572265625, -0.289306640625, -0.42236328125, 0.41748046875, -0.1845703125, -0.128173828125, 1.05859375, 0.458740234375, -0.052093505859375, 0.153564453125, -0.2420654296875, -0.317138671875, -0.5361328125, 0.09454345703125, 0.37451171875, -0.2249755859375, -0.11468505859375, -0.26318359375, 0.448974609375, -1.19140625, 0.35791015625, -0.335693359375, -0.09747314453125, -0.12353515625, -0.08770751953125, 0.57763671875, 1.15625, -0.428955078125, 0.190673828125, -0.2095947265625, 0.1287841796875, 0.291748046875, 0.1778564453125, -0.431884765625, 0.7255859375, 0.36474609375, -0.72314453125, -0.0867919921875, 0.15576171875, 0.25341796875, 0.436767578125, -0.3193359375, -0.85107421875, -1.0126953125, -0.26318359375, 0.123291015625, 0.2320556640625, 0.53125, -0.44140625, -0.38330078125, -0.322998046875, -0.697265625, 0.419677734375, -1.0283203125, -1.1669921875, 0.4970703125, 0.040283203125, -0.5625, -0.00664520263671875, -0.43896484375, -0.3349609375, -0.045166015625, 0.2236328125, -0.6572265625, 0.66845703125, -0.2374267578125, 0.35107421875, 0.02777099609375, -0.25, -0.04473876953125, 0.837890625, -0.734375, -0.45361328125, -0.28662109375, 0.8232421875, 0.1490478515625, -0.280517578125, -0.58544921875, 0.1707763671875, 0.424560546875, 0.083251953125, -0.53125, -0.047210693359375, -0.345947265625, 0.79345703125, -1.109375, 0.08123779296875, 0.10418701171875, 0.55810546875, 0.24951171875, -0.07257080078125, -0.367431640625, 0.87890625, 0.87060546875, 0.1217041015625, 0.86865234375, 0.1444091796875, 0.580078125, 0.2166748046875, 0.005584716796875, -0.365966796875, 0.75244140625, 0.75830078125, 0.8740234375, -0.194091796875, 0.14404296875, 0.7509765625, 0.335205078125, -0.44921875, 0.666015625, -0.0601806640625, -0.01453399658203125, -0.1422119140625, -0.202880859375, 0.007274627685546875, 0.0743408203125, -0.49267578125, 0.58642578125, -0.98291015625, -0.268798828125, -0.344482421875, -0.51611328125, 0.79443359375, -0.08917236328125, 0.0299835205078125, -0.10174560546875, -0.35595703125, 0.409423828125, 0.25732421875, -0.357421875, -0.02886962890625, 1.1357421875, 0.480712890625, 0.1873779296875, 0.79248046875, 0.14306640625, 0.5390625, -0.56884765625, 0.115234375, 0.006275177001953125, -0.33642578125, -0.424560546875, -0.68505859375, -0.96630859375, 0.7451171875, -0.262939453125, -0.2115478515625, 0.81640625, -0.96044921875, 0.03619384765625, -0.3955078125, 0.66796875, -0.46923828125, 0.356201171875, 0.384521484375, -0.44189453125, -1.044921875, 0.9091796875, -0.19287109375, 0.3974609375, 0.190673828125, 0.82275390625, 0.1466064453125, 1.4306640625, 0.72705078125, -0.0009636878967285156, 0.2403564453125, 0.3935546875, -0.3505859375, -0.60400390625, -0.466796875, -0.1690673828125, 0.1466064453125, -0.59033203125, -0.39794921875, 0.0770263671875, 0.478271484375, 0.32763671875, -1.0380859375, -0.29931640625, 0.40087890625, -1.0234375, 0.65283203125, 0.375, 0.307861328125, 0.3134765625, -0.2822265625, -0.329833984375, -0.515625, 0.27734375, -0.80029296875, 0.4580078125, -0.76220703125, -0.56298828125, -0.471435546875, -0.55126953125, -0.1785888671875, -0.10223388671875, -0.281982421875, -0.83251953125, 0.671875, 0.35107421875, 0.303466796875, 0.328369140625, -0.440185546875, 0.316650390625, 0.8662109375, 0.77685546875, 0.023345947265625, 0.84716796875, 0.365478515625, 0.04595947265625, 0.2030029296875, -0.1290283203125, 0.4580078125, -0.414306640625, 0.3818359375, -0.56005859375, 0.341796875, -0.9052734375, -1.166015625, 0.0938720703125, 0.290771484375, 0.2313232421875, -0.463623046875, -1.048828125, -0.3203125, -0.8525390625, -0.198486328125, -0.7958984375, 0.79931640625, -0.403076171875, 0.070068359375, -0.00281524658203125, -1.283203125, 4.2421875, 1.0029296875, 0.806640625, 0.299072265625, 0.1961669921875, 0.7861328125, 0.1798095703125, -0.7490234375, -0.1011962890625, -0.2880859375, 0.5654296875, -0.52734375, -0.0955810546875, 0.828125, 0.69287109375, 0.61474609375, -0.55419921875, -0.15771484375, 0.080810546875, -0.8681640625, -0.84326171875, 0.42431640625, 0.007404327392578125, 0.285400390625, 0.0712890625, 0.1668701171875, 0.57421875, -0.76611328125, -0.063232421875, -0.7939453125, 0.2230224609375, -0.56982421875, 0.96923828125, 0.1729736328125, -0.2137451171875, 0.66259765625, 0.1268310546875, -0.11468505859375, 0.07000732421875, 0.2177734375, -0.3173828125, -0.18359375, 0.496337890625, -0.7236328125, -0.300537109375, 0.3310546875, -0.63037109375, 0.3681640625, -0.01377105712890625, -0.9853515625, 1.0087890625, -0.2685546875, 0.1612548828125, -0.671875, -0.81982421875, -0.138671875, -0.044097900390625, -0.398193359375, -0.09259033203125, 0.423583984375, 0.59423828125, 0.630859375, 0.1700439453125, 0.6923828125, -1.5341796875, 0.63818359375, -0.058502197265625, 0.58935546875, -0.65185546875, 0.020965576171875, -0.5146484375, -0.374755859375, -0.260009765625, -0.383544921875, 0.84521484375, 0.1268310546875, -0.1971435546875, 1.029296875, 0.8369140625, -0.424560546875, 0.3046875, -0.137451171875, -0.288818359375, -0.51513671875, 1.123046875, 1.484375, -0.86962890625, -0.290283203125, -0.1295166015625, 0.47998046875, 0.255126953125, 0.77783203125, 0.310791015625, -0.473876953125, -0.4423828125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Tags: bitmasks, brute force, hashing, string suffix structures, strings, two pointers Correct Solution: ``` # Author: yumtam # Created at: 2020-12-30 16:53 def solve(): n, k = [int(t) for t in input().split()] A = [int(c) for c in input()] for i in range(n): A[i] = 1 - A[i] ctz = [] zeros = 0 for x in reversed(A): if x == 0: zeros += 1 else: zeros = 0 ctz.append(zeros) ctz = ctz[::-1] S = n - k + 1 L = S.bit_length() V = set() for i in range(n-k+1): if ctz[i] >= k - L: v = 0 d = 1 pos = i+k-1 for _ in range(min(L, k)): v += d * A[pos] pos -= 1 d *= 2 V.add(v) for ans in range(2**k): if ans not in V: print("YES") res = bin(ans)[2:] res = '0'*(k-len(res)) + res print(res) break else: print("NO") import sys, os, io input = lambda: sys.stdin.readline().rstrip('\r\n') stdout = io.BytesIO() sys.stdout.write = lambda s: stdout.write(s.encode("ascii")) for _ in range(int(input())): solve() os.write(1, stdout.getvalue()) ```
107,242
[ 0.29541015625, -0.2432861328125, 0.1929931640625, 0.10858154296875, -0.342041015625, -0.495849609375, 0.12274169921875, 0.053955078125, -0.11297607421875, 0.537109375, 0.52392578125, -0.2119140625, -0.274169921875, -1.0546875, -0.6845703125, 0.0264739990234375, -0.351318359375, -0.38916015625, -0.364013671875, -0.297607421875, -0.09588623046875, -0.08154296875, -1.142578125, 0.05133056640625, -0.201904296875, 1.1103515625, 0.55859375, 0.04052734375, 1.197265625, 0.966796875, -0.5751953125, -0.49951171875, 0.54443359375, -1.142578125, -0.46044921875, -0.59228515625, 0.8232421875, -0.95458984375, -0.253173828125, -0.2783203125, 0.465576171875, -0.318359375, 0.5, -0.732421875, -1.365234375, 0.099609375, -0.058013916015625, -0.3017578125, -0.20166015625, -0.7890625, 0.0141143798828125, -0.316650390625, 0.2471923828125, -0.2000732421875, 0.03302001953125, 0.3076171875, 0.28173828125, -0.396484375, -0.31787109375, 0.60546875, -0.1971435546875, 0.353515625, 0.1466064453125, -0.6796875, -0.08258056640625, 0.1776123046875, -0.2247314453125, -0.44482421875, -0.1412353515625, -1.083984375, 0.066162109375, 0.0863037109375, -0.384033203125, -0.5771484375, -0.044036865234375, -0.0215911865234375, 0.09722900390625, -0.1658935546875, -0.444580078125, 0.62060546875, -0.1370849609375, 1.0322265625, 0.42919921875, 0.43505859375, -0.412841796875, -0.6904296875, 0.04266357421875, 0.221435546875, 0.35986328125, 0.076416015625, -0.20166015625, 0.460205078125, -0.6103515625, -0.1248779296875, 0.56396484375, 0.363037109375, 0.091552734375, 0.09161376953125, 0.27978515625, 0.289794921875, 0.62646484375, 1.037109375, -0.12274169921875, 1.328125, -0.9541015625, -0.106201171875, -0.26806640625, -0.0022869110107421875, -0.287841796875, -0.0228271484375, -0.12115478515625, -0.163818359375, 0.60107421875, 0.5146484375, -0.269287109375, 0.7646484375, -0.0189208984375, 0.5859375, -1.181640625, 0.318359375, 0.54736328125, 0.294677734375, 0.77099609375, -0.1480712890625, -0.0010004043579101562, -0.1942138671875, -0.51171875, 1.1337890625, -0.2919921875, -0.163818359375, 0.396240234375, -0.078369140625, -0.05316162109375, 0.058380126953125, 0.06353759765625, 0.4970703125, -0.0699462890625, 0.1951904296875, 0.81298828125, -0.50537109375, 0.6767578125, -0.46337890625, -0.265625, 1.5283203125, 0.414794921875, -0.13232421875, 1.09375, 0.217041015625, -0.8212890625, 0.66357421875, -0.994140625, 0.381591796875, -0.170654296875, 0.2239990234375, 0.1256103515625, -0.0239105224609375, -0.37841796875, 0.164306640625, 0.20263671875, -0.2890625, -0.427490234375, 0.1480712890625, -0.0565185546875, 0.9443359375, -0.332763671875, 0.88623046875, -0.494873046875, -0.56640625, -0.07647705078125, -0.348388671875, 0.0095062255859375, -0.326416015625, -0.2890625, 0.7900390625, 0.58251953125, 1.2177734375, 1.01171875, -0.30859375, 0.488037109375, 0.3271484375, -0.388671875, 0.302978515625, 0.24755859375, 0.7841796875, -0.259765625, 0.2117919921875, 0.0574951171875, -0.332275390625, -0.95849609375, -0.6884765625, 0.07781982421875, 0.68310546875, -0.42138671875, 0.0243377685546875, 0.2587890625, 0.1312255859375, -0.78857421875, -0.29296875, -0.19873046875, -1.037109375, -0.71240234375, 0.6123046875, -0.22021484375, 0.47509765625, -0.5244140625, -0.51318359375, 0.353515625, 1.0546875, -0.023681640625, 0.265869140625, 0.367431640625, -0.1817626953125, -0.07452392578125, 0.22021484375, -0.0762939453125, -0.216796875, -0.5703125, 0.9970703125, -0.183837890625, -0.05364990234375, 0.039794921875, 1.0126953125, 0.54248046875, 0.63720703125, -0.35205078125, -0.2418212890625, 0.22216796875, 1.2421875, 0.11151123046875, 0.378173828125, 0.340576171875, 1.0107421875, 0.78173828125, 0.5888671875, 0.424560546875, 0.73046875, 0.740234375, 0.74951171875, 0.193359375, 0.160888671875, -0.09515380859375, 0.3701171875, 0.1937255859375, 0.61572265625, 0.417236328125, 0.283935546875, -0.09515380859375, 0.141845703125, -0.463134765625, 0.5517578125, -0.1357421875, 0.849609375, 0.104736328125, 0.65771484375, -0.59130859375, -0.55810546875, 0.110107421875, 0.71533203125, -1.021484375, -0.337890625, -0.1627197265625, -0.048736572265625, -0.0894775390625, 0.025482177734375, 0.348876953125, 0.453125, 0.310791015625, 0.65185546875, -0.1015625, -0.2431640625, -0.982421875, -0.68798828125, -1.0859375, -0.0877685546875, -0.5888671875, 0.11090087890625, 0.290771484375, -0.884765625, 0.1962890625, -0.623046875, -0.384765625, 0.376708984375, -0.55908203125, 0.4521484375, -0.064208984375, 0.335205078125, -0.83203125, 0.480712890625, 0.1065673828125, 1.2861328125, -0.58935546875, -0.13037109375, -0.1368408203125, -0.6279296875, 0.3154296875, -0.143310546875, 0.0264434814453125, -0.037078857421875, -0.6982421875, -0.94970703125, -0.460693359375, -0.04254150390625, -0.264404296875, -0.08319091796875, -0.51953125, 0.93212890625, 0.5751953125, -0.658203125, 0.6162109375, 0.763671875, -0.970703125, 0.3193359375, 0.411865234375, -0.0784912109375, -0.93212890625, 1.3671875, 0.492431640625, 0.207763671875, -0.407958984375, -0.476806640625, -0.312744140625, -0.0296783447265625, 0.0623779296875, -0.422607421875, -0.064697265625, 0.74462890625, -0.0322265625, -1.150390625, 0.27978515625, -0.6171875, -0.2279052734375, -0.238037109375, -0.2320556640625, 0.8154296875, 0.80029296875, 0.2958984375, 0.12274169921875, -0.0802001953125, 0.0051727294921875, 0.494140625, 0.3271484375, -0.290283203125, -0.204345703125, 0.89892578125, 0.19970703125, 0.218994140625, -0.03912353515625, -0.10382080078125, -0.07049560546875, 0.240234375, 0.0819091796875, 0.9306640625, 0.177978515625, 0.54638671875, 0.15234375, 0.8271484375, -0.837890625, -0.384033203125, 0.006099700927734375, 0.55029296875, 0.66748046875, 0.3603515625, 0.60888671875, -0.1573486328125, -0.293212890625, -1.4248046875, 0.34375, 0.006900787353515625, 0.91064453125, -0.6298828125, 1.1259765625, 0.169921875, -0.339111328125, 0.85595703125, -0.68408203125, -0.1468505859375, 0.91357421875, -0.0772705078125, 0.681640625, -0.3974609375, 0.14453125, -0.1826171875, -0.11712646484375, 0.54345703125, 0.70849609375, 0.89697265625, -0.46875, -0.5625, -0.33740234375, -0.2071533203125, -0.00873565673828125, -0.289794921875, 0.146240234375, -0.23095703125, -0.11016845703125, -0.8369140625, 0.08660888671875, 0.6650390625, 0.90771484375, -0.03424072265625, 0.2115478515625, 0.52880859375, 0.44482421875, 1.064453125, -0.4970703125, 0.264404296875, -0.72314453125, 0.7216796875, 0.0182037353515625, -0.2196044921875, -0.8369140625, -0.3642578125, -0.200439453125, 0.120849609375, -0.047760009765625, -0.377197265625, -1.2216796875, 0.353759765625, -0.5625, 0.58447265625, -0.72265625, 0.1162109375, -0.6103515625, 0.302734375, 0.150390625, -0.93798828125, -0.0765380859375, -0.491455078125, 0.45166015625, 0.216552734375, -0.2296142578125, -0.42138671875, -0.7607421875, -0.449462890625, -0.8779296875, 0.6005859375, 1.0185546875, 0.031463623046875, 0.218505859375, -1.431640625, 0.5263671875, 0.48095703125, -0.57275390625, 0.099365234375, -0.1356201171875, 0.6689453125, 0.3388671875, 0.8291015625, -0.313232421875, -0.69287109375, -0.12298583984375, -1.291015625, 0.252197265625, -0.40576171875, 0.69091796875, 0.034912109375, -0.125732421875, -0.086669921875, 0.1697998046875, 0.131103515625, 0.409912109375, -0.379638671875, 0.254638671875, -0.8330078125, -0.85498046875, 0.6767578125, -0.405029296875, -0.41064453125, 1.236328125, -0.09515380859375, -0.176513671875, 0.3349609375, 0.66552734375, -0.3310546875, 0.57470703125, -0.488525390625, 0.2247314453125, -0.52734375, -0.320556640625, -0.425048828125, -0.3759765625, 0.8916015625, 0.1551513671875, -0.60546875, -0.08331298828125, -1.009765625, -0.327880859375, 0.14404296875, -0.3505859375, 0.23828125, -0.2183837890625, -0.06781005859375, -0.283203125, -0.12078857421875, -0.63818359375, -0.223388671875, -0.546875, -0.5263671875, 0.319580078125, 0.33056640625, 0.796875, 0.357666015625, -0.392822265625, -0.0333251953125, -0.032806396484375, 0.159423828125, -0.38525390625, -0.284423828125, -0.44970703125, -0.257568359375, -0.369384765625, 0.01800537109375, 0.4140625, 0.11773681640625, 0.4296875, 0.34716796875, 0.5390625, 0.466552734375, -0.70068359375, 0.890625, 0.242919921875, -0.87109375, -0.061981201171875, 0.5693359375, -0.0858154296875, 0.6728515625, -0.0105133056640625, -0.90625, -0.7451171875, -0.78369140625, 0.38623046875, -0.54931640625, -0.1771240234375, -1.0908203125, -0.263671875, -0.5166015625, 0.67041015625, -0.04522705078125, -0.345703125, 0.16748046875, -1.380859375, -0.31884765625, -0.69287109375, -0.286865234375, -0.9189453125, -0.281982421875, -0.352783203125, 0.73193359375, -0.1893310546875, 0.39990234375, -0.16796875, 0.099365234375, 0.29150390625, 0.3466796875, -0.466796875, -0.37890625, -0.307861328125, 0.2318115234375, -0.1715087890625, -0.07537841796875, -0.7890625, 0.72705078125, -0.89501953125, 0.269775390625, -0.2376708984375, 0.09637451171875, -0.32275390625, -0.302001953125, 1.1162109375, -0.36083984375, -0.3974609375, -0.1685791015625, 0.191650390625, 0.67138671875, -0.483642578125, -0.272216796875, -1.17578125, -0.48193359375, -0.89599609375, 0.56298828125, -0.2352294921875, -0.1217041015625, -0.49169921875, -0.60498046875, 1.08984375, -0.490478515625, 0.2216796875, 1.09765625, -0.0033664703369140625, 0.1920166015625, -0.75146484375, 0.6630859375, 0.7099609375, -0.64892578125, 0.104736328125, 0.1851806640625, -0.76220703125, 0.1785888671875, -0.371826171875, -1.0478515625, -0.431396484375, 0.51611328125, 1.0830078125, -0.353759765625, 0.60498046875, 0.1273193359375, -1.212890625, -0.5361328125, 1.255859375, 0.43310546875, 0.08447265625, 0.79150390625, -0.022796630859375, 0.023681640625, -0.3037109375, -0.7490234375, -0.2177734375, -0.54833984375, 1.400390625, -0.669921875, -0.470703125, 1.1025390625, 0.89990234375, -1.55078125, -0.87890625, 0.001617431640625, 0.2041015625, 0.08905029296875, -0.80810546875, -0.036468505859375, 0.492919921875, -0.5107421875, -0.1708984375, 0.173095703125, -0.034637451171875, 0.37255859375, 0.1270751953125, 0.67724609375, -0.66064453125, 0.52001953125, 0.93603515625, -0.435302734375, -0.239013671875, -0.7880859375, -0.35302734375, -0.4482421875, 0.06890869140625, 0.92626953125, -0.30322265625, -0.0751953125, 0.55029296875, -0.146484375, 0.99951171875, -0.501953125, 0.0233154296875, 0.400146484375, -0.65576171875, -0.51904296875, -0.07794189453125, 0.1239013671875, 0.0216217041015625, 0.63134765625, -0.927734375, 0.026458740234375, -0.061492919921875, 0.169677734375, -0.537109375, -0.65625, -0.3359375, -1.0595703125, -0.480224609375, -0.85986328125, -0.93603515625, -0.3720703125, 0.2685546875, 0.251220703125, -0.529296875, 0.030609130859375, 0.62890625, -0.57958984375, 1.1484375, -0.755859375, 0.332763671875, -0.1290283203125, -0.08819580078125, -0.54345703125, 0.0877685546875, -0.59619140625, 0.24072265625, -0.9853515625, 0.10003662109375, 0.11767578125, 0.68310546875, -0.12420654296875, 0.86572265625, -0.289306640625, -0.42236328125, 0.41748046875, -0.1845703125, -0.128173828125, 1.05859375, 0.458740234375, -0.052093505859375, 0.153564453125, -0.2420654296875, -0.317138671875, -0.5361328125, 0.09454345703125, 0.37451171875, -0.2249755859375, -0.11468505859375, -0.26318359375, 0.448974609375, -1.19140625, 0.35791015625, -0.335693359375, -0.09747314453125, -0.12353515625, -0.08770751953125, 0.57763671875, 1.15625, -0.428955078125, 0.190673828125, -0.2095947265625, 0.1287841796875, 0.291748046875, 0.1778564453125, -0.431884765625, 0.7255859375, 0.36474609375, -0.72314453125, -0.0867919921875, 0.15576171875, 0.25341796875, 0.436767578125, -0.3193359375, -0.85107421875, -1.0126953125, -0.26318359375, 0.123291015625, 0.2320556640625, 0.53125, -0.44140625, -0.38330078125, -0.322998046875, -0.697265625, 0.419677734375, -1.0283203125, -1.1669921875, 0.4970703125, 0.040283203125, -0.5625, -0.00664520263671875, -0.43896484375, -0.3349609375, -0.045166015625, 0.2236328125, -0.6572265625, 0.66845703125, -0.2374267578125, 0.35107421875, 0.02777099609375, -0.25, -0.04473876953125, 0.837890625, -0.734375, -0.45361328125, -0.28662109375, 0.8232421875, 0.1490478515625, -0.280517578125, -0.58544921875, 0.1707763671875, 0.424560546875, 0.083251953125, -0.53125, -0.047210693359375, -0.345947265625, 0.79345703125, -1.109375, 0.08123779296875, 0.10418701171875, 0.55810546875, 0.24951171875, -0.07257080078125, -0.367431640625, 0.87890625, 0.87060546875, 0.1217041015625, 0.86865234375, 0.1444091796875, 0.580078125, 0.2166748046875, 0.005584716796875, -0.365966796875, 0.75244140625, 0.75830078125, 0.8740234375, -0.194091796875, 0.14404296875, 0.7509765625, 0.335205078125, -0.44921875, 0.666015625, -0.0601806640625, -0.01453399658203125, -0.1422119140625, -0.202880859375, 0.007274627685546875, 0.0743408203125, -0.49267578125, 0.58642578125, -0.98291015625, -0.268798828125, -0.344482421875, -0.51611328125, 0.79443359375, -0.08917236328125, 0.0299835205078125, -0.10174560546875, -0.35595703125, 0.409423828125, 0.25732421875, -0.357421875, -0.02886962890625, 1.1357421875, 0.480712890625, 0.1873779296875, 0.79248046875, 0.14306640625, 0.5390625, -0.56884765625, 0.115234375, 0.006275177001953125, -0.33642578125, -0.424560546875, -0.68505859375, -0.96630859375, 0.7451171875, -0.262939453125, -0.2115478515625, 0.81640625, -0.96044921875, 0.03619384765625, -0.3955078125, 0.66796875, -0.46923828125, 0.356201171875, 0.384521484375, -0.44189453125, -1.044921875, 0.9091796875, -0.19287109375, 0.3974609375, 0.190673828125, 0.82275390625, 0.1466064453125, 1.4306640625, 0.72705078125, -0.0009636878967285156, 0.2403564453125, 0.3935546875, -0.3505859375, -0.60400390625, -0.466796875, -0.1690673828125, 0.1466064453125, -0.59033203125, -0.39794921875, 0.0770263671875, 0.478271484375, 0.32763671875, -1.0380859375, -0.29931640625, 0.40087890625, -1.0234375, 0.65283203125, 0.375, 0.307861328125, 0.3134765625, -0.2822265625, -0.329833984375, -0.515625, 0.27734375, -0.80029296875, 0.4580078125, -0.76220703125, -0.56298828125, -0.471435546875, -0.55126953125, -0.1785888671875, -0.10223388671875, -0.281982421875, -0.83251953125, 0.671875, 0.35107421875, 0.303466796875, 0.328369140625, -0.440185546875, 0.316650390625, 0.8662109375, 0.77685546875, 0.023345947265625, 0.84716796875, 0.365478515625, 0.04595947265625, 0.2030029296875, -0.1290283203125, 0.4580078125, -0.414306640625, 0.3818359375, -0.56005859375, 0.341796875, -0.9052734375, -1.166015625, 0.0938720703125, 0.290771484375, 0.2313232421875, -0.463623046875, -1.048828125, -0.3203125, -0.8525390625, -0.198486328125, -0.7958984375, 0.79931640625, -0.403076171875, 0.070068359375, -0.00281524658203125, -1.283203125, 4.2421875, 1.0029296875, 0.806640625, 0.299072265625, 0.1961669921875, 0.7861328125, 0.1798095703125, -0.7490234375, -0.1011962890625, -0.2880859375, 0.5654296875, -0.52734375, -0.0955810546875, 0.828125, 0.69287109375, 0.61474609375, -0.55419921875, -0.15771484375, 0.080810546875, -0.8681640625, -0.84326171875, 0.42431640625, 0.007404327392578125, 0.285400390625, 0.0712890625, 0.1668701171875, 0.57421875, -0.76611328125, -0.063232421875, -0.7939453125, 0.2230224609375, -0.56982421875, 0.96923828125, 0.1729736328125, -0.2137451171875, 0.66259765625, 0.1268310546875, -0.11468505859375, 0.07000732421875, 0.2177734375, -0.3173828125, -0.18359375, 0.496337890625, -0.7236328125, -0.300537109375, 0.3310546875, -0.63037109375, 0.3681640625, -0.01377105712890625, -0.9853515625, 1.0087890625, -0.2685546875, 0.1612548828125, -0.671875, -0.81982421875, -0.138671875, -0.044097900390625, -0.398193359375, -0.09259033203125, 0.423583984375, 0.59423828125, 0.630859375, 0.1700439453125, 0.6923828125, -1.5341796875, 0.63818359375, -0.058502197265625, 0.58935546875, -0.65185546875, 0.020965576171875, -0.5146484375, -0.374755859375, -0.260009765625, -0.383544921875, 0.84521484375, 0.1268310546875, -0.1971435546875, 1.029296875, 0.8369140625, -0.424560546875, 0.3046875, -0.137451171875, -0.288818359375, -0.51513671875, 1.123046875, 1.484375, -0.86962890625, -0.290283203125, -0.1295166015625, 0.47998046875, 0.255126953125, 0.77783203125, 0.310791015625, -0.473876953125, -0.4423828125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Submitted Solution: ``` from sys import stdin t = int(stdin.readline()) for _ in range(t): n, k = map(int, stdin.readline().split()) maxx_digit = min(21, k) maxx_so = 2 ** maxx_digit arr = stdin.readline() so = 0 to = 2 ** k dct = {} lientiep = 0 for i in range(k): so = so * 2 + 1 - int(arr[i]) if so >= maxx_so: so -= maxx_so for j in range(k - maxx_digit): if arr[j] == '1': lientiep += 1 else: lientiep = 0 dau = k - maxx_digit if lientiep >= k - maxx_digit: dct[so] = 1 for i in range(k, n): so = so * 2 + 1 - int(arr[i]) if so >= maxx_so: so -= maxx_so if arr[dau] == '1': lientiep += 1 else: lientiep = 0 if lientiep >= k - maxx_digit: dct[so] = 1 dau += 1 ans = 0 while ans in dct: ans += 1 ans = bin(ans)[2:] if k < len(ans): print('NO') else: ans = '0' * (k - len(ans)) + ans print('YES') print(ans) ``` Yes
107,243
[ 0.298583984375, -0.2012939453125, 0.2039794921875, 0.053497314453125, -0.486083984375, -0.43017578125, 0.09051513671875, 0.11016845703125, -0.05255126953125, 0.53466796875, 0.438720703125, -0.145263671875, -0.2283935546875, -1.001953125, -0.6826171875, -0.04876708984375, -0.3544921875, -0.45654296875, -0.392578125, -0.3173828125, -0.06396484375, -0.06890869140625, -1.1689453125, 0.060943603515625, -0.2890625, 1.013671875, 0.5341796875, 0.0814208984375, 1.17578125, 0.83251953125, -0.5810546875, -0.415283203125, 0.498779296875, -0.95166015625, -0.443115234375, -0.71044921875, 0.8583984375, -0.8896484375, -0.304931640625, -0.35693359375, 0.38134765625, -0.2274169921875, 0.450439453125, -0.7177734375, -1.3447265625, -0.0287933349609375, 0.0123748779296875, -0.322021484375, -0.221435546875, -0.70361328125, 0.002651214599609375, -0.2978515625, 0.1512451171875, -0.2384033203125, 0.11029052734375, 0.494873046875, 0.295654296875, -0.339599609375, -0.451904296875, 0.52294921875, -0.0182037353515625, 0.431396484375, 0.072509765625, -0.75, -0.0712890625, 0.175537109375, -0.1864013671875, -0.429443359375, -0.101806640625, -0.84716796875, -0.00580596923828125, -0.0014238357543945312, -0.398193359375, -0.448486328125, -0.12261962890625, 0.021514892578125, 0.14306640625, -0.12384033203125, -0.57470703125, 0.6611328125, -0.1922607421875, 1.064453125, 0.462890625, 0.469482421875, -0.44775390625, -0.529296875, 0.2130126953125, 0.247802734375, 0.36669921875, 0.07110595703125, -0.156494140625, 0.36181640625, -0.587890625, -0.09759521484375, 0.6162109375, 0.341064453125, -0.01220703125, 0.09100341796875, 0.2196044921875, 0.332763671875, 0.66796875, 0.87890625, -0.037811279296875, 1.3671875, -0.9521484375, -0.132080078125, -0.22119140625, -0.08074951171875, -0.193359375, -0.0660400390625, -0.0823974609375, -0.2218017578125, 0.54931640625, 0.44970703125, -0.368896484375, 0.75634765625, 0.04669189453125, 0.56494140625, -1.0380859375, 0.2447509765625, 0.61328125, 0.2081298828125, 0.72119140625, -0.1904296875, 0.091552734375, -0.2578125, -0.52099609375, 1.052734375, -0.315185546875, -0.2340087890625, 0.390625, -0.06365966796875, -0.11810302734375, 0.050750732421875, 0.037872314453125, 0.455078125, -0.0115814208984375, 0.259521484375, 0.78271484375, -0.53759765625, 0.728515625, -0.41650390625, -0.1829833984375, 1.5625, 0.339111328125, -0.196533203125, 0.9345703125, 0.19384765625, -0.81982421875, 0.55615234375, -0.91064453125, 0.48486328125, -0.2099609375, 0.16748046875, 0.02679443359375, 0.01031494140625, -0.32666015625, 0.038055419921875, 0.3447265625, -0.3671875, -0.391357421875, 0.1307373046875, -0.15771484375, 0.94580078125, -0.316162109375, 0.7998046875, -0.441650390625, -0.45361328125, -0.07568359375, -0.28857421875, -0.007274627685546875, -0.2958984375, -0.1417236328125, 0.8251953125, 0.55126953125, 1.2734375, 1.0400390625, -0.2890625, 0.3603515625, 0.322021484375, -0.398193359375, 0.2117919921875, 0.339599609375, 0.9150390625, -0.1876220703125, 0.34619140625, 0.052978515625, -0.2010498046875, -0.84033203125, -0.78271484375, 0.0771484375, 0.76611328125, -0.515625, 0.11956787109375, 0.05810546875, 0.208740234375, -0.72265625, -0.365234375, -0.13818359375, -1.04296875, -0.70458984375, 0.5283203125, -0.1300048828125, 0.415283203125, -0.4560546875, -0.478515625, 0.282470703125, 1.0166015625, -0.003631591796875, 0.300537109375, 0.3359375, -0.0192718505859375, -0.1279296875, 0.1357421875, 0.0195465087890625, -0.160888671875, -0.556640625, 0.8583984375, -0.071044921875, -0.114013671875, 0.04718017578125, 0.94775390625, 0.478271484375, 0.57470703125, -0.4462890625, -0.3330078125, 0.181396484375, 1.2548828125, -0.00682830810546875, 0.457763671875, 0.326416015625, 1.009765625, 0.7353515625, 0.64208984375, 0.463623046875, 0.61083984375, 0.86083984375, 0.6806640625, -0.06640625, 0.2275390625, -0.08587646484375, 0.4150390625, 0.1617431640625, 0.6337890625, 0.419921875, 0.3212890625, -0.0406494140625, 0.0784912109375, -0.3681640625, 0.5576171875, -0.2115478515625, 0.8662109375, 0.043731689453125, 0.7216796875, -0.51806640625, -0.525390625, 0.245849609375, 0.64697265625, -1.0107421875, -0.49853515625, -0.060943603515625, -0.0753173828125, -0.08770751953125, 0.1435546875, 0.2244873046875, 0.41455078125, 0.2646484375, 0.6396484375, -0.2548828125, -0.322265625, -0.9736328125, -0.6552734375, -1.1904296875, -0.0611572265625, -0.62451171875, 0.0770263671875, 0.20458984375, -0.8193359375, 0.16455078125, -0.66748046875, -0.32763671875, 0.24267578125, -0.48388671875, 0.483154296875, -0.041168212890625, 0.39599609375, -0.8076171875, 0.390869140625, 0.143310546875, 1.1865234375, -0.64501953125, -0.060577392578125, -0.1474609375, -0.60546875, 0.348876953125, -0.1461181640625, 0.0740966796875, 0.0238800048828125, -0.623046875, -0.97802734375, -0.395263671875, -0.002712249755859375, -0.2181396484375, -0.082763671875, -0.55908203125, 0.99853515625, 0.4833984375, -0.6796875, 0.54345703125, 0.7412109375, -0.97216796875, 0.3388671875, 0.43798828125, -0.037322998046875, -0.84375, 1.3583984375, 0.458740234375, 0.232421875, -0.458740234375, -0.52197265625, -0.29833984375, -0.01239013671875, 0.1324462890625, -0.53466796875, -0.1475830078125, 0.77001953125, -0.0201263427734375, -1.1103515625, 0.34033203125, -0.6875, -0.351806640625, -0.1600341796875, -0.3525390625, 0.86962890625, 0.87548828125, 0.388916015625, 0.14990234375, -0.2095947265625, -0.07598876953125, 0.482177734375, 0.414306640625, -0.39599609375, -0.2388916015625, 0.876953125, 0.1898193359375, 0.280517578125, -0.038909912109375, -0.1446533203125, -0.051849365234375, 0.190185546875, -0.03729248046875, 0.96435546875, 0.10015869140625, 0.51220703125, 0.103271484375, 0.888671875, -0.8447265625, -0.381103515625, -0.14453125, 0.5986328125, 0.67578125, 0.52001953125, 0.5908203125, -0.03118896484375, -0.391357421875, -1.263671875, 0.242919921875, -0.096435546875, 0.88916015625, -0.5166015625, 1.076171875, 0.0987548828125, -0.413818359375, 0.9013671875, -0.642578125, -0.04998779296875, 0.873046875, -0.0132598876953125, 0.71435546875, -0.444580078125, 0.09967041015625, -0.160400390625, -0.187255859375, 0.50537109375, 0.5517578125, 0.8642578125, -0.4169921875, -0.44921875, -0.342041015625, -0.1177978515625, -0.057647705078125, -0.30029296875, 0.037750244140625, -0.169677734375, -0.1910400390625, -0.8828125, 0.2203369140625, 0.493408203125, 0.88232421875, 0.06585693359375, 0.2196044921875, 0.427490234375, 0.419189453125, 0.96533203125, -0.4140625, 0.199462890625, -0.6865234375, 0.67236328125, 0.0130462646484375, -0.331787109375, -0.77197265625, -0.3720703125, -0.131591796875, 0.1453857421875, -0.053955078125, -0.380615234375, -1.17578125, 0.445068359375, -0.440673828125, 0.5947265625, -0.7490234375, 0.11077880859375, -0.497314453125, 0.2724609375, 0.244140625, -0.9658203125, 0.057708740234375, -0.5908203125, 0.304931640625, 0.37060546875, -0.23291015625, -0.49853515625, -0.6416015625, -0.69482421875, -1.001953125, 0.54638671875, 1.0205078125, 0.0118408203125, 0.07977294921875, -1.4619140625, 0.52685546875, 0.64501953125, -0.60546875, 0.13330078125, -0.250732421875, 0.48193359375, 0.275146484375, 0.84130859375, -0.3359375, -0.64794921875, -0.10064697265625, -1.240234375, 0.26708984375, -0.43896484375, 0.6875, 0.05609130859375, -0.11016845703125, -0.09423828125, 0.34228515625, 0.118896484375, 0.380859375, -0.341552734375, 0.336669921875, -0.87353515625, -0.87255859375, 0.66943359375, -0.31201171875, -0.42333984375, 1.1748046875, -0.12469482421875, -0.3173828125, 0.38671875, 0.57470703125, -0.3271484375, 0.634765625, -0.374755859375, 0.25732421875, -0.446533203125, -0.329345703125, -0.364990234375, -0.367431640625, 0.97412109375, 0.0411376953125, -0.6513671875, -0.11016845703125, -1.0302734375, -0.2213134765625, 0.16943359375, -0.421875, 0.310791015625, -0.141357421875, -0.0282135009765625, -0.258544921875, -0.1473388671875, -0.72119140625, -0.216796875, -0.45703125, -0.46240234375, 0.2408447265625, 0.328857421875, 0.6572265625, 0.3291015625, -0.361328125, -0.11859130859375, 0.007289886474609375, 0.141845703125, -0.383056640625, -0.291015625, -0.32421875, -0.318115234375, -0.427001953125, 0.12054443359375, 0.327392578125, 0.1817626953125, 0.435791015625, 0.3154296875, 0.60107421875, 0.450439453125, -0.77490234375, 0.94775390625, 0.11480712890625, -0.94287109375, -0.080322265625, 0.5927734375, 0.03271484375, 0.70849609375, -0.0712890625, -0.7998046875, -0.728515625, -0.8525390625, 0.38427734375, -0.56787109375, -0.304443359375, -1.1015625, -0.3505859375, -0.435302734375, 0.64404296875, -0.08770751953125, -0.4208984375, 0.1417236328125, -1.4287109375, -0.2047119140625, -0.796875, -0.2286376953125, -0.95458984375, -0.2335205078125, -0.390380859375, 0.85205078125, -0.07647705078125, 0.40966796875, -0.1673583984375, 0.12396240234375, 0.1998291015625, 0.31005859375, -0.45654296875, -0.4150390625, -0.25927734375, 0.08880615234375, -0.1258544921875, -0.0899658203125, -0.69140625, 0.7509765625, -0.791015625, 0.28271484375, -0.181396484375, 0.00614166259765625, -0.27001953125, -0.41796875, 1.169921875, -0.39892578125, -0.296875, -0.2054443359375, 0.1622314453125, 0.712890625, -0.54443359375, -0.3115234375, -1.0712890625, -0.3994140625, -0.93603515625, 0.548828125, -0.31640625, -0.04388427734375, -0.50048828125, -0.55517578125, 1.150390625, -0.59619140625, 0.26220703125, 1.158203125, 0.1163330078125, 0.266357421875, -0.77392578125, 0.66552734375, 0.75634765625, -0.59765625, 0.058013916015625, 0.11822509765625, -0.73974609375, 0.0694580078125, -0.390625, -1.068359375, -0.5107421875, 0.50830078125, 0.99951171875, -0.345947265625, 0.63232421875, 0.15966796875, -1.236328125, -0.478271484375, 1.23046875, 0.298095703125, 0.0875244140625, 0.83251953125, 0.118896484375, -0.08636474609375, -0.27978515625, -0.728515625, -0.244384765625, -0.473388671875, 1.4111328125, -0.65087890625, -0.5458984375, 1.0908203125, 0.8955078125, -1.5341796875, -0.89794921875, 0.0968017578125, 0.16455078125, 0.1800537109375, -0.8125, 0.06195068359375, 0.433837890625, -0.485107421875, -0.09130859375, 0.1273193359375, -0.04351806640625, 0.39453125, 0.040374755859375, 0.71484375, -0.720703125, 0.414794921875, 1.0458984375, -0.485595703125, -0.33349609375, -0.837890625, -0.2325439453125, -0.435791015625, -0.01473236083984375, 0.90576171875, -0.2498779296875, -0.0250091552734375, 0.61474609375, -0.142333984375, 0.95947265625, -0.6201171875, 0.04901123046875, 0.288330078125, -0.6787109375, -0.52294921875, -0.1474609375, 0.1884765625, 0.09381103515625, 0.63330078125, -0.892578125, 0.03564453125, 0.012786865234375, 0.2310791015625, -0.3876953125, -0.58447265625, -0.402587890625, -0.97802734375, -0.501953125, -0.81689453125, -0.8701171875, -0.35009765625, 0.302490234375, 0.2734375, -0.498046875, 0.1026611328125, 0.71240234375, -0.57568359375, 1.07421875, -0.7919921875, 0.2196044921875, -0.2325439453125, -0.174560546875, -0.5576171875, 0.09368896484375, -0.6533203125, 0.27197265625, -0.89794921875, 0.08001708984375, 0.08392333984375, 0.64453125, -0.251220703125, 0.84814453125, -0.2486572265625, -0.3125, 0.49853515625, -0.1475830078125, -0.317138671875, 1.0537109375, 0.372802734375, -0.0055999755859375, 0.0867919921875, -0.31884765625, -0.2406005859375, -0.33544921875, 0.25390625, 0.310546875, -0.2205810546875, -0.09600830078125, -0.05426025390625, 0.1986083984375, -1.1494140625, 0.419189453125, -0.3017578125, -0.08526611328125, -0.0302276611328125, -0.2044677734375, 0.5732421875, 1.10546875, -0.49609375, 0.2578125, -0.1517333984375, 0.10784912109375, 0.3583984375, 0.19970703125, -0.371826171875, 0.6865234375, 0.32177734375, -0.71533203125, 0.0355224609375, 0.30078125, 0.35498046875, 0.476806640625, -0.370849609375, -0.861328125, -1.0810546875, -0.198486328125, -0.0189666748046875, 0.221435546875, 0.4765625, -0.401611328125, -0.279541015625, -0.33544921875, -0.67578125, 0.5361328125, -1.1484375, -1.1474609375, 0.57470703125, -0.053497314453125, -0.60595703125, 0.048126220703125, -0.462158203125, -0.181396484375, 0.07073974609375, 0.1702880859375, -0.5986328125, 0.61767578125, -0.1925048828125, 0.38134765625, 0.0133819580078125, -0.302978515625, -0.0287322998046875, 0.7470703125, -0.748046875, -0.50390625, -0.223876953125, 0.9248046875, 0.11328125, -0.328369140625, -0.5751953125, 0.2108154296875, 0.287109375, -0.013427734375, -0.431396484375, -0.0201416015625, -0.2685546875, 0.7724609375, -0.95458984375, 0.1021728515625, -0.0244293212890625, 0.491943359375, 0.13671875, -0.13427734375, -0.44580078125, 0.79248046875, 0.865234375, 0.040863037109375, 0.69287109375, 0.125244140625, 0.6171875, 0.1705322265625, -0.06158447265625, -0.27978515625, 0.7705078125, 0.7275390625, 0.8564453125, -0.069091796875, 0.147705078125, 0.73681640625, 0.36328125, -0.25, 0.6298828125, -0.053314208984375, -0.00804901123046875, -0.12841796875, -0.249755859375, -0.00783538818359375, 0.109375, -0.4560546875, 0.533203125, -0.8779296875, -0.286865234375, -0.325927734375, -0.5068359375, 0.814453125, -0.0799560546875, 0.048187255859375, -0.123291015625, -0.327880859375, 0.6064453125, 0.28076171875, -0.263916015625, -0.018402099609375, 1.0751953125, 0.646484375, 0.351318359375, 0.86083984375, 0.1875, 0.409912109375, -0.62158203125, -0.0277252197265625, 0.1572265625, -0.32373046875, -0.3359375, -0.59716796875, -0.978515625, 0.80517578125, -0.1719970703125, -0.1866455078125, 0.64111328125, -0.97216796875, 0.07501220703125, -0.36474609375, 0.6767578125, -0.5400390625, 0.33056640625, 0.369384765625, -0.4375, -1.0439453125, 0.86572265625, -0.060455322265625, 0.37646484375, 0.226806640625, 0.82373046875, 0.1695556640625, 1.4052734375, 0.81298828125, -0.03753662109375, 0.2271728515625, 0.4091796875, -0.30712890625, -0.50927734375, -0.41259765625, -0.202392578125, 0.08984375, -0.66064453125, -0.401123046875, 0.0080718994140625, 0.45654296875, 0.3271484375, -1.029296875, -0.345458984375, 0.35205078125, -0.91796875, 0.6611328125, 0.290771484375, 0.321533203125, 0.265625, -0.1728515625, -0.415283203125, -0.4716796875, 0.26171875, -0.64892578125, 0.404052734375, -0.734375, -0.42333984375, -0.48681640625, -0.43896484375, -0.0911865234375, -0.0760498046875, -0.353271484375, -0.6865234375, 0.6298828125, 0.377197265625, 0.2230224609375, 0.233154296875, -0.45263671875, 0.24560546875, 0.8818359375, 0.81689453125, -0.0007815361022949219, 0.8671875, 0.4091796875, 0.01947021484375, 0.1185302734375, -0.1861572265625, 0.43212890625, -0.40771484375, 0.255859375, -0.6533203125, 0.352783203125, -0.8994140625, -1.08203125, 0.004913330078125, 0.35693359375, 0.2069091796875, -0.41162109375, -1.1337890625, -0.489990234375, -0.85400390625, -0.1873779296875, -0.76904296875, 0.783203125, -0.37939453125, -0.046051025390625, -0.0701904296875, -1.2763671875, 4.31640625, 0.91796875, 0.74951171875, 0.36181640625, 0.18798828125, 0.68310546875, 0.2496337890625, -0.8662109375, 0.05908203125, -0.3525390625, 0.55078125, -0.505859375, -0.08856201171875, 0.87158203125, 0.64453125, 0.55810546875, -0.59033203125, -0.263916015625, 0.24951171875, -0.9248046875, -0.87451171875, 0.489990234375, 0.032562255859375, 0.20166015625, 0.12078857421875, 0.2177734375, 0.7177734375, -0.818359375, -0.146240234375, -0.80224609375, 0.234375, -0.49755859375, 1, 0.1280517578125, -0.165771484375, 0.62841796875, 0.215087890625, -0.1572265625, -0.0189361572265625, 0.275146484375, -0.322509765625, -0.1435546875, 0.52490234375, -0.73681640625, -0.280517578125, 0.430908203125, -0.70556640625, 0.447509765625, 0.0204620361328125, -0.982421875, 1.001953125, -0.1575927734375, 0.2047119140625, -0.62548828125, -0.85546875, -0.1279296875, -0.01461029052734375, -0.327880859375, -0.0653076171875, 0.39208984375, 0.52685546875, 0.57568359375, 0.04644775390625, 0.8212890625, -1.5625, 0.556640625, -0.0147857666015625, 0.472412109375, -0.6376953125, -0.0181884765625, -0.61328125, -0.420654296875, -0.1324462890625, -0.50244140625, 0.68505859375, 0.2200927734375, -0.195556640625, 0.923828125, 0.80419921875, -0.466796875, 0.326171875, -0.10626220703125, -0.2470703125, -0.68310546875, 1.1630859375, 1.384765625, -0.86865234375, -0.377197265625, -0.221435546875, 0.46630859375, 0.30224609375, 0.806640625, 0.335205078125, -0.45263671875, -0.46826171875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Submitted Solution: ``` import sys input = sys.stdin.readline t = int(input()) for case in range(t): n, k0 = [int(x) for x in input().split(' ')] start_inds = set([i for i in range(n-k0+1)]) s = input() k = min(20, k0) if k < k0: next_0 = [] curr_0 = n for i in range(n-1,-1,-1): if s[i] == '0': curr_0 = i next_0.append(curr_0) next_0.reverse() for i in range(n-k0+1): if next_0[i] < i + k0 - 20: start_inds.remove(i) Z = 1 << k avoid = set() for i in start_inds: r = int(s[i + k0 - k:i + k0], 2) avoid.add(Z - 1 - r) j = 0 while j in avoid and j < Z: j += 1 ans = bin(j)[2:] if j == Z: print("NO") else: print("YES") ans = '0' * (k0 - len(ans)) + ans print(ans) ``` Yes
107,244
[ 0.298583984375, -0.2012939453125, 0.2039794921875, 0.053497314453125, -0.486083984375, -0.43017578125, 0.09051513671875, 0.11016845703125, -0.05255126953125, 0.53466796875, 0.438720703125, -0.145263671875, -0.2283935546875, -1.001953125, -0.6826171875, -0.04876708984375, -0.3544921875, -0.45654296875, -0.392578125, -0.3173828125, -0.06396484375, -0.06890869140625, -1.1689453125, 0.060943603515625, -0.2890625, 1.013671875, 0.5341796875, 0.0814208984375, 1.17578125, 0.83251953125, -0.5810546875, -0.415283203125, 0.498779296875, -0.95166015625, -0.443115234375, -0.71044921875, 0.8583984375, -0.8896484375, -0.304931640625, -0.35693359375, 0.38134765625, -0.2274169921875, 0.450439453125, -0.7177734375, -1.3447265625, -0.0287933349609375, 0.0123748779296875, -0.322021484375, -0.221435546875, -0.70361328125, 0.002651214599609375, -0.2978515625, 0.1512451171875, -0.2384033203125, 0.11029052734375, 0.494873046875, 0.295654296875, -0.339599609375, -0.451904296875, 0.52294921875, -0.0182037353515625, 0.431396484375, 0.072509765625, -0.75, -0.0712890625, 0.175537109375, -0.1864013671875, -0.429443359375, -0.101806640625, -0.84716796875, -0.00580596923828125, -0.0014238357543945312, -0.398193359375, -0.448486328125, -0.12261962890625, 0.021514892578125, 0.14306640625, -0.12384033203125, -0.57470703125, 0.6611328125, -0.1922607421875, 1.064453125, 0.462890625, 0.469482421875, -0.44775390625, -0.529296875, 0.2130126953125, 0.247802734375, 0.36669921875, 0.07110595703125, -0.156494140625, 0.36181640625, -0.587890625, -0.09759521484375, 0.6162109375, 0.341064453125, -0.01220703125, 0.09100341796875, 0.2196044921875, 0.332763671875, 0.66796875, 0.87890625, -0.037811279296875, 1.3671875, -0.9521484375, -0.132080078125, -0.22119140625, -0.08074951171875, -0.193359375, -0.0660400390625, -0.0823974609375, -0.2218017578125, 0.54931640625, 0.44970703125, -0.368896484375, 0.75634765625, 0.04669189453125, 0.56494140625, -1.0380859375, 0.2447509765625, 0.61328125, 0.2081298828125, 0.72119140625, -0.1904296875, 0.091552734375, -0.2578125, -0.52099609375, 1.052734375, -0.315185546875, -0.2340087890625, 0.390625, -0.06365966796875, -0.11810302734375, 0.050750732421875, 0.037872314453125, 0.455078125, -0.0115814208984375, 0.259521484375, 0.78271484375, -0.53759765625, 0.728515625, -0.41650390625, -0.1829833984375, 1.5625, 0.339111328125, -0.196533203125, 0.9345703125, 0.19384765625, -0.81982421875, 0.55615234375, -0.91064453125, 0.48486328125, -0.2099609375, 0.16748046875, 0.02679443359375, 0.01031494140625, -0.32666015625, 0.038055419921875, 0.3447265625, -0.3671875, -0.391357421875, 0.1307373046875, -0.15771484375, 0.94580078125, -0.316162109375, 0.7998046875, -0.441650390625, -0.45361328125, -0.07568359375, -0.28857421875, -0.007274627685546875, -0.2958984375, -0.1417236328125, 0.8251953125, 0.55126953125, 1.2734375, 1.0400390625, -0.2890625, 0.3603515625, 0.322021484375, -0.398193359375, 0.2117919921875, 0.339599609375, 0.9150390625, -0.1876220703125, 0.34619140625, 0.052978515625, -0.2010498046875, -0.84033203125, -0.78271484375, 0.0771484375, 0.76611328125, -0.515625, 0.11956787109375, 0.05810546875, 0.208740234375, -0.72265625, -0.365234375, -0.13818359375, -1.04296875, -0.70458984375, 0.5283203125, -0.1300048828125, 0.415283203125, -0.4560546875, -0.478515625, 0.282470703125, 1.0166015625, -0.003631591796875, 0.300537109375, 0.3359375, -0.0192718505859375, -0.1279296875, 0.1357421875, 0.0195465087890625, -0.160888671875, -0.556640625, 0.8583984375, -0.071044921875, -0.114013671875, 0.04718017578125, 0.94775390625, 0.478271484375, 0.57470703125, -0.4462890625, -0.3330078125, 0.181396484375, 1.2548828125, -0.00682830810546875, 0.457763671875, 0.326416015625, 1.009765625, 0.7353515625, 0.64208984375, 0.463623046875, 0.61083984375, 0.86083984375, 0.6806640625, -0.06640625, 0.2275390625, -0.08587646484375, 0.4150390625, 0.1617431640625, 0.6337890625, 0.419921875, 0.3212890625, -0.0406494140625, 0.0784912109375, -0.3681640625, 0.5576171875, -0.2115478515625, 0.8662109375, 0.043731689453125, 0.7216796875, -0.51806640625, -0.525390625, 0.245849609375, 0.64697265625, -1.0107421875, -0.49853515625, -0.060943603515625, -0.0753173828125, -0.08770751953125, 0.1435546875, 0.2244873046875, 0.41455078125, 0.2646484375, 0.6396484375, -0.2548828125, -0.322265625, -0.9736328125, -0.6552734375, -1.1904296875, -0.0611572265625, -0.62451171875, 0.0770263671875, 0.20458984375, -0.8193359375, 0.16455078125, -0.66748046875, -0.32763671875, 0.24267578125, -0.48388671875, 0.483154296875, -0.041168212890625, 0.39599609375, -0.8076171875, 0.390869140625, 0.143310546875, 1.1865234375, -0.64501953125, -0.060577392578125, -0.1474609375, -0.60546875, 0.348876953125, -0.1461181640625, 0.0740966796875, 0.0238800048828125, -0.623046875, -0.97802734375, -0.395263671875, -0.002712249755859375, -0.2181396484375, -0.082763671875, -0.55908203125, 0.99853515625, 0.4833984375, -0.6796875, 0.54345703125, 0.7412109375, -0.97216796875, 0.3388671875, 0.43798828125, -0.037322998046875, -0.84375, 1.3583984375, 0.458740234375, 0.232421875, -0.458740234375, -0.52197265625, -0.29833984375, -0.01239013671875, 0.1324462890625, -0.53466796875, -0.1475830078125, 0.77001953125, -0.0201263427734375, -1.1103515625, 0.34033203125, -0.6875, -0.351806640625, -0.1600341796875, -0.3525390625, 0.86962890625, 0.87548828125, 0.388916015625, 0.14990234375, -0.2095947265625, -0.07598876953125, 0.482177734375, 0.414306640625, -0.39599609375, -0.2388916015625, 0.876953125, 0.1898193359375, 0.280517578125, -0.038909912109375, -0.1446533203125, -0.051849365234375, 0.190185546875, -0.03729248046875, 0.96435546875, 0.10015869140625, 0.51220703125, 0.103271484375, 0.888671875, -0.8447265625, -0.381103515625, -0.14453125, 0.5986328125, 0.67578125, 0.52001953125, 0.5908203125, -0.03118896484375, -0.391357421875, -1.263671875, 0.242919921875, -0.096435546875, 0.88916015625, -0.5166015625, 1.076171875, 0.0987548828125, -0.413818359375, 0.9013671875, -0.642578125, -0.04998779296875, 0.873046875, -0.0132598876953125, 0.71435546875, -0.444580078125, 0.09967041015625, -0.160400390625, -0.187255859375, 0.50537109375, 0.5517578125, 0.8642578125, -0.4169921875, -0.44921875, -0.342041015625, -0.1177978515625, -0.057647705078125, -0.30029296875, 0.037750244140625, -0.169677734375, -0.1910400390625, -0.8828125, 0.2203369140625, 0.493408203125, 0.88232421875, 0.06585693359375, 0.2196044921875, 0.427490234375, 0.419189453125, 0.96533203125, -0.4140625, 0.199462890625, -0.6865234375, 0.67236328125, 0.0130462646484375, -0.331787109375, -0.77197265625, -0.3720703125, -0.131591796875, 0.1453857421875, -0.053955078125, -0.380615234375, -1.17578125, 0.445068359375, -0.440673828125, 0.5947265625, -0.7490234375, 0.11077880859375, -0.497314453125, 0.2724609375, 0.244140625, -0.9658203125, 0.057708740234375, -0.5908203125, 0.304931640625, 0.37060546875, -0.23291015625, -0.49853515625, -0.6416015625, -0.69482421875, -1.001953125, 0.54638671875, 1.0205078125, 0.0118408203125, 0.07977294921875, -1.4619140625, 0.52685546875, 0.64501953125, -0.60546875, 0.13330078125, -0.250732421875, 0.48193359375, 0.275146484375, 0.84130859375, -0.3359375, -0.64794921875, -0.10064697265625, -1.240234375, 0.26708984375, -0.43896484375, 0.6875, 0.05609130859375, -0.11016845703125, -0.09423828125, 0.34228515625, 0.118896484375, 0.380859375, -0.341552734375, 0.336669921875, -0.87353515625, -0.87255859375, 0.66943359375, -0.31201171875, -0.42333984375, 1.1748046875, -0.12469482421875, -0.3173828125, 0.38671875, 0.57470703125, -0.3271484375, 0.634765625, -0.374755859375, 0.25732421875, -0.446533203125, -0.329345703125, -0.364990234375, -0.367431640625, 0.97412109375, 0.0411376953125, -0.6513671875, -0.11016845703125, -1.0302734375, -0.2213134765625, 0.16943359375, -0.421875, 0.310791015625, -0.141357421875, -0.0282135009765625, -0.258544921875, -0.1473388671875, -0.72119140625, -0.216796875, -0.45703125, -0.46240234375, 0.2408447265625, 0.328857421875, 0.6572265625, 0.3291015625, -0.361328125, -0.11859130859375, 0.007289886474609375, 0.141845703125, -0.383056640625, -0.291015625, -0.32421875, -0.318115234375, -0.427001953125, 0.12054443359375, 0.327392578125, 0.1817626953125, 0.435791015625, 0.3154296875, 0.60107421875, 0.450439453125, -0.77490234375, 0.94775390625, 0.11480712890625, -0.94287109375, -0.080322265625, 0.5927734375, 0.03271484375, 0.70849609375, -0.0712890625, -0.7998046875, -0.728515625, -0.8525390625, 0.38427734375, -0.56787109375, -0.304443359375, -1.1015625, -0.3505859375, -0.435302734375, 0.64404296875, -0.08770751953125, -0.4208984375, 0.1417236328125, -1.4287109375, -0.2047119140625, -0.796875, -0.2286376953125, -0.95458984375, -0.2335205078125, -0.390380859375, 0.85205078125, -0.07647705078125, 0.40966796875, -0.1673583984375, 0.12396240234375, 0.1998291015625, 0.31005859375, -0.45654296875, -0.4150390625, -0.25927734375, 0.08880615234375, -0.1258544921875, -0.0899658203125, -0.69140625, 0.7509765625, -0.791015625, 0.28271484375, -0.181396484375, 0.00614166259765625, -0.27001953125, -0.41796875, 1.169921875, -0.39892578125, -0.296875, -0.2054443359375, 0.1622314453125, 0.712890625, -0.54443359375, -0.3115234375, -1.0712890625, -0.3994140625, -0.93603515625, 0.548828125, -0.31640625, -0.04388427734375, -0.50048828125, -0.55517578125, 1.150390625, -0.59619140625, 0.26220703125, 1.158203125, 0.1163330078125, 0.266357421875, -0.77392578125, 0.66552734375, 0.75634765625, -0.59765625, 0.058013916015625, 0.11822509765625, -0.73974609375, 0.0694580078125, -0.390625, -1.068359375, -0.5107421875, 0.50830078125, 0.99951171875, -0.345947265625, 0.63232421875, 0.15966796875, -1.236328125, -0.478271484375, 1.23046875, 0.298095703125, 0.0875244140625, 0.83251953125, 0.118896484375, -0.08636474609375, -0.27978515625, -0.728515625, -0.244384765625, -0.473388671875, 1.4111328125, -0.65087890625, -0.5458984375, 1.0908203125, 0.8955078125, -1.5341796875, -0.89794921875, 0.0968017578125, 0.16455078125, 0.1800537109375, -0.8125, 0.06195068359375, 0.433837890625, -0.485107421875, -0.09130859375, 0.1273193359375, -0.04351806640625, 0.39453125, 0.040374755859375, 0.71484375, -0.720703125, 0.414794921875, 1.0458984375, -0.485595703125, -0.33349609375, -0.837890625, -0.2325439453125, -0.435791015625, -0.01473236083984375, 0.90576171875, -0.2498779296875, -0.0250091552734375, 0.61474609375, -0.142333984375, 0.95947265625, -0.6201171875, 0.04901123046875, 0.288330078125, -0.6787109375, -0.52294921875, -0.1474609375, 0.1884765625, 0.09381103515625, 0.63330078125, -0.892578125, 0.03564453125, 0.012786865234375, 0.2310791015625, -0.3876953125, -0.58447265625, -0.402587890625, -0.97802734375, -0.501953125, -0.81689453125, -0.8701171875, -0.35009765625, 0.302490234375, 0.2734375, -0.498046875, 0.1026611328125, 0.71240234375, -0.57568359375, 1.07421875, -0.7919921875, 0.2196044921875, -0.2325439453125, -0.174560546875, -0.5576171875, 0.09368896484375, -0.6533203125, 0.27197265625, -0.89794921875, 0.08001708984375, 0.08392333984375, 0.64453125, -0.251220703125, 0.84814453125, -0.2486572265625, -0.3125, 0.49853515625, -0.1475830078125, -0.317138671875, 1.0537109375, 0.372802734375, -0.0055999755859375, 0.0867919921875, -0.31884765625, -0.2406005859375, -0.33544921875, 0.25390625, 0.310546875, -0.2205810546875, -0.09600830078125, -0.05426025390625, 0.1986083984375, -1.1494140625, 0.419189453125, -0.3017578125, -0.08526611328125, -0.0302276611328125, -0.2044677734375, 0.5732421875, 1.10546875, -0.49609375, 0.2578125, -0.1517333984375, 0.10784912109375, 0.3583984375, 0.19970703125, -0.371826171875, 0.6865234375, 0.32177734375, -0.71533203125, 0.0355224609375, 0.30078125, 0.35498046875, 0.476806640625, -0.370849609375, -0.861328125, -1.0810546875, -0.198486328125, -0.0189666748046875, 0.221435546875, 0.4765625, -0.401611328125, -0.279541015625, -0.33544921875, -0.67578125, 0.5361328125, -1.1484375, -1.1474609375, 0.57470703125, -0.053497314453125, -0.60595703125, 0.048126220703125, -0.462158203125, -0.181396484375, 0.07073974609375, 0.1702880859375, -0.5986328125, 0.61767578125, -0.1925048828125, 0.38134765625, 0.0133819580078125, -0.302978515625, -0.0287322998046875, 0.7470703125, -0.748046875, -0.50390625, -0.223876953125, 0.9248046875, 0.11328125, -0.328369140625, -0.5751953125, 0.2108154296875, 0.287109375, -0.013427734375, -0.431396484375, -0.0201416015625, -0.2685546875, 0.7724609375, -0.95458984375, 0.1021728515625, -0.0244293212890625, 0.491943359375, 0.13671875, -0.13427734375, -0.44580078125, 0.79248046875, 0.865234375, 0.040863037109375, 0.69287109375, 0.125244140625, 0.6171875, 0.1705322265625, -0.06158447265625, -0.27978515625, 0.7705078125, 0.7275390625, 0.8564453125, -0.069091796875, 0.147705078125, 0.73681640625, 0.36328125, -0.25, 0.6298828125, -0.053314208984375, -0.00804901123046875, -0.12841796875, -0.249755859375, -0.00783538818359375, 0.109375, -0.4560546875, 0.533203125, -0.8779296875, -0.286865234375, -0.325927734375, -0.5068359375, 0.814453125, -0.0799560546875, 0.048187255859375, -0.123291015625, -0.327880859375, 0.6064453125, 0.28076171875, -0.263916015625, -0.018402099609375, 1.0751953125, 0.646484375, 0.351318359375, 0.86083984375, 0.1875, 0.409912109375, -0.62158203125, -0.0277252197265625, 0.1572265625, -0.32373046875, -0.3359375, -0.59716796875, -0.978515625, 0.80517578125, -0.1719970703125, -0.1866455078125, 0.64111328125, -0.97216796875, 0.07501220703125, -0.36474609375, 0.6767578125, -0.5400390625, 0.33056640625, 0.369384765625, -0.4375, -1.0439453125, 0.86572265625, -0.060455322265625, 0.37646484375, 0.226806640625, 0.82373046875, 0.1695556640625, 1.4052734375, 0.81298828125, -0.03753662109375, 0.2271728515625, 0.4091796875, -0.30712890625, -0.50927734375, -0.41259765625, -0.202392578125, 0.08984375, -0.66064453125, -0.401123046875, 0.0080718994140625, 0.45654296875, 0.3271484375, -1.029296875, -0.345458984375, 0.35205078125, -0.91796875, 0.6611328125, 0.290771484375, 0.321533203125, 0.265625, -0.1728515625, -0.415283203125, -0.4716796875, 0.26171875, -0.64892578125, 0.404052734375, -0.734375, -0.42333984375, -0.48681640625, -0.43896484375, -0.0911865234375, -0.0760498046875, -0.353271484375, -0.6865234375, 0.6298828125, 0.377197265625, 0.2230224609375, 0.233154296875, -0.45263671875, 0.24560546875, 0.8818359375, 0.81689453125, -0.0007815361022949219, 0.8671875, 0.4091796875, 0.01947021484375, 0.1185302734375, -0.1861572265625, 0.43212890625, -0.40771484375, 0.255859375, -0.6533203125, 0.352783203125, -0.8994140625, -1.08203125, 0.004913330078125, 0.35693359375, 0.2069091796875, -0.41162109375, -1.1337890625, -0.489990234375, -0.85400390625, -0.1873779296875, -0.76904296875, 0.783203125, -0.37939453125, -0.046051025390625, -0.0701904296875, -1.2763671875, 4.31640625, 0.91796875, 0.74951171875, 0.36181640625, 0.18798828125, 0.68310546875, 0.2496337890625, -0.8662109375, 0.05908203125, -0.3525390625, 0.55078125, -0.505859375, -0.08856201171875, 0.87158203125, 0.64453125, 0.55810546875, -0.59033203125, -0.263916015625, 0.24951171875, -0.9248046875, -0.87451171875, 0.489990234375, 0.032562255859375, 0.20166015625, 0.12078857421875, 0.2177734375, 0.7177734375, -0.818359375, -0.146240234375, -0.80224609375, 0.234375, -0.49755859375, 1, 0.1280517578125, -0.165771484375, 0.62841796875, 0.215087890625, -0.1572265625, -0.0189361572265625, 0.275146484375, -0.322509765625, -0.1435546875, 0.52490234375, -0.73681640625, -0.280517578125, 0.430908203125, -0.70556640625, 0.447509765625, 0.0204620361328125, -0.982421875, 1.001953125, -0.1575927734375, 0.2047119140625, -0.62548828125, -0.85546875, -0.1279296875, -0.01461029052734375, -0.327880859375, -0.0653076171875, 0.39208984375, 0.52685546875, 0.57568359375, 0.04644775390625, 0.8212890625, -1.5625, 0.556640625, -0.0147857666015625, 0.472412109375, -0.6376953125, -0.0181884765625, -0.61328125, -0.420654296875, -0.1324462890625, -0.50244140625, 0.68505859375, 0.2200927734375, -0.195556640625, 0.923828125, 0.80419921875, -0.466796875, 0.326171875, -0.10626220703125, -0.2470703125, -0.68310546875, 1.1630859375, 1.384765625, -0.86865234375, -0.377197265625, -0.221435546875, 0.46630859375, 0.30224609375, 0.806640625, 0.335205078125, -0.45263671875, -0.46826171875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Submitted Solution: ``` from itertools import accumulate, chain BITS = 20 for _ in range(int(input())): n, k = map(int, input().split()) s = input() antis = [1 - int(si) for si in s] antis_s = ''.join(map(str, antis)) antis_sums = tuple(chain((0,), accumulate(antis))) fbd = set() for i in range(n + 1 - k): if k < BITS or antis_sums[i] == antis_sums[i + k - BITS]: cur = int(antis_s[max(i, i + k - BITS):i + k], base=2) fbd.add(cur) ans = 0 while ans in fbd: ans += 1 t = bin(ans)[2:] if len(t) > k: print("NO") else: print("YES") print(t.rjust(k, '0')) ``` Yes
107,245
[ 0.298583984375, -0.2012939453125, 0.2039794921875, 0.053497314453125, -0.486083984375, -0.43017578125, 0.09051513671875, 0.11016845703125, -0.05255126953125, 0.53466796875, 0.438720703125, -0.145263671875, -0.2283935546875, -1.001953125, -0.6826171875, -0.04876708984375, -0.3544921875, -0.45654296875, -0.392578125, -0.3173828125, -0.06396484375, -0.06890869140625, -1.1689453125, 0.060943603515625, -0.2890625, 1.013671875, 0.5341796875, 0.0814208984375, 1.17578125, 0.83251953125, -0.5810546875, -0.415283203125, 0.498779296875, -0.95166015625, -0.443115234375, -0.71044921875, 0.8583984375, -0.8896484375, -0.304931640625, -0.35693359375, 0.38134765625, -0.2274169921875, 0.450439453125, -0.7177734375, -1.3447265625, -0.0287933349609375, 0.0123748779296875, -0.322021484375, -0.221435546875, -0.70361328125, 0.002651214599609375, -0.2978515625, 0.1512451171875, -0.2384033203125, 0.11029052734375, 0.494873046875, 0.295654296875, -0.339599609375, -0.451904296875, 0.52294921875, -0.0182037353515625, 0.431396484375, 0.072509765625, -0.75, -0.0712890625, 0.175537109375, -0.1864013671875, -0.429443359375, -0.101806640625, -0.84716796875, -0.00580596923828125, -0.0014238357543945312, -0.398193359375, -0.448486328125, -0.12261962890625, 0.021514892578125, 0.14306640625, -0.12384033203125, -0.57470703125, 0.6611328125, -0.1922607421875, 1.064453125, 0.462890625, 0.469482421875, -0.44775390625, -0.529296875, 0.2130126953125, 0.247802734375, 0.36669921875, 0.07110595703125, -0.156494140625, 0.36181640625, -0.587890625, -0.09759521484375, 0.6162109375, 0.341064453125, -0.01220703125, 0.09100341796875, 0.2196044921875, 0.332763671875, 0.66796875, 0.87890625, -0.037811279296875, 1.3671875, -0.9521484375, -0.132080078125, -0.22119140625, -0.08074951171875, -0.193359375, -0.0660400390625, -0.0823974609375, -0.2218017578125, 0.54931640625, 0.44970703125, -0.368896484375, 0.75634765625, 0.04669189453125, 0.56494140625, -1.0380859375, 0.2447509765625, 0.61328125, 0.2081298828125, 0.72119140625, -0.1904296875, 0.091552734375, -0.2578125, -0.52099609375, 1.052734375, -0.315185546875, -0.2340087890625, 0.390625, -0.06365966796875, -0.11810302734375, 0.050750732421875, 0.037872314453125, 0.455078125, -0.0115814208984375, 0.259521484375, 0.78271484375, -0.53759765625, 0.728515625, -0.41650390625, -0.1829833984375, 1.5625, 0.339111328125, -0.196533203125, 0.9345703125, 0.19384765625, -0.81982421875, 0.55615234375, -0.91064453125, 0.48486328125, -0.2099609375, 0.16748046875, 0.02679443359375, 0.01031494140625, -0.32666015625, 0.038055419921875, 0.3447265625, -0.3671875, -0.391357421875, 0.1307373046875, -0.15771484375, 0.94580078125, -0.316162109375, 0.7998046875, -0.441650390625, -0.45361328125, -0.07568359375, -0.28857421875, -0.007274627685546875, -0.2958984375, -0.1417236328125, 0.8251953125, 0.55126953125, 1.2734375, 1.0400390625, -0.2890625, 0.3603515625, 0.322021484375, -0.398193359375, 0.2117919921875, 0.339599609375, 0.9150390625, -0.1876220703125, 0.34619140625, 0.052978515625, -0.2010498046875, -0.84033203125, -0.78271484375, 0.0771484375, 0.76611328125, -0.515625, 0.11956787109375, 0.05810546875, 0.208740234375, -0.72265625, -0.365234375, -0.13818359375, -1.04296875, -0.70458984375, 0.5283203125, -0.1300048828125, 0.415283203125, -0.4560546875, -0.478515625, 0.282470703125, 1.0166015625, -0.003631591796875, 0.300537109375, 0.3359375, -0.0192718505859375, -0.1279296875, 0.1357421875, 0.0195465087890625, -0.160888671875, -0.556640625, 0.8583984375, -0.071044921875, -0.114013671875, 0.04718017578125, 0.94775390625, 0.478271484375, 0.57470703125, -0.4462890625, -0.3330078125, 0.181396484375, 1.2548828125, -0.00682830810546875, 0.457763671875, 0.326416015625, 1.009765625, 0.7353515625, 0.64208984375, 0.463623046875, 0.61083984375, 0.86083984375, 0.6806640625, -0.06640625, 0.2275390625, -0.08587646484375, 0.4150390625, 0.1617431640625, 0.6337890625, 0.419921875, 0.3212890625, -0.0406494140625, 0.0784912109375, -0.3681640625, 0.5576171875, -0.2115478515625, 0.8662109375, 0.043731689453125, 0.7216796875, -0.51806640625, -0.525390625, 0.245849609375, 0.64697265625, -1.0107421875, -0.49853515625, -0.060943603515625, -0.0753173828125, -0.08770751953125, 0.1435546875, 0.2244873046875, 0.41455078125, 0.2646484375, 0.6396484375, -0.2548828125, -0.322265625, -0.9736328125, -0.6552734375, -1.1904296875, -0.0611572265625, -0.62451171875, 0.0770263671875, 0.20458984375, -0.8193359375, 0.16455078125, -0.66748046875, -0.32763671875, 0.24267578125, -0.48388671875, 0.483154296875, -0.041168212890625, 0.39599609375, -0.8076171875, 0.390869140625, 0.143310546875, 1.1865234375, -0.64501953125, -0.060577392578125, -0.1474609375, -0.60546875, 0.348876953125, -0.1461181640625, 0.0740966796875, 0.0238800048828125, -0.623046875, -0.97802734375, -0.395263671875, -0.002712249755859375, -0.2181396484375, -0.082763671875, -0.55908203125, 0.99853515625, 0.4833984375, -0.6796875, 0.54345703125, 0.7412109375, -0.97216796875, 0.3388671875, 0.43798828125, -0.037322998046875, -0.84375, 1.3583984375, 0.458740234375, 0.232421875, -0.458740234375, -0.52197265625, -0.29833984375, -0.01239013671875, 0.1324462890625, -0.53466796875, -0.1475830078125, 0.77001953125, -0.0201263427734375, -1.1103515625, 0.34033203125, -0.6875, -0.351806640625, -0.1600341796875, -0.3525390625, 0.86962890625, 0.87548828125, 0.388916015625, 0.14990234375, -0.2095947265625, -0.07598876953125, 0.482177734375, 0.414306640625, -0.39599609375, -0.2388916015625, 0.876953125, 0.1898193359375, 0.280517578125, -0.038909912109375, -0.1446533203125, -0.051849365234375, 0.190185546875, -0.03729248046875, 0.96435546875, 0.10015869140625, 0.51220703125, 0.103271484375, 0.888671875, -0.8447265625, -0.381103515625, -0.14453125, 0.5986328125, 0.67578125, 0.52001953125, 0.5908203125, -0.03118896484375, -0.391357421875, -1.263671875, 0.242919921875, -0.096435546875, 0.88916015625, -0.5166015625, 1.076171875, 0.0987548828125, -0.413818359375, 0.9013671875, -0.642578125, -0.04998779296875, 0.873046875, -0.0132598876953125, 0.71435546875, -0.444580078125, 0.09967041015625, -0.160400390625, -0.187255859375, 0.50537109375, 0.5517578125, 0.8642578125, -0.4169921875, -0.44921875, -0.342041015625, -0.1177978515625, -0.057647705078125, -0.30029296875, 0.037750244140625, -0.169677734375, -0.1910400390625, -0.8828125, 0.2203369140625, 0.493408203125, 0.88232421875, 0.06585693359375, 0.2196044921875, 0.427490234375, 0.419189453125, 0.96533203125, -0.4140625, 0.199462890625, -0.6865234375, 0.67236328125, 0.0130462646484375, -0.331787109375, -0.77197265625, -0.3720703125, -0.131591796875, 0.1453857421875, -0.053955078125, -0.380615234375, -1.17578125, 0.445068359375, -0.440673828125, 0.5947265625, -0.7490234375, 0.11077880859375, -0.497314453125, 0.2724609375, 0.244140625, -0.9658203125, 0.057708740234375, -0.5908203125, 0.304931640625, 0.37060546875, -0.23291015625, -0.49853515625, -0.6416015625, -0.69482421875, -1.001953125, 0.54638671875, 1.0205078125, 0.0118408203125, 0.07977294921875, -1.4619140625, 0.52685546875, 0.64501953125, -0.60546875, 0.13330078125, -0.250732421875, 0.48193359375, 0.275146484375, 0.84130859375, -0.3359375, -0.64794921875, -0.10064697265625, -1.240234375, 0.26708984375, -0.43896484375, 0.6875, 0.05609130859375, -0.11016845703125, -0.09423828125, 0.34228515625, 0.118896484375, 0.380859375, -0.341552734375, 0.336669921875, -0.87353515625, -0.87255859375, 0.66943359375, -0.31201171875, -0.42333984375, 1.1748046875, -0.12469482421875, -0.3173828125, 0.38671875, 0.57470703125, -0.3271484375, 0.634765625, -0.374755859375, 0.25732421875, -0.446533203125, -0.329345703125, -0.364990234375, -0.367431640625, 0.97412109375, 0.0411376953125, -0.6513671875, -0.11016845703125, -1.0302734375, -0.2213134765625, 0.16943359375, -0.421875, 0.310791015625, -0.141357421875, -0.0282135009765625, -0.258544921875, -0.1473388671875, -0.72119140625, -0.216796875, -0.45703125, -0.46240234375, 0.2408447265625, 0.328857421875, 0.6572265625, 0.3291015625, -0.361328125, -0.11859130859375, 0.007289886474609375, 0.141845703125, -0.383056640625, -0.291015625, -0.32421875, -0.318115234375, -0.427001953125, 0.12054443359375, 0.327392578125, 0.1817626953125, 0.435791015625, 0.3154296875, 0.60107421875, 0.450439453125, -0.77490234375, 0.94775390625, 0.11480712890625, -0.94287109375, -0.080322265625, 0.5927734375, 0.03271484375, 0.70849609375, -0.0712890625, -0.7998046875, -0.728515625, -0.8525390625, 0.38427734375, -0.56787109375, -0.304443359375, -1.1015625, -0.3505859375, -0.435302734375, 0.64404296875, -0.08770751953125, -0.4208984375, 0.1417236328125, -1.4287109375, -0.2047119140625, -0.796875, -0.2286376953125, -0.95458984375, -0.2335205078125, -0.390380859375, 0.85205078125, -0.07647705078125, 0.40966796875, -0.1673583984375, 0.12396240234375, 0.1998291015625, 0.31005859375, -0.45654296875, -0.4150390625, -0.25927734375, 0.08880615234375, -0.1258544921875, -0.0899658203125, -0.69140625, 0.7509765625, -0.791015625, 0.28271484375, -0.181396484375, 0.00614166259765625, -0.27001953125, -0.41796875, 1.169921875, -0.39892578125, -0.296875, -0.2054443359375, 0.1622314453125, 0.712890625, -0.54443359375, -0.3115234375, -1.0712890625, -0.3994140625, -0.93603515625, 0.548828125, -0.31640625, -0.04388427734375, -0.50048828125, -0.55517578125, 1.150390625, -0.59619140625, 0.26220703125, 1.158203125, 0.1163330078125, 0.266357421875, -0.77392578125, 0.66552734375, 0.75634765625, -0.59765625, 0.058013916015625, 0.11822509765625, -0.73974609375, 0.0694580078125, -0.390625, -1.068359375, -0.5107421875, 0.50830078125, 0.99951171875, -0.345947265625, 0.63232421875, 0.15966796875, -1.236328125, -0.478271484375, 1.23046875, 0.298095703125, 0.0875244140625, 0.83251953125, 0.118896484375, -0.08636474609375, -0.27978515625, -0.728515625, -0.244384765625, -0.473388671875, 1.4111328125, -0.65087890625, -0.5458984375, 1.0908203125, 0.8955078125, -1.5341796875, -0.89794921875, 0.0968017578125, 0.16455078125, 0.1800537109375, -0.8125, 0.06195068359375, 0.433837890625, -0.485107421875, -0.09130859375, 0.1273193359375, -0.04351806640625, 0.39453125, 0.040374755859375, 0.71484375, -0.720703125, 0.414794921875, 1.0458984375, -0.485595703125, -0.33349609375, -0.837890625, -0.2325439453125, -0.435791015625, -0.01473236083984375, 0.90576171875, -0.2498779296875, -0.0250091552734375, 0.61474609375, -0.142333984375, 0.95947265625, -0.6201171875, 0.04901123046875, 0.288330078125, -0.6787109375, -0.52294921875, -0.1474609375, 0.1884765625, 0.09381103515625, 0.63330078125, -0.892578125, 0.03564453125, 0.012786865234375, 0.2310791015625, -0.3876953125, -0.58447265625, -0.402587890625, -0.97802734375, -0.501953125, -0.81689453125, -0.8701171875, -0.35009765625, 0.302490234375, 0.2734375, -0.498046875, 0.1026611328125, 0.71240234375, -0.57568359375, 1.07421875, -0.7919921875, 0.2196044921875, -0.2325439453125, -0.174560546875, -0.5576171875, 0.09368896484375, -0.6533203125, 0.27197265625, -0.89794921875, 0.08001708984375, 0.08392333984375, 0.64453125, -0.251220703125, 0.84814453125, -0.2486572265625, -0.3125, 0.49853515625, -0.1475830078125, -0.317138671875, 1.0537109375, 0.372802734375, -0.0055999755859375, 0.0867919921875, -0.31884765625, -0.2406005859375, -0.33544921875, 0.25390625, 0.310546875, -0.2205810546875, -0.09600830078125, -0.05426025390625, 0.1986083984375, -1.1494140625, 0.419189453125, -0.3017578125, -0.08526611328125, -0.0302276611328125, -0.2044677734375, 0.5732421875, 1.10546875, -0.49609375, 0.2578125, -0.1517333984375, 0.10784912109375, 0.3583984375, 0.19970703125, -0.371826171875, 0.6865234375, 0.32177734375, -0.71533203125, 0.0355224609375, 0.30078125, 0.35498046875, 0.476806640625, -0.370849609375, -0.861328125, -1.0810546875, -0.198486328125, -0.0189666748046875, 0.221435546875, 0.4765625, -0.401611328125, -0.279541015625, -0.33544921875, -0.67578125, 0.5361328125, -1.1484375, -1.1474609375, 0.57470703125, -0.053497314453125, -0.60595703125, 0.048126220703125, -0.462158203125, -0.181396484375, 0.07073974609375, 0.1702880859375, -0.5986328125, 0.61767578125, -0.1925048828125, 0.38134765625, 0.0133819580078125, -0.302978515625, -0.0287322998046875, 0.7470703125, -0.748046875, -0.50390625, -0.223876953125, 0.9248046875, 0.11328125, -0.328369140625, -0.5751953125, 0.2108154296875, 0.287109375, -0.013427734375, -0.431396484375, -0.0201416015625, -0.2685546875, 0.7724609375, -0.95458984375, 0.1021728515625, -0.0244293212890625, 0.491943359375, 0.13671875, -0.13427734375, -0.44580078125, 0.79248046875, 0.865234375, 0.040863037109375, 0.69287109375, 0.125244140625, 0.6171875, 0.1705322265625, -0.06158447265625, -0.27978515625, 0.7705078125, 0.7275390625, 0.8564453125, -0.069091796875, 0.147705078125, 0.73681640625, 0.36328125, -0.25, 0.6298828125, -0.053314208984375, -0.00804901123046875, -0.12841796875, -0.249755859375, -0.00783538818359375, 0.109375, -0.4560546875, 0.533203125, -0.8779296875, -0.286865234375, -0.325927734375, -0.5068359375, 0.814453125, -0.0799560546875, 0.048187255859375, -0.123291015625, -0.327880859375, 0.6064453125, 0.28076171875, -0.263916015625, -0.018402099609375, 1.0751953125, 0.646484375, 0.351318359375, 0.86083984375, 0.1875, 0.409912109375, -0.62158203125, -0.0277252197265625, 0.1572265625, -0.32373046875, -0.3359375, -0.59716796875, -0.978515625, 0.80517578125, -0.1719970703125, -0.1866455078125, 0.64111328125, -0.97216796875, 0.07501220703125, -0.36474609375, 0.6767578125, -0.5400390625, 0.33056640625, 0.369384765625, -0.4375, -1.0439453125, 0.86572265625, -0.060455322265625, 0.37646484375, 0.226806640625, 0.82373046875, 0.1695556640625, 1.4052734375, 0.81298828125, -0.03753662109375, 0.2271728515625, 0.4091796875, -0.30712890625, -0.50927734375, -0.41259765625, -0.202392578125, 0.08984375, -0.66064453125, -0.401123046875, 0.0080718994140625, 0.45654296875, 0.3271484375, -1.029296875, -0.345458984375, 0.35205078125, -0.91796875, 0.6611328125, 0.290771484375, 0.321533203125, 0.265625, -0.1728515625, -0.415283203125, -0.4716796875, 0.26171875, -0.64892578125, 0.404052734375, -0.734375, -0.42333984375, -0.48681640625, -0.43896484375, -0.0911865234375, -0.0760498046875, -0.353271484375, -0.6865234375, 0.6298828125, 0.377197265625, 0.2230224609375, 0.233154296875, -0.45263671875, 0.24560546875, 0.8818359375, 0.81689453125, -0.0007815361022949219, 0.8671875, 0.4091796875, 0.01947021484375, 0.1185302734375, -0.1861572265625, 0.43212890625, -0.40771484375, 0.255859375, -0.6533203125, 0.352783203125, -0.8994140625, -1.08203125, 0.004913330078125, 0.35693359375, 0.2069091796875, -0.41162109375, -1.1337890625, -0.489990234375, -0.85400390625, -0.1873779296875, -0.76904296875, 0.783203125, -0.37939453125, -0.046051025390625, -0.0701904296875, -1.2763671875, 4.31640625, 0.91796875, 0.74951171875, 0.36181640625, 0.18798828125, 0.68310546875, 0.2496337890625, -0.8662109375, 0.05908203125, -0.3525390625, 0.55078125, -0.505859375, -0.08856201171875, 0.87158203125, 0.64453125, 0.55810546875, -0.59033203125, -0.263916015625, 0.24951171875, -0.9248046875, -0.87451171875, 0.489990234375, 0.032562255859375, 0.20166015625, 0.12078857421875, 0.2177734375, 0.7177734375, -0.818359375, -0.146240234375, -0.80224609375, 0.234375, -0.49755859375, 1, 0.1280517578125, -0.165771484375, 0.62841796875, 0.215087890625, -0.1572265625, -0.0189361572265625, 0.275146484375, -0.322509765625, -0.1435546875, 0.52490234375, -0.73681640625, -0.280517578125, 0.430908203125, -0.70556640625, 0.447509765625, 0.0204620361328125, -0.982421875, 1.001953125, -0.1575927734375, 0.2047119140625, -0.62548828125, -0.85546875, -0.1279296875, -0.01461029052734375, -0.327880859375, -0.0653076171875, 0.39208984375, 0.52685546875, 0.57568359375, 0.04644775390625, 0.8212890625, -1.5625, 0.556640625, -0.0147857666015625, 0.472412109375, -0.6376953125, -0.0181884765625, -0.61328125, -0.420654296875, -0.1324462890625, -0.50244140625, 0.68505859375, 0.2200927734375, -0.195556640625, 0.923828125, 0.80419921875, -0.466796875, 0.326171875, -0.10626220703125, -0.2470703125, -0.68310546875, 1.1630859375, 1.384765625, -0.86865234375, -0.377197265625, -0.221435546875, 0.46630859375, 0.30224609375, 0.806640625, 0.335205078125, -0.45263671875, -0.46826171875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Submitted Solution: ``` T = int(input()) ans = [] for t in range(T): n,k = map(int,input().split()) s = list(input()) for i in range(n): if s[i]=="0": s[i]="1" else: s[i]="0" count1 = 0 if k > 20: count1 = s[0:k-20].count("1") s = "".join(s) dic = {} for i in range(n-k+1): if k <= 20: dic[int(s[i:i+k],2)]=0 else: if count1==0: dic[int(s[i+k-20:i+k],2)]=0 count1 -= int(s[i]) count1 += int(s[i+k-20]) tmpans=10**10 for i in range(0,n+1): if not(i in dic): tmpans=i break if tmpans < pow(2,k): ans.append("YES") ans.append(format(tmpans,"0"+str(k)+"b")) else: ans.append("NO") for i in range(len(ans)): print(ans[i]) ``` Yes
107,246
[ 0.298583984375, -0.2012939453125, 0.2039794921875, 0.053497314453125, -0.486083984375, -0.43017578125, 0.09051513671875, 0.11016845703125, -0.05255126953125, 0.53466796875, 0.438720703125, -0.145263671875, -0.2283935546875, -1.001953125, -0.6826171875, -0.04876708984375, -0.3544921875, -0.45654296875, -0.392578125, -0.3173828125, -0.06396484375, -0.06890869140625, -1.1689453125, 0.060943603515625, -0.2890625, 1.013671875, 0.5341796875, 0.0814208984375, 1.17578125, 0.83251953125, -0.5810546875, -0.415283203125, 0.498779296875, -0.95166015625, -0.443115234375, -0.71044921875, 0.8583984375, -0.8896484375, -0.304931640625, -0.35693359375, 0.38134765625, -0.2274169921875, 0.450439453125, -0.7177734375, -1.3447265625, -0.0287933349609375, 0.0123748779296875, -0.322021484375, -0.221435546875, -0.70361328125, 0.002651214599609375, -0.2978515625, 0.1512451171875, -0.2384033203125, 0.11029052734375, 0.494873046875, 0.295654296875, -0.339599609375, -0.451904296875, 0.52294921875, -0.0182037353515625, 0.431396484375, 0.072509765625, -0.75, -0.0712890625, 0.175537109375, -0.1864013671875, -0.429443359375, -0.101806640625, -0.84716796875, -0.00580596923828125, -0.0014238357543945312, -0.398193359375, -0.448486328125, -0.12261962890625, 0.021514892578125, 0.14306640625, -0.12384033203125, -0.57470703125, 0.6611328125, -0.1922607421875, 1.064453125, 0.462890625, 0.469482421875, -0.44775390625, -0.529296875, 0.2130126953125, 0.247802734375, 0.36669921875, 0.07110595703125, -0.156494140625, 0.36181640625, -0.587890625, -0.09759521484375, 0.6162109375, 0.341064453125, -0.01220703125, 0.09100341796875, 0.2196044921875, 0.332763671875, 0.66796875, 0.87890625, -0.037811279296875, 1.3671875, -0.9521484375, -0.132080078125, -0.22119140625, -0.08074951171875, -0.193359375, -0.0660400390625, -0.0823974609375, -0.2218017578125, 0.54931640625, 0.44970703125, -0.368896484375, 0.75634765625, 0.04669189453125, 0.56494140625, -1.0380859375, 0.2447509765625, 0.61328125, 0.2081298828125, 0.72119140625, -0.1904296875, 0.091552734375, -0.2578125, -0.52099609375, 1.052734375, -0.315185546875, -0.2340087890625, 0.390625, -0.06365966796875, -0.11810302734375, 0.050750732421875, 0.037872314453125, 0.455078125, -0.0115814208984375, 0.259521484375, 0.78271484375, -0.53759765625, 0.728515625, -0.41650390625, -0.1829833984375, 1.5625, 0.339111328125, -0.196533203125, 0.9345703125, 0.19384765625, -0.81982421875, 0.55615234375, -0.91064453125, 0.48486328125, -0.2099609375, 0.16748046875, 0.02679443359375, 0.01031494140625, -0.32666015625, 0.038055419921875, 0.3447265625, -0.3671875, -0.391357421875, 0.1307373046875, -0.15771484375, 0.94580078125, -0.316162109375, 0.7998046875, -0.441650390625, -0.45361328125, -0.07568359375, -0.28857421875, -0.007274627685546875, -0.2958984375, -0.1417236328125, 0.8251953125, 0.55126953125, 1.2734375, 1.0400390625, -0.2890625, 0.3603515625, 0.322021484375, -0.398193359375, 0.2117919921875, 0.339599609375, 0.9150390625, -0.1876220703125, 0.34619140625, 0.052978515625, -0.2010498046875, -0.84033203125, -0.78271484375, 0.0771484375, 0.76611328125, -0.515625, 0.11956787109375, 0.05810546875, 0.208740234375, -0.72265625, -0.365234375, -0.13818359375, -1.04296875, -0.70458984375, 0.5283203125, -0.1300048828125, 0.415283203125, -0.4560546875, -0.478515625, 0.282470703125, 1.0166015625, -0.003631591796875, 0.300537109375, 0.3359375, -0.0192718505859375, -0.1279296875, 0.1357421875, 0.0195465087890625, -0.160888671875, -0.556640625, 0.8583984375, -0.071044921875, -0.114013671875, 0.04718017578125, 0.94775390625, 0.478271484375, 0.57470703125, -0.4462890625, -0.3330078125, 0.181396484375, 1.2548828125, -0.00682830810546875, 0.457763671875, 0.326416015625, 1.009765625, 0.7353515625, 0.64208984375, 0.463623046875, 0.61083984375, 0.86083984375, 0.6806640625, -0.06640625, 0.2275390625, -0.08587646484375, 0.4150390625, 0.1617431640625, 0.6337890625, 0.419921875, 0.3212890625, -0.0406494140625, 0.0784912109375, -0.3681640625, 0.5576171875, -0.2115478515625, 0.8662109375, 0.043731689453125, 0.7216796875, -0.51806640625, -0.525390625, 0.245849609375, 0.64697265625, -1.0107421875, -0.49853515625, -0.060943603515625, -0.0753173828125, -0.08770751953125, 0.1435546875, 0.2244873046875, 0.41455078125, 0.2646484375, 0.6396484375, -0.2548828125, -0.322265625, -0.9736328125, -0.6552734375, -1.1904296875, -0.0611572265625, -0.62451171875, 0.0770263671875, 0.20458984375, -0.8193359375, 0.16455078125, -0.66748046875, -0.32763671875, 0.24267578125, -0.48388671875, 0.483154296875, -0.041168212890625, 0.39599609375, -0.8076171875, 0.390869140625, 0.143310546875, 1.1865234375, -0.64501953125, -0.060577392578125, -0.1474609375, -0.60546875, 0.348876953125, -0.1461181640625, 0.0740966796875, 0.0238800048828125, -0.623046875, -0.97802734375, -0.395263671875, -0.002712249755859375, -0.2181396484375, -0.082763671875, -0.55908203125, 0.99853515625, 0.4833984375, -0.6796875, 0.54345703125, 0.7412109375, -0.97216796875, 0.3388671875, 0.43798828125, -0.037322998046875, -0.84375, 1.3583984375, 0.458740234375, 0.232421875, -0.458740234375, -0.52197265625, -0.29833984375, -0.01239013671875, 0.1324462890625, -0.53466796875, -0.1475830078125, 0.77001953125, -0.0201263427734375, -1.1103515625, 0.34033203125, -0.6875, -0.351806640625, -0.1600341796875, -0.3525390625, 0.86962890625, 0.87548828125, 0.388916015625, 0.14990234375, -0.2095947265625, -0.07598876953125, 0.482177734375, 0.414306640625, -0.39599609375, -0.2388916015625, 0.876953125, 0.1898193359375, 0.280517578125, -0.038909912109375, -0.1446533203125, -0.051849365234375, 0.190185546875, -0.03729248046875, 0.96435546875, 0.10015869140625, 0.51220703125, 0.103271484375, 0.888671875, -0.8447265625, -0.381103515625, -0.14453125, 0.5986328125, 0.67578125, 0.52001953125, 0.5908203125, -0.03118896484375, -0.391357421875, -1.263671875, 0.242919921875, -0.096435546875, 0.88916015625, -0.5166015625, 1.076171875, 0.0987548828125, -0.413818359375, 0.9013671875, -0.642578125, -0.04998779296875, 0.873046875, -0.0132598876953125, 0.71435546875, -0.444580078125, 0.09967041015625, -0.160400390625, -0.187255859375, 0.50537109375, 0.5517578125, 0.8642578125, -0.4169921875, -0.44921875, -0.342041015625, -0.1177978515625, -0.057647705078125, -0.30029296875, 0.037750244140625, -0.169677734375, -0.1910400390625, -0.8828125, 0.2203369140625, 0.493408203125, 0.88232421875, 0.06585693359375, 0.2196044921875, 0.427490234375, 0.419189453125, 0.96533203125, -0.4140625, 0.199462890625, -0.6865234375, 0.67236328125, 0.0130462646484375, -0.331787109375, -0.77197265625, -0.3720703125, -0.131591796875, 0.1453857421875, -0.053955078125, -0.380615234375, -1.17578125, 0.445068359375, -0.440673828125, 0.5947265625, -0.7490234375, 0.11077880859375, -0.497314453125, 0.2724609375, 0.244140625, -0.9658203125, 0.057708740234375, -0.5908203125, 0.304931640625, 0.37060546875, -0.23291015625, -0.49853515625, -0.6416015625, -0.69482421875, -1.001953125, 0.54638671875, 1.0205078125, 0.0118408203125, 0.07977294921875, -1.4619140625, 0.52685546875, 0.64501953125, -0.60546875, 0.13330078125, -0.250732421875, 0.48193359375, 0.275146484375, 0.84130859375, -0.3359375, -0.64794921875, -0.10064697265625, -1.240234375, 0.26708984375, -0.43896484375, 0.6875, 0.05609130859375, -0.11016845703125, -0.09423828125, 0.34228515625, 0.118896484375, 0.380859375, -0.341552734375, 0.336669921875, -0.87353515625, -0.87255859375, 0.66943359375, -0.31201171875, -0.42333984375, 1.1748046875, -0.12469482421875, -0.3173828125, 0.38671875, 0.57470703125, -0.3271484375, 0.634765625, -0.374755859375, 0.25732421875, -0.446533203125, -0.329345703125, -0.364990234375, -0.367431640625, 0.97412109375, 0.0411376953125, -0.6513671875, -0.11016845703125, -1.0302734375, -0.2213134765625, 0.16943359375, -0.421875, 0.310791015625, -0.141357421875, -0.0282135009765625, -0.258544921875, -0.1473388671875, -0.72119140625, -0.216796875, -0.45703125, -0.46240234375, 0.2408447265625, 0.328857421875, 0.6572265625, 0.3291015625, -0.361328125, -0.11859130859375, 0.007289886474609375, 0.141845703125, -0.383056640625, -0.291015625, -0.32421875, -0.318115234375, -0.427001953125, 0.12054443359375, 0.327392578125, 0.1817626953125, 0.435791015625, 0.3154296875, 0.60107421875, 0.450439453125, -0.77490234375, 0.94775390625, 0.11480712890625, -0.94287109375, -0.080322265625, 0.5927734375, 0.03271484375, 0.70849609375, -0.0712890625, -0.7998046875, -0.728515625, -0.8525390625, 0.38427734375, -0.56787109375, -0.304443359375, -1.1015625, -0.3505859375, -0.435302734375, 0.64404296875, -0.08770751953125, -0.4208984375, 0.1417236328125, -1.4287109375, -0.2047119140625, -0.796875, -0.2286376953125, -0.95458984375, -0.2335205078125, -0.390380859375, 0.85205078125, -0.07647705078125, 0.40966796875, -0.1673583984375, 0.12396240234375, 0.1998291015625, 0.31005859375, -0.45654296875, -0.4150390625, -0.25927734375, 0.08880615234375, -0.1258544921875, -0.0899658203125, -0.69140625, 0.7509765625, -0.791015625, 0.28271484375, -0.181396484375, 0.00614166259765625, -0.27001953125, -0.41796875, 1.169921875, -0.39892578125, -0.296875, -0.2054443359375, 0.1622314453125, 0.712890625, -0.54443359375, -0.3115234375, -1.0712890625, -0.3994140625, -0.93603515625, 0.548828125, -0.31640625, -0.04388427734375, -0.50048828125, -0.55517578125, 1.150390625, -0.59619140625, 0.26220703125, 1.158203125, 0.1163330078125, 0.266357421875, -0.77392578125, 0.66552734375, 0.75634765625, -0.59765625, 0.058013916015625, 0.11822509765625, -0.73974609375, 0.0694580078125, -0.390625, -1.068359375, -0.5107421875, 0.50830078125, 0.99951171875, -0.345947265625, 0.63232421875, 0.15966796875, -1.236328125, -0.478271484375, 1.23046875, 0.298095703125, 0.0875244140625, 0.83251953125, 0.118896484375, -0.08636474609375, -0.27978515625, -0.728515625, -0.244384765625, -0.473388671875, 1.4111328125, -0.65087890625, -0.5458984375, 1.0908203125, 0.8955078125, -1.5341796875, -0.89794921875, 0.0968017578125, 0.16455078125, 0.1800537109375, -0.8125, 0.06195068359375, 0.433837890625, -0.485107421875, -0.09130859375, 0.1273193359375, -0.04351806640625, 0.39453125, 0.040374755859375, 0.71484375, -0.720703125, 0.414794921875, 1.0458984375, -0.485595703125, -0.33349609375, -0.837890625, -0.2325439453125, -0.435791015625, -0.01473236083984375, 0.90576171875, -0.2498779296875, -0.0250091552734375, 0.61474609375, -0.142333984375, 0.95947265625, -0.6201171875, 0.04901123046875, 0.288330078125, -0.6787109375, -0.52294921875, -0.1474609375, 0.1884765625, 0.09381103515625, 0.63330078125, -0.892578125, 0.03564453125, 0.012786865234375, 0.2310791015625, -0.3876953125, -0.58447265625, -0.402587890625, -0.97802734375, -0.501953125, -0.81689453125, -0.8701171875, -0.35009765625, 0.302490234375, 0.2734375, -0.498046875, 0.1026611328125, 0.71240234375, -0.57568359375, 1.07421875, -0.7919921875, 0.2196044921875, -0.2325439453125, -0.174560546875, -0.5576171875, 0.09368896484375, -0.6533203125, 0.27197265625, -0.89794921875, 0.08001708984375, 0.08392333984375, 0.64453125, -0.251220703125, 0.84814453125, -0.2486572265625, -0.3125, 0.49853515625, -0.1475830078125, -0.317138671875, 1.0537109375, 0.372802734375, -0.0055999755859375, 0.0867919921875, -0.31884765625, -0.2406005859375, -0.33544921875, 0.25390625, 0.310546875, -0.2205810546875, -0.09600830078125, -0.05426025390625, 0.1986083984375, -1.1494140625, 0.419189453125, -0.3017578125, -0.08526611328125, -0.0302276611328125, -0.2044677734375, 0.5732421875, 1.10546875, -0.49609375, 0.2578125, -0.1517333984375, 0.10784912109375, 0.3583984375, 0.19970703125, -0.371826171875, 0.6865234375, 0.32177734375, -0.71533203125, 0.0355224609375, 0.30078125, 0.35498046875, 0.476806640625, -0.370849609375, -0.861328125, -1.0810546875, -0.198486328125, -0.0189666748046875, 0.221435546875, 0.4765625, -0.401611328125, -0.279541015625, -0.33544921875, -0.67578125, 0.5361328125, -1.1484375, -1.1474609375, 0.57470703125, -0.053497314453125, -0.60595703125, 0.048126220703125, -0.462158203125, -0.181396484375, 0.07073974609375, 0.1702880859375, -0.5986328125, 0.61767578125, -0.1925048828125, 0.38134765625, 0.0133819580078125, -0.302978515625, -0.0287322998046875, 0.7470703125, -0.748046875, -0.50390625, -0.223876953125, 0.9248046875, 0.11328125, -0.328369140625, -0.5751953125, 0.2108154296875, 0.287109375, -0.013427734375, -0.431396484375, -0.0201416015625, -0.2685546875, 0.7724609375, -0.95458984375, 0.1021728515625, -0.0244293212890625, 0.491943359375, 0.13671875, -0.13427734375, -0.44580078125, 0.79248046875, 0.865234375, 0.040863037109375, 0.69287109375, 0.125244140625, 0.6171875, 0.1705322265625, -0.06158447265625, -0.27978515625, 0.7705078125, 0.7275390625, 0.8564453125, -0.069091796875, 0.147705078125, 0.73681640625, 0.36328125, -0.25, 0.6298828125, -0.053314208984375, -0.00804901123046875, -0.12841796875, -0.249755859375, -0.00783538818359375, 0.109375, -0.4560546875, 0.533203125, -0.8779296875, -0.286865234375, -0.325927734375, -0.5068359375, 0.814453125, -0.0799560546875, 0.048187255859375, -0.123291015625, -0.327880859375, 0.6064453125, 0.28076171875, -0.263916015625, -0.018402099609375, 1.0751953125, 0.646484375, 0.351318359375, 0.86083984375, 0.1875, 0.409912109375, -0.62158203125, -0.0277252197265625, 0.1572265625, -0.32373046875, -0.3359375, -0.59716796875, -0.978515625, 0.80517578125, -0.1719970703125, -0.1866455078125, 0.64111328125, -0.97216796875, 0.07501220703125, -0.36474609375, 0.6767578125, -0.5400390625, 0.33056640625, 0.369384765625, -0.4375, -1.0439453125, 0.86572265625, -0.060455322265625, 0.37646484375, 0.226806640625, 0.82373046875, 0.1695556640625, 1.4052734375, 0.81298828125, -0.03753662109375, 0.2271728515625, 0.4091796875, -0.30712890625, -0.50927734375, -0.41259765625, -0.202392578125, 0.08984375, -0.66064453125, -0.401123046875, 0.0080718994140625, 0.45654296875, 0.3271484375, -1.029296875, -0.345458984375, 0.35205078125, -0.91796875, 0.6611328125, 0.290771484375, 0.321533203125, 0.265625, -0.1728515625, -0.415283203125, -0.4716796875, 0.26171875, -0.64892578125, 0.404052734375, -0.734375, -0.42333984375, -0.48681640625, -0.43896484375, -0.0911865234375, -0.0760498046875, -0.353271484375, -0.6865234375, 0.6298828125, 0.377197265625, 0.2230224609375, 0.233154296875, -0.45263671875, 0.24560546875, 0.8818359375, 0.81689453125, -0.0007815361022949219, 0.8671875, 0.4091796875, 0.01947021484375, 0.1185302734375, -0.1861572265625, 0.43212890625, -0.40771484375, 0.255859375, -0.6533203125, 0.352783203125, -0.8994140625, -1.08203125, 0.004913330078125, 0.35693359375, 0.2069091796875, -0.41162109375, -1.1337890625, -0.489990234375, -0.85400390625, -0.1873779296875, -0.76904296875, 0.783203125, -0.37939453125, -0.046051025390625, -0.0701904296875, -1.2763671875, 4.31640625, 0.91796875, 0.74951171875, 0.36181640625, 0.18798828125, 0.68310546875, 0.2496337890625, -0.8662109375, 0.05908203125, -0.3525390625, 0.55078125, -0.505859375, -0.08856201171875, 0.87158203125, 0.64453125, 0.55810546875, -0.59033203125, -0.263916015625, 0.24951171875, -0.9248046875, -0.87451171875, 0.489990234375, 0.032562255859375, 0.20166015625, 0.12078857421875, 0.2177734375, 0.7177734375, -0.818359375, -0.146240234375, -0.80224609375, 0.234375, -0.49755859375, 1, 0.1280517578125, -0.165771484375, 0.62841796875, 0.215087890625, -0.1572265625, -0.0189361572265625, 0.275146484375, -0.322509765625, -0.1435546875, 0.52490234375, -0.73681640625, -0.280517578125, 0.430908203125, -0.70556640625, 0.447509765625, 0.0204620361328125, -0.982421875, 1.001953125, -0.1575927734375, 0.2047119140625, -0.62548828125, -0.85546875, -0.1279296875, -0.01461029052734375, -0.327880859375, -0.0653076171875, 0.39208984375, 0.52685546875, 0.57568359375, 0.04644775390625, 0.8212890625, -1.5625, 0.556640625, -0.0147857666015625, 0.472412109375, -0.6376953125, -0.0181884765625, -0.61328125, -0.420654296875, -0.1324462890625, -0.50244140625, 0.68505859375, 0.2200927734375, -0.195556640625, 0.923828125, 0.80419921875, -0.466796875, 0.326171875, -0.10626220703125, -0.2470703125, -0.68310546875, 1.1630859375, 1.384765625, -0.86865234375, -0.377197265625, -0.221435546875, 0.46630859375, 0.30224609375, 0.806640625, 0.335205078125, -0.45263671875, -0.46826171875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Submitted Solution: ``` import sys input = sys.stdin.readline from collections import Counter import math t = int(input()) for _ in range(t): n,m = list(map(int,input().split())) k = min(21,m) s = input().rstrip() D = set() v = 2**k - 1 for i in range(len(s)-k+1): temp = s[i:i+k] #print(temp) D.add(v - int(temp,2)) ok = 0 if s[:m].count('1')==0 and m>len(s)//2: print('YES') print('0' * m) ok = 1 else: for i in range(v+1): if i not in D: ans = (bin(i))[2:] ans = (m - len(ans)) * '0' + ans print('YES') print(ans) ok = 1 break if ok==0: print('NO') ``` No
107,247
[ 0.298583984375, -0.2012939453125, 0.2039794921875, 0.053497314453125, -0.486083984375, -0.43017578125, 0.09051513671875, 0.11016845703125, -0.05255126953125, 0.53466796875, 0.438720703125, -0.145263671875, -0.2283935546875, -1.001953125, -0.6826171875, -0.04876708984375, -0.3544921875, -0.45654296875, -0.392578125, -0.3173828125, -0.06396484375, -0.06890869140625, -1.1689453125, 0.060943603515625, -0.2890625, 1.013671875, 0.5341796875, 0.0814208984375, 1.17578125, 0.83251953125, -0.5810546875, -0.415283203125, 0.498779296875, -0.95166015625, -0.443115234375, -0.71044921875, 0.8583984375, -0.8896484375, -0.304931640625, -0.35693359375, 0.38134765625, -0.2274169921875, 0.450439453125, -0.7177734375, -1.3447265625, -0.0287933349609375, 0.0123748779296875, -0.322021484375, -0.221435546875, -0.70361328125, 0.002651214599609375, -0.2978515625, 0.1512451171875, -0.2384033203125, 0.11029052734375, 0.494873046875, 0.295654296875, -0.339599609375, -0.451904296875, 0.52294921875, -0.0182037353515625, 0.431396484375, 0.072509765625, -0.75, -0.0712890625, 0.175537109375, -0.1864013671875, -0.429443359375, -0.101806640625, -0.84716796875, -0.00580596923828125, -0.0014238357543945312, -0.398193359375, -0.448486328125, -0.12261962890625, 0.021514892578125, 0.14306640625, -0.12384033203125, -0.57470703125, 0.6611328125, -0.1922607421875, 1.064453125, 0.462890625, 0.469482421875, -0.44775390625, -0.529296875, 0.2130126953125, 0.247802734375, 0.36669921875, 0.07110595703125, -0.156494140625, 0.36181640625, -0.587890625, -0.09759521484375, 0.6162109375, 0.341064453125, -0.01220703125, 0.09100341796875, 0.2196044921875, 0.332763671875, 0.66796875, 0.87890625, -0.037811279296875, 1.3671875, -0.9521484375, -0.132080078125, -0.22119140625, -0.08074951171875, -0.193359375, -0.0660400390625, -0.0823974609375, -0.2218017578125, 0.54931640625, 0.44970703125, -0.368896484375, 0.75634765625, 0.04669189453125, 0.56494140625, -1.0380859375, 0.2447509765625, 0.61328125, 0.2081298828125, 0.72119140625, -0.1904296875, 0.091552734375, -0.2578125, -0.52099609375, 1.052734375, -0.315185546875, -0.2340087890625, 0.390625, -0.06365966796875, -0.11810302734375, 0.050750732421875, 0.037872314453125, 0.455078125, -0.0115814208984375, 0.259521484375, 0.78271484375, -0.53759765625, 0.728515625, -0.41650390625, -0.1829833984375, 1.5625, 0.339111328125, -0.196533203125, 0.9345703125, 0.19384765625, -0.81982421875, 0.55615234375, -0.91064453125, 0.48486328125, -0.2099609375, 0.16748046875, 0.02679443359375, 0.01031494140625, -0.32666015625, 0.038055419921875, 0.3447265625, -0.3671875, -0.391357421875, 0.1307373046875, -0.15771484375, 0.94580078125, -0.316162109375, 0.7998046875, -0.441650390625, -0.45361328125, -0.07568359375, -0.28857421875, -0.007274627685546875, -0.2958984375, -0.1417236328125, 0.8251953125, 0.55126953125, 1.2734375, 1.0400390625, -0.2890625, 0.3603515625, 0.322021484375, -0.398193359375, 0.2117919921875, 0.339599609375, 0.9150390625, -0.1876220703125, 0.34619140625, 0.052978515625, -0.2010498046875, -0.84033203125, -0.78271484375, 0.0771484375, 0.76611328125, -0.515625, 0.11956787109375, 0.05810546875, 0.208740234375, -0.72265625, -0.365234375, -0.13818359375, -1.04296875, -0.70458984375, 0.5283203125, -0.1300048828125, 0.415283203125, -0.4560546875, -0.478515625, 0.282470703125, 1.0166015625, -0.003631591796875, 0.300537109375, 0.3359375, -0.0192718505859375, -0.1279296875, 0.1357421875, 0.0195465087890625, -0.160888671875, -0.556640625, 0.8583984375, -0.071044921875, -0.114013671875, 0.04718017578125, 0.94775390625, 0.478271484375, 0.57470703125, -0.4462890625, -0.3330078125, 0.181396484375, 1.2548828125, -0.00682830810546875, 0.457763671875, 0.326416015625, 1.009765625, 0.7353515625, 0.64208984375, 0.463623046875, 0.61083984375, 0.86083984375, 0.6806640625, -0.06640625, 0.2275390625, -0.08587646484375, 0.4150390625, 0.1617431640625, 0.6337890625, 0.419921875, 0.3212890625, -0.0406494140625, 0.0784912109375, -0.3681640625, 0.5576171875, -0.2115478515625, 0.8662109375, 0.043731689453125, 0.7216796875, -0.51806640625, -0.525390625, 0.245849609375, 0.64697265625, -1.0107421875, -0.49853515625, -0.060943603515625, -0.0753173828125, -0.08770751953125, 0.1435546875, 0.2244873046875, 0.41455078125, 0.2646484375, 0.6396484375, -0.2548828125, -0.322265625, -0.9736328125, -0.6552734375, -1.1904296875, -0.0611572265625, -0.62451171875, 0.0770263671875, 0.20458984375, -0.8193359375, 0.16455078125, -0.66748046875, -0.32763671875, 0.24267578125, -0.48388671875, 0.483154296875, -0.041168212890625, 0.39599609375, -0.8076171875, 0.390869140625, 0.143310546875, 1.1865234375, -0.64501953125, -0.060577392578125, -0.1474609375, -0.60546875, 0.348876953125, -0.1461181640625, 0.0740966796875, 0.0238800048828125, -0.623046875, -0.97802734375, -0.395263671875, -0.002712249755859375, -0.2181396484375, -0.082763671875, -0.55908203125, 0.99853515625, 0.4833984375, -0.6796875, 0.54345703125, 0.7412109375, -0.97216796875, 0.3388671875, 0.43798828125, -0.037322998046875, -0.84375, 1.3583984375, 0.458740234375, 0.232421875, -0.458740234375, -0.52197265625, -0.29833984375, -0.01239013671875, 0.1324462890625, -0.53466796875, -0.1475830078125, 0.77001953125, -0.0201263427734375, -1.1103515625, 0.34033203125, -0.6875, -0.351806640625, -0.1600341796875, -0.3525390625, 0.86962890625, 0.87548828125, 0.388916015625, 0.14990234375, -0.2095947265625, -0.07598876953125, 0.482177734375, 0.414306640625, -0.39599609375, -0.2388916015625, 0.876953125, 0.1898193359375, 0.280517578125, -0.038909912109375, -0.1446533203125, -0.051849365234375, 0.190185546875, -0.03729248046875, 0.96435546875, 0.10015869140625, 0.51220703125, 0.103271484375, 0.888671875, -0.8447265625, -0.381103515625, -0.14453125, 0.5986328125, 0.67578125, 0.52001953125, 0.5908203125, -0.03118896484375, -0.391357421875, -1.263671875, 0.242919921875, -0.096435546875, 0.88916015625, -0.5166015625, 1.076171875, 0.0987548828125, -0.413818359375, 0.9013671875, -0.642578125, -0.04998779296875, 0.873046875, -0.0132598876953125, 0.71435546875, -0.444580078125, 0.09967041015625, -0.160400390625, -0.187255859375, 0.50537109375, 0.5517578125, 0.8642578125, -0.4169921875, -0.44921875, -0.342041015625, -0.1177978515625, -0.057647705078125, -0.30029296875, 0.037750244140625, -0.169677734375, -0.1910400390625, -0.8828125, 0.2203369140625, 0.493408203125, 0.88232421875, 0.06585693359375, 0.2196044921875, 0.427490234375, 0.419189453125, 0.96533203125, -0.4140625, 0.199462890625, -0.6865234375, 0.67236328125, 0.0130462646484375, -0.331787109375, -0.77197265625, -0.3720703125, -0.131591796875, 0.1453857421875, -0.053955078125, -0.380615234375, -1.17578125, 0.445068359375, -0.440673828125, 0.5947265625, -0.7490234375, 0.11077880859375, -0.497314453125, 0.2724609375, 0.244140625, -0.9658203125, 0.057708740234375, -0.5908203125, 0.304931640625, 0.37060546875, -0.23291015625, -0.49853515625, -0.6416015625, -0.69482421875, -1.001953125, 0.54638671875, 1.0205078125, 0.0118408203125, 0.07977294921875, -1.4619140625, 0.52685546875, 0.64501953125, -0.60546875, 0.13330078125, -0.250732421875, 0.48193359375, 0.275146484375, 0.84130859375, -0.3359375, -0.64794921875, -0.10064697265625, -1.240234375, 0.26708984375, -0.43896484375, 0.6875, 0.05609130859375, -0.11016845703125, -0.09423828125, 0.34228515625, 0.118896484375, 0.380859375, -0.341552734375, 0.336669921875, -0.87353515625, -0.87255859375, 0.66943359375, -0.31201171875, -0.42333984375, 1.1748046875, -0.12469482421875, -0.3173828125, 0.38671875, 0.57470703125, -0.3271484375, 0.634765625, -0.374755859375, 0.25732421875, -0.446533203125, -0.329345703125, -0.364990234375, -0.367431640625, 0.97412109375, 0.0411376953125, -0.6513671875, -0.11016845703125, -1.0302734375, -0.2213134765625, 0.16943359375, -0.421875, 0.310791015625, -0.141357421875, -0.0282135009765625, -0.258544921875, -0.1473388671875, -0.72119140625, -0.216796875, -0.45703125, -0.46240234375, 0.2408447265625, 0.328857421875, 0.6572265625, 0.3291015625, -0.361328125, -0.11859130859375, 0.007289886474609375, 0.141845703125, -0.383056640625, -0.291015625, -0.32421875, -0.318115234375, -0.427001953125, 0.12054443359375, 0.327392578125, 0.1817626953125, 0.435791015625, 0.3154296875, 0.60107421875, 0.450439453125, -0.77490234375, 0.94775390625, 0.11480712890625, -0.94287109375, -0.080322265625, 0.5927734375, 0.03271484375, 0.70849609375, -0.0712890625, -0.7998046875, -0.728515625, -0.8525390625, 0.38427734375, -0.56787109375, -0.304443359375, -1.1015625, -0.3505859375, -0.435302734375, 0.64404296875, -0.08770751953125, -0.4208984375, 0.1417236328125, -1.4287109375, -0.2047119140625, -0.796875, -0.2286376953125, -0.95458984375, -0.2335205078125, -0.390380859375, 0.85205078125, -0.07647705078125, 0.40966796875, -0.1673583984375, 0.12396240234375, 0.1998291015625, 0.31005859375, -0.45654296875, -0.4150390625, -0.25927734375, 0.08880615234375, -0.1258544921875, -0.0899658203125, -0.69140625, 0.7509765625, -0.791015625, 0.28271484375, -0.181396484375, 0.00614166259765625, -0.27001953125, -0.41796875, 1.169921875, -0.39892578125, -0.296875, -0.2054443359375, 0.1622314453125, 0.712890625, -0.54443359375, -0.3115234375, -1.0712890625, -0.3994140625, -0.93603515625, 0.548828125, -0.31640625, -0.04388427734375, -0.50048828125, -0.55517578125, 1.150390625, -0.59619140625, 0.26220703125, 1.158203125, 0.1163330078125, 0.266357421875, -0.77392578125, 0.66552734375, 0.75634765625, -0.59765625, 0.058013916015625, 0.11822509765625, -0.73974609375, 0.0694580078125, -0.390625, -1.068359375, -0.5107421875, 0.50830078125, 0.99951171875, -0.345947265625, 0.63232421875, 0.15966796875, -1.236328125, -0.478271484375, 1.23046875, 0.298095703125, 0.0875244140625, 0.83251953125, 0.118896484375, -0.08636474609375, -0.27978515625, -0.728515625, -0.244384765625, -0.473388671875, 1.4111328125, -0.65087890625, -0.5458984375, 1.0908203125, 0.8955078125, -1.5341796875, -0.89794921875, 0.0968017578125, 0.16455078125, 0.1800537109375, -0.8125, 0.06195068359375, 0.433837890625, -0.485107421875, -0.09130859375, 0.1273193359375, -0.04351806640625, 0.39453125, 0.040374755859375, 0.71484375, -0.720703125, 0.414794921875, 1.0458984375, -0.485595703125, -0.33349609375, -0.837890625, -0.2325439453125, -0.435791015625, -0.01473236083984375, 0.90576171875, -0.2498779296875, -0.0250091552734375, 0.61474609375, -0.142333984375, 0.95947265625, -0.6201171875, 0.04901123046875, 0.288330078125, -0.6787109375, -0.52294921875, -0.1474609375, 0.1884765625, 0.09381103515625, 0.63330078125, -0.892578125, 0.03564453125, 0.012786865234375, 0.2310791015625, -0.3876953125, -0.58447265625, -0.402587890625, -0.97802734375, -0.501953125, -0.81689453125, -0.8701171875, -0.35009765625, 0.302490234375, 0.2734375, -0.498046875, 0.1026611328125, 0.71240234375, -0.57568359375, 1.07421875, -0.7919921875, 0.2196044921875, -0.2325439453125, -0.174560546875, -0.5576171875, 0.09368896484375, -0.6533203125, 0.27197265625, -0.89794921875, 0.08001708984375, 0.08392333984375, 0.64453125, -0.251220703125, 0.84814453125, -0.2486572265625, -0.3125, 0.49853515625, -0.1475830078125, -0.317138671875, 1.0537109375, 0.372802734375, -0.0055999755859375, 0.0867919921875, -0.31884765625, -0.2406005859375, -0.33544921875, 0.25390625, 0.310546875, -0.2205810546875, -0.09600830078125, -0.05426025390625, 0.1986083984375, -1.1494140625, 0.419189453125, -0.3017578125, -0.08526611328125, -0.0302276611328125, -0.2044677734375, 0.5732421875, 1.10546875, -0.49609375, 0.2578125, -0.1517333984375, 0.10784912109375, 0.3583984375, 0.19970703125, -0.371826171875, 0.6865234375, 0.32177734375, -0.71533203125, 0.0355224609375, 0.30078125, 0.35498046875, 0.476806640625, -0.370849609375, -0.861328125, -1.0810546875, -0.198486328125, -0.0189666748046875, 0.221435546875, 0.4765625, -0.401611328125, -0.279541015625, -0.33544921875, -0.67578125, 0.5361328125, -1.1484375, -1.1474609375, 0.57470703125, -0.053497314453125, -0.60595703125, 0.048126220703125, -0.462158203125, -0.181396484375, 0.07073974609375, 0.1702880859375, -0.5986328125, 0.61767578125, -0.1925048828125, 0.38134765625, 0.0133819580078125, -0.302978515625, -0.0287322998046875, 0.7470703125, -0.748046875, -0.50390625, -0.223876953125, 0.9248046875, 0.11328125, -0.328369140625, -0.5751953125, 0.2108154296875, 0.287109375, -0.013427734375, -0.431396484375, -0.0201416015625, -0.2685546875, 0.7724609375, -0.95458984375, 0.1021728515625, -0.0244293212890625, 0.491943359375, 0.13671875, -0.13427734375, -0.44580078125, 0.79248046875, 0.865234375, 0.040863037109375, 0.69287109375, 0.125244140625, 0.6171875, 0.1705322265625, -0.06158447265625, -0.27978515625, 0.7705078125, 0.7275390625, 0.8564453125, -0.069091796875, 0.147705078125, 0.73681640625, 0.36328125, -0.25, 0.6298828125, -0.053314208984375, -0.00804901123046875, -0.12841796875, -0.249755859375, -0.00783538818359375, 0.109375, -0.4560546875, 0.533203125, -0.8779296875, -0.286865234375, -0.325927734375, -0.5068359375, 0.814453125, -0.0799560546875, 0.048187255859375, -0.123291015625, -0.327880859375, 0.6064453125, 0.28076171875, -0.263916015625, -0.018402099609375, 1.0751953125, 0.646484375, 0.351318359375, 0.86083984375, 0.1875, 0.409912109375, -0.62158203125, -0.0277252197265625, 0.1572265625, -0.32373046875, -0.3359375, -0.59716796875, -0.978515625, 0.80517578125, -0.1719970703125, -0.1866455078125, 0.64111328125, -0.97216796875, 0.07501220703125, -0.36474609375, 0.6767578125, -0.5400390625, 0.33056640625, 0.369384765625, -0.4375, -1.0439453125, 0.86572265625, -0.060455322265625, 0.37646484375, 0.226806640625, 0.82373046875, 0.1695556640625, 1.4052734375, 0.81298828125, -0.03753662109375, 0.2271728515625, 0.4091796875, -0.30712890625, -0.50927734375, -0.41259765625, -0.202392578125, 0.08984375, -0.66064453125, -0.401123046875, 0.0080718994140625, 0.45654296875, 0.3271484375, -1.029296875, -0.345458984375, 0.35205078125, -0.91796875, 0.6611328125, 0.290771484375, 0.321533203125, 0.265625, -0.1728515625, -0.415283203125, -0.4716796875, 0.26171875, -0.64892578125, 0.404052734375, -0.734375, -0.42333984375, -0.48681640625, -0.43896484375, -0.0911865234375, -0.0760498046875, -0.353271484375, -0.6865234375, 0.6298828125, 0.377197265625, 0.2230224609375, 0.233154296875, -0.45263671875, 0.24560546875, 0.8818359375, 0.81689453125, -0.0007815361022949219, 0.8671875, 0.4091796875, 0.01947021484375, 0.1185302734375, -0.1861572265625, 0.43212890625, -0.40771484375, 0.255859375, -0.6533203125, 0.352783203125, -0.8994140625, -1.08203125, 0.004913330078125, 0.35693359375, 0.2069091796875, -0.41162109375, -1.1337890625, -0.489990234375, -0.85400390625, -0.1873779296875, -0.76904296875, 0.783203125, -0.37939453125, -0.046051025390625, -0.0701904296875, -1.2763671875, 4.31640625, 0.91796875, 0.74951171875, 0.36181640625, 0.18798828125, 0.68310546875, 0.2496337890625, -0.8662109375, 0.05908203125, -0.3525390625, 0.55078125, -0.505859375, -0.08856201171875, 0.87158203125, 0.64453125, 0.55810546875, -0.59033203125, -0.263916015625, 0.24951171875, -0.9248046875, -0.87451171875, 0.489990234375, 0.032562255859375, 0.20166015625, 0.12078857421875, 0.2177734375, 0.7177734375, -0.818359375, -0.146240234375, -0.80224609375, 0.234375, -0.49755859375, 1, 0.1280517578125, -0.165771484375, 0.62841796875, 0.215087890625, -0.1572265625, -0.0189361572265625, 0.275146484375, -0.322509765625, -0.1435546875, 0.52490234375, -0.73681640625, -0.280517578125, 0.430908203125, -0.70556640625, 0.447509765625, 0.0204620361328125, -0.982421875, 1.001953125, -0.1575927734375, 0.2047119140625, -0.62548828125, -0.85546875, -0.1279296875, -0.01461029052734375, -0.327880859375, -0.0653076171875, 0.39208984375, 0.52685546875, 0.57568359375, 0.04644775390625, 0.8212890625, -1.5625, 0.556640625, -0.0147857666015625, 0.472412109375, -0.6376953125, -0.0181884765625, -0.61328125, -0.420654296875, -0.1324462890625, -0.50244140625, 0.68505859375, 0.2200927734375, -0.195556640625, 0.923828125, 0.80419921875, -0.466796875, 0.326171875, -0.10626220703125, -0.2470703125, -0.68310546875, 1.1630859375, 1.384765625, -0.86865234375, -0.377197265625, -0.221435546875, 0.46630859375, 0.30224609375, 0.806640625, 0.335205078125, -0.45263671875, -0.46826171875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Submitted Solution: ``` from sys import stdin, gettrace, stdout if gettrace(): def inputi(): return input() else: def input(): return next(stdin)[:-1] def inputi(): return stdin.buffer.readline() def solve(ob): n, k = map(int, inputi().split()) ss = inputi() kk = min((n - k + 1).bit_length(), k) asize = 1<<kk mask = asize - 1 found = bytearray(asize) v = 0 for s in ss[0:kk-1]: v <<=1 if s == 0x31: v += 1 for s in ss[kk-1:n]: v <<=1 v &= mask if s == 0x31: v += 1 found[v] = 1 ndx = found.rfind(0) if ndx == -1: ob.write(b'NO\n') return else: ob.write(b'YES\n') v = asize - ndx - 1 res = bytearray(k) for i in range(k-1, -1, -1): res[i] = (v&1) + 0x30 v >>= 1 ob.write(res) ob.write(b'\n') def main(): t = int(inputi()) ob = stdout.buffer for _ in range(t): solve(ob) if __name__ == "__main__": main() ``` No
107,248
[ 0.298583984375, -0.2012939453125, 0.2039794921875, 0.053497314453125, -0.486083984375, -0.43017578125, 0.09051513671875, 0.11016845703125, -0.05255126953125, 0.53466796875, 0.438720703125, -0.145263671875, -0.2283935546875, -1.001953125, -0.6826171875, -0.04876708984375, -0.3544921875, -0.45654296875, -0.392578125, -0.3173828125, -0.06396484375, -0.06890869140625, -1.1689453125, 0.060943603515625, -0.2890625, 1.013671875, 0.5341796875, 0.0814208984375, 1.17578125, 0.83251953125, -0.5810546875, -0.415283203125, 0.498779296875, -0.95166015625, -0.443115234375, -0.71044921875, 0.8583984375, -0.8896484375, -0.304931640625, -0.35693359375, 0.38134765625, -0.2274169921875, 0.450439453125, -0.7177734375, -1.3447265625, -0.0287933349609375, 0.0123748779296875, -0.322021484375, -0.221435546875, -0.70361328125, 0.002651214599609375, -0.2978515625, 0.1512451171875, -0.2384033203125, 0.11029052734375, 0.494873046875, 0.295654296875, -0.339599609375, -0.451904296875, 0.52294921875, -0.0182037353515625, 0.431396484375, 0.072509765625, -0.75, -0.0712890625, 0.175537109375, -0.1864013671875, -0.429443359375, -0.101806640625, -0.84716796875, -0.00580596923828125, -0.0014238357543945312, -0.398193359375, -0.448486328125, -0.12261962890625, 0.021514892578125, 0.14306640625, -0.12384033203125, -0.57470703125, 0.6611328125, -0.1922607421875, 1.064453125, 0.462890625, 0.469482421875, -0.44775390625, -0.529296875, 0.2130126953125, 0.247802734375, 0.36669921875, 0.07110595703125, -0.156494140625, 0.36181640625, -0.587890625, -0.09759521484375, 0.6162109375, 0.341064453125, -0.01220703125, 0.09100341796875, 0.2196044921875, 0.332763671875, 0.66796875, 0.87890625, -0.037811279296875, 1.3671875, -0.9521484375, -0.132080078125, -0.22119140625, -0.08074951171875, -0.193359375, -0.0660400390625, -0.0823974609375, -0.2218017578125, 0.54931640625, 0.44970703125, -0.368896484375, 0.75634765625, 0.04669189453125, 0.56494140625, -1.0380859375, 0.2447509765625, 0.61328125, 0.2081298828125, 0.72119140625, -0.1904296875, 0.091552734375, -0.2578125, -0.52099609375, 1.052734375, -0.315185546875, -0.2340087890625, 0.390625, -0.06365966796875, -0.11810302734375, 0.050750732421875, 0.037872314453125, 0.455078125, -0.0115814208984375, 0.259521484375, 0.78271484375, -0.53759765625, 0.728515625, -0.41650390625, -0.1829833984375, 1.5625, 0.339111328125, -0.196533203125, 0.9345703125, 0.19384765625, -0.81982421875, 0.55615234375, -0.91064453125, 0.48486328125, -0.2099609375, 0.16748046875, 0.02679443359375, 0.01031494140625, -0.32666015625, 0.038055419921875, 0.3447265625, -0.3671875, -0.391357421875, 0.1307373046875, -0.15771484375, 0.94580078125, -0.316162109375, 0.7998046875, -0.441650390625, -0.45361328125, -0.07568359375, -0.28857421875, -0.007274627685546875, -0.2958984375, -0.1417236328125, 0.8251953125, 0.55126953125, 1.2734375, 1.0400390625, -0.2890625, 0.3603515625, 0.322021484375, -0.398193359375, 0.2117919921875, 0.339599609375, 0.9150390625, -0.1876220703125, 0.34619140625, 0.052978515625, -0.2010498046875, -0.84033203125, -0.78271484375, 0.0771484375, 0.76611328125, -0.515625, 0.11956787109375, 0.05810546875, 0.208740234375, -0.72265625, -0.365234375, -0.13818359375, -1.04296875, -0.70458984375, 0.5283203125, -0.1300048828125, 0.415283203125, -0.4560546875, -0.478515625, 0.282470703125, 1.0166015625, -0.003631591796875, 0.300537109375, 0.3359375, -0.0192718505859375, -0.1279296875, 0.1357421875, 0.0195465087890625, -0.160888671875, -0.556640625, 0.8583984375, -0.071044921875, -0.114013671875, 0.04718017578125, 0.94775390625, 0.478271484375, 0.57470703125, -0.4462890625, -0.3330078125, 0.181396484375, 1.2548828125, -0.00682830810546875, 0.457763671875, 0.326416015625, 1.009765625, 0.7353515625, 0.64208984375, 0.463623046875, 0.61083984375, 0.86083984375, 0.6806640625, -0.06640625, 0.2275390625, -0.08587646484375, 0.4150390625, 0.1617431640625, 0.6337890625, 0.419921875, 0.3212890625, -0.0406494140625, 0.0784912109375, -0.3681640625, 0.5576171875, -0.2115478515625, 0.8662109375, 0.043731689453125, 0.7216796875, -0.51806640625, -0.525390625, 0.245849609375, 0.64697265625, -1.0107421875, -0.49853515625, -0.060943603515625, -0.0753173828125, -0.08770751953125, 0.1435546875, 0.2244873046875, 0.41455078125, 0.2646484375, 0.6396484375, -0.2548828125, -0.322265625, -0.9736328125, -0.6552734375, -1.1904296875, -0.0611572265625, -0.62451171875, 0.0770263671875, 0.20458984375, -0.8193359375, 0.16455078125, -0.66748046875, -0.32763671875, 0.24267578125, -0.48388671875, 0.483154296875, -0.041168212890625, 0.39599609375, -0.8076171875, 0.390869140625, 0.143310546875, 1.1865234375, -0.64501953125, -0.060577392578125, -0.1474609375, -0.60546875, 0.348876953125, -0.1461181640625, 0.0740966796875, 0.0238800048828125, -0.623046875, -0.97802734375, -0.395263671875, -0.002712249755859375, -0.2181396484375, -0.082763671875, -0.55908203125, 0.99853515625, 0.4833984375, -0.6796875, 0.54345703125, 0.7412109375, -0.97216796875, 0.3388671875, 0.43798828125, -0.037322998046875, -0.84375, 1.3583984375, 0.458740234375, 0.232421875, -0.458740234375, -0.52197265625, -0.29833984375, -0.01239013671875, 0.1324462890625, -0.53466796875, -0.1475830078125, 0.77001953125, -0.0201263427734375, -1.1103515625, 0.34033203125, -0.6875, -0.351806640625, -0.1600341796875, -0.3525390625, 0.86962890625, 0.87548828125, 0.388916015625, 0.14990234375, -0.2095947265625, -0.07598876953125, 0.482177734375, 0.414306640625, -0.39599609375, -0.2388916015625, 0.876953125, 0.1898193359375, 0.280517578125, -0.038909912109375, -0.1446533203125, -0.051849365234375, 0.190185546875, -0.03729248046875, 0.96435546875, 0.10015869140625, 0.51220703125, 0.103271484375, 0.888671875, -0.8447265625, -0.381103515625, -0.14453125, 0.5986328125, 0.67578125, 0.52001953125, 0.5908203125, -0.03118896484375, -0.391357421875, -1.263671875, 0.242919921875, -0.096435546875, 0.88916015625, -0.5166015625, 1.076171875, 0.0987548828125, -0.413818359375, 0.9013671875, -0.642578125, -0.04998779296875, 0.873046875, -0.0132598876953125, 0.71435546875, -0.444580078125, 0.09967041015625, -0.160400390625, -0.187255859375, 0.50537109375, 0.5517578125, 0.8642578125, -0.4169921875, -0.44921875, -0.342041015625, -0.1177978515625, -0.057647705078125, -0.30029296875, 0.037750244140625, -0.169677734375, -0.1910400390625, -0.8828125, 0.2203369140625, 0.493408203125, 0.88232421875, 0.06585693359375, 0.2196044921875, 0.427490234375, 0.419189453125, 0.96533203125, -0.4140625, 0.199462890625, -0.6865234375, 0.67236328125, 0.0130462646484375, -0.331787109375, -0.77197265625, -0.3720703125, -0.131591796875, 0.1453857421875, -0.053955078125, -0.380615234375, -1.17578125, 0.445068359375, -0.440673828125, 0.5947265625, -0.7490234375, 0.11077880859375, -0.497314453125, 0.2724609375, 0.244140625, -0.9658203125, 0.057708740234375, -0.5908203125, 0.304931640625, 0.37060546875, -0.23291015625, -0.49853515625, -0.6416015625, -0.69482421875, -1.001953125, 0.54638671875, 1.0205078125, 0.0118408203125, 0.07977294921875, -1.4619140625, 0.52685546875, 0.64501953125, -0.60546875, 0.13330078125, -0.250732421875, 0.48193359375, 0.275146484375, 0.84130859375, -0.3359375, -0.64794921875, -0.10064697265625, -1.240234375, 0.26708984375, -0.43896484375, 0.6875, 0.05609130859375, -0.11016845703125, -0.09423828125, 0.34228515625, 0.118896484375, 0.380859375, -0.341552734375, 0.336669921875, -0.87353515625, -0.87255859375, 0.66943359375, -0.31201171875, -0.42333984375, 1.1748046875, -0.12469482421875, -0.3173828125, 0.38671875, 0.57470703125, -0.3271484375, 0.634765625, -0.374755859375, 0.25732421875, -0.446533203125, -0.329345703125, -0.364990234375, -0.367431640625, 0.97412109375, 0.0411376953125, -0.6513671875, -0.11016845703125, -1.0302734375, -0.2213134765625, 0.16943359375, -0.421875, 0.310791015625, -0.141357421875, -0.0282135009765625, -0.258544921875, -0.1473388671875, -0.72119140625, -0.216796875, -0.45703125, -0.46240234375, 0.2408447265625, 0.328857421875, 0.6572265625, 0.3291015625, -0.361328125, -0.11859130859375, 0.007289886474609375, 0.141845703125, -0.383056640625, -0.291015625, -0.32421875, -0.318115234375, -0.427001953125, 0.12054443359375, 0.327392578125, 0.1817626953125, 0.435791015625, 0.3154296875, 0.60107421875, 0.450439453125, -0.77490234375, 0.94775390625, 0.11480712890625, -0.94287109375, -0.080322265625, 0.5927734375, 0.03271484375, 0.70849609375, -0.0712890625, -0.7998046875, -0.728515625, -0.8525390625, 0.38427734375, -0.56787109375, -0.304443359375, -1.1015625, -0.3505859375, -0.435302734375, 0.64404296875, -0.08770751953125, -0.4208984375, 0.1417236328125, -1.4287109375, -0.2047119140625, -0.796875, -0.2286376953125, -0.95458984375, -0.2335205078125, -0.390380859375, 0.85205078125, -0.07647705078125, 0.40966796875, -0.1673583984375, 0.12396240234375, 0.1998291015625, 0.31005859375, -0.45654296875, -0.4150390625, -0.25927734375, 0.08880615234375, -0.1258544921875, -0.0899658203125, -0.69140625, 0.7509765625, -0.791015625, 0.28271484375, -0.181396484375, 0.00614166259765625, -0.27001953125, -0.41796875, 1.169921875, -0.39892578125, -0.296875, -0.2054443359375, 0.1622314453125, 0.712890625, -0.54443359375, -0.3115234375, -1.0712890625, -0.3994140625, -0.93603515625, 0.548828125, -0.31640625, -0.04388427734375, -0.50048828125, -0.55517578125, 1.150390625, -0.59619140625, 0.26220703125, 1.158203125, 0.1163330078125, 0.266357421875, -0.77392578125, 0.66552734375, 0.75634765625, -0.59765625, 0.058013916015625, 0.11822509765625, -0.73974609375, 0.0694580078125, -0.390625, -1.068359375, -0.5107421875, 0.50830078125, 0.99951171875, -0.345947265625, 0.63232421875, 0.15966796875, -1.236328125, -0.478271484375, 1.23046875, 0.298095703125, 0.0875244140625, 0.83251953125, 0.118896484375, -0.08636474609375, -0.27978515625, -0.728515625, -0.244384765625, -0.473388671875, 1.4111328125, -0.65087890625, -0.5458984375, 1.0908203125, 0.8955078125, -1.5341796875, -0.89794921875, 0.0968017578125, 0.16455078125, 0.1800537109375, -0.8125, 0.06195068359375, 0.433837890625, -0.485107421875, -0.09130859375, 0.1273193359375, -0.04351806640625, 0.39453125, 0.040374755859375, 0.71484375, -0.720703125, 0.414794921875, 1.0458984375, -0.485595703125, -0.33349609375, -0.837890625, -0.2325439453125, -0.435791015625, -0.01473236083984375, 0.90576171875, -0.2498779296875, -0.0250091552734375, 0.61474609375, -0.142333984375, 0.95947265625, -0.6201171875, 0.04901123046875, 0.288330078125, -0.6787109375, -0.52294921875, -0.1474609375, 0.1884765625, 0.09381103515625, 0.63330078125, -0.892578125, 0.03564453125, 0.012786865234375, 0.2310791015625, -0.3876953125, -0.58447265625, -0.402587890625, -0.97802734375, -0.501953125, -0.81689453125, -0.8701171875, -0.35009765625, 0.302490234375, 0.2734375, -0.498046875, 0.1026611328125, 0.71240234375, -0.57568359375, 1.07421875, -0.7919921875, 0.2196044921875, -0.2325439453125, -0.174560546875, -0.5576171875, 0.09368896484375, -0.6533203125, 0.27197265625, -0.89794921875, 0.08001708984375, 0.08392333984375, 0.64453125, -0.251220703125, 0.84814453125, -0.2486572265625, -0.3125, 0.49853515625, -0.1475830078125, -0.317138671875, 1.0537109375, 0.372802734375, -0.0055999755859375, 0.0867919921875, -0.31884765625, -0.2406005859375, -0.33544921875, 0.25390625, 0.310546875, -0.2205810546875, -0.09600830078125, -0.05426025390625, 0.1986083984375, -1.1494140625, 0.419189453125, -0.3017578125, -0.08526611328125, -0.0302276611328125, -0.2044677734375, 0.5732421875, 1.10546875, -0.49609375, 0.2578125, -0.1517333984375, 0.10784912109375, 0.3583984375, 0.19970703125, -0.371826171875, 0.6865234375, 0.32177734375, -0.71533203125, 0.0355224609375, 0.30078125, 0.35498046875, 0.476806640625, -0.370849609375, -0.861328125, -1.0810546875, -0.198486328125, -0.0189666748046875, 0.221435546875, 0.4765625, -0.401611328125, -0.279541015625, -0.33544921875, -0.67578125, 0.5361328125, -1.1484375, -1.1474609375, 0.57470703125, -0.053497314453125, -0.60595703125, 0.048126220703125, -0.462158203125, -0.181396484375, 0.07073974609375, 0.1702880859375, -0.5986328125, 0.61767578125, -0.1925048828125, 0.38134765625, 0.0133819580078125, -0.302978515625, -0.0287322998046875, 0.7470703125, -0.748046875, -0.50390625, -0.223876953125, 0.9248046875, 0.11328125, -0.328369140625, -0.5751953125, 0.2108154296875, 0.287109375, -0.013427734375, -0.431396484375, -0.0201416015625, -0.2685546875, 0.7724609375, -0.95458984375, 0.1021728515625, -0.0244293212890625, 0.491943359375, 0.13671875, -0.13427734375, -0.44580078125, 0.79248046875, 0.865234375, 0.040863037109375, 0.69287109375, 0.125244140625, 0.6171875, 0.1705322265625, -0.06158447265625, -0.27978515625, 0.7705078125, 0.7275390625, 0.8564453125, -0.069091796875, 0.147705078125, 0.73681640625, 0.36328125, -0.25, 0.6298828125, -0.053314208984375, -0.00804901123046875, -0.12841796875, -0.249755859375, -0.00783538818359375, 0.109375, -0.4560546875, 0.533203125, -0.8779296875, -0.286865234375, -0.325927734375, -0.5068359375, 0.814453125, -0.0799560546875, 0.048187255859375, -0.123291015625, -0.327880859375, 0.6064453125, 0.28076171875, -0.263916015625, -0.018402099609375, 1.0751953125, 0.646484375, 0.351318359375, 0.86083984375, 0.1875, 0.409912109375, -0.62158203125, -0.0277252197265625, 0.1572265625, -0.32373046875, -0.3359375, -0.59716796875, -0.978515625, 0.80517578125, -0.1719970703125, -0.1866455078125, 0.64111328125, -0.97216796875, 0.07501220703125, -0.36474609375, 0.6767578125, -0.5400390625, 0.33056640625, 0.369384765625, -0.4375, -1.0439453125, 0.86572265625, -0.060455322265625, 0.37646484375, 0.226806640625, 0.82373046875, 0.1695556640625, 1.4052734375, 0.81298828125, -0.03753662109375, 0.2271728515625, 0.4091796875, -0.30712890625, -0.50927734375, -0.41259765625, -0.202392578125, 0.08984375, -0.66064453125, -0.401123046875, 0.0080718994140625, 0.45654296875, 0.3271484375, -1.029296875, -0.345458984375, 0.35205078125, -0.91796875, 0.6611328125, 0.290771484375, 0.321533203125, 0.265625, -0.1728515625, -0.415283203125, -0.4716796875, 0.26171875, -0.64892578125, 0.404052734375, -0.734375, -0.42333984375, -0.48681640625, -0.43896484375, -0.0911865234375, -0.0760498046875, -0.353271484375, -0.6865234375, 0.6298828125, 0.377197265625, 0.2230224609375, 0.233154296875, -0.45263671875, 0.24560546875, 0.8818359375, 0.81689453125, -0.0007815361022949219, 0.8671875, 0.4091796875, 0.01947021484375, 0.1185302734375, -0.1861572265625, 0.43212890625, -0.40771484375, 0.255859375, -0.6533203125, 0.352783203125, -0.8994140625, -1.08203125, 0.004913330078125, 0.35693359375, 0.2069091796875, -0.41162109375, -1.1337890625, -0.489990234375, -0.85400390625, -0.1873779296875, -0.76904296875, 0.783203125, -0.37939453125, -0.046051025390625, -0.0701904296875, -1.2763671875, 4.31640625, 0.91796875, 0.74951171875, 0.36181640625, 0.18798828125, 0.68310546875, 0.2496337890625, -0.8662109375, 0.05908203125, -0.3525390625, 0.55078125, -0.505859375, -0.08856201171875, 0.87158203125, 0.64453125, 0.55810546875, -0.59033203125, -0.263916015625, 0.24951171875, -0.9248046875, -0.87451171875, 0.489990234375, 0.032562255859375, 0.20166015625, 0.12078857421875, 0.2177734375, 0.7177734375, -0.818359375, -0.146240234375, -0.80224609375, 0.234375, -0.49755859375, 1, 0.1280517578125, -0.165771484375, 0.62841796875, 0.215087890625, -0.1572265625, -0.0189361572265625, 0.275146484375, -0.322509765625, -0.1435546875, 0.52490234375, -0.73681640625, -0.280517578125, 0.430908203125, -0.70556640625, 0.447509765625, 0.0204620361328125, -0.982421875, 1.001953125, -0.1575927734375, 0.2047119140625, -0.62548828125, -0.85546875, -0.1279296875, -0.01461029052734375, -0.327880859375, -0.0653076171875, 0.39208984375, 0.52685546875, 0.57568359375, 0.04644775390625, 0.8212890625, -1.5625, 0.556640625, -0.0147857666015625, 0.472412109375, -0.6376953125, -0.0181884765625, -0.61328125, -0.420654296875, -0.1324462890625, -0.50244140625, 0.68505859375, 0.2200927734375, -0.195556640625, 0.923828125, 0.80419921875, -0.466796875, 0.326171875, -0.10626220703125, -0.2470703125, -0.68310546875, 1.1630859375, 1.384765625, -0.86865234375, -0.377197265625, -0.221435546875, 0.46630859375, 0.30224609375, 0.806640625, 0.335205078125, -0.45263671875, -0.46826171875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Submitted Solution: ``` import bisect import sys input=sys.stdin.readline from math import ceil t=int(input()) while t: n,k=map(int,input().split()) s=input().split()[0] z=[] for i in range(n): if(s[i]=='0'): z.append(i) co=0 cz=0 l=0 r=k-1 lol=0 for i in range(k): if(s[i]=='0'): cz+=1 else: co+=1 lol1=0 comp=[0]*k if(co==k): lol=1 if(cz==k): lol1=1 #print(cz,co) if(cz==1): ind=bisect.bisect_left(z,r) ind-=1 #print(ind,"ind") comp[ind]=1 while r<n: if(s[l]=='0'): cz-=1 else: co-=1 l+=1 r+=1 if(r==n): break if(s[r]=='0'): cz+=1 else: co+=1 if(co==k): lol=1 if(cz==k): lol1=1 if(cz==1): #print(r) ind=bisect.bisect_right(z,r) ind-=1 #print(ind,"ind") ind = ind-l+1 comp[ind]=1 yes=0 for i in range(k): if(comp[i]==1): comp[i]='0' else: yes=1 comp[i]='1' if(lol==1 and yes==0): if(lol1==0): print("YES") print("1"*k) else: print("NO") elif(lol==1 and yes==1): print("YES") print("".join(comp)) else: print("YES") print('0'*k) t-=1 ``` No
107,249
[ 0.298583984375, -0.2012939453125, 0.2039794921875, 0.053497314453125, -0.486083984375, -0.43017578125, 0.09051513671875, 0.11016845703125, -0.05255126953125, 0.53466796875, 0.438720703125, -0.145263671875, -0.2283935546875, -1.001953125, -0.6826171875, -0.04876708984375, -0.3544921875, -0.45654296875, -0.392578125, -0.3173828125, -0.06396484375, -0.06890869140625, -1.1689453125, 0.060943603515625, -0.2890625, 1.013671875, 0.5341796875, 0.0814208984375, 1.17578125, 0.83251953125, -0.5810546875, -0.415283203125, 0.498779296875, -0.95166015625, -0.443115234375, -0.71044921875, 0.8583984375, -0.8896484375, -0.304931640625, -0.35693359375, 0.38134765625, -0.2274169921875, 0.450439453125, -0.7177734375, -1.3447265625, -0.0287933349609375, 0.0123748779296875, -0.322021484375, -0.221435546875, -0.70361328125, 0.002651214599609375, -0.2978515625, 0.1512451171875, -0.2384033203125, 0.11029052734375, 0.494873046875, 0.295654296875, -0.339599609375, -0.451904296875, 0.52294921875, -0.0182037353515625, 0.431396484375, 0.072509765625, -0.75, -0.0712890625, 0.175537109375, -0.1864013671875, -0.429443359375, -0.101806640625, -0.84716796875, -0.00580596923828125, -0.0014238357543945312, -0.398193359375, -0.448486328125, -0.12261962890625, 0.021514892578125, 0.14306640625, -0.12384033203125, -0.57470703125, 0.6611328125, -0.1922607421875, 1.064453125, 0.462890625, 0.469482421875, -0.44775390625, -0.529296875, 0.2130126953125, 0.247802734375, 0.36669921875, 0.07110595703125, -0.156494140625, 0.36181640625, -0.587890625, -0.09759521484375, 0.6162109375, 0.341064453125, -0.01220703125, 0.09100341796875, 0.2196044921875, 0.332763671875, 0.66796875, 0.87890625, -0.037811279296875, 1.3671875, -0.9521484375, -0.132080078125, -0.22119140625, -0.08074951171875, -0.193359375, -0.0660400390625, -0.0823974609375, -0.2218017578125, 0.54931640625, 0.44970703125, -0.368896484375, 0.75634765625, 0.04669189453125, 0.56494140625, -1.0380859375, 0.2447509765625, 0.61328125, 0.2081298828125, 0.72119140625, -0.1904296875, 0.091552734375, -0.2578125, -0.52099609375, 1.052734375, -0.315185546875, -0.2340087890625, 0.390625, -0.06365966796875, -0.11810302734375, 0.050750732421875, 0.037872314453125, 0.455078125, -0.0115814208984375, 0.259521484375, 0.78271484375, -0.53759765625, 0.728515625, -0.41650390625, -0.1829833984375, 1.5625, 0.339111328125, -0.196533203125, 0.9345703125, 0.19384765625, -0.81982421875, 0.55615234375, -0.91064453125, 0.48486328125, -0.2099609375, 0.16748046875, 0.02679443359375, 0.01031494140625, -0.32666015625, 0.038055419921875, 0.3447265625, -0.3671875, -0.391357421875, 0.1307373046875, -0.15771484375, 0.94580078125, -0.316162109375, 0.7998046875, -0.441650390625, -0.45361328125, -0.07568359375, -0.28857421875, -0.007274627685546875, -0.2958984375, -0.1417236328125, 0.8251953125, 0.55126953125, 1.2734375, 1.0400390625, -0.2890625, 0.3603515625, 0.322021484375, -0.398193359375, 0.2117919921875, 0.339599609375, 0.9150390625, -0.1876220703125, 0.34619140625, 0.052978515625, -0.2010498046875, -0.84033203125, -0.78271484375, 0.0771484375, 0.76611328125, -0.515625, 0.11956787109375, 0.05810546875, 0.208740234375, -0.72265625, -0.365234375, -0.13818359375, -1.04296875, -0.70458984375, 0.5283203125, -0.1300048828125, 0.415283203125, -0.4560546875, -0.478515625, 0.282470703125, 1.0166015625, -0.003631591796875, 0.300537109375, 0.3359375, -0.0192718505859375, -0.1279296875, 0.1357421875, 0.0195465087890625, -0.160888671875, -0.556640625, 0.8583984375, -0.071044921875, -0.114013671875, 0.04718017578125, 0.94775390625, 0.478271484375, 0.57470703125, -0.4462890625, -0.3330078125, 0.181396484375, 1.2548828125, -0.00682830810546875, 0.457763671875, 0.326416015625, 1.009765625, 0.7353515625, 0.64208984375, 0.463623046875, 0.61083984375, 0.86083984375, 0.6806640625, -0.06640625, 0.2275390625, -0.08587646484375, 0.4150390625, 0.1617431640625, 0.6337890625, 0.419921875, 0.3212890625, -0.0406494140625, 0.0784912109375, -0.3681640625, 0.5576171875, -0.2115478515625, 0.8662109375, 0.043731689453125, 0.7216796875, -0.51806640625, -0.525390625, 0.245849609375, 0.64697265625, -1.0107421875, -0.49853515625, -0.060943603515625, -0.0753173828125, -0.08770751953125, 0.1435546875, 0.2244873046875, 0.41455078125, 0.2646484375, 0.6396484375, -0.2548828125, -0.322265625, -0.9736328125, -0.6552734375, -1.1904296875, -0.0611572265625, -0.62451171875, 0.0770263671875, 0.20458984375, -0.8193359375, 0.16455078125, -0.66748046875, -0.32763671875, 0.24267578125, -0.48388671875, 0.483154296875, -0.041168212890625, 0.39599609375, -0.8076171875, 0.390869140625, 0.143310546875, 1.1865234375, -0.64501953125, -0.060577392578125, -0.1474609375, -0.60546875, 0.348876953125, -0.1461181640625, 0.0740966796875, 0.0238800048828125, -0.623046875, -0.97802734375, -0.395263671875, -0.002712249755859375, -0.2181396484375, -0.082763671875, -0.55908203125, 0.99853515625, 0.4833984375, -0.6796875, 0.54345703125, 0.7412109375, -0.97216796875, 0.3388671875, 0.43798828125, -0.037322998046875, -0.84375, 1.3583984375, 0.458740234375, 0.232421875, -0.458740234375, -0.52197265625, -0.29833984375, -0.01239013671875, 0.1324462890625, -0.53466796875, -0.1475830078125, 0.77001953125, -0.0201263427734375, -1.1103515625, 0.34033203125, -0.6875, -0.351806640625, -0.1600341796875, -0.3525390625, 0.86962890625, 0.87548828125, 0.388916015625, 0.14990234375, -0.2095947265625, -0.07598876953125, 0.482177734375, 0.414306640625, -0.39599609375, -0.2388916015625, 0.876953125, 0.1898193359375, 0.280517578125, -0.038909912109375, -0.1446533203125, -0.051849365234375, 0.190185546875, -0.03729248046875, 0.96435546875, 0.10015869140625, 0.51220703125, 0.103271484375, 0.888671875, -0.8447265625, -0.381103515625, -0.14453125, 0.5986328125, 0.67578125, 0.52001953125, 0.5908203125, -0.03118896484375, -0.391357421875, -1.263671875, 0.242919921875, -0.096435546875, 0.88916015625, -0.5166015625, 1.076171875, 0.0987548828125, -0.413818359375, 0.9013671875, -0.642578125, -0.04998779296875, 0.873046875, -0.0132598876953125, 0.71435546875, -0.444580078125, 0.09967041015625, -0.160400390625, -0.187255859375, 0.50537109375, 0.5517578125, 0.8642578125, -0.4169921875, -0.44921875, -0.342041015625, -0.1177978515625, -0.057647705078125, -0.30029296875, 0.037750244140625, -0.169677734375, -0.1910400390625, -0.8828125, 0.2203369140625, 0.493408203125, 0.88232421875, 0.06585693359375, 0.2196044921875, 0.427490234375, 0.419189453125, 0.96533203125, -0.4140625, 0.199462890625, -0.6865234375, 0.67236328125, 0.0130462646484375, -0.331787109375, -0.77197265625, -0.3720703125, -0.131591796875, 0.1453857421875, -0.053955078125, -0.380615234375, -1.17578125, 0.445068359375, -0.440673828125, 0.5947265625, -0.7490234375, 0.11077880859375, -0.497314453125, 0.2724609375, 0.244140625, -0.9658203125, 0.057708740234375, -0.5908203125, 0.304931640625, 0.37060546875, -0.23291015625, -0.49853515625, -0.6416015625, -0.69482421875, -1.001953125, 0.54638671875, 1.0205078125, 0.0118408203125, 0.07977294921875, -1.4619140625, 0.52685546875, 0.64501953125, -0.60546875, 0.13330078125, -0.250732421875, 0.48193359375, 0.275146484375, 0.84130859375, -0.3359375, -0.64794921875, -0.10064697265625, -1.240234375, 0.26708984375, -0.43896484375, 0.6875, 0.05609130859375, -0.11016845703125, -0.09423828125, 0.34228515625, 0.118896484375, 0.380859375, -0.341552734375, 0.336669921875, -0.87353515625, -0.87255859375, 0.66943359375, -0.31201171875, -0.42333984375, 1.1748046875, -0.12469482421875, -0.3173828125, 0.38671875, 0.57470703125, -0.3271484375, 0.634765625, -0.374755859375, 0.25732421875, -0.446533203125, -0.329345703125, -0.364990234375, -0.367431640625, 0.97412109375, 0.0411376953125, -0.6513671875, -0.11016845703125, -1.0302734375, -0.2213134765625, 0.16943359375, -0.421875, 0.310791015625, -0.141357421875, -0.0282135009765625, -0.258544921875, -0.1473388671875, -0.72119140625, -0.216796875, -0.45703125, -0.46240234375, 0.2408447265625, 0.328857421875, 0.6572265625, 0.3291015625, -0.361328125, -0.11859130859375, 0.007289886474609375, 0.141845703125, -0.383056640625, -0.291015625, -0.32421875, -0.318115234375, -0.427001953125, 0.12054443359375, 0.327392578125, 0.1817626953125, 0.435791015625, 0.3154296875, 0.60107421875, 0.450439453125, -0.77490234375, 0.94775390625, 0.11480712890625, -0.94287109375, -0.080322265625, 0.5927734375, 0.03271484375, 0.70849609375, -0.0712890625, -0.7998046875, -0.728515625, -0.8525390625, 0.38427734375, -0.56787109375, -0.304443359375, -1.1015625, -0.3505859375, -0.435302734375, 0.64404296875, -0.08770751953125, -0.4208984375, 0.1417236328125, -1.4287109375, -0.2047119140625, -0.796875, -0.2286376953125, -0.95458984375, -0.2335205078125, -0.390380859375, 0.85205078125, -0.07647705078125, 0.40966796875, -0.1673583984375, 0.12396240234375, 0.1998291015625, 0.31005859375, -0.45654296875, -0.4150390625, -0.25927734375, 0.08880615234375, -0.1258544921875, -0.0899658203125, -0.69140625, 0.7509765625, -0.791015625, 0.28271484375, -0.181396484375, 0.00614166259765625, -0.27001953125, -0.41796875, 1.169921875, -0.39892578125, -0.296875, -0.2054443359375, 0.1622314453125, 0.712890625, -0.54443359375, -0.3115234375, -1.0712890625, -0.3994140625, -0.93603515625, 0.548828125, -0.31640625, -0.04388427734375, -0.50048828125, -0.55517578125, 1.150390625, -0.59619140625, 0.26220703125, 1.158203125, 0.1163330078125, 0.266357421875, -0.77392578125, 0.66552734375, 0.75634765625, -0.59765625, 0.058013916015625, 0.11822509765625, -0.73974609375, 0.0694580078125, -0.390625, -1.068359375, -0.5107421875, 0.50830078125, 0.99951171875, -0.345947265625, 0.63232421875, 0.15966796875, -1.236328125, -0.478271484375, 1.23046875, 0.298095703125, 0.0875244140625, 0.83251953125, 0.118896484375, -0.08636474609375, -0.27978515625, -0.728515625, -0.244384765625, -0.473388671875, 1.4111328125, -0.65087890625, -0.5458984375, 1.0908203125, 0.8955078125, -1.5341796875, -0.89794921875, 0.0968017578125, 0.16455078125, 0.1800537109375, -0.8125, 0.06195068359375, 0.433837890625, -0.485107421875, -0.09130859375, 0.1273193359375, -0.04351806640625, 0.39453125, 0.040374755859375, 0.71484375, -0.720703125, 0.414794921875, 1.0458984375, -0.485595703125, -0.33349609375, -0.837890625, -0.2325439453125, -0.435791015625, -0.01473236083984375, 0.90576171875, -0.2498779296875, -0.0250091552734375, 0.61474609375, -0.142333984375, 0.95947265625, -0.6201171875, 0.04901123046875, 0.288330078125, -0.6787109375, -0.52294921875, -0.1474609375, 0.1884765625, 0.09381103515625, 0.63330078125, -0.892578125, 0.03564453125, 0.012786865234375, 0.2310791015625, -0.3876953125, -0.58447265625, -0.402587890625, -0.97802734375, -0.501953125, -0.81689453125, -0.8701171875, -0.35009765625, 0.302490234375, 0.2734375, -0.498046875, 0.1026611328125, 0.71240234375, -0.57568359375, 1.07421875, -0.7919921875, 0.2196044921875, -0.2325439453125, -0.174560546875, -0.5576171875, 0.09368896484375, -0.6533203125, 0.27197265625, -0.89794921875, 0.08001708984375, 0.08392333984375, 0.64453125, -0.251220703125, 0.84814453125, -0.2486572265625, -0.3125, 0.49853515625, -0.1475830078125, -0.317138671875, 1.0537109375, 0.372802734375, -0.0055999755859375, 0.0867919921875, -0.31884765625, -0.2406005859375, -0.33544921875, 0.25390625, 0.310546875, -0.2205810546875, -0.09600830078125, -0.05426025390625, 0.1986083984375, -1.1494140625, 0.419189453125, -0.3017578125, -0.08526611328125, -0.0302276611328125, -0.2044677734375, 0.5732421875, 1.10546875, -0.49609375, 0.2578125, -0.1517333984375, 0.10784912109375, 0.3583984375, 0.19970703125, -0.371826171875, 0.6865234375, 0.32177734375, -0.71533203125, 0.0355224609375, 0.30078125, 0.35498046875, 0.476806640625, -0.370849609375, -0.861328125, -1.0810546875, -0.198486328125, -0.0189666748046875, 0.221435546875, 0.4765625, -0.401611328125, -0.279541015625, -0.33544921875, -0.67578125, 0.5361328125, -1.1484375, -1.1474609375, 0.57470703125, -0.053497314453125, -0.60595703125, 0.048126220703125, -0.462158203125, -0.181396484375, 0.07073974609375, 0.1702880859375, -0.5986328125, 0.61767578125, -0.1925048828125, 0.38134765625, 0.0133819580078125, -0.302978515625, -0.0287322998046875, 0.7470703125, -0.748046875, -0.50390625, -0.223876953125, 0.9248046875, 0.11328125, -0.328369140625, -0.5751953125, 0.2108154296875, 0.287109375, -0.013427734375, -0.431396484375, -0.0201416015625, -0.2685546875, 0.7724609375, -0.95458984375, 0.1021728515625, -0.0244293212890625, 0.491943359375, 0.13671875, -0.13427734375, -0.44580078125, 0.79248046875, 0.865234375, 0.040863037109375, 0.69287109375, 0.125244140625, 0.6171875, 0.1705322265625, -0.06158447265625, -0.27978515625, 0.7705078125, 0.7275390625, 0.8564453125, -0.069091796875, 0.147705078125, 0.73681640625, 0.36328125, -0.25, 0.6298828125, -0.053314208984375, -0.00804901123046875, -0.12841796875, -0.249755859375, -0.00783538818359375, 0.109375, -0.4560546875, 0.533203125, -0.8779296875, -0.286865234375, -0.325927734375, -0.5068359375, 0.814453125, -0.0799560546875, 0.048187255859375, -0.123291015625, -0.327880859375, 0.6064453125, 0.28076171875, -0.263916015625, -0.018402099609375, 1.0751953125, 0.646484375, 0.351318359375, 0.86083984375, 0.1875, 0.409912109375, -0.62158203125, -0.0277252197265625, 0.1572265625, -0.32373046875, -0.3359375, -0.59716796875, -0.978515625, 0.80517578125, -0.1719970703125, -0.1866455078125, 0.64111328125, -0.97216796875, 0.07501220703125, -0.36474609375, 0.6767578125, -0.5400390625, 0.33056640625, 0.369384765625, -0.4375, -1.0439453125, 0.86572265625, -0.060455322265625, 0.37646484375, 0.226806640625, 0.82373046875, 0.1695556640625, 1.4052734375, 0.81298828125, -0.03753662109375, 0.2271728515625, 0.4091796875, -0.30712890625, -0.50927734375, -0.41259765625, -0.202392578125, 0.08984375, -0.66064453125, -0.401123046875, 0.0080718994140625, 0.45654296875, 0.3271484375, -1.029296875, -0.345458984375, 0.35205078125, -0.91796875, 0.6611328125, 0.290771484375, 0.321533203125, 0.265625, -0.1728515625, -0.415283203125, -0.4716796875, 0.26171875, -0.64892578125, 0.404052734375, -0.734375, -0.42333984375, -0.48681640625, -0.43896484375, -0.0911865234375, -0.0760498046875, -0.353271484375, -0.6865234375, 0.6298828125, 0.377197265625, 0.2230224609375, 0.233154296875, -0.45263671875, 0.24560546875, 0.8818359375, 0.81689453125, -0.0007815361022949219, 0.8671875, 0.4091796875, 0.01947021484375, 0.1185302734375, -0.1861572265625, 0.43212890625, -0.40771484375, 0.255859375, -0.6533203125, 0.352783203125, -0.8994140625, -1.08203125, 0.004913330078125, 0.35693359375, 0.2069091796875, -0.41162109375, -1.1337890625, -0.489990234375, -0.85400390625, -0.1873779296875, -0.76904296875, 0.783203125, -0.37939453125, -0.046051025390625, -0.0701904296875, -1.2763671875, 4.31640625, 0.91796875, 0.74951171875, 0.36181640625, 0.18798828125, 0.68310546875, 0.2496337890625, -0.8662109375, 0.05908203125, -0.3525390625, 0.55078125, -0.505859375, -0.08856201171875, 0.87158203125, 0.64453125, 0.55810546875, -0.59033203125, -0.263916015625, 0.24951171875, -0.9248046875, -0.87451171875, 0.489990234375, 0.032562255859375, 0.20166015625, 0.12078857421875, 0.2177734375, 0.7177734375, -0.818359375, -0.146240234375, -0.80224609375, 0.234375, -0.49755859375, 1, 0.1280517578125, -0.165771484375, 0.62841796875, 0.215087890625, -0.1572265625, -0.0189361572265625, 0.275146484375, -0.322509765625, -0.1435546875, 0.52490234375, -0.73681640625, -0.280517578125, 0.430908203125, -0.70556640625, 0.447509765625, 0.0204620361328125, -0.982421875, 1.001953125, -0.1575927734375, 0.2047119140625, -0.62548828125, -0.85546875, -0.1279296875, -0.01461029052734375, -0.327880859375, -0.0653076171875, 0.39208984375, 0.52685546875, 0.57568359375, 0.04644775390625, 0.8212890625, -1.5625, 0.556640625, -0.0147857666015625, 0.472412109375, -0.6376953125, -0.0181884765625, -0.61328125, -0.420654296875, -0.1324462890625, -0.50244140625, 0.68505859375, 0.2200927734375, -0.195556640625, 0.923828125, 0.80419921875, -0.466796875, 0.326171875, -0.10626220703125, -0.2470703125, -0.68310546875, 1.1630859375, 1.384765625, -0.86865234375, -0.377197265625, -0.221435546875, 0.46630859375, 0.30224609375, 0.806640625, 0.335205078125, -0.45263671875, -0.46826171875 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let's call two strings a and b (both of length k) a bit similar if they have the same character in some position, i. e. there exists at least one i ∈ [1, k] such that a_i = b_i. You are given a binary string s of length n (a string of n characters 0 and/or 1) and an integer k. Let's denote the string s[i..j] as the substring of s starting from the i-th character and ending with the j-th character (that is, s[i..j] = s_i s_{i + 1} s_{i + 2} ... s_{j - 1} s_j). Let's call a binary string t of length k beautiful if it is a bit similar to all substrings of s having length exactly k; that is, it is a bit similar to s[1..k], s[2..k+1], ..., s[n-k+1..n]. Your goal is to find the lexicographically smallest string t that is beautiful, or report that no such string exists. String x is lexicographically less than string y if either x is a prefix of y (and x β‰  y), or there exists such i (1 ≀ i ≀ min(|x|, |y|)), that x_i < y_i, and for any j (1 ≀ j < i) x_j = y_j. Input The first line contains one integer q (1 ≀ q ≀ 10000) β€” the number of test cases. Each test case consists of two lines. The first line of each test case contains two integers n and k (1 ≀ k ≀ n ≀ 10^6). The second line contains the string s, consisting of n characters (each character is either 0 or 1). It is guaranteed that the sum of n over all test cases does not exceed 10^6. Output For each test case, print the answer as follows: * if it is impossible to construct a beautiful string, print one line containing the string NO (note: exactly in upper case, you can't print No, for example); * otherwise, print two lines. The first line should contain the string YES (exactly in upper case as well); the second line β€” the lexicographically smallest beautiful string, consisting of k characters 0 and/or 1. Example Input 7 4 2 0110 4 2 1001 9 3 010001110 9 3 101110001 10 3 0101110001 10 10 1111111111 11 10 11111111110 Output YES 11 YES 00 YES 010 YES 101 NO YES 0000000001 YES 0000000010 Submitted Solution: ``` import sys input = sys.stdin.readline for _ in range(int(input())): N, K = map(int, input().split()) S = list(map(int, list(input())[: -1])) res = [0] * K ln = min(K, 25) s = set() for i in range(N - K + 1): t = S[i + K - ln: i + K] x = 0 for j in range(ln): x |= t[j] << (ln - j - 1) s.add(x) for x in range((1 << ln) - 1, -1, -1): if x in s: continue print("YES") bn = list(bin(x))[2: ] bn = [0] * (ln - len(bn)) + bn print("".join([str(int(i) ^ 1) for i in bn]).zfill(K)) break else: print("NO") ``` No
107,250
[ 0.298583984375, -0.2012939453125, 0.2039794921875, 0.053497314453125, -0.486083984375, -0.43017578125, 0.09051513671875, 0.11016845703125, -0.05255126953125, 0.53466796875, 0.438720703125, -0.145263671875, -0.2283935546875, -1.001953125, -0.6826171875, -0.04876708984375, -0.3544921875, -0.45654296875, -0.392578125, -0.3173828125, -0.06396484375, -0.06890869140625, -1.1689453125, 0.060943603515625, -0.2890625, 1.013671875, 0.5341796875, 0.0814208984375, 1.17578125, 0.83251953125, -0.5810546875, -0.415283203125, 0.498779296875, -0.95166015625, -0.443115234375, -0.71044921875, 0.8583984375, -0.8896484375, -0.304931640625, -0.35693359375, 0.38134765625, -0.2274169921875, 0.450439453125, -0.7177734375, -1.3447265625, -0.0287933349609375, 0.0123748779296875, -0.322021484375, -0.221435546875, -0.70361328125, 0.002651214599609375, -0.2978515625, 0.1512451171875, -0.2384033203125, 0.11029052734375, 0.494873046875, 0.295654296875, -0.339599609375, -0.451904296875, 0.52294921875, -0.0182037353515625, 0.431396484375, 0.072509765625, -0.75, -0.0712890625, 0.175537109375, -0.1864013671875, -0.429443359375, -0.101806640625, -0.84716796875, -0.00580596923828125, -0.0014238357543945312, -0.398193359375, -0.448486328125, -0.12261962890625, 0.021514892578125, 0.14306640625, -0.12384033203125, -0.57470703125, 0.6611328125, -0.1922607421875, 1.064453125, 0.462890625, 0.469482421875, -0.44775390625, -0.529296875, 0.2130126953125, 0.247802734375, 0.36669921875, 0.07110595703125, -0.156494140625, 0.36181640625, -0.587890625, -0.09759521484375, 0.6162109375, 0.341064453125, -0.01220703125, 0.09100341796875, 0.2196044921875, 0.332763671875, 0.66796875, 0.87890625, -0.037811279296875, 1.3671875, -0.9521484375, -0.132080078125, -0.22119140625, -0.08074951171875, -0.193359375, -0.0660400390625, -0.0823974609375, -0.2218017578125, 0.54931640625, 0.44970703125, -0.368896484375, 0.75634765625, 0.04669189453125, 0.56494140625, -1.0380859375, 0.2447509765625, 0.61328125, 0.2081298828125, 0.72119140625, -0.1904296875, 0.091552734375, -0.2578125, -0.52099609375, 1.052734375, -0.315185546875, -0.2340087890625, 0.390625, -0.06365966796875, -0.11810302734375, 0.050750732421875, 0.037872314453125, 0.455078125, -0.0115814208984375, 0.259521484375, 0.78271484375, -0.53759765625, 0.728515625, -0.41650390625, -0.1829833984375, 1.5625, 0.339111328125, -0.196533203125, 0.9345703125, 0.19384765625, -0.81982421875, 0.55615234375, -0.91064453125, 0.48486328125, -0.2099609375, 0.16748046875, 0.02679443359375, 0.01031494140625, -0.32666015625, 0.038055419921875, 0.3447265625, -0.3671875, -0.391357421875, 0.1307373046875, -0.15771484375, 0.94580078125, -0.316162109375, 0.7998046875, -0.441650390625, -0.45361328125, -0.07568359375, -0.28857421875, -0.007274627685546875, -0.2958984375, -0.1417236328125, 0.8251953125, 0.55126953125, 1.2734375, 1.0400390625, -0.2890625, 0.3603515625, 0.322021484375, -0.398193359375, 0.2117919921875, 0.339599609375, 0.9150390625, -0.1876220703125, 0.34619140625, 0.052978515625, -0.2010498046875, -0.84033203125, -0.78271484375, 0.0771484375, 0.76611328125, -0.515625, 0.11956787109375, 0.05810546875, 0.208740234375, -0.72265625, -0.365234375, -0.13818359375, -1.04296875, -0.70458984375, 0.5283203125, -0.1300048828125, 0.415283203125, -0.4560546875, -0.478515625, 0.282470703125, 1.0166015625, -0.003631591796875, 0.300537109375, 0.3359375, -0.0192718505859375, -0.1279296875, 0.1357421875, 0.0195465087890625, -0.160888671875, -0.556640625, 0.8583984375, -0.071044921875, -0.114013671875, 0.04718017578125, 0.94775390625, 0.478271484375, 0.57470703125, -0.4462890625, -0.3330078125, 0.181396484375, 1.2548828125, -0.00682830810546875, 0.457763671875, 0.326416015625, 1.009765625, 0.7353515625, 0.64208984375, 0.463623046875, 0.61083984375, 0.86083984375, 0.6806640625, -0.06640625, 0.2275390625, -0.08587646484375, 0.4150390625, 0.1617431640625, 0.6337890625, 0.419921875, 0.3212890625, -0.0406494140625, 0.0784912109375, -0.3681640625, 0.5576171875, -0.2115478515625, 0.8662109375, 0.043731689453125, 0.7216796875, -0.51806640625, -0.525390625, 0.245849609375, 0.64697265625, -1.0107421875, -0.49853515625, -0.060943603515625, -0.0753173828125, -0.08770751953125, 0.1435546875, 0.2244873046875, 0.41455078125, 0.2646484375, 0.6396484375, -0.2548828125, -0.322265625, -0.9736328125, -0.6552734375, -1.1904296875, -0.0611572265625, -0.62451171875, 0.0770263671875, 0.20458984375, -0.8193359375, 0.16455078125, -0.66748046875, -0.32763671875, 0.24267578125, -0.48388671875, 0.483154296875, -0.041168212890625, 0.39599609375, -0.8076171875, 0.390869140625, 0.143310546875, 1.1865234375, -0.64501953125, -0.060577392578125, -0.1474609375, -0.60546875, 0.348876953125, -0.1461181640625, 0.0740966796875, 0.0238800048828125, -0.623046875, -0.97802734375, -0.395263671875, -0.002712249755859375, -0.2181396484375, -0.082763671875, -0.55908203125, 0.99853515625, 0.4833984375, -0.6796875, 0.54345703125, 0.7412109375, -0.97216796875, 0.3388671875, 0.43798828125, -0.037322998046875, -0.84375, 1.3583984375, 0.458740234375, 0.232421875, -0.458740234375, -0.52197265625, -0.29833984375, -0.01239013671875, 0.1324462890625, -0.53466796875, -0.1475830078125, 0.77001953125, -0.0201263427734375, -1.1103515625, 0.34033203125, -0.6875, -0.351806640625, -0.1600341796875, -0.3525390625, 0.86962890625, 0.87548828125, 0.388916015625, 0.14990234375, -0.2095947265625, -0.07598876953125, 0.482177734375, 0.414306640625, -0.39599609375, -0.2388916015625, 0.876953125, 0.1898193359375, 0.280517578125, -0.038909912109375, -0.1446533203125, -0.051849365234375, 0.190185546875, -0.03729248046875, 0.96435546875, 0.10015869140625, 0.51220703125, 0.103271484375, 0.888671875, -0.8447265625, -0.381103515625, -0.14453125, 0.5986328125, 0.67578125, 0.52001953125, 0.5908203125, -0.03118896484375, -0.391357421875, -1.263671875, 0.242919921875, -0.096435546875, 0.88916015625, -0.5166015625, 1.076171875, 0.0987548828125, -0.413818359375, 0.9013671875, -0.642578125, -0.04998779296875, 0.873046875, -0.0132598876953125, 0.71435546875, -0.444580078125, 0.09967041015625, -0.160400390625, -0.187255859375, 0.50537109375, 0.5517578125, 0.8642578125, -0.4169921875, -0.44921875, -0.342041015625, -0.1177978515625, -0.057647705078125, -0.30029296875, 0.037750244140625, -0.169677734375, -0.1910400390625, -0.8828125, 0.2203369140625, 0.493408203125, 0.88232421875, 0.06585693359375, 0.2196044921875, 0.427490234375, 0.419189453125, 0.96533203125, -0.4140625, 0.199462890625, -0.6865234375, 0.67236328125, 0.0130462646484375, -0.331787109375, -0.77197265625, -0.3720703125, -0.131591796875, 0.1453857421875, -0.053955078125, -0.380615234375, -1.17578125, 0.445068359375, -0.440673828125, 0.5947265625, -0.7490234375, 0.11077880859375, -0.497314453125, 0.2724609375, 0.244140625, -0.9658203125, 0.057708740234375, -0.5908203125, 0.304931640625, 0.37060546875, -0.23291015625, -0.49853515625, -0.6416015625, -0.69482421875, -1.001953125, 0.54638671875, 1.0205078125, 0.0118408203125, 0.07977294921875, -1.4619140625, 0.52685546875, 0.64501953125, -0.60546875, 0.13330078125, -0.250732421875, 0.48193359375, 0.275146484375, 0.84130859375, -0.3359375, -0.64794921875, -0.10064697265625, -1.240234375, 0.26708984375, -0.43896484375, 0.6875, 0.05609130859375, -0.11016845703125, -0.09423828125, 0.34228515625, 0.118896484375, 0.380859375, -0.341552734375, 0.336669921875, -0.87353515625, -0.87255859375, 0.66943359375, -0.31201171875, -0.42333984375, 1.1748046875, -0.12469482421875, -0.3173828125, 0.38671875, 0.57470703125, -0.3271484375, 0.634765625, -0.374755859375, 0.25732421875, -0.446533203125, -0.329345703125, -0.364990234375, -0.367431640625, 0.97412109375, 0.0411376953125, -0.6513671875, -0.11016845703125, -1.0302734375, -0.2213134765625, 0.16943359375, -0.421875, 0.310791015625, -0.141357421875, -0.0282135009765625, -0.258544921875, -0.1473388671875, -0.72119140625, -0.216796875, -0.45703125, -0.46240234375, 0.2408447265625, 0.328857421875, 0.6572265625, 0.3291015625, -0.361328125, -0.11859130859375, 0.007289886474609375, 0.141845703125, -0.383056640625, -0.291015625, -0.32421875, -0.318115234375, -0.427001953125, 0.12054443359375, 0.327392578125, 0.1817626953125, 0.435791015625, 0.3154296875, 0.60107421875, 0.450439453125, -0.77490234375, 0.94775390625, 0.11480712890625, -0.94287109375, -0.080322265625, 0.5927734375, 0.03271484375, 0.70849609375, -0.0712890625, -0.7998046875, -0.728515625, -0.8525390625, 0.38427734375, -0.56787109375, -0.304443359375, -1.1015625, -0.3505859375, -0.435302734375, 0.64404296875, -0.08770751953125, -0.4208984375, 0.1417236328125, -1.4287109375, -0.2047119140625, -0.796875, -0.2286376953125, -0.95458984375, -0.2335205078125, -0.390380859375, 0.85205078125, -0.07647705078125, 0.40966796875, -0.1673583984375, 0.12396240234375, 0.1998291015625, 0.31005859375, -0.45654296875, -0.4150390625, -0.25927734375, 0.08880615234375, -0.1258544921875, -0.0899658203125, -0.69140625, 0.7509765625, -0.791015625, 0.28271484375, -0.181396484375, 0.00614166259765625, -0.27001953125, -0.41796875, 1.169921875, -0.39892578125, -0.296875, -0.2054443359375, 0.1622314453125, 0.712890625, -0.54443359375, -0.3115234375, -1.0712890625, -0.3994140625, -0.93603515625, 0.548828125, -0.31640625, -0.04388427734375, -0.50048828125, -0.55517578125, 1.150390625, -0.59619140625, 0.26220703125, 1.158203125, 0.1163330078125, 0.266357421875, -0.77392578125, 0.66552734375, 0.75634765625, -0.59765625, 0.058013916015625, 0.11822509765625, -0.73974609375, 0.0694580078125, -0.390625, -1.068359375, -0.5107421875, 0.50830078125, 0.99951171875, -0.345947265625, 0.63232421875, 0.15966796875, -1.236328125, -0.478271484375, 1.23046875, 0.298095703125, 0.0875244140625, 0.83251953125, 0.118896484375, -0.08636474609375, -0.27978515625, -0.728515625, -0.244384765625, -0.473388671875, 1.4111328125, -0.65087890625, -0.5458984375, 1.0908203125, 0.8955078125, -1.5341796875, -0.89794921875, 0.0968017578125, 0.16455078125, 0.1800537109375, -0.8125, 0.06195068359375, 0.433837890625, -0.485107421875, -0.09130859375, 0.1273193359375, -0.04351806640625, 0.39453125, 0.040374755859375, 0.71484375, -0.720703125, 0.414794921875, 1.0458984375, -0.485595703125, -0.33349609375, -0.837890625, -0.2325439453125, -0.435791015625, -0.01473236083984375, 0.90576171875, -0.2498779296875, -0.0250091552734375, 0.61474609375, -0.142333984375, 0.95947265625, -0.6201171875, 0.04901123046875, 0.288330078125, -0.6787109375, -0.52294921875, -0.1474609375, 0.1884765625, 0.09381103515625, 0.63330078125, -0.892578125, 0.03564453125, 0.012786865234375, 0.2310791015625, -0.3876953125, -0.58447265625, -0.402587890625, -0.97802734375, -0.501953125, -0.81689453125, -0.8701171875, -0.35009765625, 0.302490234375, 0.2734375, -0.498046875, 0.1026611328125, 0.71240234375, -0.57568359375, 1.07421875, -0.7919921875, 0.2196044921875, -0.2325439453125, -0.174560546875, -0.5576171875, 0.09368896484375, -0.6533203125, 0.27197265625, -0.89794921875, 0.08001708984375, 0.08392333984375, 0.64453125, -0.251220703125, 0.84814453125, -0.2486572265625, -0.3125, 0.49853515625, -0.1475830078125, -0.317138671875, 1.0537109375, 0.372802734375, -0.0055999755859375, 0.0867919921875, -0.31884765625, -0.2406005859375, -0.33544921875, 0.25390625, 0.310546875, -0.2205810546875, -0.09600830078125, -0.05426025390625, 0.1986083984375, -1.1494140625, 0.419189453125, -0.3017578125, -0.08526611328125, -0.0302276611328125, -0.2044677734375, 0.5732421875, 1.10546875, -0.49609375, 0.2578125, -0.1517333984375, 0.10784912109375, 0.3583984375, 0.19970703125, -0.371826171875, 0.6865234375, 0.32177734375, -0.71533203125, 0.0355224609375, 0.30078125, 0.35498046875, 0.476806640625, -0.370849609375, -0.861328125, -1.0810546875, -0.198486328125, -0.0189666748046875, 0.221435546875, 0.4765625, -0.401611328125, -0.279541015625, -0.33544921875, -0.67578125, 0.5361328125, -1.1484375, -1.1474609375, 0.57470703125, -0.053497314453125, -0.60595703125, 0.048126220703125, -0.462158203125, -0.181396484375, 0.07073974609375, 0.1702880859375, -0.5986328125, 0.61767578125, -0.1925048828125, 0.38134765625, 0.0133819580078125, -0.302978515625, -0.0287322998046875, 0.7470703125, -0.748046875, -0.50390625, -0.223876953125, 0.9248046875, 0.11328125, -0.328369140625, -0.5751953125, 0.2108154296875, 0.287109375, -0.013427734375, -0.431396484375, -0.0201416015625, -0.2685546875, 0.7724609375, -0.95458984375, 0.1021728515625, -0.0244293212890625, 0.491943359375, 0.13671875, -0.13427734375, -0.44580078125, 0.79248046875, 0.865234375, 0.040863037109375, 0.69287109375, 0.125244140625, 0.6171875, 0.1705322265625, -0.06158447265625, -0.27978515625, 0.7705078125, 0.7275390625, 0.8564453125, -0.069091796875, 0.147705078125, 0.73681640625, 0.36328125, -0.25, 0.6298828125, -0.053314208984375, -0.00804901123046875, -0.12841796875, -0.249755859375, -0.00783538818359375, 0.109375, -0.4560546875, 0.533203125, -0.8779296875, -0.286865234375, -0.325927734375, -0.5068359375, 0.814453125, -0.0799560546875, 0.048187255859375, -0.123291015625, -0.327880859375, 0.6064453125, 0.28076171875, -0.263916015625, -0.018402099609375, 1.0751953125, 0.646484375, 0.351318359375, 0.86083984375, 0.1875, 0.409912109375, -0.62158203125, -0.0277252197265625, 0.1572265625, -0.32373046875, -0.3359375, -0.59716796875, -0.978515625, 0.80517578125, -0.1719970703125, -0.1866455078125, 0.64111328125, -0.97216796875, 0.07501220703125, -0.36474609375, 0.6767578125, -0.5400390625, 0.33056640625, 0.369384765625, -0.4375, -1.0439453125, 0.86572265625, -0.060455322265625, 0.37646484375, 0.226806640625, 0.82373046875, 0.1695556640625, 1.4052734375, 0.81298828125, -0.03753662109375, 0.2271728515625, 0.4091796875, -0.30712890625, -0.50927734375, -0.41259765625, -0.202392578125, 0.08984375, -0.66064453125, -0.401123046875, 0.0080718994140625, 0.45654296875, 0.3271484375, -1.029296875, -0.345458984375, 0.35205078125, -0.91796875, 0.6611328125, 0.290771484375, 0.321533203125, 0.265625, -0.1728515625, -0.415283203125, -0.4716796875, 0.26171875, -0.64892578125, 0.404052734375, -0.734375, -0.42333984375, -0.48681640625, -0.43896484375, -0.0911865234375, -0.0760498046875, -0.353271484375, -0.6865234375, 0.6298828125, 0.377197265625, 0.2230224609375, 0.233154296875, -0.45263671875, 0.24560546875, 0.8818359375, 0.81689453125, -0.0007815361022949219, 0.8671875, 0.4091796875, 0.01947021484375, 0.1185302734375, -0.1861572265625, 0.43212890625, -0.40771484375, 0.255859375, -0.6533203125, 0.352783203125, -0.8994140625, -1.08203125, 0.004913330078125, 0.35693359375, 0.2069091796875, -0.41162109375, -1.1337890625, -0.489990234375, -0.85400390625, -0.1873779296875, -0.76904296875, 0.783203125, -0.37939453125, -0.046051025390625, -0.0701904296875, -1.2763671875, 4.31640625, 0.91796875, 0.74951171875, 0.36181640625, 0.18798828125, 0.68310546875, 0.2496337890625, -0.8662109375, 0.05908203125, -0.3525390625, 0.55078125, -0.505859375, -0.08856201171875, 0.87158203125, 0.64453125, 0.55810546875, -0.59033203125, -0.263916015625, 0.24951171875, -0.9248046875, -0.87451171875, 0.489990234375, 0.032562255859375, 0.20166015625, 0.12078857421875, 0.2177734375, 0.7177734375, -0.818359375, -0.146240234375, -0.80224609375, 0.234375, -0.49755859375, 1, 0.1280517578125, -0.165771484375, 0.62841796875, 0.215087890625, -0.1572265625, -0.0189361572265625, 0.275146484375, -0.322509765625, -0.1435546875, 0.52490234375, -0.73681640625, -0.280517578125, 0.430908203125, -0.70556640625, 0.447509765625, 0.0204620361328125, -0.982421875, 1.001953125, -0.1575927734375, 0.2047119140625, -0.62548828125, -0.85546875, -0.1279296875, -0.01461029052734375, -0.327880859375, -0.0653076171875, 0.39208984375, 0.52685546875, 0.57568359375, 0.04644775390625, 0.8212890625, -1.5625, 0.556640625, -0.0147857666015625, 0.472412109375, -0.6376953125, -0.0181884765625, -0.61328125, -0.420654296875, -0.1324462890625, -0.50244140625, 0.68505859375, 0.2200927734375, -0.195556640625, 0.923828125, 0.80419921875, -0.466796875, 0.326171875, -0.10626220703125, -0.2470703125, -0.68310546875, 1.1630859375, 1.384765625, -0.86865234375, -0.377197265625, -0.221435546875, 0.46630859375, 0.30224609375, 0.806640625, 0.335205078125, -0.45263671875, -0.46826171875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: 1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si β‰  si + 1(1 ≀ i < n). 3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. Help him find such string or state that such string doesn't exist. String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes. Input A single line contains two positive integers n and k (1 ≀ n ≀ 106, 1 ≀ k ≀ 26) β€” the string's length and the number of distinct letters. Output In a single line print the required string. If there isn't such string, print "-1" (without the quotes). Examples Input 7 4 Output ababacd Input 4 7 Output -1 Tags: greedy Correct Solution: ``` #!/usr/bin/python3 n, k = map(int, input().split()) if n < k: print(-1) exit(0) if k == 1 and n == 1: print("a") exit(0) if k == 1: print(-1) exit(0) ans = [] b = 0 for i in range(n): if i + k - 2 >= n: ans.append(chr(ord('a') + k - (n - i))) else: ans.append(chr(ord('a') + b)) b ^= 1 print(''.join(ans)) ```
107,306
[ 0.46484375, -0.134765625, 0.58056640625, 0.300048828125, -0.191162109375, -0.50390625, 0.176025390625, 0.08001708984375, 0.3583984375, 0.78369140625, 0.75439453125, -0.1517333984375, 0.098388671875, -0.71875, -0.56201171875, 0.0875244140625, -0.6015625, -0.4462890625, -0.368896484375, 0.12103271484375, 0.0533447265625, -0.1075439453125, -1.5205078125, -0.0404052734375, -0.283447265625, 0.9853515625, 0.36279296875, 0.10430908203125, 1.0908203125, 0.98828125, -0.2685546875, -0.47119140625, 0.428466796875, -1.01953125, -0.61328125, -0.447509765625, 0.57763671875, -1.0400390625, -0.397705078125, -0.5966796875, 0.1148681640625, -0.72314453125, 0.4931640625, -0.69873046875, -1.181640625, -0.06378173828125, -0.583984375, -0.3779296875, -0.18115234375, -0.85498046875, 0.11370849609375, -0.217529296875, 0.533203125, -0.453125, 0.006366729736328125, 0.2442626953125, 0.2445068359375, -0.239013671875, -0.420166015625, 0.3330078125, -0.269287109375, 0.28515625, 0.090087890625, -0.505859375, -0.3212890625, -0.063232421875, -0.111083984375, -0.401611328125, 0.041473388671875, -0.71630859375, -0.2337646484375, 0.231689453125, -0.64111328125, -0.3486328125, -0.2021484375, 0.199462890625, 0.344482421875, -0.00678253173828125, -0.488037109375, 0.95703125, 0.5107421875, 1.455078125, 0.491943359375, 0.357666015625, -0.07550048828125, -0.5771484375, 0.07000732421875, 0.59375, 0.25732421875, -0.27099609375, 0.1888427734375, 0.53515625, -0.84423828125, 0.22705078125, 0.51171875, 0.41748046875, 0.103759765625, 0.427001953125, 0.29833984375, -0.121337890625, 0.85107421875, 1.033203125, -0.291259765625, 0.96728515625, -0.5703125, 0.346923828125, -0.02972412109375, -0.21435546875, -0.2203369140625, -0.37109375, -0.2191162109375, -0.1368408203125, 0.7158203125, 0.209716796875, -0.349365234375, 0.98193359375, -0.1297607421875, 0.255615234375, -0.80517578125, -0.05572509765625, 0.463134765625, 0.393310546875, 0.77197265625, 0.03271484375, -0.1373291015625, -0.222900390625, -0.67041015625, 0.9375, -0.65625, 0.23046875, 0.40380859375, 0.08245849609375, 0.0171966552734375, 0.09381103515625, 0.217041015625, 0.5966796875, -0.1265869140625, 0.51123046875, 0.5576171875, -0.45556640625, 0.80224609375, -0.30712890625, -0.06463623046875, 1.45703125, 0.4970703125, -0.2041015625, 0.76513671875, 0.1839599609375, -0.8076171875, 0.32861328125, -1.19921875, 0.62451171875, -0.07012939453125, 0.089599609375, -0.1156005859375, 0.267822265625, -0.343994140625, 0.24853515625, 0.41845703125, 0.2357177734375, -0.58203125, 0.11944580078125, -0.155029296875, 0.62939453125, -0.310546875, 0.72900390625, -0.5869140625, -0.12091064453125, 0.06048583984375, -0.2900390625, 0.26708984375, -0.10302734375, -0.281005859375, 0.87890625, 0.724609375, 1.1875, 0.9931640625, -0.27880859375, 0.171142578125, 0.423095703125, -0.479736328125, 0.051116943359375, 0.2213134765625, 0.444091796875, 0.091796875, 0.3427734375, -0.0225982666015625, -0.5126953125, -0.9501953125, -0.671875, -0.025787353515625, 0.31591796875, -0.209716796875, 0.399169921875, -0.032501220703125, -0.0203857421875, -0.666015625, -0.2259521484375, -0.28466796875, -1.0859375, -0.302978515625, 0.68701171875, -0.1317138671875, 0.450439453125, -0.49267578125, -0.258056640625, 0.4873046875, 0.9970703125, -0.41455078125, 0.08135986328125, 0.1981201171875, 0.059814453125, -0.1287841796875, 0.1644287109375, 0.254150390625, 0.2003173828125, -0.8291015625, 0.78515625, -0.265380859375, 0.10626220703125, 0.265380859375, 0.8818359375, 0.1173095703125, 0.498779296875, -0.248046875, -0.10797119140625, 0.6103515625, 0.8212890625, 0.0196685791015625, 0.6875, 0.34619140625, 1.212890625, 0.7666015625, 0.456787109375, 0.5478515625, 0.65185546875, 0.61962890625, 1.0712890625, 0.06781005859375, 0.316162109375, -0.1563720703125, 0.4521484375, -0.1265869140625, 0.3916015625, 0.30322265625, 0.471435546875, -0.050445556640625, 0.07940673828125, -0.217041015625, 0.2496337890625, -0.0305328369140625, 0.88525390625, 0.146240234375, 0.408447265625, -0.474609375, -0.36669921875, 0.04351806640625, 0.81591796875, -0.544921875, -0.433349609375, -0.172119140625, 0.143310546875, -0.006694793701171875, -0.2249755859375, 0.208251953125, 0.291015625, 0.47607421875, 0.07867431640625, -0.335693359375, -0.220458984375, -1.2646484375, -0.5576171875, -1.20703125, -0.12274169921875, -0.71044921875, 0.128173828125, 0.49365234375, -0.9833984375, 0.06951904296875, -0.328369140625, -0.27294921875, 0.189208984375, -0.7529296875, 0.53759765625, 0.08624267578125, 0.473876953125, -0.52783203125, 0.450927734375, 0.0740966796875, 0.93994140625, -0.30615234375, -0.268798828125, 0.0283355712890625, -0.40380859375, 0.35205078125, -0.212890625, 0.471923828125, 0.039276123046875, -0.427734375, -0.94580078125, -0.54052734375, -0.08880615234375, -0.2366943359375, 0.1522216796875, -0.282470703125, 1.0693359375, 0.533203125, -0.787109375, 0.5224609375, 0.7099609375, -0.857421875, 0.485107421875, 0.390625, 0.1898193359375, -0.85498046875, 1.455078125, 0.3310546875, -0.04229736328125, -0.61279296875, -0.548828125, -0.363037109375, 0.275146484375, 0.08380126953125, -0.437744140625, 0.049957275390625, 0.47607421875, 0.193115234375, -1.216796875, 0.77001953125, -1.017578125, -0.5390625, -0.5048828125, -0.188720703125, 0.71240234375, 0.5126953125, 0.292236328125, -0.1334228515625, -0.398193359375, -0.449951171875, 0.41650390625, 0.349853515625, -0.7109375, -0.16064453125, 0.50390625, -0.421875, 0.19677734375, 0.0019321441650390625, -0.094482421875, 0.04022216796875, -0.140380859375, 0.221435546875, 0.904296875, 0.303955078125, 0.0670166015625, 0.30126953125, 0.9580078125, -0.63134765625, -0.357666015625, -0.54345703125, 0.681640625, 0.28173828125, 0.828125, 0.38232421875, -0.2998046875, -0.25732421875, -1.4326171875, 0.27587890625, -0.156982421875, 0.775390625, -0.5068359375, 1.02734375, 0.60400390625, -0.4560546875, 0.49853515625, -0.498046875, -0.285888671875, 1.2109375, -0.02294921875, 0.8115234375, -0.378173828125, 0.45068359375, -0.2083740234375, -0.330078125, 0.62109375, 0.280517578125, 0.77490234375, -0.373779296875, -0.642578125, -0.455078125, -0.5458984375, 0.04168701171875, -0.5732421875, 0.28759765625, -0.4130859375, -0.222412109375, -0.33984375, 0.293212890625, 0.7353515625, 0.51220703125, 0.0758056640625, 0.461181640625, 0.029876708984375, 0.29052734375, 0.33056640625, -0.5517578125, -0.0200653076171875, -0.372314453125, 0.73486328125, 0.235595703125, -0.1805419921875, -0.87255859375, -0.5126953125, 0.04571533203125, -0.212158203125, -0.056304931640625, -0.48876953125, -0.7392578125, 0.197998046875, -0.2403564453125, 0.37841796875, -0.55224609375, -0.486328125, -0.2919921875, 0.398193359375, 0.43310546875, -1.0009765625, 0.1268310546875, -0.52001953125, 0.4375, 0.368408203125, -0.058349609375, -0.287109375, -0.52001953125, -0.66357421875, -0.6962890625, 0.24462890625, 0.72802734375, -0.0252227783203125, 0.1868896484375, -1.43359375, 0.48291015625, 0.1678466796875, 0.047210693359375, 0.144775390625, 0.2335205078125, 0.46630859375, 0.2064208984375, 0.83544921875, -0.458740234375, -0.86083984375, 0.1951904296875, -1.3291015625, 0.544921875, -0.63427734375, 0.247314453125, 0.042327880859375, 0.151611328125, -0.1641845703125, 0.51904296875, -0.174072265625, 0.351806640625, 0.0347900390625, 0.402099609375, -1.0009765625, -0.50537109375, 0.56396484375, -0.40576171875, -0.2685546875, 1.330078125, -0.159423828125, -0.50048828125, 0.5830078125, 0.54931640625, -0.32177734375, 0.1844482421875, -0.344970703125, 0.5693359375, -0.3603515625, -0.206298828125, -0.030120849609375, -0.457763671875, 0.9443359375, -0.1414794921875, -0.94189453125, -0.362060546875, -1.2529296875, -0.189697265625, -0.2227783203125, -0.30517578125, 0.335205078125, -0.1932373046875, -0.08642578125, -0.265625, -0.53271484375, -0.3583984375, -0.2486572265625, -0.167724609375, -0.2269287109375, 0.274658203125, 0.724609375, 0.3125, 0.33056640625, -0.484130859375, 0.152099609375, -0.188232421875, -0.1566162109375, -0.3251953125, -0.06121826171875, -0.2275390625, -0.09820556640625, -0.1610107421875, 0.0406494140625, 0.308349609375, 0.6064453125, 0.533203125, 0.41845703125, 0.64208984375, 0.52587890625, -0.62060546875, 0.86572265625, 0.2130126953125, -1.01953125, -0.564453125, 0.611328125, -0.1402587890625, 0.505859375, 0.4443359375, -0.81494140625, -0.64404296875, -0.8740234375, 0.1973876953125, -0.3525390625, -0.2479248046875, -0.89990234375, 0.22607421875, -0.363037109375, 0.5380859375, -0.024017333984375, -0.56494140625, 0.0518798828125, -1.3046875, 0.1861572265625, -0.68359375, -0.35009765625, -0.58251953125, -0.3251953125, 0.060394287109375, 0.96044921875, 0.0565185546875, 0.194580078125, -0.243408203125, -0.2364501953125, 0.37890625, -0.0272369384765625, -0.345703125, -0.384521484375, -0.2213134765625, 0.252685546875, -0.157470703125, 0.01049041748046875, -0.10400390625, 0.662109375, -0.7607421875, 0.050933837890625, -0.47119140625, -0.1788330078125, -0.3984375, -0.1517333984375, 0.94775390625, -0.289794921875, -0.3837890625, -0.0230712890625, 0.1383056640625, 0.7080078125, -0.387939453125, -0.1947021484375, -0.8681640625, -0.166015625, -0.68115234375, 0.57763671875, -0.193115234375, -0.0706787109375, -0.75830078125, -0.364501953125, 1.1748046875, -0.58740234375, 0.2420654296875, 1.2294921875, 0.19921875, 0.2802734375, -0.72021484375, 0.1734619140625, 0.53564453125, -0.60205078125, -0.049896240234375, 0.1334228515625, -0.7294921875, 0.443115234375, -0.20703125, -1.18359375, -0.56103515625, 0.32373046875, 1.4716796875, -0.2607421875, 0.6328125, 0.2110595703125, -1.2314453125, -0.6015625, 0.65185546875, -0.0408935546875, 0.317138671875, 1.0546875, -0.251953125, -0.26123046875, 0.075439453125, -0.1617431640625, -0.485595703125, -0.416015625, 1.36328125, -0.56494140625, -0.363525390625, 0.955078125, 1.2861328125, -0.96630859375, -1.05078125, -0.023345947265625, -0.0055999755859375, -0.468017578125, -0.9140625, 0.150390625, 0.6796875, -1.0224609375, -0.0955810546875, 0.25634765625, -0.2366943359375, 0.6865234375, -0.037384033203125, 0.26708984375, -0.478271484375, 0.42822265625, 0.646484375, -0.51416015625, -0.0163116455078125, -0.430419921875, -0.2052001953125, -0.263671875, -0.11395263671875, 0.55615234375, -0.578125, 0.1004638671875, 0.327392578125, 0.0743408203125, 0.422607421875, -0.290771484375, -0.60791015625, 0.12139892578125, -0.951171875, -0.3212890625, 0.0694580078125, 0.41650390625, -0.294677734375, 0.42041015625, -0.9130859375, -0.158447265625, 0.103759765625, 0.1658935546875, -0.4443359375, -0.68603515625, -0.233642578125, -1.1005859375, -0.52197265625, -0.47705078125, -0.859375, -0.453125, -0.1422119140625, 0.232177734375, -0.370361328125, 0.2626953125, 0.488525390625, -0.6640625, 0.8916015625, -0.75244140625, 0.50146484375, -0.77685546875, -0.1917724609375, -0.62890625, -0.06146240234375, -0.5068359375, 0.2734375, -0.99853515625, 0.1876220703125, 0.068115234375, 0.4814453125, -0.4423828125, 0.290283203125, -0.2430419921875, -0.6103515625, 0.07476806640625, 0.36376953125, -0.6650390625, 0.66796875, 0.2401123046875, 0.1605224609375, -0.058929443359375, -0.345947265625, -0.65966796875, -0.375732421875, 0.5048828125, 0.332763671875, -0.0005598068237304688, 0.1314697265625, -0.546875, 0.11669921875, -1.0888671875, 0.0928955078125, -0.40380859375, -0.044403076171875, 0.1981201171875, -0.517578125, 0.6162109375, 1.048828125, -0.35986328125, 0.462890625, -0.251708984375, 0.05950927734375, 0.3623046875, 0.203369140625, -0.306640625, 0.28466796875, 0.4091796875, -0.1614990234375, -0.09619140625, 0.474365234375, -0.0491943359375, 0.221923828125, 0.1846923828125, -0.685546875, -0.9091796875, -0.260498046875, -0.404052734375, 0.42333984375, 0.2447509765625, -0.4892578125, -0.08636474609375, -0.1412353515625, -0.37255859375, 0.3681640625, -1.2294921875, -0.8701171875, 0.212158203125, 0.11480712890625, -0.51171875, 0.132568359375, -0.8125, -0.1170654296875, 0.12249755859375, 0.60107421875, -0.2081298828125, 0.68408203125, -0.310546875, 0.0732421875, -0.1961669921875, -0.2373046875, 0.11328125, 0.50927734375, -0.556640625, -0.452880859375, 0.085693359375, 0.978515625, 0.2646484375, -0.06427001953125, -0.62255859375, 0.31640625, 0.15625, 0.0968017578125, -0.38525390625, 0.1190185546875, -0.434814453125, 0.60205078125, -0.9296875, -0.01494598388671875, 0.098876953125, 0.8212890625, 0.281005859375, -0.463623046875, -0.428955078125, 0.6669921875, 1.109375, -0.329345703125, 0.57861328125, 0.367431640625, 0.44921875, -0.168701171875, -0.1737060546875, -0.332763671875, 0.833984375, 0.4638671875, 0.5009765625, -0.013885498046875, 0.2237548828125, 0.8203125, -0.047393798828125, -0.468017578125, 0.45751953125, -0.253662109375, 0.0235748291015625, 0.0216522216796875, -0.0814208984375, -0.32373046875, 0.1405029296875, -0.75244140625, 0.6259765625, -0.537109375, -0.35888671875, -0.1739501953125, -0.55810546875, 1.0380859375, -0.484375, -0.0821533203125, 0.136474609375, -0.254638671875, 0.1365966796875, 0.6630859375, 0.1395263671875, 0.2061767578125, 1.0263671875, 0.44677734375, 0.27294921875, 0.7138671875, 0.33642578125, 0.65869140625, -0.7109375, 0.0001863241195678711, -0.07421875, -0.1904296875, -0.206298828125, -0.568359375, -1.0419921875, 0.595703125, -0.07623291015625, -0.379638671875, 0.7216796875, -0.6689453125, 0.048004150390625, -0.2822265625, 0.796875, -0.47900390625, 0.33642578125, -0.128662109375, -0.31982421875, -0.488525390625, 0.8720703125, -0.12322998046875, 0.30078125, 0.27734375, 0.90966796875, -0.13525390625, 1.5107421875, 0.2181396484375, 0.054473876953125, 0.1307373046875, 0.338134765625, -0.65478515625, -0.66796875, -0.2421875, -0.30859375, 0.08905029296875, -0.7529296875, -0.363037109375, -0.154541015625, 0.8720703125, 0.282470703125, -0.759765625, -0.5, 0.19775390625, -0.91650390625, 0.350830078125, 0.3662109375, 0.2427978515625, 0.09527587890625, -0.0203857421875, -0.284423828125, -0.70654296875, 0.1370849609375, -0.79443359375, 0.263671875, -0.6337890625, -0.53076171875, -0.137939453125, -0.4228515625, -0.40576171875, -0.360107421875, -0.07666015625, -0.83984375, 0.77001953125, 0.295654296875, 0.53125, 0.53662109375, -0.140625, 0.34326171875, 0.9599609375, 0.84814453125, -0.2099609375, 0.4892578125, 0.11981201171875, -0.05523681640625, 0.39794921875, -0.470703125, 0.415771484375, -0.13134765625, 0.5947265625, -0.568359375, 0.5380859375, -0.80078125, -1.240234375, 0.1475830078125, 0.3671875, 0.493408203125, -0.658203125, -0.8349609375, -0.124755859375, -1.0263671875, -0.143310546875, -0.265380859375, 0.791015625, -0.36865234375, 0.07403564453125, -0.17236328125, -1.0986328125, 4.453125, 1.0517578125, 0.6591796875, 0.263671875, 0.177490234375, 0.6357421875, 0.315673828125, -0.796875, -0.135498046875, -0.1590576171875, 0.609375, -0.1104736328125, 0.050018310546875, 0.8525390625, 0.346435546875, 0.490478515625, -0.5009765625, -0.061676025390625, -0.022430419921875, -0.62744140625, -0.7880859375, 0.1373291015625, 0.009124755859375, 0.3662109375, -0.2166748046875, 0.3251953125, 0.365234375, -0.869140625, -0.44873046875, -0.6689453125, 0.211669921875, -0.450927734375, 1.044921875, -0.477783203125, -0.1019287109375, 0.5849609375, -0.04461669921875, -0.521484375, -0.400146484375, 0.256103515625, 0.2078857421875, -0.01190948486328125, 0.73779296875, -0.96923828125, 0.0052032470703125, 0.26904296875, -0.64990234375, 0.20068359375, 0.039764404296875, -0.9833984375, 0.487548828125, -0.127197265625, 0.225830078125, -0.494140625, -1.06640625, 0.1484375, 0.3095703125, -0.01102447509765625, -0.11724853515625, 0.46484375, 0.55517578125, 0.120849609375, 0.10662841796875, 0.66552734375, -1.177734375, 1.109375, -0.03094482421875, 0.6064453125, -0.64990234375, 0.05157470703125, -0.428466796875, -0.449951171875, -0.43798828125, -0.1441650390625, 0.94921875, 0.2322998046875, -0.2469482421875, 0.326904296875, 0.4130859375, -0.63232421875, 0.333251953125, 0.0965576171875, -0.37841796875, -0.1949462890625, 0.767578125, 1.1083984375, -0.62353515625, -0.4013671875, -0.325439453125, 0.455078125, 0.288330078125, 0.461181640625, 0.2230224609375, -0.55078125, -0.5087890625 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: 1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si β‰  si + 1(1 ≀ i < n). 3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. Help him find such string or state that such string doesn't exist. String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes. Input A single line contains two positive integers n and k (1 ≀ n ≀ 106, 1 ≀ k ≀ 26) β€” the string's length and the number of distinct letters. Output In a single line print the required string. If there isn't such string, print "-1" (without the quotes). Examples Input 7 4 Output ababacd Input 4 7 Output -1 Tags: greedy Correct Solution: ``` a=list(map(int,input().split())) if(a[0]>1)&(a[1]==1):print(-1) elif a[0]==a[1]==1:print('a') elif a[1]>a[0]:print(-1) else:print('ab'*((a[0]+2-a[1])//2)+'a'*((a[0]-a[1])%2)+''.join(map(lambda x:chr(ord('c')+x),range(a[1]-2)))) ```
107,307
[ 0.42431640625, -0.10845947265625, 0.59765625, 0.259521484375, -0.1971435546875, -0.48876953125, 0.140869140625, 0.0751953125, 0.397705078125, 0.76708984375, 0.74072265625, -0.071044921875, 0.099365234375, -0.75634765625, -0.56005859375, 0.040496826171875, -0.60546875, -0.446044921875, -0.384765625, 0.12054443359375, -0.0109710693359375, -0.1331787109375, -1.4912109375, -0.073974609375, -0.28662109375, 0.9794921875, 0.37939453125, 0.06634521484375, 1.0908203125, 1.021484375, -0.2435302734375, -0.470703125, 0.402099609375, -0.97119140625, -0.57373046875, -0.394287109375, 0.5595703125, -1.0498046875, -0.370361328125, -0.623046875, 0.1082763671875, -0.72021484375, 0.454345703125, -0.70361328125, -1.2109375, -0.100341796875, -0.57080078125, -0.37451171875, -0.199462890625, -0.96337890625, 0.0855712890625, -0.2255859375, 0.52978515625, -0.3857421875, -0.00913238525390625, 0.252685546875, 0.19970703125, -0.27978515625, -0.4091796875, 0.41259765625, -0.259521484375, 0.35791015625, 0.0723876953125, -0.53173828125, -0.31103515625, -0.06182861328125, -0.11651611328125, -0.4150390625, 0.023590087890625, -0.70703125, -0.1990966796875, 0.2252197265625, -0.55126953125, -0.346923828125, -0.27392578125, 0.1649169921875, 0.337158203125, -0.007328033447265625, -0.468017578125, 0.9306640625, 0.459716796875, 1.4326171875, 0.457763671875, 0.283447265625, -0.08758544921875, -0.548828125, 0.12286376953125, 0.615234375, 0.2822265625, -0.3095703125, 0.168212890625, 0.52685546875, -0.83056640625, 0.2489013671875, 0.466796875, 0.426513671875, 0.062744140625, 0.433349609375, 0.306884765625, -0.0389404296875, 0.8505859375, 1.0068359375, -0.2890625, 0.95703125, -0.58203125, 0.3125, -0.0288238525390625, -0.25439453125, -0.2139892578125, -0.35595703125, -0.26220703125, -0.1654052734375, 0.728515625, 0.2239990234375, -0.285888671875, 0.962890625, -0.163330078125, 0.273681640625, -0.82421875, -0.07647705078125, 0.436279296875, 0.39111328125, 0.76513671875, 0.0076751708984375, -0.09844970703125, -0.233154296875, -0.60546875, 0.9228515625, -0.63671875, 0.229736328125, 0.413818359375, 0.05120849609375, 0.04998779296875, 0.10723876953125, 0.1812744140625, 0.62841796875, -0.09967041015625, 0.55419921875, 0.580078125, -0.443115234375, 0.8349609375, -0.31494140625, -0.05377197265625, 1.4267578125, 0.5341796875, -0.186767578125, 0.77880859375, 0.176513671875, -0.8359375, 0.3642578125, -1.154296875, 0.630859375, -0.07958984375, 0.10565185546875, -0.1156005859375, 0.262451171875, -0.330078125, 0.2149658203125, 0.468017578125, 0.1973876953125, -0.55029296875, 0.164794921875, -0.174072265625, 0.703125, -0.334716796875, 0.76953125, -0.56201171875, -0.1231689453125, 0.10528564453125, -0.2744140625, 0.2271728515625, -0.1124267578125, -0.298583984375, 0.91796875, 0.71923828125, 1.13671875, 0.96435546875, -0.274658203125, 0.1824951171875, 0.394287109375, -0.49951171875, 0.04827880859375, 0.19873046875, 0.50634765625, 0.0986328125, 0.3134765625, 0.016845703125, -0.5283203125, -0.9462890625, -0.67578125, -0.01494598388671875, 0.3291015625, -0.222900390625, 0.394775390625, -0.0008511543273925781, -0.0200042724609375, -0.66748046875, -0.254638671875, -0.318603515625, -1.0576171875, -0.352294921875, 0.68408203125, -0.141845703125, 0.501953125, -0.52294921875, -0.30859375, 0.460205078125, 1.0126953125, -0.42041015625, 0.015594482421875, 0.197998046875, 0.08404541015625, -0.1273193359375, 0.15869140625, 0.2291259765625, 0.2362060546875, -0.77392578125, 0.7939453125, -0.236328125, 0.18603515625, 0.1915283203125, 0.8310546875, 0.1820068359375, 0.494873046875, -0.2275390625, -0.11029052734375, 0.529296875, 0.7802734375, 0.01166534423828125, 0.64794921875, 0.3408203125, 1.224609375, 0.7587890625, 0.489501953125, 0.58984375, 0.583984375, 0.56640625, 1.0615234375, 0.033294677734375, 0.334228515625, -0.11279296875, 0.4482421875, -0.10009765625, 0.392578125, 0.25, 0.4658203125, -0.024169921875, 0.2008056640625, -0.2381591796875, 0.25048828125, -0.021087646484375, 0.82568359375, 0.1351318359375, 0.433837890625, -0.462890625, -0.37451171875, -0.00934600830078125, 0.7900390625, -0.54443359375, -0.40576171875, -0.234619140625, 0.1517333984375, 0.01242828369140625, -0.2235107421875, 0.258056640625, 0.2484130859375, 0.50927734375, 0.0638427734375, -0.326171875, -0.28564453125, -1.2392578125, -0.58935546875, -1.2431640625, -0.10406494140625, -0.6953125, 0.13330078125, 0.449951171875, -0.919921875, 0.110595703125, -0.340087890625, -0.257568359375, 0.2174072265625, -0.77392578125, 0.59326171875, 0.1024169921875, 0.494384765625, -0.51513671875, 0.4033203125, 0.1341552734375, 0.93212890625, -0.292236328125, -0.2822265625, 0.0523681640625, -0.416015625, 0.31884765625, -0.1728515625, 0.449951171875, 0.061492919921875, -0.452880859375, -0.95263671875, -0.54296875, -0.031646728515625, -0.28466796875, 0.1346435546875, -0.33203125, 1.1376953125, 0.5244140625, -0.80810546875, 0.51318359375, 0.7568359375, -0.81689453125, 0.541015625, 0.3349609375, 0.1754150390625, -0.841796875, 1.490234375, 0.3623046875, -0.04681396484375, -0.6181640625, -0.5322265625, -0.32763671875, 0.308349609375, 0.12396240234375, -0.56298828125, 0.024261474609375, 0.50390625, 0.2169189453125, -1.2470703125, 0.7939453125, -0.9912109375, -0.5498046875, -0.51171875, -0.2269287109375, 0.63525390625, 0.525390625, 0.314453125, -0.13232421875, -0.400390625, -0.41259765625, 0.43359375, 0.356201171875, -0.662109375, -0.168701171875, 0.4814453125, -0.36376953125, 0.1934814453125, 0.0012502670288085938, -0.15625, 0.0799560546875, -0.090576171875, 0.2216796875, 0.892578125, 0.27880859375, 0.02197265625, 0.2841796875, 0.91357421875, -0.5986328125, -0.352783203125, -0.51123046875, 0.6376953125, 0.3056640625, 0.83935546875, 0.37890625, -0.3193359375, -0.294189453125, -1.4091796875, 0.27197265625, -0.1602783203125, 0.80615234375, -0.529296875, 1.005859375, 0.58203125, -0.490234375, 0.448486328125, -0.533203125, -0.306396484375, 1.1748046875, -0.042327880859375, 0.80126953125, -0.35693359375, 0.45068359375, -0.21728515625, -0.306640625, 0.6279296875, 0.272705078125, 0.744140625, -0.391845703125, -0.62353515625, -0.473876953125, -0.5400390625, -0.0244293212890625, -0.525390625, 0.22900390625, -0.36376953125, -0.2083740234375, -0.36572265625, 0.34619140625, 0.74609375, 0.51806640625, 0.06011962890625, 0.465576171875, 0.022064208984375, 0.2900390625, 0.35205078125, -0.541015625, -0.06134033203125, -0.3486328125, 0.7158203125, 0.19384765625, -0.1920166015625, -0.828125, -0.50830078125, 0.0246734619140625, -0.184814453125, -0.00460052490234375, -0.48193359375, -0.78857421875, 0.1739501953125, -0.23974609375, 0.360595703125, -0.53759765625, -0.50146484375, -0.302734375, 0.373779296875, 0.441162109375, -0.99951171875, 0.1419677734375, -0.53125, 0.44140625, 0.416748046875, -0.10595703125, -0.28955078125, -0.552734375, -0.68505859375, -0.6943359375, 0.2548828125, 0.7216796875, -0.0182342529296875, 0.174560546875, -1.39453125, 0.4892578125, 0.2342529296875, 0.06561279296875, 0.154296875, 0.213134765625, 0.462890625, 0.17724609375, 0.88720703125, -0.48779296875, -0.91064453125, 0.1539306640625, -1.3193359375, 0.5400390625, -0.64404296875, 0.239501953125, -0.0271759033203125, 0.10980224609375, -0.166259765625, 0.53369140625, -0.205322265625, 0.31298828125, 0.0081329345703125, 0.409423828125, -0.9677734375, -0.50634765625, 0.51318359375, -0.37841796875, -0.2474365234375, 1.2412109375, -0.189697265625, -0.52001953125, 0.59423828125, 0.5908203125, -0.33642578125, 0.2288818359375, -0.26708984375, 0.5439453125, -0.34375, -0.2239990234375, 0.0030727386474609375, -0.390380859375, 0.9375, -0.06109619140625, -0.9384765625, -0.3984375, -1.2646484375, -0.174072265625, -0.219482421875, -0.287353515625, 0.31640625, -0.1983642578125, -0.10498046875, -0.220703125, -0.49169921875, -0.3525390625, -0.2509765625, -0.1490478515625, -0.250732421875, 0.283447265625, 0.7138671875, 0.322265625, 0.307373046875, -0.46533203125, 0.106201171875, -0.1514892578125, -0.1195068359375, -0.327880859375, -0.108154296875, -0.192138671875, -0.0732421875, -0.19580078125, 0.0305023193359375, 0.2548828125, 0.55615234375, 0.525390625, 0.44970703125, 0.61669921875, 0.46728515625, -0.671875, 0.77978515625, 0.21484375, -1.033203125, -0.59375, 0.58837890625, -0.10919189453125, 0.454833984375, 0.401611328125, -0.8056640625, -0.59326171875, -0.93212890625, 0.10272216796875, -0.360595703125, -0.25634765625, -0.9169921875, 0.1661376953125, -0.31298828125, 0.55419921875, -0.0460205078125, -0.5751953125, 0.08184814453125, -1.3447265625, 0.21337890625, -0.65966796875, -0.289306640625, -0.6337890625, -0.33740234375, 0.043243408203125, 0.94580078125, 0.1197509765625, 0.198974609375, -0.220703125, -0.19287109375, 0.429443359375, 0.04425048828125, -0.374755859375, -0.39599609375, -0.25830078125, 0.2235107421875, -0.11260986328125, 0.0088958740234375, -0.1236572265625, 0.67822265625, -0.75, 0.046417236328125, -0.50634765625, -0.2047119140625, -0.36767578125, -0.15234375, 0.98876953125, -0.252197265625, -0.345947265625, -0.07470703125, 0.208740234375, 0.720703125, -0.382568359375, -0.25634765625, -0.853515625, -0.27978515625, -0.6630859375, 0.59619140625, -0.212158203125, -0.10076904296875, -0.7744140625, -0.353515625, 1.1591796875, -0.541015625, 0.2379150390625, 1.294921875, 0.17236328125, 0.2919921875, -0.74951171875, 0.1871337890625, 0.50537109375, -0.59326171875, -0.053680419921875, 0.10687255859375, -0.68798828125, 0.350341796875, -0.2327880859375, -1.15234375, -0.56591796875, 0.307861328125, 1.490234375, -0.29833984375, 0.6953125, 0.114013671875, -1.1806640625, -0.6083984375, 0.6669921875, 0.00667572021484375, 0.32470703125, 1.095703125, -0.244873046875, -0.2181396484375, 0.017242431640625, -0.131591796875, -0.51806640625, -0.439208984375, 1.341796875, -0.505859375, -0.33984375, 0.931640625, 1.2802734375, -1.0126953125, -1.0830078125, -0.054595947265625, -0.00783538818359375, -0.52978515625, -0.93798828125, 0.180908203125, 0.67041015625, -1.0048828125, -0.043212890625, 0.303466796875, -0.2705078125, 0.63232421875, -0.0300445556640625, 0.275390625, -0.50146484375, 0.3740234375, 0.6806640625, -0.5380859375, -0.07427978515625, -0.47607421875, -0.19677734375, -0.228759765625, -0.10418701171875, 0.55615234375, -0.55126953125, 0.08050537109375, 0.40283203125, 0.11737060546875, 0.42822265625, -0.281982421875, -0.62255859375, 0.080810546875, -0.99755859375, -0.32470703125, 0.032012939453125, 0.431396484375, -0.23388671875, 0.4228515625, -0.8955078125, -0.10723876953125, 0.101806640625, 0.1822509765625, -0.457275390625, -0.68212890625, -0.2587890625, -1.130859375, -0.529296875, -0.55224609375, -0.7861328125, -0.43798828125, -0.1337890625, 0.2076416015625, -0.424560546875, 0.323974609375, 0.46630859375, -0.650390625, 0.87548828125, -0.73388671875, 0.47265625, -0.751953125, -0.248291015625, -0.59326171875, -0.0999755859375, -0.441162109375, 0.343505859375, -0.9755859375, 0.21240234375, 0.026702880859375, 0.54052734375, -0.370361328125, 0.284912109375, -0.224365234375, -0.6396484375, 0.0814208984375, 0.34423828125, -0.66455078125, 0.6884765625, 0.1976318359375, 0.13818359375, -0.072998046875, -0.4091796875, -0.64501953125, -0.39697265625, 0.465576171875, 0.310302734375, 0.06512451171875, 0.17333984375, -0.5576171875, 0.0849609375, -1.0224609375, 0.0919189453125, -0.403564453125, -0.06463623046875, 0.2022705078125, -0.51025390625, 0.62109375, 1.041015625, -0.3994140625, 0.48583984375, -0.23681640625, 0.0104522705078125, 0.363525390625, 0.1956787109375, -0.3115234375, 0.1834716796875, 0.399169921875, -0.11663818359375, -0.11737060546875, 0.5185546875, -0.078369140625, 0.268310546875, 0.16748046875, -0.65380859375, -0.89111328125, -0.2724609375, -0.325439453125, 0.40771484375, 0.1842041015625, -0.42333984375, -0.07501220703125, -0.119873046875, -0.360595703125, 0.348876953125, -1.2431640625, -0.85595703125, 0.2509765625, 0.136962890625, -0.53564453125, 0.135986328125, -0.86181640625, -0.06414794921875, 0.138427734375, 0.595703125, -0.2449951171875, 0.69482421875, -0.318115234375, 0.08648681640625, -0.238037109375, -0.1856689453125, 0.050994873046875, 0.4814453125, -0.5419921875, -0.482421875, 0.1180419921875, 0.96533203125, 0.2342529296875, -0.079833984375, -0.56494140625, 0.393310546875, 0.140869140625, 0.12103271484375, -0.38427734375, 0.1317138671875, -0.4453125, 0.63671875, -0.85595703125, -0.0224456787109375, 0.0880126953125, 0.779296875, 0.31494140625, -0.3994140625, -0.405029296875, 0.6572265625, 1.078125, -0.3203125, 0.57568359375, 0.361083984375, 0.460205078125, -0.2030029296875, -0.194580078125, -0.308349609375, 0.86669921875, 0.42529296875, 0.51220703125, -0.0125732421875, 0.2025146484375, 0.77197265625, -0.05194091796875, -0.454833984375, 0.418701171875, -0.295166015625, -0.0159759521484375, 0.0251312255859375, -0.131103515625, -0.3056640625, 0.18896484375, -0.78076171875, 0.6083984375, -0.57568359375, -0.427978515625, -0.200927734375, -0.54541015625, 1.03125, -0.448486328125, -0.024566650390625, 0.16748046875, -0.281982421875, 0.1326904296875, 0.689453125, 0.1839599609375, 0.1904296875, 1.005859375, 0.45361328125, 0.28857421875, 0.6953125, 0.3076171875, 0.71044921875, -0.662109375, -0.004352569580078125, -0.038177490234375, -0.1988525390625, -0.2210693359375, -0.57958984375, -1.017578125, 0.58251953125, -0.110595703125, -0.44775390625, 0.70263671875, -0.6806640625, -0.004817962646484375, -0.26025390625, 0.775390625, -0.466796875, 0.3447265625, -0.11700439453125, -0.324462890625, -0.479248046875, 0.83837890625, -0.08441162109375, 0.329833984375, 0.252685546875, 0.84619140625, -0.1541748046875, 1.50390625, 0.2109375, 0.050872802734375, 0.1351318359375, 0.3681640625, -0.61376953125, -0.685546875, -0.2763671875, -0.371826171875, 0.1697998046875, -0.77197265625, -0.381591796875, -0.1558837890625, 0.8486328125, 0.319091796875, -0.78125, -0.448486328125, 0.253173828125, -0.93701171875, 0.36279296875, 0.458251953125, 0.2098388671875, 0.053070068359375, -0.00920867919921875, -0.33203125, -0.703125, 0.1302490234375, -0.8671875, 0.327392578125, -0.603515625, -0.496826171875, -0.1881103515625, -0.33935546875, -0.36376953125, -0.350830078125, -0.0947265625, -0.806640625, 0.7900390625, 0.310546875, 0.52734375, 0.546875, -0.09381103515625, 0.324951171875, 0.9755859375, 0.81787109375, -0.16064453125, 0.456298828125, 0.13623046875, -0.07666015625, 0.38720703125, -0.496337890625, 0.435546875, -0.11273193359375, 0.61376953125, -0.62060546875, 0.53271484375, -0.81591796875, -1.212890625, 0.1806640625, 0.369140625, 0.5283203125, -0.619140625, -0.912109375, -0.1158447265625, -1.0126953125, -0.1572265625, -0.23486328125, 0.7490234375, -0.279052734375, 0.0252532958984375, -0.159423828125, -1.0546875, 4.47265625, 1.060546875, 0.69384765625, 0.323974609375, 0.175537109375, 0.6337890625, 0.29443359375, -0.78564453125, -0.06884765625, -0.1278076171875, 0.61572265625, -0.1280517578125, 0.095947265625, 0.90185546875, 0.365234375, 0.5185546875, -0.473876953125, -0.0648193359375, -0.03521728515625, -0.60400390625, -0.84033203125, 0.1160888671875, -0.04742431640625, 0.374755859375, -0.11822509765625, 0.33349609375, 0.3310546875, -0.88623046875, -0.466796875, -0.63037109375, 0.1737060546875, -0.409912109375, 1.052734375, -0.42236328125, -0.1251220703125, 0.63037109375, -0.0075531005859375, -0.468017578125, -0.413330078125, 0.210693359375, 0.175048828125, 0.0419921875, 0.81396484375, -0.94677734375, -0.0523681640625, 0.32861328125, -0.6630859375, 0.1728515625, -0.01316070556640625, -0.95068359375, 0.483642578125, -0.138671875, 0.264892578125, -0.509765625, -1.0537109375, 0.12890625, 0.26513671875, 0.060546875, -0.1077880859375, 0.473876953125, 0.64453125, 0.1534423828125, 0.07830810546875, 0.61767578125, -1.166015625, 1.0966796875, -0.032958984375, 0.615234375, -0.650390625, 0.043212890625, -0.490478515625, -0.363037109375, -0.34814453125, -0.2198486328125, 0.98046875, 0.308349609375, -0.309814453125, 0.258544921875, 0.361572265625, -0.6328125, 0.326171875, 0.048248291015625, -0.404296875, -0.228271484375, 0.8046875, 1.0625, -0.59521484375, -0.4384765625, -0.321044921875, 0.45556640625, 0.27099609375, 0.453369140625, 0.224853515625, -0.465087890625, -0.49462890625 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: 1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si β‰  si + 1(1 ≀ i < n). 3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. Help him find such string or state that such string doesn't exist. String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes. Input A single line contains two positive integers n and k (1 ≀ n ≀ 106, 1 ≀ k ≀ 26) β€” the string's length and the number of distinct letters. Output In a single line print the required string. If there isn't such string, print "-1" (without the quotes). Examples Input 7 4 Output ababacd Input 4 7 Output -1 Tags: greedy Correct Solution: ``` X = list(map(int, input().split())) Temp = "".join([chr(ord("a") + i) for i in range(X[1])]) if X[1] == 1 and X[0] == 1: print("a") elif X[1] > X[0] or X[1] == 1: print(-1) else: print("ab" * ((X[0] - X[1] + 2) // 2) + "a" * ((X[0] - X[1] + 2) % 2) + Temp[2:]) # Hope the best for Ravens # Never give up ```
107,309
[ 0.426513671875, -0.10260009765625, 0.6201171875, 0.254638671875, -0.1646728515625, -0.482421875, 0.11456298828125, 0.05865478515625, 0.416259765625, 0.77490234375, 0.74560546875, -0.06768798828125, 0.0841064453125, -0.72802734375, -0.57568359375, 0.04443359375, -0.56787109375, -0.447265625, -0.3876953125, 0.117431640625, -0.0062255859375, -0.1463623046875, -1.498046875, -0.0443115234375, -0.3017578125, 0.9677734375, 0.39111328125, 0.0687255859375, 1.068359375, 1.0224609375, -0.248291015625, -0.47412109375, 0.404052734375, -0.9873046875, -0.587890625, -0.3837890625, 0.58203125, -1.04296875, -0.360595703125, -0.5986328125, 0.093505859375, -0.7421875, 0.486328125, -0.70458984375, -1.201171875, -0.10614013671875, -0.58203125, -0.356689453125, -0.19189453125, -0.97705078125, 0.11602783203125, -0.193603515625, 0.51025390625, -0.392822265625, -0.0173492431640625, 0.267822265625, 0.208984375, -0.286865234375, -0.40673828125, 0.402587890625, -0.2432861328125, 0.32080078125, 0.097412109375, -0.5537109375, -0.28369140625, -0.0322265625, -0.14404296875, -0.398681640625, 0.031494140625, -0.7138671875, -0.1773681640625, 0.22412109375, -0.56591796875, -0.31884765625, -0.26611328125, 0.154052734375, 0.354736328125, -0.019805908203125, -0.48193359375, 0.935546875, 0.462890625, 1.42578125, 0.455322265625, 0.302490234375, -0.089599609375, -0.54931640625, 0.11651611328125, 0.5673828125, 0.270751953125, -0.29736328125, 0.167236328125, 0.53857421875, -0.84130859375, 0.2685546875, 0.472412109375, 0.41943359375, 0.041259765625, 0.44091796875, 0.296630859375, -0.046661376953125, 0.83935546875, 1.0361328125, -0.302734375, 0.94921875, -0.6044921875, 0.333251953125, -0.0477294921875, -0.23095703125, -0.2008056640625, -0.35205078125, -0.253662109375, -0.17333984375, 0.70703125, 0.2210693359375, -0.27294921875, 0.95361328125, -0.144775390625, 0.2841796875, -0.82666015625, -0.074951171875, 0.42041015625, 0.39501953125, 0.775390625, 0.0170135498046875, -0.069580078125, -0.2186279296875, -0.62060546875, 0.916015625, -0.6416015625, 0.25244140625, 0.40478515625, 0.054595947265625, 0.04168701171875, 0.11260986328125, 0.1614990234375, 0.63623046875, -0.093017578125, 0.55810546875, 0.58251953125, -0.451904296875, 0.8505859375, -0.326416015625, -0.07464599609375, 1.439453125, 0.5390625, -0.1923828125, 0.81494140625, 0.1661376953125, -0.8212890625, 0.3828125, -1.1474609375, 0.6455078125, -0.0673828125, 0.1051025390625, -0.111328125, 0.28564453125, -0.293701171875, 0.2286376953125, 0.463623046875, 0.198486328125, -0.56396484375, 0.1551513671875, -0.144287109375, 0.68896484375, -0.3349609375, 0.77197265625, -0.53759765625, -0.1375732421875, 0.0643310546875, -0.283935546875, 0.2100830078125, -0.08746337890625, -0.28515625, 0.9052734375, 0.67529296875, 1.1416015625, 0.9775390625, -0.263671875, 0.155517578125, 0.402099609375, -0.521484375, 0.041748046875, 0.2244873046875, 0.497802734375, 0.11676025390625, 0.301513671875, 0.048370361328125, -0.51513671875, -0.9716796875, -0.7021484375, -0.01580810546875, 0.346923828125, -0.238037109375, 0.3857421875, 0.0104217529296875, -0.01212310791015625, -0.66064453125, -0.29150390625, -0.359619140625, -1.052734375, -0.328857421875, 0.6650390625, -0.12054443359375, 0.5078125, -0.54296875, -0.32275390625, 0.47607421875, 0.9931640625, -0.453857421875, -0.0235748291015625, 0.1978759765625, 0.0810546875, -0.13427734375, 0.154052734375, 0.22705078125, 0.21728515625, -0.78857421875, 0.78466796875, -0.2421875, 0.1785888671875, 0.184326171875, 0.80322265625, 0.221435546875, 0.51904296875, -0.222900390625, -0.09075927734375, 0.50341796875, 0.7666015625, 0.003047943115234375, 0.6396484375, 0.30322265625, 1.20703125, 0.77099609375, 0.49609375, 0.58154296875, 0.58740234375, 0.56591796875, 1.037109375, 0.080810546875, 0.35498046875, -0.1334228515625, 0.446533203125, -0.10546875, 0.369873046875, 0.26171875, 0.490478515625, 0.0089569091796875, 0.165283203125, -0.2176513671875, 0.2120361328125, -0.0063934326171875, 0.84130859375, 0.13623046875, 0.4189453125, -0.4931640625, -0.394287109375, 0.0194854736328125, 0.7919921875, -0.5927734375, -0.398193359375, -0.246337890625, 0.156982421875, -0.01308441162109375, -0.21923828125, 0.28466796875, 0.259521484375, 0.492431640625, 0.06329345703125, -0.32861328125, -0.3046875, -1.2666015625, -0.58154296875, -1.216796875, -0.1246337890625, -0.697265625, 0.1414794921875, 0.4501953125, -0.923828125, 0.1170654296875, -0.335693359375, -0.264404296875, 0.2332763671875, -0.76953125, 0.57275390625, 0.11163330078125, 0.51806640625, -0.52880859375, 0.404541015625, 0.1441650390625, 0.9443359375, -0.28466796875, -0.2705078125, 0.038543701171875, -0.4462890625, 0.299072265625, -0.1627197265625, 0.461669921875, 0.04425048828125, -0.4384765625, -0.921875, -0.5361328125, -0.020355224609375, -0.3046875, 0.1016845703125, -0.340087890625, 1.10546875, 0.5439453125, -0.81298828125, 0.5068359375, 0.7548828125, -0.802734375, 0.5498046875, 0.318115234375, 0.1572265625, -0.81982421875, 1.462890625, 0.382568359375, -0.0236663818359375, -0.61572265625, -0.5078125, -0.333984375, 0.291748046875, 0.1070556640625, -0.53759765625, 0.0022830963134765625, 0.496337890625, 0.2149658203125, -1.244140625, 0.7626953125, -0.9765625, -0.59326171875, -0.50634765625, -0.2454833984375, 0.6328125, 0.517578125, 0.33447265625, -0.1123046875, -0.392822265625, -0.402099609375, 0.416015625, 0.364501953125, -0.63134765625, -0.13671875, 0.498046875, -0.371826171875, 0.1639404296875, -0.02728271484375, -0.164794921875, 0.076171875, -0.056365966796875, 0.2183837890625, 0.8681640625, 0.27783203125, 0.038330078125, 0.27880859375, 0.9130859375, -0.6220703125, -0.355712890625, -0.51953125, 0.62841796875, 0.337646484375, 0.828125, 0.356689453125, -0.331787109375, -0.288818359375, -1.390625, 0.2763671875, -0.151123046875, 0.80908203125, -0.5341796875, 1.013671875, 0.607421875, -0.493408203125, 0.472412109375, -0.53173828125, -0.300537109375, 1.1689453125, -0.033599853515625, 0.8134765625, -0.362060546875, 0.448486328125, -0.1986083984375, -0.28857421875, 0.61962890625, 0.270263671875, 0.740234375, -0.387939453125, -0.6083984375, -0.444091796875, -0.52392578125, -0.029876708984375, -0.50439453125, 0.2685546875, -0.37060546875, -0.2021484375, -0.388671875, 0.361572265625, 0.71044921875, 0.5126953125, 0.08837890625, 0.461669921875, 0.0237579345703125, 0.289794921875, 0.322265625, -0.53662109375, -0.042449951171875, -0.337890625, 0.7138671875, 0.173095703125, -0.2088623046875, -0.89453125, -0.494384765625, 0.0345458984375, -0.1761474609375, -0.01233673095703125, -0.470947265625, -0.8037109375, 0.2052001953125, -0.2578125, 0.36376953125, -0.52978515625, -0.4990234375, -0.277099609375, 0.37939453125, 0.4560546875, -0.99853515625, 0.20263671875, -0.53125, 0.434326171875, 0.422119140625, -0.0958251953125, -0.277099609375, -0.578125, -0.658203125, -0.69384765625, 0.25146484375, 0.732421875, -0.010040283203125, 0.1492919921875, -1.3671875, 0.480712890625, 0.236328125, 0.093505859375, 0.144775390625, 0.194580078125, 0.457763671875, 0.15478515625, 0.88720703125, -0.45849609375, -0.8818359375, 0.190185546875, -1.32421875, 0.5458984375, -0.66650390625, 0.2247314453125, 0.00614166259765625, 0.15576171875, -0.1771240234375, 0.52783203125, -0.2137451171875, 0.341796875, -0.00045990943908691406, 0.39208984375, -0.947265625, -0.50732421875, 0.51025390625, -0.40625, -0.2474365234375, 1.240234375, -0.182861328125, -0.5166015625, 0.6181640625, 0.6064453125, -0.35546875, 0.19970703125, -0.2454833984375, 0.564453125, -0.376708984375, -0.2275390625, 0.0158233642578125, -0.389892578125, 0.92724609375, -0.0323486328125, -0.9462890625, -0.38720703125, -1.2451171875, -0.187744140625, -0.1959228515625, -0.273193359375, 0.313720703125, -0.1810302734375, -0.1259765625, -0.2325439453125, -0.488037109375, -0.350830078125, -0.27783203125, -0.1683349609375, -0.25439453125, 0.27734375, 0.7138671875, 0.343505859375, 0.31982421875, -0.481201171875, 0.113525390625, -0.12646484375, -0.08612060546875, -0.33447265625, -0.08465576171875, -0.207275390625, -0.057586669921875, -0.177734375, 0.018707275390625, 0.24853515625, 0.54052734375, 0.5, 0.46484375, 0.60595703125, 0.484375, -0.65966796875, 0.76220703125, 0.2166748046875, -1.0224609375, -0.59716796875, 0.56787109375, -0.09222412109375, 0.430908203125, 0.433349609375, -0.79296875, -0.6005859375, -0.892578125, 0.09649658203125, -0.3662109375, -0.2354736328125, -0.916015625, 0.1492919921875, -0.30517578125, 0.53857421875, -0.0032367706298828125, -0.58203125, 0.09637451171875, -1.3388671875, 0.2073974609375, -0.6796875, -0.27490234375, -0.59619140625, -0.323486328125, 0.060028076171875, 0.931640625, 0.0963134765625, 0.20361328125, -0.2421875, -0.199462890625, 0.44873046875, 0.0347900390625, -0.365478515625, -0.37744140625, -0.261962890625, 0.2137451171875, -0.10443115234375, 0.0029392242431640625, -0.1273193359375, 0.68310546875, -0.7333984375, 0.028472900390625, -0.484130859375, -0.208984375, -0.413818359375, -0.1358642578125, 1.00390625, -0.2232666015625, -0.3212890625, -0.054656982421875, 0.2451171875, 0.68310546875, -0.396240234375, -0.251220703125, -0.8720703125, -0.2705078125, -0.64111328125, 0.58935546875, -0.2041015625, -0.11688232421875, -0.73583984375, -0.3623046875, 1.1318359375, -0.57177734375, 0.236328125, 1.267578125, 0.1807861328125, 0.282958984375, -0.71240234375, 0.1953125, 0.493896484375, -0.58154296875, -0.06658935546875, 0.0711669921875, -0.693359375, 0.352783203125, -0.2017822265625, -1.1376953125, -0.56005859375, 0.28466796875, 1.478515625, -0.2900390625, 0.7099609375, 0.1256103515625, -1.19921875, -0.5986328125, 0.68310546875, -0.002655029296875, 0.313720703125, 1.091796875, -0.248779296875, -0.2276611328125, 0.004352569580078125, -0.1551513671875, -0.52001953125, -0.43115234375, 1.3359375, -0.51220703125, -0.330078125, 0.93701171875, 1.2861328125, -1.005859375, -1.0634765625, -0.056732177734375, -0.03363037109375, -0.521484375, -0.8935546875, 0.1829833984375, 0.65869140625, -1.044921875, -0.0438232421875, 0.313720703125, -0.28271484375, 0.6279296875, -0.05535888671875, 0.271240234375, -0.497314453125, 0.38916015625, 0.6689453125, -0.51123046875, -0.06402587890625, -0.45849609375, -0.1888427734375, -0.236083984375, -0.10772705078125, 0.5283203125, -0.58544921875, 0.064697265625, 0.390869140625, 0.1025390625, 0.424560546875, -0.29248046875, -0.65673828125, 0.03887939453125, -0.9814453125, -0.3583984375, 0.037261962890625, 0.437744140625, -0.2208251953125, 0.400634765625, -0.90185546875, -0.0869140625, 0.1197509765625, 0.1617431640625, -0.425537109375, -0.68994140625, -0.2479248046875, -1.1171875, -0.52978515625, -0.5537109375, -0.8076171875, -0.43212890625, -0.1414794921875, 0.1824951171875, -0.471435546875, 0.307861328125, 0.440185546875, -0.65087890625, 0.859375, -0.720703125, 0.46826171875, -0.748046875, -0.296142578125, -0.5810546875, -0.10626220703125, -0.4501953125, 0.336181640625, -0.99609375, 0.2138671875, 0.0002613067626953125, 0.552734375, -0.342041015625, 0.2998046875, -0.2291259765625, -0.66552734375, 0.09307861328125, 0.328125, -0.6455078125, 0.7080078125, 0.1910400390625, 0.1414794921875, -0.0640869140625, -0.380615234375, -0.6318359375, -0.406005859375, 0.469482421875, 0.351806640625, 0.06744384765625, 0.1632080078125, -0.53857421875, 0.10498046875, -1.0439453125, 0.115234375, -0.35498046875, -0.0232696533203125, 0.1922607421875, -0.52783203125, 0.615234375, 1.041015625, -0.391357421875, 0.5, -0.2479248046875, -0.006557464599609375, 0.38525390625, 0.19921875, -0.323486328125, 0.21533203125, 0.38916015625, -0.1123046875, -0.09844970703125, 0.53466796875, -0.06982421875, 0.263916015625, 0.16748046875, -0.6279296875, -0.8857421875, -0.270751953125, -0.3095703125, 0.401123046875, 0.193603515625, -0.43310546875, -0.09136962890625, -0.11553955078125, -0.348388671875, 0.34423828125, -1.2451171875, -0.8251953125, 0.2529296875, 0.143310546875, -0.53857421875, 0.1322021484375, -0.826171875, -0.07708740234375, 0.1341552734375, 0.57080078125, -0.24658203125, 0.69091796875, -0.322265625, 0.114990234375, -0.236572265625, -0.1844482421875, 0.0458984375, 0.482666015625, -0.564453125, -0.49658203125, 0.13916015625, 0.947265625, 0.25048828125, -0.07135009765625, -0.5517578125, 0.38720703125, 0.1251220703125, 0.11016845703125, -0.435791015625, 0.11541748046875, -0.430419921875, 0.65185546875, -0.85009765625, -0.00032258033752441406, 0.06329345703125, 0.77197265625, 0.288330078125, -0.40771484375, -0.372802734375, 0.65380859375, 1.0693359375, -0.33203125, 0.56787109375, 0.33935546875, 0.459228515625, -0.1904296875, -0.239013671875, -0.315673828125, 0.873046875, 0.4228515625, 0.51953125, -0.0085296630859375, 0.2110595703125, 0.77099609375, -0.0265350341796875, -0.46826171875, 0.42236328125, -0.275146484375, -0.0205535888671875, 0.03411865234375, -0.11016845703125, -0.3046875, 0.2039794921875, -0.76513671875, 0.625, -0.56494140625, -0.445556640625, -0.203125, -0.54052734375, 1.0302734375, -0.4345703125, -0.031646728515625, 0.17529296875, -0.297607421875, 0.095703125, 0.6796875, 0.157470703125, 0.17822265625, 1.0029296875, 0.480712890625, 0.291259765625, 0.7080078125, 0.29052734375, 0.69970703125, -0.6591796875, -0.0251312255859375, -0.0239410400390625, -0.1787109375, -0.2364501953125, -0.5966796875, -1.0185546875, 0.55615234375, -0.13818359375, -0.465087890625, 0.72802734375, -0.6513671875, -0.0165252685546875, -0.26220703125, 0.74169921875, -0.478759765625, 0.3369140625, -0.1094970703125, -0.342041015625, -0.4951171875, 0.8330078125, -0.09637451171875, 0.31982421875, 0.2318115234375, 0.857421875, -0.179931640625, 1.5009765625, 0.181884765625, 0.04608154296875, 0.09552001953125, 0.3740234375, -0.625, -0.69384765625, -0.256591796875, -0.400146484375, 0.1859130859375, -0.76611328125, -0.368896484375, -0.1466064453125, 0.8125, 0.33251953125, -0.76025390625, -0.443603515625, 0.2425537109375, -0.9375, 0.33447265625, 0.423828125, 0.1986083984375, 0.004558563232421875, 0.002410888671875, -0.344970703125, -0.7021484375, 0.1495361328125, -0.908203125, 0.304931640625, -0.62939453125, -0.481201171875, -0.17236328125, -0.33984375, -0.374755859375, -0.35546875, -0.11309814453125, -0.83056640625, 0.79345703125, 0.335205078125, 0.533203125, 0.529296875, -0.085693359375, 0.31201171875, 0.97021484375, 0.828125, -0.1607666015625, 0.43212890625, 0.10650634765625, -0.0546875, 0.3857421875, -0.50341796875, 0.4150390625, -0.1031494140625, 0.609375, -0.623046875, 0.53759765625, -0.796875, -1.203125, 0.177978515625, 0.360107421875, 0.515625, -0.60546875, -0.88134765625, -0.10113525390625, -1.025390625, -0.1519775390625, -0.2401123046875, 0.75537109375, -0.27880859375, 0.031707763671875, -0.1558837890625, -1.0927734375, 4.484375, 1.0576171875, 0.69921875, 0.324462890625, 0.1583251953125, 0.6318359375, 0.306396484375, -0.78466796875, -0.10479736328125, -0.1429443359375, 0.64404296875, -0.134765625, 0.082275390625, 0.8916015625, 0.35595703125, 0.52685546875, -0.478759765625, -0.0312347412109375, -0.0310211181640625, -0.62158203125, -0.83349609375, 0.1697998046875, -0.038970947265625, 0.390380859375, -0.1273193359375, 0.33544921875, 0.35302734375, -0.8837890625, -0.450927734375, -0.6240234375, 0.2120361328125, -0.40185546875, 1.0673828125, -0.4287109375, -0.10540771484375, 0.64453125, -0.020294189453125, -0.496826171875, -0.396240234375, 0.21044921875, 0.1480712890625, 0.0023288726806640625, 0.81005859375, -0.951171875, -0.0311737060546875, 0.287353515625, -0.64306640625, 0.1522216796875, -0.0033416748046875, -0.9541015625, 0.490478515625, -0.15478515625, 0.2392578125, -0.51708984375, -1.029296875, 0.141357421875, 0.282470703125, 0.044586181640625, -0.1126708984375, 0.456298828125, 0.67626953125, 0.117431640625, 0.0953369140625, 0.63671875, -1.146484375, 1.091796875, -0.0307769775390625, 0.59814453125, -0.681640625, 0.02008056640625, -0.485595703125, -0.359375, -0.35009765625, -0.2159423828125, 0.9912109375, 0.285400390625, -0.3037109375, 0.264892578125, 0.369873046875, -0.62744140625, 0.32275390625, 0.06427001953125, -0.396484375, -0.2225341796875, 0.79541015625, 1.064453125, -0.58251953125, -0.416259765625, -0.353515625, 0.449951171875, 0.272216796875, 0.447998046875, 0.23193359375, -0.478271484375, -0.467529296875 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: 1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si β‰  si + 1(1 ≀ i < n). 3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. Help him find such string or state that such string doesn't exist. String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes. Input A single line contains two positive integers n and k (1 ≀ n ≀ 106, 1 ≀ k ≀ 26) β€” the string's length and the number of distinct letters. Output In a single line print the required string. If there isn't such string, print "-1" (without the quotes). Examples Input 7 4 Output ababacd Input 4 7 Output -1 Tags: greedy Correct Solution: ``` def fastio(): import sys from io import StringIO from atexit import register global input sys.stdin = StringIO(sys.stdin.read()) input = lambda : sys.stdin.readline().rstrip('\r\n') sys.stdout = StringIO() register(lambda : sys.__stdout__.write(sys.stdout.getvalue())) fastio() MOD = 10**9 + 7 I = lambda:list(map(int,input().split())) n, k = I() c = [chr(i + 97) for i in range(k)] if n < k or (k == 1 and n > 1): print(-1) exit() if n == 1: print(c[0]) exit() m = n - k + 2 ans = 'ab'*(m//2) + 'a'*(m%2) print(ans + ''.join(c[2:])) ```
107,311
[ 0.263916015625, -0.125244140625, 0.36083984375, 0.38671875, -0.322998046875, -0.50048828125, 0.051513671875, 0.1376953125, 0.447998046875, 0.8203125, 0.6142578125, 0.049560546875, 0.00907135009765625, -0.70458984375, -0.60595703125, 0.12359619140625, -0.5859375, -0.5341796875, -0.4443359375, 0.1656494140625, 0.12481689453125, -0.2073974609375, -1.453125, 0.038055419921875, -0.33203125, 0.9560546875, 0.33740234375, 0.050384521484375, 1.197265625, 0.87841796875, -0.279052734375, -0.439208984375, 0.54736328125, -1.01171875, -0.59814453125, -0.4296875, 0.57080078125, -0.93017578125, -0.4638671875, -0.77783203125, 0.1666259765625, -0.73095703125, 0.54736328125, -0.7080078125, -1.1826171875, -0.1480712890625, -0.455078125, -0.51611328125, -0.30224609375, -0.71728515625, -0.02349853515625, -0.14794921875, 0.47412109375, -0.330078125, -0.047149658203125, 0.27099609375, 0.197265625, -0.2548828125, -0.40234375, 0.490966796875, -0.2108154296875, 0.316162109375, 0.07611083984375, -0.57080078125, -0.220947265625, 0.05224609375, -0.1329345703125, -0.366943359375, -0.122314453125, -0.64453125, -0.1597900390625, 0.25048828125, -0.39404296875, -0.44775390625, -0.2491455078125, 0.24951171875, 0.432861328125, 0.0311737060546875, -0.456787109375, 0.87158203125, 0.44140625, 1.41015625, 0.35888671875, 0.2177734375, -0.126708984375, -0.477294921875, -0.0124359130859375, 0.341064453125, 0.1256103515625, -0.2666015625, 0.240966796875, 0.54931640625, -0.7470703125, 0.32958984375, 0.5419921875, 0.459716796875, -0.0859375, 0.419189453125, 0.285400390625, 0.052734375, 0.86181640625, 0.9794921875, -0.1602783203125, 0.84912109375, -0.6748046875, 0.31787109375, 0.09478759765625, -0.2366943359375, -0.270751953125, -0.416748046875, -0.289794921875, -0.1624755859375, 0.7978515625, 0.36181640625, -0.131591796875, 0.8583984375, -0.2239990234375, 0.276123046875, -0.83447265625, -0.13671875, 0.289306640625, 0.387451171875, 0.8115234375, -0.035369873046875, -0.11639404296875, -0.28271484375, -0.62158203125, 0.93359375, -0.7490234375, 0.333251953125, 0.3115234375, 0.0400390625, 0.09027099609375, 0.213623046875, 0.178466796875, 0.6513671875, -0.0728759765625, 0.40869140625, 0.68359375, -0.46826171875, 0.9072265625, -0.2322998046875, -0.03582763671875, 1.50390625, 0.41015625, -0.11968994140625, 0.6650390625, 0.283447265625, -0.837890625, 0.431884765625, -1.123046875, 0.429931640625, -0.11004638671875, 0.269775390625, -0.184814453125, 0.27392578125, -0.38818359375, 0.333740234375, 0.5078125, 0.2305908203125, -0.7744140625, 0.189697265625, -0.1649169921875, 0.7216796875, -0.314208984375, 0.7451171875, -0.57763671875, -0.095947265625, 0.264892578125, -0.1865234375, 0.305419921875, -0.15478515625, -0.348876953125, 0.791015625, 0.69677734375, 1.0068359375, 1.033203125, -0.35546875, 0.201171875, 0.438232421875, -0.669921875, 0.083251953125, 0.310791015625, 0.303955078125, 0.2379150390625, 0.431396484375, 0.08544921875, -0.456298828125, -0.92041015625, -0.6962890625, 0.04931640625, 0.39013671875, -0.203125, 0.478759765625, -0.09332275390625, 0.002044677734375, -0.7255859375, -0.2042236328125, -0.4150390625, -1.0966796875, -0.298583984375, 0.6865234375, -0.0692138671875, 0.473876953125, -0.333984375, -0.342041015625, 0.486083984375, 1.0048828125, -0.33837890625, 0.2000732421875, 0.36767578125, -0.08502197265625, -0.295166015625, 0.361083984375, 0.252685546875, 0.266845703125, -0.6865234375, 0.77099609375, -0.11663818359375, 0.21826171875, 0.300537109375, 0.86376953125, 0.14892578125, 0.375, -0.2110595703125, -0.026580810546875, 0.496337890625, 0.79833984375, 0.05743408203125, 0.57666015625, 0.35009765625, 1.2265625, 0.6513671875, 0.412353515625, 0.5888671875, 0.37451171875, 0.56103515625, 1.001953125, -0.1943359375, 0.363525390625, -0.1790771484375, 0.51220703125, -0.1551513671875, 0.30078125, 0.233154296875, 0.402587890625, 0.1383056640625, 0.20556640625, -0.2332763671875, 0.12188720703125, -0.0312347412109375, 0.908203125, -0.035736083984375, 0.3408203125, -0.468994140625, -0.435791015625, 0.07354736328125, 0.71826171875, -0.5830078125, -0.353271484375, -0.08575439453125, 0.1871337890625, -0.055999755859375, -0.088134765625, 0.1280517578125, 0.36376953125, 0.53515625, 0.181396484375, -0.411376953125, -0.256591796875, -1.2626953125, -0.49267578125, -1.16796875, -0.2203369140625, -0.59521484375, 0.171142578125, 0.392578125, -0.99072265625, 0.09716796875, -0.4384765625, -0.1883544921875, 0.09893798828125, -0.724609375, 0.5537109375, 0.03106689453125, 0.5966796875, -0.50927734375, 0.391845703125, -0.0303497314453125, 1.1201171875, -0.163330078125, -0.2427978515625, -0.0190582275390625, -0.54541015625, 0.307373046875, -0.204833984375, 0.45751953125, 0.08740234375, -0.385498046875, -1.0009765625, -0.56298828125, -0.1278076171875, -0.2330322265625, 0.10089111328125, -0.318115234375, 1.0703125, 0.3974609375, -0.857421875, 0.607421875, 0.73486328125, -0.63623046875, 0.68359375, 0.264892578125, 0.195556640625, -0.89892578125, 1.3515625, 0.0816650390625, -0.06390380859375, -0.796875, -0.63623046875, -0.301513671875, 0.26953125, 0.127197265625, -0.5791015625, -0.034393310546875, 0.54248046875, 0.1546630859375, -1.2509765625, 0.783203125, -0.9599609375, -0.40966796875, -0.4365234375, -0.34814453125, 0.50390625, 0.5078125, 0.387451171875, -0.312744140625, -0.356689453125, -0.476318359375, 0.309814453125, 0.406982421875, -0.72998046875, -0.1905517578125, 0.548828125, -0.41748046875, 0.104248046875, 0.2037353515625, -0.283447265625, -0.064208984375, -0.034088134765625, 0.09747314453125, 0.986328125, 0.1953125, 0.13232421875, 0.31298828125, 0.93505859375, -0.69482421875, -0.2646484375, -0.43408203125, 0.52099609375, 0.266845703125, 0.671875, 0.28955078125, -0.19970703125, -0.2587890625, -1.3671875, 0.327880859375, -0.0163726806640625, 0.7861328125, -0.4609375, 1.017578125, 0.42138671875, -0.53125, 0.46533203125, -0.5009765625, -0.27587890625, 1.1240234375, -0.21240234375, 0.8203125, -0.354736328125, 0.469482421875, -0.1358642578125, -0.2509765625, 0.62646484375, 0.1365966796875, 0.6611328125, -0.32177734375, -0.69775390625, -0.55810546875, -0.556640625, -0.0115966796875, -0.2978515625, 0.17578125, -0.311279296875, -0.18212890625, -0.387451171875, 0.367919921875, 0.90478515625, 0.59716796875, 0.09857177734375, 0.362060546875, -0.0927734375, 0.1383056640625, 0.41259765625, -0.56103515625, 0.1131591796875, -0.416015625, 0.76025390625, 0.13720703125, -0.1671142578125, -0.7255859375, -0.61865234375, -0.035552978515625, -0.2098388671875, -0.044525146484375, -0.36376953125, -0.82958984375, 0.176513671875, -0.1278076171875, 0.341064453125, -0.5986328125, -0.472900390625, -0.45703125, 0.517578125, 0.413330078125, -0.873046875, 0.0151824951171875, -0.421875, 0.34521484375, 0.392333984375, -0.125732421875, -0.23193359375, -0.5126953125, -0.63427734375, -0.7490234375, 0.394775390625, 0.6015625, 0.06787109375, 0.20703125, -1.330078125, 0.54052734375, 0.1805419921875, -0.18603515625, 0.07550048828125, 0.1466064453125, 0.484375, 0.27783203125, 0.6279296875, -0.42626953125, -0.744140625, 0.24755859375, -1.3369140625, 0.5380859375, -0.75537109375, 0.2008056640625, -0.1871337890625, 0.0068511962890625, -0.15380859375, 0.56494140625, -0.142822265625, 0.2127685546875, -0.08062744140625, 0.6748046875, -0.9384765625, -0.6796875, 0.609375, -0.368896484375, -0.310791015625, 1.0986328125, 0.0240325927734375, -0.5888671875, 0.748046875, 0.763671875, -0.313720703125, 0.2467041015625, -0.381103515625, 0.464111328125, -0.451416015625, -0.251953125, -0.170654296875, -0.472412109375, 0.88330078125, 0.19921875, -1.0322265625, -0.3349609375, -1.2060546875, -0.253662109375, -0.1763916015625, -0.197509765625, 0.37255859375, -0.3115234375, -0.179931640625, -0.236328125, -0.494873046875, -0.464111328125, -0.24951171875, -0.1951904296875, -0.300537109375, 0.3994140625, 0.798828125, 0.31298828125, 0.341064453125, -0.50634765625, -0.06268310546875, -0.3447265625, -0.4189453125, -0.337646484375, -0.08258056640625, -0.1578369140625, -0.08856201171875, -0.236328125, 0.042205810546875, 0.332763671875, 0.5673828125, 0.456298828125, 0.484619140625, 0.69775390625, 0.67138671875, -0.732421875, 0.7353515625, 0.1556396484375, -0.96240234375, -0.4912109375, 0.6318359375, -0.280517578125, 0.45068359375, 0.258056640625, -0.779296875, -0.6591796875, -1.0107421875, 0.284912109375, -0.2900390625, -0.12347412109375, -0.96044921875, 0.19384765625, -0.4111328125, 0.447998046875, 0.021575927734375, -0.62890625, -0.00788116455078125, -1.248046875, 0.1802978515625, -0.6396484375, -0.331298828125, -0.59423828125, -0.39404296875, 0.128173828125, 0.9521484375, 0.020263671875, 0.2149658203125, -0.32373046875, 0.018646240234375, 0.28076171875, -0.035491943359375, -0.317626953125, -0.2998046875, -0.255126953125, 0.22314453125, -0.2469482421875, 0.10235595703125, -0.23193359375, 0.47705078125, -0.6806640625, -0.0390625, -0.425048828125, -0.1378173828125, -0.341796875, 0.0364990234375, 1.021484375, -0.402587890625, -0.262451171875, 0.0276031494140625, 0.263916015625, 0.615234375, -0.2457275390625, -0.380126953125, -0.91552734375, -0.255859375, -0.9033203125, 0.414794921875, -0.27734375, -0.087646484375, -0.7216796875, -0.215576171875, 0.97802734375, -0.52099609375, 0.324951171875, 1.23046875, 0.1695556640625, 0.17333984375, -0.8193359375, 0.46630859375, 0.5859375, -0.5185546875, 0.10205078125, 0.18603515625, -0.7880859375, 0.40283203125, -0.27392578125, -1.185546875, -0.5888671875, 0.1922607421875, 1.5068359375, -0.2301025390625, 0.75048828125, 0.17333984375, -1.0673828125, -0.6201171875, 0.63134765625, -0.0494384765625, 0.2191162109375, 1.0634765625, -0.2724609375, -0.11279296875, 0.1343994140625, -0.02593994140625, -0.3603515625, -0.48095703125, 1.279296875, -0.5654296875, -0.354736328125, 1.1044921875, 1.0849609375, -1.0244140625, -1.1357421875, -0.18017578125, 0.191162109375, -0.338623046875, -0.8916015625, 0.01096343994140625, 0.701171875, -1.044921875, -0.1788330078125, 0.264404296875, -0.338134765625, 0.75, 0.00475311279296875, 0.316650390625, -0.58837890625, 0.26025390625, 0.537109375, -0.431884765625, -0.07861328125, -0.5498046875, -0.08270263671875, -0.331298828125, -0.060577392578125, 0.51708984375, -0.5693359375, 0.1507568359375, 0.333740234375, 0.1331787109375, 0.195556640625, -0.11053466796875, -0.6416015625, 0.170654296875, -0.97509765625, -0.372314453125, 0.1312255859375, 0.3671875, -0.17138671875, 0.42333984375, -0.88623046875, 0.01412200927734375, 0.26611328125, 0.2069091796875, -0.33251953125, -0.822265625, -0.30126953125, -1.0283203125, -0.44091796875, -0.330078125, -0.8916015625, -0.449462890625, -0.26513671875, 0.1944580078125, -0.50244140625, 0.35986328125, 0.42919921875, -0.41552734375, 0.685546875, -0.7783203125, 0.472900390625, -0.740234375, -0.111328125, -0.5986328125, 0.0032253265380859375, -0.3896484375, 0.287109375, -1.017578125, 0.07244873046875, 0.04144287109375, 0.599609375, -0.288330078125, 0.308837890625, -0.292236328125, -0.479248046875, -0.06317138671875, 0.374267578125, -0.6416015625, 0.87109375, 0.1617431640625, 0.127685546875, -0.0202178955078125, -0.355712890625, -0.460693359375, -0.392578125, 0.38037109375, 0.26416015625, -0.052398681640625, 0.01226043701171875, -0.5771484375, 0.117919921875, -0.9091796875, 0.0804443359375, -0.44091796875, -0.030853271484375, 0.1968994140625, -0.41455078125, 0.46044921875, 0.99365234375, -0.41455078125, 0.51513671875, -0.327392578125, 0.0002880096435546875, 0.404541015625, 0.07745361328125, -0.2269287109375, 0.261962890625, 0.248779296875, -0.253173828125, -0.06146240234375, 0.6123046875, -0.08935546875, 0.38427734375, 0.13232421875, -0.52001953125, -0.87109375, -0.275390625, -0.173828125, 0.324462890625, 0.1805419921875, -0.53173828125, -0.22509765625, -0.051361083984375, -0.40869140625, 0.423095703125, -1.1796875, -0.7939453125, 0.1534423828125, 0.10546875, -0.4375, 0.1353759765625, -0.8408203125, -0.11834716796875, 0.17822265625, 0.398681640625, -0.2225341796875, 0.634765625, -0.18017578125, 0.049835205078125, -0.424072265625, -0.1988525390625, 0.1776123046875, 0.3984375, -0.56787109375, -0.5009765625, 0.222900390625, 1.021484375, 0.1650390625, -0.006725311279296875, -0.6240234375, 0.324951171875, 0.1578369140625, 0.162109375, -0.334716796875, 0.1304931640625, -0.436767578125, 0.60986328125, -0.9287109375, 0.047332763671875, 0.1971435546875, 0.70361328125, 0.258056640625, -0.43701171875, -0.55859375, 0.650390625, 1.119140625, -0.1517333984375, 0.572265625, 0.268798828125, 0.5341796875, -0.230224609375, -0.301513671875, -0.443359375, 0.939453125, 0.434326171875, 0.54931640625, -0.0633544921875, 0.34375, 0.802734375, -0.1314697265625, -0.49365234375, 0.395263671875, -0.223876953125, -0.1534423828125, 0.11553955078125, -0.261474609375, -0.34326171875, 0.0650634765625, -0.8359375, 0.6943359375, -0.60791015625, -0.360595703125, -0.10198974609375, -0.537109375, 0.8466796875, -0.4462890625, -0.10888671875, 0.302734375, -0.432861328125, 0.253173828125, 0.65283203125, 0.253173828125, 0.11541748046875, 1.099609375, 0.4443359375, 0.2578125, 0.74951171875, 0.430908203125, 0.77880859375, -0.66552734375, -0.1124267578125, -0.06427001953125, -0.1776123046875, -0.1680908203125, -0.2978515625, -1.0517578125, 0.498291015625, -0.0919189453125, -0.423828125, 0.6513671875, -0.58251953125, 0.08154296875, -0.28125, 0.69384765625, -0.427734375, 0.3798828125, -0.07928466796875, -0.1463623046875, -0.53564453125, 0.78759765625, -0.0633544921875, 0.274658203125, 0.405029296875, 0.90380859375, -0.0626220703125, 1.546875, 0.251953125, -0.09832763671875, -0.0321044921875, 0.38134765625, -0.6015625, -0.75439453125, -0.1689453125, -0.239013671875, 0.1875, -0.576171875, -0.3603515625, -0.056671142578125, 0.7763671875, 0.34228515625, -0.6669921875, -0.45166015625, 0.10491943359375, -0.9228515625, 0.42041015625, 0.5166015625, 0.322021484375, 0.08013916015625, 0.08331298828125, -0.2462158203125, -0.8779296875, 0.20849609375, -0.82568359375, 0.42822265625, -0.615234375, -0.5205078125, -0.2349853515625, -0.318359375, -0.411865234375, -0.447265625, 0.02716064453125, -0.80712890625, 0.7763671875, 0.306396484375, 0.36279296875, 0.4599609375, 0.0274810791015625, 0.488525390625, 1.103515625, 0.89501953125, -0.1693115234375, 0.58154296875, 0.09259033203125, -0.056365966796875, 0.27880859375, -0.313232421875, 0.46728515625, -0.049224853515625, 0.4697265625, -0.5380859375, 0.5732421875, -0.87646484375, -1.2177734375, 0.1859130859375, 0.24755859375, 0.61328125, -0.705078125, -0.8994140625, -0.1436767578125, -1.1328125, -0.210205078125, -0.337158203125, 0.6474609375, -0.346435546875, 0.031402587890625, -0.138671875, -0.96337890625, 4.49609375, 1.1318359375, 0.689453125, 0.333740234375, 0.1962890625, 0.67919921875, 0.28271484375, -0.6904296875, -0.13818359375, -0.2342529296875, 0.64990234375, -0.1285400390625, -0.0426025390625, 0.9541015625, 0.498779296875, 0.46240234375, -0.37353515625, -0.2041015625, 0.052032470703125, -0.5263671875, -0.70361328125, 0.053955078125, 0.07025146484375, 0.284912109375, -0.152587890625, 0.343017578125, 0.398193359375, -0.91552734375, -0.372314453125, -0.56396484375, 0.25244140625, -0.36962890625, 0.927734375, -0.458984375, 0.0836181640625, 0.64892578125, 0.099365234375, -0.44287109375, -0.4111328125, 0.2376708984375, -0.0219879150390625, 0.058135986328125, 0.57470703125, -0.89306640625, 0.050811767578125, 0.28662109375, -0.58740234375, 0.359375, 0.162109375, -0.9677734375, 0.463623046875, -0.2489013671875, 0.20703125, -0.544921875, -0.958984375, 0.16943359375, 0.19677734375, -0.042266845703125, -0.375, 0.52880859375, 0.75341796875, 0.140625, 0.00615692138671875, 0.517578125, -1.08984375, 1.091796875, -0.0253448486328125, 0.8408203125, -0.7216796875, 0.022552490234375, -0.61962890625, -0.263671875, -0.251220703125, -0.1690673828125, 0.98583984375, 0.2139892578125, -0.3779296875, 0.326416015625, 0.302978515625, -0.499267578125, 0.34619140625, -0.017578125, -0.478271484375, -0.213623046875, 0.927734375, 1.271484375, -0.5654296875, -0.431396484375, -0.5947265625, 0.495361328125, 0.385986328125, 0.41796875, 0.25927734375, -0.64453125, -0.444580078125 ]
0
Provide tags and a correct Python 3 solution for this coding contest problem. Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: 1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si β‰  si + 1(1 ≀ i < n). 3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. Help him find such string or state that such string doesn't exist. String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes. Input A single line contains two positive integers n and k (1 ≀ n ≀ 106, 1 ≀ k ≀ 26) β€” the string's length and the number of distinct letters. Output In a single line print the required string. If there isn't such string, print "-1" (without the quotes). Examples Input 7 4 Output ababacd Input 4 7 Output -1 Tags: greedy Correct Solution: ``` import sys import math n, k = [int(x) for x in (sys.stdin.readline()).split()] if(k == 1 and n == 1): print("a") exit() if(k == 1 or k > n): print(-1) exit() res = ['a', 'b'] * (int(n / 2)) if(n % 2 != 0): res.append('a') t = 2 for i in range(n - (k - 2), n): res[i] = (chr(t + 97)) t += 1 """t = 2 for i in range(n): if(n - (k - 2) > i): if(i % 2 == 0): res.append('a') else: res.append('b') else: res.append(chr(t + 97)) t += 1""" print("".join(res)) ```
107,313
[ 0.417724609375, -0.09368896484375, 0.6044921875, 0.272216796875, -0.2021484375, -0.481689453125, 0.113037109375, 0.041473388671875, 0.365478515625, 0.779296875, 0.74658203125, -0.10467529296875, 0.0655517578125, -0.74755859375, -0.55126953125, 0.09344482421875, -0.59716796875, -0.5009765625, -0.37109375, 0.1337890625, 0.025970458984375, -0.1339111328125, -1.49609375, -0.05328369140625, -0.28173828125, 0.978515625, 0.388916015625, 0.07147216796875, 1.0830078125, 1.0107421875, -0.266357421875, -0.45849609375, 0.421142578125, -0.97265625, -0.6083984375, -0.403564453125, 0.58984375, -1.03125, -0.385009765625, -0.62451171875, 0.0684814453125, -0.7646484375, 0.463623046875, -0.73828125, -1.19140625, -0.08428955078125, -0.58154296875, -0.3984375, -0.140380859375, -0.88818359375, 0.10174560546875, -0.214111328125, 0.497802734375, -0.432861328125, -0.0302276611328125, 0.258056640625, 0.2415771484375, -0.2413330078125, -0.4208984375, 0.37646484375, -0.25439453125, 0.322998046875, 0.10357666015625, -0.52734375, -0.259765625, -0.03839111328125, -0.172607421875, -0.42822265625, 0.0181427001953125, -0.70947265625, -0.2286376953125, 0.231689453125, -0.56591796875, -0.375244140625, -0.244384765625, 0.1982421875, 0.36376953125, 0.0179901123046875, -0.477783203125, 0.94580078125, 0.488525390625, 1.4267578125, 0.480712890625, 0.301025390625, -0.109619140625, -0.52197265625, 0.12335205078125, 0.5576171875, 0.2354736328125, -0.2861328125, 0.1805419921875, 0.51904296875, -0.83544921875, 0.251708984375, 0.464111328125, 0.427978515625, 0.06280517578125, 0.42626953125, 0.2744140625, -0.07489013671875, 0.8515625, 1.0107421875, -0.313232421875, 0.9609375, -0.61181640625, 0.34521484375, -0.0101470947265625, -0.2296142578125, -0.19921875, -0.35888671875, -0.21923828125, -0.1787109375, 0.7216796875, 0.268798828125, -0.3017578125, 0.9287109375, -0.169189453125, 0.2802734375, -0.82568359375, -0.0802001953125, 0.4208984375, 0.42333984375, 0.79541015625, -0.0017147064208984375, -0.1019287109375, -0.204345703125, -0.63623046875, 0.896484375, -0.62451171875, 0.1976318359375, 0.373291015625, 0.048095703125, 0.03619384765625, 0.1217041015625, 0.2008056640625, 0.61865234375, -0.0667724609375, 0.52294921875, 0.5634765625, -0.398193359375, 0.85302734375, -0.335693359375, -0.043121337890625, 1.46484375, 0.51513671875, -0.199951171875, 0.7626953125, 0.198486328125, -0.7587890625, 0.3798828125, -1.1552734375, 0.59033203125, -0.0972900390625, 0.12371826171875, -0.07977294921875, 0.275390625, -0.3515625, 0.2685546875, 0.4619140625, 0.2479248046875, -0.57958984375, 0.17041015625, -0.1312255859375, 0.67041015625, -0.333740234375, 0.7626953125, -0.5625, -0.11846923828125, 0.0771484375, -0.263671875, 0.2354736328125, -0.12335205078125, -0.29736328125, 0.86328125, 0.7158203125, 1.15625, 0.93701171875, -0.280029296875, 0.1292724609375, 0.402099609375, -0.51953125, 0.046844482421875, 0.2178955078125, 0.468994140625, 0.09527587890625, 0.336669921875, 0.0290374755859375, -0.47802734375, -0.947265625, -0.6669921875, -0.004535675048828125, 0.317626953125, -0.2052001953125, 0.3828125, -0.031494140625, -0.03692626953125, -0.67724609375, -0.284423828125, -0.342041015625, -1.0576171875, -0.343505859375, 0.71630859375, -0.1143798828125, 0.50439453125, -0.509765625, -0.316162109375, 0.455810546875, 1.0185546875, -0.428955078125, 0.029754638671875, 0.204345703125, 0.07745361328125, -0.1470947265625, 0.15576171875, 0.236328125, 0.2117919921875, -0.8125, 0.74658203125, -0.2244873046875, 0.171875, 0.2286376953125, 0.8515625, 0.1614990234375, 0.49853515625, -0.23583984375, -0.06524658203125, 0.55517578125, 0.7705078125, 0.01119232177734375, 0.666015625, 0.314208984375, 1.2236328125, 0.74072265625, 0.483154296875, 0.568359375, 0.58349609375, 0.61376953125, 1.0693359375, 0.051239013671875, 0.348876953125, -0.16650390625, 0.473876953125, -0.1466064453125, 0.412841796875, 0.2476806640625, 0.44287109375, -0.00970458984375, 0.1373291015625, -0.198974609375, 0.21435546875, -0.03533935546875, 0.86376953125, 0.10821533203125, 0.38818359375, -0.5009765625, -0.3515625, 0.045074462890625, 0.75048828125, -0.5712890625, -0.40771484375, -0.196533203125, 0.1588134765625, -0.03729248046875, -0.20751953125, 0.233642578125, 0.2493896484375, 0.46044921875, 0.047698974609375, -0.336181640625, -0.276611328125, -1.2197265625, -0.59033203125, -1.263671875, -0.1153564453125, -0.69677734375, 0.1201171875, 0.460205078125, -0.91552734375, 0.0675048828125, -0.316650390625, -0.2347412109375, 0.240234375, -0.76220703125, 0.5625, 0.08270263671875, 0.48681640625, -0.5166015625, 0.453369140625, 0.092041015625, 0.93505859375, -0.2900390625, -0.264404296875, 0.049957275390625, -0.416748046875, 0.339599609375, -0.2310791015625, 0.467041015625, 0.03656005859375, -0.397705078125, -0.974609375, -0.58935546875, -0.09100341796875, -0.275390625, 0.07861328125, -0.294921875, 1.0908203125, 0.51171875, -0.81298828125, 0.5390625, 0.7236328125, -0.8388671875, 0.50048828125, 0.316650390625, 0.1903076171875, -0.8388671875, 1.4609375, 0.33251953125, -0.047027587890625, -0.61962890625, -0.533203125, -0.322998046875, 0.31103515625, 0.09552001953125, -0.5048828125, 0.043182373046875, 0.4921875, 0.237548828125, -1.2333984375, 0.78955078125, -1, -0.580078125, -0.513671875, -0.25146484375, 0.67626953125, 0.488037109375, 0.287353515625, -0.152587890625, -0.407958984375, -0.44775390625, 0.369140625, 0.376708984375, -0.669921875, -0.1767578125, 0.461669921875, -0.385986328125, 0.1529541015625, 0.023529052734375, -0.1500244140625, 0.06072998046875, -0.12078857421875, 0.2193603515625, 0.88671875, 0.31298828125, 0.0836181640625, 0.28955078125, 0.94580078125, -0.64453125, -0.39404296875, -0.51318359375, 0.630859375, 0.289306640625, 0.80224609375, 0.38330078125, -0.300537109375, -0.271728515625, -1.44140625, 0.26171875, -0.1787109375, 0.796875, -0.51318359375, 1.021484375, 0.53955078125, -0.51123046875, 0.48828125, -0.51513671875, -0.293212890625, 1.1796875, -0.031951904296875, 0.79541015625, -0.360107421875, 0.4375, -0.2064208984375, -0.346923828125, 0.64599609375, 0.2491455078125, 0.72900390625, -0.361083984375, -0.62744140625, -0.491455078125, -0.50146484375, -0.017120361328125, -0.5439453125, 0.24609375, -0.391845703125, -0.2235107421875, -0.40283203125, 0.345458984375, 0.7294921875, 0.5087890625, 0.0751953125, 0.448974609375, 0.004364013671875, 0.27685546875, 0.338623046875, -0.56787109375, 0.006694793701171875, -0.367431640625, 0.75244140625, 0.193115234375, -0.1888427734375, -0.85400390625, -0.51904296875, 0.052947998046875, -0.1728515625, -0.044769287109375, -0.439208984375, -0.76953125, 0.1981201171875, -0.22265625, 0.320068359375, -0.58203125, -0.4853515625, -0.3173828125, 0.4052734375, 0.46240234375, -1.0185546875, 0.126953125, -0.56640625, 0.42431640625, 0.39794921875, -0.09375, -0.2822265625, -0.5048828125, -0.66796875, -0.68115234375, 0.244140625, 0.70654296875, -0.016937255859375, 0.166259765625, -1.388671875, 0.494873046875, 0.227783203125, 0.0302886962890625, 0.130859375, 0.2327880859375, 0.4560546875, 0.1756591796875, 0.85498046875, -0.453369140625, -0.841796875, 0.1580810546875, -1.3046875, 0.556640625, -0.64453125, 0.2418212890625, 0.007171630859375, 0.1512451171875, -0.1810302734375, 0.53369140625, -0.2353515625, 0.324951171875, 0.033111572265625, 0.4208984375, -0.98828125, -0.53857421875, 0.53173828125, -0.39306640625, -0.257080078125, 1.2822265625, -0.14111328125, -0.50146484375, 0.61767578125, 0.5888671875, -0.313720703125, 0.229248046875, -0.30859375, 0.53564453125, -0.37060546875, -0.190673828125, -0.058135986328125, -0.411376953125, 0.93212890625, -0.035858154296875, -0.927734375, -0.397705078125, -1.23828125, -0.1922607421875, -0.21630859375, -0.2802734375, 0.305419921875, -0.232421875, -0.12744140625, -0.218994140625, -0.52392578125, -0.362060546875, -0.2109375, -0.159912109375, -0.234375, 0.28173828125, 0.7197265625, 0.32861328125, 0.310302734375, -0.4443359375, 0.09625244140625, -0.18701171875, -0.1644287109375, -0.344482421875, -0.10595703125, -0.250732421875, -0.057708740234375, -0.19677734375, 0.0560302734375, 0.281494140625, 0.57763671875, 0.52197265625, 0.4921875, 0.64013671875, 0.52294921875, -0.63427734375, 0.80615234375, 0.1854248046875, -1.0498046875, -0.58251953125, 0.5908203125, -0.1539306640625, 0.47265625, 0.36669921875, -0.8251953125, -0.603515625, -0.8740234375, 0.1451416015625, -0.377685546875, -0.269775390625, -0.89208984375, 0.1614990234375, -0.339111328125, 0.55224609375, -0.03033447265625, -0.5517578125, 0.07464599609375, -1.3212890625, 0.20263671875, -0.6787109375, -0.3076171875, -0.5751953125, -0.350341796875, 0.0753173828125, 1.00390625, 0.06829833984375, 0.20166015625, -0.216552734375, -0.14599609375, 0.394775390625, 0.033966064453125, -0.3388671875, -0.41552734375, -0.24755859375, 0.24365234375, -0.139404296875, 0.04498291015625, -0.1400146484375, 0.64599609375, -0.73291015625, 0.0401611328125, -0.498779296875, -0.189453125, -0.3671875, -0.11846923828125, 0.98876953125, -0.28369140625, -0.304931640625, -0.025299072265625, 0.180908203125, 0.73583984375, -0.363037109375, -0.1962890625, -0.8515625, -0.238037109375, -0.681640625, 0.5869140625, -0.2069091796875, -0.072265625, -0.7568359375, -0.358154296875, 1.1298828125, -0.5732421875, 0.2406005859375, 1.283203125, 0.207763671875, 0.29345703125, -0.73388671875, 0.19287109375, 0.53125, -0.6064453125, -0.0242919921875, 0.132080078125, -0.71484375, 0.3779296875, -0.225830078125, -1.1669921875, -0.55224609375, 0.267578125, 1.462890625, -0.27294921875, 0.68603515625, 0.1544189453125, -1.2177734375, -0.59228515625, 0.65478515625, -0.0181121826171875, 0.31787109375, 1.0908203125, -0.2275390625, -0.2333984375, 0.08453369140625, -0.16162109375, -0.473388671875, -0.433837890625, 1.3642578125, -0.56103515625, -0.34130859375, 0.96435546875, 1.2509765625, -0.9814453125, -1.0986328125, -0.06988525390625, -0.0005216598510742188, -0.5087890625, -0.94091796875, 0.17041015625, 0.65625, -1.001953125, -0.0478515625, 0.29638671875, -0.265869140625, 0.66845703125, -0.0338134765625, 0.287841796875, -0.465087890625, 0.407958984375, 0.6689453125, -0.475830078125, -0.055694580078125, -0.469970703125, -0.1864013671875, -0.254150390625, -0.11737060546875, 0.5390625, -0.5888671875, 0.109619140625, 0.354248046875, 0.097900390625, 0.4248046875, -0.263916015625, -0.6044921875, 0.07574462890625, -0.984375, -0.3330078125, 0.05316162109375, 0.3837890625, -0.266357421875, 0.453857421875, -0.935546875, -0.0865478515625, 0.09783935546875, 0.1636962890625, -0.425537109375, -0.67041015625, -0.251708984375, -1.1240234375, -0.51806640625, -0.52490234375, -0.82666015625, -0.429931640625, -0.134521484375, 0.256103515625, -0.413818359375, 0.302978515625, 0.46435546875, -0.63671875, 0.85009765625, -0.728515625, 0.492431640625, -0.72119140625, -0.26220703125, -0.638671875, -0.070556640625, -0.48486328125, 0.298095703125, -0.99267578125, 0.1881103515625, 0.024566650390625, 0.51611328125, -0.3486328125, 0.2626953125, -0.2293701171875, -0.62255859375, 0.1068115234375, 0.35791015625, -0.703125, 0.7060546875, 0.1807861328125, 0.1600341796875, -0.037445068359375, -0.36474609375, -0.6240234375, -0.37353515625, 0.488525390625, 0.322265625, 0.0582275390625, 0.1490478515625, -0.5546875, 0.07598876953125, -1.029296875, 0.14404296875, -0.362060546875, -0.029449462890625, 0.1651611328125, -0.552734375, 0.583984375, 1.0791015625, -0.3623046875, 0.468505859375, -0.2122802734375, 0.0285491943359375, 0.36474609375, 0.1685791015625, -0.32958984375, 0.2459716796875, 0.400390625, -0.10992431640625, -0.10162353515625, 0.481689453125, -0.06622314453125, 0.2449951171875, 0.1881103515625, -0.6455078125, -0.89892578125, -0.267822265625, -0.349365234375, 0.418701171875, 0.2425537109375, -0.47509765625, -0.10394287109375, -0.1588134765625, -0.34912109375, 0.343505859375, -1.224609375, -0.86962890625, 0.2354736328125, 0.10498046875, -0.5263671875, 0.1754150390625, -0.8349609375, -0.07232666015625, 0.1103515625, 0.54443359375, -0.200927734375, 0.7177734375, -0.28271484375, 0.1014404296875, -0.21630859375, -0.1805419921875, 0.0472412109375, 0.487060546875, -0.53955078125, -0.496826171875, 0.1224365234375, 0.9599609375, 0.262451171875, -0.08807373046875, -0.60546875, 0.34423828125, 0.15380859375, 0.1336669921875, -0.391845703125, 0.1300048828125, -0.429443359375, 0.671875, -0.86572265625, 0.0008592605590820312, 0.0927734375, 0.77685546875, 0.267578125, -0.40869140625, -0.4189453125, 0.67822265625, 1.1455078125, -0.318359375, 0.5908203125, 0.36865234375, 0.460693359375, -0.1683349609375, -0.19970703125, -0.3173828125, 0.83642578125, 0.43212890625, 0.52880859375, -0.020538330078125, 0.2376708984375, 0.7939453125, -0.0215606689453125, -0.47607421875, 0.403076171875, -0.298828125, -0.0218963623046875, 0.050445556640625, -0.1025390625, -0.319091796875, 0.1666259765625, -0.79443359375, 0.61376953125, -0.595703125, -0.398193359375, -0.195556640625, -0.51708984375, 1.0380859375, -0.49267578125, -0.0364990234375, 0.1820068359375, -0.280517578125, 0.15380859375, 0.662109375, 0.1849365234375, 0.212646484375, 1.015625, 0.464599609375, 0.278564453125, 0.66455078125, 0.3603515625, 0.6796875, -0.7080078125, -0.021209716796875, -0.02679443359375, -0.18603515625, -0.2100830078125, -0.5380859375, -1.056640625, 0.57763671875, -0.095458984375, -0.427978515625, 0.68994140625, -0.66015625, -0.003429412841796875, -0.28955078125, 0.767578125, -0.47802734375, 0.305908203125, -0.11798095703125, -0.296875, -0.501953125, 0.8349609375, -0.07171630859375, 0.30712890625, 0.28076171875, 0.86181640625, -0.1693115234375, 1.5244140625, 0.2381591796875, 0.0657958984375, 0.08984375, 0.360107421875, -0.640625, -0.6796875, -0.242919921875, -0.331787109375, 0.13525390625, -0.7314453125, -0.377685546875, -0.11322021484375, 0.8388671875, 0.322509765625, -0.72802734375, -0.496826171875, 0.2183837890625, -0.91943359375, 0.3515625, 0.406494140625, 0.256591796875, 0.02490234375, -0.02777099609375, -0.345703125, -0.74658203125, 0.15234375, -0.85498046875, 0.33837890625, -0.59521484375, -0.496826171875, -0.20751953125, -0.32861328125, -0.3720703125, -0.3359375, -0.06805419921875, -0.82373046875, 0.833984375, 0.275146484375, 0.48095703125, 0.48974609375, -0.09527587890625, 0.30908203125, 0.982421875, 0.826171875, -0.2078857421875, 0.478759765625, 0.1085205078125, -0.051666259765625, 0.371337890625, -0.45703125, 0.42138671875, -0.097412109375, 0.580078125, -0.62744140625, 0.552734375, -0.83447265625, -1.2060546875, 0.148193359375, 0.332275390625, 0.50732421875, -0.60498046875, -0.90771484375, -0.1568603515625, -1.0517578125, -0.1551513671875, -0.2435302734375, 0.763671875, -0.31005859375, 0.06451416015625, -0.151611328125, -1.07421875, 4.48046875, 1.0810546875, 0.6572265625, 0.2958984375, 0.1783447265625, 0.65478515625, 0.3193359375, -0.81201171875, -0.063232421875, -0.1898193359375, 0.63427734375, -0.1429443359375, 0.05621337890625, 0.87353515625, 0.36083984375, 0.53369140625, -0.5048828125, -0.1097412109375, -0.01432037353515625, -0.62255859375, -0.80126953125, 0.1473388671875, -0.0185089111328125, 0.3134765625, -0.149169921875, 0.3857421875, 0.352783203125, -0.8857421875, -0.4326171875, -0.611328125, 0.2427978515625, -0.389404296875, 1.0224609375, -0.4423828125, -0.09637451171875, 0.65380859375, -0.027679443359375, -0.486572265625, -0.402099609375, 0.2298583984375, 0.1751708984375, 0.0853271484375, 0.77685546875, -0.94482421875, -0.01617431640625, 0.321044921875, -0.62548828125, 0.1546630859375, 0.0296478271484375, -0.96630859375, 0.499267578125, -0.139404296875, 0.2218017578125, -0.463623046875, -1.0361328125, 0.177490234375, 0.28857421875, 0.0533447265625, -0.13330078125, 0.46142578125, 0.642578125, 0.12261962890625, 0.09423828125, 0.66357421875, -1.1357421875, 1.0751953125, -0.0011911392211914062, 0.62890625, -0.64599609375, 0.04901123046875, -0.4912109375, -0.427001953125, -0.40625, -0.18359375, 0.99267578125, 0.307861328125, -0.2998046875, 0.2496337890625, 0.376953125, -0.59326171875, 0.3193359375, 0.07781982421875, -0.3603515625, -0.224609375, 0.77392578125, 1.0693359375, -0.59033203125, -0.423583984375, -0.3515625, 0.41650390625, 0.27001953125, 0.46142578125, 0.2509765625, -0.515625, -0.5048828125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: 1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si β‰  si + 1(1 ≀ i < n). 3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. Help him find such string or state that such string doesn't exist. String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes. Input A single line contains two positive integers n and k (1 ≀ n ≀ 106, 1 ≀ k ≀ 26) β€” the string's length and the number of distinct letters. Output In a single line print the required string. If there isn't such string, print "-1" (without the quotes). Examples Input 7 4 Output ababacd Input 4 7 Output -1 Submitted Solution: ``` import sys (n,k)=map(int,sys.stdin.readline().split()) if (k==1 and n!=1) or k>n: print(-1) elif n==1: print('a') else: tmp=n-k+2 s="ab"*(tmp//2) if tmp%2==1: s+="a" for i in range(2,k): s+=chr(ord('a')+i) print (s) ``` Yes
107,314
[ 0.46826171875, -0.153564453125, 0.505859375, 0.2130126953125, -0.3427734375, -0.356689453125, -0.0043182373046875, 0.1494140625, 0.230712890625, 0.7841796875, 0.63427734375, -0.019195556640625, 0.006008148193359375, -0.791015625, -0.56494140625, 0.06231689453125, -0.578125, -0.456298828125, -0.29443359375, 0.07720947265625, -0.0361328125, -0.162109375, -1.482421875, 0.04864501953125, -0.298583984375, 0.89013671875, 0.357177734375, 0.0338134765625, 1.1591796875, 0.88671875, -0.302978515625, -0.5224609375, 0.486328125, -0.849609375, -0.50634765625, -0.498779296875, 0.65478515625, -0.97705078125, -0.44677734375, -0.6171875, 0.01218414306640625, -0.65185546875, 0.438232421875, -0.6611328125, -1.2509765625, -0.1173095703125, -0.54638671875, -0.334716796875, -0.23486328125, -0.89111328125, 0.08135986328125, -0.2200927734375, 0.40185546875, -0.71533203125, 0.07220458984375, 0.390625, 0.21337890625, -0.1773681640625, -0.43505859375, 0.321533203125, -0.18701171875, 0.44384765625, 0.05419921875, -0.61572265625, -0.22900390625, 0.055206298828125, -0.09234619140625, -0.38232421875, 0.0721435546875, -0.51513671875, -0.284912109375, 0.01503753662109375, -0.58984375, -0.274658203125, -0.3125, 0.181884765625, 0.370849609375, 0.051788330078125, -0.640625, 0.8427734375, 0.3701171875, 1.4345703125, 0.5302734375, 0.326416015625, -0.1197509765625, -0.4677734375, 0.2064208984375, 0.52490234375, 0.26171875, -0.1781005859375, 0.281494140625, 0.3896484375, -0.78857421875, 0.09783935546875, 0.546875, 0.413818359375, 0.047149658203125, 0.39111328125, 0.26171875, -0.030487060546875, 0.87890625, 0.86328125, -0.1812744140625, 1.0927734375, -0.6005859375, 0.296142578125, -0.12261962890625, -0.37841796875, -0.1949462890625, -0.429443359375, -0.231201171875, -0.1556396484375, 0.6240234375, 0.306884765625, -0.381103515625, 0.88134765625, -0.07354736328125, 0.3544921875, -0.79150390625, -0.0665283203125, 0.46630859375, 0.338134765625, 0.75634765625, 0.04339599609375, 0.01119232177734375, -0.25439453125, -0.748046875, 0.880859375, -0.56396484375, 0.12469482421875, 0.41455078125, 0.06988525390625, -0.176025390625, 0.050567626953125, 0.140380859375, 0.5908203125, 0.01165008544921875, 0.53271484375, 0.6015625, -0.49072265625, 0.91064453125, -0.257568359375, 0.023590087890625, 1.505859375, 0.5068359375, -0.322265625, 0.62353515625, 0.1768798828125, -0.76904296875, 0.469482421875, -1.0859375, 0.60302734375, -0.1588134765625, -0.05712890625, -0.1763916015625, 0.1856689453125, -0.27587890625, 0.25390625, 0.54736328125, 0.2408447265625, -0.435791015625, 0.2369384765625, -0.304443359375, 0.56298828125, -0.33984375, 0.6279296875, -0.53955078125, -0.1827392578125, 0.102294921875, -0.24609375, 0.2203369140625, -0.1336669921875, -0.11505126953125, 0.904296875, 0.78564453125, 1.2451171875, 0.92138671875, -0.2142333984375, 0.1368408203125, 0.44970703125, -0.57568359375, -0.00789642333984375, 0.2822265625, 0.5341796875, 0.0859375, 0.357421875, 0.0008082389831542969, -0.501953125, -0.73974609375, -0.70068359375, -0.050811767578125, 0.38623046875, -0.1756591796875, 0.46484375, -0.1182861328125, -0.051605224609375, -0.7373046875, -0.302490234375, -0.2425537109375, -1.119140625, -0.435791015625, 0.6044921875, -0.07159423828125, 0.50732421875, -0.623046875, -0.303466796875, 0.403564453125, 1.046875, -0.3544921875, 0.1414794921875, 0.2340087890625, 0.162109375, -0.1549072265625, 0.043304443359375, 0.343994140625, 0.234130859375, -0.74462890625, 0.61376953125, -0.281494140625, 0.09149169921875, 0.1363525390625, 0.8515625, 0.12646484375, 0.375732421875, -0.33935546875, -0.1046142578125, 0.404296875, 0.89013671875, -0.0504150390625, 0.68017578125, 0.47265625, 1.1533203125, 0.7431640625, 0.58251953125, 0.5791015625, 0.54345703125, 0.77978515625, 1.0380859375, -0.0880126953125, 0.3583984375, -0.261474609375, 0.493408203125, -0.030670166015625, 0.587890625, 0.30224609375, 0.350341796875, -0.0219268798828125, 0.0736083984375, -0.2318115234375, 0.253173828125, -0.1046142578125, 0.74755859375, -0.0061187744140625, 0.451904296875, -0.449951171875, -0.3837890625, 0.1219482421875, 0.7548828125, -0.70361328125, -0.56884765625, -0.112060546875, 0.11370849609375, -0.0458984375, -0.183837890625, 0.04388427734375, 0.11676025390625, 0.52294921875, 0.14208984375, -0.303466796875, -0.27099609375, -1.1435546875, -0.68408203125, -1.3720703125, -0.1771240234375, -0.76220703125, 0.1312255859375, 0.462890625, -0.9189453125, 0.12176513671875, -0.50146484375, -0.1405029296875, 0.050933837890625, -0.6103515625, 0.65625, 0.07965087890625, 0.406494140625, -0.53759765625, 0.410400390625, 0.13427734375, 0.9365234375, -0.43798828125, -0.241455078125, -0.06500244140625, -0.351318359375, 0.3056640625, -0.3291015625, 0.53759765625, 0.0860595703125, -0.39990234375, -1.0302734375, -0.46875, -0.0134429931640625, -0.263671875, -0.0227203369140625, -0.347412109375, 1.2109375, 0.377197265625, -0.87255859375, 0.5380859375, 0.64794921875, -0.7763671875, 0.5068359375, 0.486083984375, 0.1807861328125, -0.802734375, 1.482421875, 0.306884765625, 0.0294952392578125, -0.57421875, -0.5283203125, -0.323486328125, 0.318115234375, 0.10003662109375, -0.5029296875, -0.0931396484375, 0.490966796875, 0.1829833984375, -1.1650390625, 0.8125, -1.05078125, -0.484619140625, -0.478515625, -0.3642578125, 0.63037109375, 0.51708984375, 0.320068359375, -0.10589599609375, -0.53076171875, -0.405029296875, 0.43310546875, 0.384521484375, -0.880859375, -0.1524658203125, 0.49072265625, -0.355712890625, 0.289306640625, 0.039825439453125, -0.2440185546875, 0.0254669189453125, -0.1695556640625, 0.11187744140625, 0.9912109375, 0.25244140625, 0.134033203125, 0.2283935546875, 0.990234375, -0.71630859375, -0.39453125, -0.59228515625, 0.68017578125, 0.270751953125, 0.87646484375, 0.4560546875, -0.07281494140625, -0.307861328125, -1.376953125, 0.3125, -0.2451171875, 0.7314453125, -0.435546875, 0.9697265625, 0.4033203125, -0.62060546875, 0.64794921875, -0.529296875, -0.1517333984375, 1.1943359375, -0.005023956298828125, 0.76318359375, -0.473388671875, 0.423828125, -0.1484375, -0.33544921875, 0.5625, 0.25732421875, 0.89697265625, -0.34814453125, -0.51513671875, -0.4697265625, -0.39599609375, -0.01161956787109375, -0.4501953125, 0.2056884765625, -0.31591796875, -0.39453125, -0.46240234375, 0.358154296875, 0.7216796875, 0.5146484375, 0.2188720703125, 0.38330078125, -0.027923583984375, 0.185791015625, 0.3662109375, -0.42626953125, 0.020843505859375, -0.382080078125, 0.8310546875, 0.294189453125, -0.27001953125, -0.78515625, -0.4658203125, -0.0204315185546875, -0.1920166015625, -0.08941650390625, -0.342041015625, -0.78369140625, 0.19873046875, -0.146484375, 0.4140625, -0.708984375, -0.45361328125, -0.327392578125, 0.446533203125, 0.46875, -1.046875, 0.1334228515625, -0.60107421875, 0.35546875, 0.461669921875, -0.227783203125, -0.349609375, -0.4677734375, -0.84423828125, -0.8876953125, 0.327880859375, 0.6689453125, 0.055572509765625, 0.1490478515625, -1.4287109375, 0.5380859375, 0.36279296875, -0.134033203125, 0.0985107421875, 0.01042938232421875, 0.328125, 0.28173828125, 0.74755859375, -0.44189453125, -0.7529296875, 0.11724853515625, -1.2568359375, 0.42431640625, -0.6533203125, 0.3154296875, 0.0989990234375, 0.10772705078125, -0.153076171875, 0.472412109375, -0.2509765625, 0.304443359375, -0.058746337890625, 0.459716796875, -1.0361328125, -0.599609375, 0.51123046875, -0.342529296875, -0.37939453125, 1.2861328125, -0.173095703125, -0.53564453125, 0.56787109375, 0.492919921875, -0.2354736328125, 0.341064453125, -0.31982421875, 0.4892578125, -0.189697265625, -0.194091796875, -0.06927490234375, -0.345458984375, 1.046875, -0.1859130859375, -0.798828125, -0.39453125, -1.169921875, -0.1195068359375, -0.135009765625, -0.35888671875, 0.30859375, -0.18359375, -0.09124755859375, -0.264404296875, -0.5400390625, -0.53466796875, -0.144287109375, -0.1185302734375, -0.359130859375, 0.1304931640625, 0.583984375, 0.373291015625, 0.34326171875, -0.47216796875, -0.005809783935546875, -0.31103515625, -0.155029296875, -0.41357421875, -0.1767578125, -0.15283203125, -0.214599609375, -0.22119140625, 0.1446533203125, 0.278564453125, 0.64111328125, 0.388916015625, 0.47021484375, 0.69482421875, 0.454833984375, -0.7744140625, 0.95458984375, 0.134765625, -1.1806640625, -0.4580078125, 0.60986328125, -0.0267333984375, 0.517578125, 0.287353515625, -0.74609375, -0.62744140625, -0.97216796875, 0.231201171875, -0.378662109375, -0.37451171875, -0.9111328125, 0.1328125, -0.2431640625, 0.57275390625, -0.1339111328125, -0.607421875, 0.08050537109375, -1.3681640625, 0.1561279296875, -0.6982421875, -0.382080078125, -0.60107421875, -0.29345703125, -0.005462646484375, 1.0302734375, 0.11663818359375, 0.2392578125, -0.2078857421875, -0.0758056640625, 0.279541015625, 0.0953369140625, -0.326904296875, -0.52001953125, -0.264892578125, 0.26025390625, -0.180908203125, 0.040496826171875, -0.1885986328125, 0.662109375, -0.67626953125, 0.121337890625, -0.383544921875, -0.1424560546875, -0.28173828125, -0.212646484375, 0.99462890625, -0.41015625, -0.240966796875, -0.08349609375, 0.1480712890625, 0.7412109375, -0.428466796875, -0.15380859375, -0.7080078125, -0.2130126953125, -0.744140625, 0.48876953125, -0.27685546875, -0.020782470703125, -0.7705078125, -0.28076171875, 1.1533203125, -0.61474609375, 0.274169921875, 1.3134765625, 0.2237548828125, 0.3212890625, -0.7294921875, 0.304443359375, 0.57275390625, -0.5849609375, -0.09649658203125, 0.117919921875, -0.76513671875, 0.367431640625, -0.2568359375, -1.1376953125, -0.552734375, 0.314697265625, 1.37109375, -0.2200927734375, 0.7490234375, 0.1881103515625, -1.138671875, -0.477783203125, 0.69091796875, -0.134521484375, 0.276123046875, 1.0322265625, -0.12445068359375, -0.25146484375, 0.1246337890625, -0.245361328125, -0.50341796875, -0.374755859375, 1.3544921875, -0.61376953125, -0.41650390625, 1.068359375, 1.244140625, -1.01171875, -1.07421875, -0.1326904296875, 0.0706787109375, -0.365478515625, -1.0185546875, 0.257568359375, 0.57080078125, -0.947265625, -0.061614990234375, 0.156494140625, -0.315673828125, 0.72607421875, -0.04119873046875, 0.37646484375, -0.55419921875, 0.1986083984375, 0.724609375, -0.5126953125, -0.07330322265625, -0.50634765625, -0.0758056640625, -0.20458984375, 0.0185546875, 0.5439453125, -0.47412109375, 0.1827392578125, 0.4287109375, 0.09228515625, 0.4638671875, -0.397216796875, -0.447021484375, -0.0028400421142578125, -0.9287109375, -0.346923828125, 0.044647216796875, 0.40283203125, -0.146728515625, 0.52880859375, -0.90625, -0.061126708984375, 0.147705078125, 0.2489013671875, -0.388427734375, -0.52294921875, -0.3369140625, -1.0791015625, -0.5126953125, -0.442138671875, -0.85205078125, -0.446533203125, -0.0789794921875, 0.347900390625, -0.4423828125, 0.267333984375, 0.55517578125, -0.65380859375, 0.80810546875, -0.73828125, 0.46142578125, -0.78076171875, -0.185791015625, -0.59033203125, 0.056121826171875, -0.58154296875, 0.1436767578125, -0.8984375, 0.153564453125, -0.043914794921875, 0.43798828125, -0.43408203125, 0.31396484375, -0.1455078125, -0.556640625, 0.1697998046875, 0.41015625, -0.78564453125, 0.79736328125, 0.1627197265625, 0.218994140625, 0.01312255859375, -0.5126953125, -0.52001953125, -0.1785888671875, 0.6953125, 0.337646484375, 0.07550048828125, 0.106201171875, -0.460205078125, -0.014556884765625, -0.88916015625, 0.1300048828125, -0.40673828125, 0.09814453125, 0.0693359375, -0.55859375, 0.55078125, 1.0634765625, -0.439453125, 0.416015625, -0.1541748046875, 0.07427978515625, 0.411865234375, 0.204833984375, -0.28759765625, 0.310546875, 0.3134765625, -0.0709228515625, -0.0396728515625, 0.48193359375, 0.034149169921875, 0.319580078125, -0.0364990234375, -0.7236328125, -0.947265625, -0.1776123046875, -0.333251953125, 0.39306640625, 0.26025390625, -0.465576171875, -0.1033935546875, -0.058135986328125, -0.494873046875, 0.43408203125, -1.251953125, -0.908203125, 0.346435546875, 0.09466552734375, -0.6064453125, 0.252685546875, -0.9599609375, 0.02471923828125, 0.160888671875, 0.447998046875, -0.257080078125, 0.63330078125, -0.139404296875, 0.119384765625, -0.2249755859375, -0.1739501953125, 0.12127685546875, 0.44580078125, -0.66162109375, -0.486328125, 0.1693115234375, 0.939453125, 0.1868896484375, -0.220458984375, -0.67041015625, 0.30029296875, 0.1744384765625, -0.0576171875, -0.266845703125, 0.166748046875, -0.36279296875, 0.6494140625, -0.81787109375, -0.0279998779296875, 0.041046142578125, 0.7705078125, 0.185302734375, -0.3662109375, -0.53271484375, 0.69775390625, 1.16015625, -0.266357421875, 0.5634765625, 0.324462890625, 0.57666015625, -0.11151123046875, -0.19677734375, -0.408203125, 0.8251953125, 0.58642578125, 0.58349609375, 0.0018939971923828125, 0.36376953125, 0.822265625, 0.12493896484375, -0.289306640625, 0.576171875, -0.2423095703125, -0.050750732421875, 0.0160064697265625, -0.2354736328125, -0.37158203125, 0.20556640625, -0.712890625, 0.51025390625, -0.59375, -0.287109375, -0.21240234375, -0.55615234375, 1.0283203125, -0.54443359375, -0.0097808837890625, 0.1383056640625, -0.348388671875, 0.256591796875, 0.6708984375, 0.205810546875, 0.1173095703125, 0.97021484375, 0.64990234375, 0.359375, 0.71533203125, 0.367919921875, 0.57958984375, -0.75, -0.0335693359375, 0.120361328125, -0.22509765625, -0.1962890625, -0.5029296875, -1.2041015625, 0.74609375, -0.0950927734375, -0.2958984375, 0.6015625, -0.69189453125, 0.041412353515625, -0.26806640625, 0.87353515625, -0.53515625, 0.307861328125, -0.039825439453125, -0.345458984375, -0.61669921875, 0.962890625, 0.11138916015625, 0.2939453125, 0.357177734375, 0.9091796875, -0.05303955078125, 1.4892578125, 0.2431640625, 0.08270263671875, 0.1812744140625, 0.55029296875, -0.59521484375, -0.69775390625, -0.08819580078125, -0.31640625, 0.08306884765625, -0.81298828125, -0.369384765625, -0.2078857421875, 0.87353515625, 0.37646484375, -0.68505859375, -0.572265625, 0.213623046875, -0.958984375, 0.45361328125, 0.265625, 0.2578125, 0.1702880859375, -0.088623046875, -0.38134765625, -0.78125, 0.162353515625, -0.56298828125, 0.27734375, -0.58544921875, -0.4111328125, -0.284423828125, -0.345703125, -0.291748046875, -0.31298828125, -0.1439208984375, -0.73681640625, 0.79541015625, 0.410888671875, 0.37158203125, 0.36767578125, -0.1346435546875, 0.3017578125, 0.89501953125, 0.68701171875, -0.318603515625, 0.5478515625, 0.212646484375, 0.0872802734375, 0.2607421875, -0.465087890625, 0.4169921875, -0.0309600830078125, 0.452880859375, -0.5927734375, 0.484375, -0.87744140625, -1.091796875, 0.08636474609375, 0.296875, 0.350830078125, -0.56982421875, -0.9541015625, -0.35498046875, -0.94384765625, -0.0316162109375, -0.33544921875, 0.79541015625, -0.2078857421875, -0.0999755859375, -0.12841796875, -0.9833984375, 4.44921875, 1.0927734375, 0.6005859375, 0.24072265625, 0.20263671875, 0.60498046875, 0.30615234375, -0.8740234375, -0.0247344970703125, -0.3125, 0.62744140625, -0.12158203125, 0.024505615234375, 0.97509765625, 0.4033203125, 0.57470703125, -0.48974609375, -0.35595703125, 0.1385498046875, -0.6982421875, -0.84814453125, 0.2432861328125, 0.04266357421875, 0.335693359375, -0.118408203125, 0.351806640625, 0.5732421875, -0.88623046875, -0.548828125, -0.6044921875, 0.241455078125, -0.3076171875, 1.0546875, -0.4033203125, -0.152099609375, 0.63623046875, 0.056976318359375, -0.48828125, -0.490478515625, 0.3662109375, 0.0296173095703125, 0.099609375, 0.79052734375, -0.8623046875, -0.007366180419921875, 0.443115234375, -0.6884765625, 0.265869140625, 0.04888916015625, -1.03515625, 0.51611328125, -0.1201171875, 0.22998046875, -0.403076171875, -0.98486328125, 0.1580810546875, 0.34423828125, 0.061614990234375, -0.06341552734375, 0.470703125, 0.51171875, 0.1522216796875, 0.01396942138671875, 0.8251953125, -1.2998046875, 0.9599609375, 0.1373291015625, 0.55712890625, -0.58251953125, 0.0557861328125, -0.61572265625, -0.48193359375, -0.376953125, -0.2030029296875, 0.84423828125, 0.35595703125, -0.2705078125, 0.17626953125, 0.50146484375, -0.5791015625, 0.4130859375, 0.041534423828125, -0.367919921875, -0.427490234375, 0.80615234375, 1.0498046875, -0.626953125, -0.499267578125, -0.326904296875, 0.439453125, 0.4033203125, 0.576171875, 0.294921875, -0.56640625, -0.6630859375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: 1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si β‰  si + 1(1 ≀ i < n). 3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. Help him find such string or state that such string doesn't exist. String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes. Input A single line contains two positive integers n and k (1 ≀ n ≀ 106, 1 ≀ k ≀ 26) β€” the string's length and the number of distinct letters. Output In a single line print the required string. If there isn't such string, print "-1" (without the quotes). Examples Input 7 4 Output ababacd Input 4 7 Output -1 Submitted Solution: ``` n,k=[int(x) for x in input().split()] if n<k or (k==1 and n>=2): print(-1) exit() if k==1: print('a') exit() st="" flag=1 for i in range(n-k+2): if flag: st+='a' flag=0 else: st+='b' flag=1 num=ord('c') for i in range(0,k-2): st+=chr(num+i) print(st) ``` Yes
107,315
[ 0.47265625, -0.2138671875, 0.498291015625, 0.245849609375, -0.310546875, -0.376953125, -0.00714111328125, 0.1849365234375, 0.22119140625, 0.78369140625, 0.6748046875, -0.038360595703125, -0.0093231201171875, -0.80859375, -0.56884765625, 0.08709716796875, -0.5830078125, -0.48681640625, -0.2822265625, 0.0806884765625, -0.0269775390625, -0.1600341796875, -1.498046875, 0.0543212890625, -0.3203125, 0.8994140625, 0.383056640625, -0.01117706298828125, 1.1748046875, 0.85693359375, -0.26611328125, -0.5458984375, 0.46484375, -0.861328125, -0.5380859375, -0.53955078125, 0.650390625, -0.9970703125, -0.4365234375, -0.62158203125, -0.00621795654296875, -0.6357421875, 0.4482421875, -0.6826171875, -1.265625, -0.07989501953125, -0.53466796875, -0.34375, -0.19482421875, -0.85302734375, 0.07916259765625, -0.209228515625, 0.424072265625, -0.72265625, 0.09661865234375, 0.4052734375, 0.183349609375, -0.184814453125, -0.417236328125, 0.3046875, -0.2127685546875, 0.427001953125, 0.04351806640625, -0.63330078125, -0.2347412109375, 0.0210723876953125, -0.0645751953125, -0.396484375, 0.0677490234375, -0.537109375, -0.262939453125, -0.0004031658172607422, -0.64404296875, -0.2587890625, -0.344482421875, 0.1630859375, 0.352294921875, 0.08880615234375, -0.67822265625, 0.853515625, 0.3837890625, 1.4052734375, 0.5205078125, 0.28369140625, -0.1175537109375, -0.462646484375, 0.230224609375, 0.49365234375, 0.259521484375, -0.189453125, 0.28662109375, 0.387451171875, -0.81396484375, 0.07281494140625, 0.5556640625, 0.358154296875, 0.062408447265625, 0.3994140625, 0.255859375, -0.02276611328125, 0.8984375, 0.85595703125, -0.2308349609375, 1.0615234375, -0.6181640625, 0.28515625, -0.1087646484375, -0.334716796875, -0.168212890625, -0.46484375, -0.1998291015625, -0.1846923828125, 0.591796875, 0.273193359375, -0.40283203125, 0.88232421875, -0.11932373046875, 0.33935546875, -0.77392578125, -0.040069580078125, 0.48291015625, 0.334228515625, 0.71923828125, 0.06500244140625, 0.055511474609375, -0.251953125, -0.73779296875, 0.873046875, -0.58740234375, 0.16796875, 0.4150390625, 0.01380157470703125, -0.17724609375, 0.0687255859375, 0.10491943359375, 0.57861328125, 0.0400390625, 0.53564453125, 0.63916015625, -0.471435546875, 0.88720703125, -0.24609375, 0.007404327392578125, 1.4521484375, 0.50927734375, -0.3388671875, 0.638671875, 0.155517578125, -0.74560546875, 0.4794921875, -1.1005859375, 0.5595703125, -0.1781005859375, -0.0156707763671875, -0.1297607421875, 0.221435546875, -0.29248046875, 0.244140625, 0.52392578125, 0.2392578125, -0.450927734375, 0.273193359375, -0.26220703125, 0.59716796875, -0.33251953125, 0.62451171875, -0.529296875, -0.179443359375, 0.056243896484375, -0.2442626953125, 0.211181640625, -0.10443115234375, -0.09130859375, 0.9072265625, 0.78173828125, 1.2529296875, 0.96923828125, -0.21435546875, 0.1492919921875, 0.43603515625, -0.5458984375, 0.0268402099609375, 0.2900390625, 0.5732421875, 0.04364013671875, 0.364013671875, -0.00557708740234375, -0.477294921875, -0.75341796875, -0.68603515625, -0.07183837890625, 0.37255859375, -0.1915283203125, 0.442138671875, -0.130126953125, -0.052154541015625, -0.68701171875, -0.282470703125, -0.205078125, -1.1328125, -0.42138671875, 0.65478515625, -0.08428955078125, 0.517578125, -0.609375, -0.302490234375, 0.427490234375, 0.98974609375, -0.373291015625, 0.10369873046875, 0.21435546875, 0.1810302734375, -0.1309814453125, 0.072998046875, 0.333251953125, 0.245361328125, -0.75927734375, 0.61279296875, -0.255615234375, 0.10858154296875, 0.1807861328125, 0.8203125, 0.10870361328125, 0.397216796875, -0.346923828125, -0.1265869140625, 0.36474609375, 0.94091796875, -0.053192138671875, 0.67236328125, 0.427001953125, 1.1640625, 0.7646484375, 0.56201171875, 0.5732421875, 0.55859375, 0.76953125, 1.0634765625, -0.0482177734375, 0.381103515625, -0.2496337890625, 0.4970703125, -0.00830078125, 0.5869140625, 0.26904296875, 0.336669921875, -0.0017366409301757812, 0.08624267578125, -0.1953125, 0.28515625, -0.1229248046875, 0.78857421875, -0.01490020751953125, 0.4306640625, -0.458984375, -0.375732421875, 0.1279296875, 0.74755859375, -0.68603515625, -0.52001953125, -0.10418701171875, 0.09466552734375, -0.020294189453125, -0.1895751953125, 0.0157012939453125, 0.1439208984375, 0.501953125, 0.12249755859375, -0.329833984375, -0.309326171875, -1.099609375, -0.68017578125, -1.3828125, -0.173828125, -0.71533203125, 0.170654296875, 0.397216796875, -0.91357421875, 0.1055908203125, -0.489013671875, -0.15234375, 0.042816162109375, -0.61083984375, 0.6376953125, 0.053070068359375, 0.436279296875, -0.493408203125, 0.385986328125, 0.1688232421875, 0.88037109375, -0.472412109375, -0.2137451171875, -0.04339599609375, -0.3701171875, 0.330322265625, -0.33349609375, 0.51171875, 0.135986328125, -0.395751953125, -1.0234375, -0.4697265625, 0.001918792724609375, -0.23828125, -0.0557861328125, -0.3291015625, 1.1630859375, 0.347412109375, -0.85498046875, 0.5185546875, 0.67138671875, -0.75634765625, 0.5234375, 0.5009765625, 0.1861572265625, -0.8291015625, 1.4501953125, 0.337646484375, 0.019927978515625, -0.591796875, -0.5986328125, -0.38134765625, 0.30712890625, 0.107421875, -0.4873046875, -0.0740966796875, 0.484619140625, 0.1697998046875, -1.1630859375, 0.80810546875, -0.98388671875, -0.49609375, -0.473876953125, -0.3515625, 0.6220703125, 0.52392578125, 0.35498046875, -0.047332763671875, -0.5341796875, -0.35888671875, 0.42578125, 0.375244140625, -0.853515625, -0.1497802734375, 0.43798828125, -0.39404296875, 0.283203125, 0.035675048828125, -0.2288818359375, 0.0276947021484375, -0.1883544921875, 0.10662841796875, 1.01953125, 0.2802734375, 0.1109619140625, 0.257568359375, 1.017578125, -0.71142578125, -0.3740234375, -0.60107421875, 0.6904296875, 0.258544921875, 0.82080078125, 0.436767578125, -0.05029296875, -0.326171875, -1.3544921875, 0.304931640625, -0.2369384765625, 0.68212890625, -0.4462890625, 0.94970703125, 0.42236328125, -0.62744140625, 0.64501953125, -0.55126953125, -0.1776123046875, 1.185546875, 0.03692626953125, 0.78662109375, -0.462158203125, 0.41552734375, -0.1859130859375, -0.384521484375, 0.56787109375, 0.2188720703125, 0.83154296875, -0.328857421875, -0.5048828125, -0.43115234375, -0.400390625, -0.00009298324584960938, -0.4765625, 0.1983642578125, -0.360595703125, -0.397705078125, -0.449951171875, 0.333740234375, 0.6875, 0.49609375, 0.2403564453125, 0.41845703125, 0.030242919921875, 0.1240234375, 0.372802734375, -0.454833984375, 0.0282745361328125, -0.316650390625, 0.80078125, 0.28857421875, -0.269775390625, -0.7763671875, -0.458251953125, 0.031646728515625, -0.179931640625, -0.032806396484375, -0.357177734375, -0.81591796875, 0.22802734375, -0.10870361328125, 0.425537109375, -0.72607421875, -0.420166015625, -0.276611328125, 0.425048828125, 0.449951171875, -1.0595703125, 0.1348876953125, -0.61328125, 0.333251953125, 0.424560546875, -0.1864013671875, -0.37744140625, -0.467529296875, -0.84228515625, -0.84814453125, 0.300048828125, 0.68701171875, 0.00028443336486816406, 0.1334228515625, -1.4033203125, 0.49267578125, 0.3857421875, -0.11517333984375, 0.129150390625, 0.0257415771484375, 0.34033203125, 0.2330322265625, 0.771484375, -0.485107421875, -0.7158203125, 0.10736083984375, -1.228515625, 0.411865234375, -0.607421875, 0.328857421875, 0.0809326171875, 0.1287841796875, -0.1549072265625, 0.451171875, -0.1881103515625, 0.26416015625, -0.04254150390625, 0.423095703125, -1.0615234375, -0.591796875, 0.51513671875, -0.36328125, -0.357177734375, 1.302734375, -0.2032470703125, -0.490966796875, 0.52978515625, 0.4599609375, -0.27197265625, 0.329345703125, -0.306396484375, 0.490966796875, -0.190185546875, -0.191162109375, -0.03558349609375, -0.364990234375, 1.021484375, -0.1746826171875, -0.8291015625, -0.39697265625, -1.1259765625, -0.13037109375, -0.1527099609375, -0.315673828125, 0.301513671875, -0.140380859375, -0.09490966796875, -0.28857421875, -0.53515625, -0.5283203125, -0.1553955078125, -0.09490966796875, -0.339111328125, 0.14892578125, 0.62109375, 0.3701171875, 0.41796875, -0.4697265625, 0.00567626953125, -0.339111328125, -0.100341796875, -0.384033203125, -0.1646728515625, -0.1578369140625, -0.1981201171875, -0.2169189453125, 0.147216796875, 0.289794921875, 0.60986328125, 0.411865234375, 0.445068359375, 0.67724609375, 0.498779296875, -0.7724609375, 0.89990234375, 0.0789794921875, -1.1357421875, -0.46142578125, 0.57421875, -0.020538330078125, 0.51123046875, 0.251220703125, -0.72119140625, -0.60400390625, -0.98974609375, 0.255126953125, -0.32275390625, -0.342529296875, -0.90869140625, 0.14794921875, -0.223876953125, 0.56005859375, -0.11273193359375, -0.6171875, 0.0589599609375, -1.3876953125, 0.164306640625, -0.701171875, -0.41162109375, -0.5849609375, -0.287841796875, -0.0236358642578125, 1.0009765625, 0.10382080078125, 0.2315673828125, -0.241943359375, -0.07159423828125, 0.2412109375, 0.076171875, -0.296142578125, -0.564453125, -0.285400390625, 0.263916015625, -0.1611328125, 0.01385498046875, -0.1912841796875, 0.6728515625, -0.6923828125, 0.15185546875, -0.426513671875, -0.144775390625, -0.28759765625, -0.2059326171875, 0.98095703125, -0.34716796875, -0.219970703125, -0.06597900390625, 0.1209716796875, 0.74169921875, -0.453857421875, -0.10595703125, -0.70263671875, -0.1591796875, -0.763671875, 0.4658203125, -0.2364501953125, -0.0214080810546875, -0.76220703125, -0.32275390625, 1.166015625, -0.60009765625, 0.2210693359375, 1.3017578125, 0.2200927734375, 0.298828125, -0.75537109375, 0.230224609375, 0.578125, -0.55224609375, -0.09503173828125, 0.072021484375, -0.77783203125, 0.3974609375, -0.2347412109375, -1.125, -0.57958984375, 0.33349609375, 1.388671875, -0.2418212890625, 0.7431640625, 0.1904296875, -1.1669921875, -0.44921875, 0.69921875, -0.09429931640625, 0.249267578125, 1.0087890625, -0.152587890625, -0.20263671875, 0.098876953125, -0.240478515625, -0.448974609375, -0.368408203125, 1.390625, -0.62060546875, -0.423828125, 1.046875, 1.2099609375, -1.0146484375, -1.0576171875, -0.08709716796875, 0.050262451171875, -0.29296875, -0.96044921875, 0.28369140625, 0.58349609375, -0.943359375, -0.02294921875, 0.184326171875, -0.324951171875, 0.76318359375, -0.054595947265625, 0.433837890625, -0.54638671875, 0.2362060546875, 0.70947265625, -0.53564453125, -0.034210205078125, -0.498779296875, -0.095458984375, -0.21240234375, 0.0467529296875, 0.556640625, -0.4501953125, 0.16845703125, 0.462646484375, 0.045196533203125, 0.422119140625, -0.39794921875, -0.47705078125, -0.0161590576171875, -0.93994140625, -0.3203125, 0.01418304443359375, 0.4013671875, -0.1868896484375, 0.5400390625, -0.900390625, -0.062347412109375, 0.1383056640625, 0.198486328125, -0.368408203125, -0.492919921875, -0.314453125, -1.0595703125, -0.53369140625, -0.47802734375, -0.83056640625, -0.40625, -0.06561279296875, 0.283203125, -0.423095703125, 0.279541015625, 0.5244140625, -0.6591796875, 0.82958984375, -0.72314453125, 0.43310546875, -0.759765625, -0.178955078125, -0.58837890625, 0.0299835205078125, -0.5751953125, 0.1478271484375, -0.9482421875, 0.21484375, -0.0260162353515625, 0.44140625, -0.4501953125, 0.3271484375, -0.1275634765625, -0.58984375, 0.168212890625, 0.44091796875, -0.81298828125, 0.7802734375, 0.1348876953125, 0.2076416015625, 0.032867431640625, -0.45068359375, -0.484619140625, -0.1685791015625, 0.64599609375, 0.351806640625, 0.1268310546875, 0.066650390625, -0.401611328125, 0.0081634521484375, -0.8876953125, 0.1502685546875, -0.435546875, 0.09112548828125, 0.06451416015625, -0.53271484375, 0.515625, 1.0166015625, -0.41845703125, 0.4228515625, -0.1619873046875, 0.08074951171875, 0.421630859375, 0.2073974609375, -0.295654296875, 0.307861328125, 0.291748046875, -0.078369140625, -0.026580810546875, 0.481201171875, 0.0226898193359375, 0.2939453125, 0.01161956787109375, -0.7255859375, -0.94677734375, -0.2161865234375, -0.3671875, 0.41162109375, 0.2509765625, -0.43701171875, -0.038543701171875, -0.05010986328125, -0.4541015625, 0.407470703125, -1.2978515625, -0.859375, 0.320068359375, 0.11767578125, -0.609375, 0.2476806640625, -0.95068359375, 0.030242919921875, 0.17529296875, 0.4140625, -0.197021484375, 0.587890625, -0.1578369140625, 0.1373291015625, -0.1781005859375, -0.2060546875, 0.1124267578125, 0.466552734375, -0.66650390625, -0.496337890625, 0.1702880859375, 0.9365234375, 0.1900634765625, -0.200927734375, -0.6220703125, 0.2890625, 0.1800537109375, -0.0289764404296875, -0.27099609375, 0.183837890625, -0.406982421875, 0.6318359375, -0.798828125, -0.057525634765625, 0.037445068359375, 0.7412109375, 0.132080078125, -0.368896484375, -0.5234375, 0.65234375, 1.16796875, -0.284912109375, 0.55859375, 0.28759765625, 0.57080078125, -0.094970703125, -0.18310546875, -0.38720703125, 0.8408203125, 0.54931640625, 0.56494140625, 0.005615234375, 0.3642578125, 0.76220703125, 0.11224365234375, -0.2705078125, 0.57421875, -0.2371826171875, -0.0101776123046875, 0.0179290771484375, -0.2034912109375, -0.33837890625, 0.1776123046875, -0.72412109375, 0.5009765625, -0.63037109375, -0.3134765625, -0.2203369140625, -0.52294921875, 1.03515625, -0.50732421875, 0.01027679443359375, 0.1473388671875, -0.3544921875, 0.1998291015625, 0.72216796875, 0.1796875, 0.1507568359375, 0.94091796875, 0.61962890625, 0.354736328125, 0.7392578125, 0.33251953125, 0.53564453125, -0.71630859375, 0.01009368896484375, 0.101318359375, -0.2386474609375, -0.2230224609375, -0.51416015625, -1.220703125, 0.71240234375, -0.0628662109375, -0.310302734375, 0.591796875, -0.68017578125, 0.04193115234375, -0.256103515625, 0.81201171875, -0.489990234375, 0.31787109375, -0.06585693359375, -0.323486328125, -0.58447265625, 0.96435546875, 0.0963134765625, 0.27783203125, 0.39306640625, 0.8974609375, -0.0760498046875, 1.4150390625, 0.271728515625, 0.0679931640625, 0.17578125, 0.517578125, -0.59033203125, -0.658203125, -0.07196044921875, -0.341552734375, 0.04766845703125, -0.81591796875, -0.38623046875, -0.2232666015625, 0.8681640625, 0.387451171875, -0.6904296875, -0.54638671875, 0.197509765625, -0.92529296875, 0.442626953125, 0.242431640625, 0.263427734375, 0.191162109375, -0.0667724609375, -0.347412109375, -0.77783203125, 0.1298828125, -0.6015625, 0.257568359375, -0.59033203125, -0.416015625, -0.250732421875, -0.32666015625, -0.259521484375, -0.292236328125, -0.19970703125, -0.7294921875, 0.84912109375, 0.417236328125, 0.397705078125, 0.363037109375, -0.12225341796875, 0.318359375, 0.89501953125, 0.71533203125, -0.30224609375, 0.505859375, 0.216796875, 0.09954833984375, 0.2384033203125, -0.447265625, 0.40234375, -0.054443359375, 0.42236328125, -0.57763671875, 0.52587890625, -0.8818359375, -1.0771484375, 0.06268310546875, 0.2381591796875, 0.334228515625, -0.5703125, -0.92724609375, -0.345703125, -0.93798828125, -0.07073974609375, -0.33447265625, 0.787109375, -0.2117919921875, -0.095458984375, -0.1666259765625, -0.99169921875, 4.48828125, 1.087890625, 0.5771484375, 0.240966796875, 0.193603515625, 0.59228515625, 0.24169921875, -0.86181640625, -0.038848876953125, -0.265380859375, 0.615234375, -0.157958984375, 0.0516357421875, 0.9326171875, 0.416748046875, 0.57177734375, -0.459228515625, -0.344482421875, 0.1463623046875, -0.65673828125, -0.86328125, 0.2418212890625, 0.0841064453125, 0.305908203125, -0.13818359375, 0.370361328125, 0.5419921875, -0.93017578125, -0.51513671875, -0.5830078125, 0.25537109375, -0.317138671875, 1.017578125, -0.417724609375, -0.1573486328125, 0.60400390625, 0.0210418701171875, -0.485107421875, -0.4521484375, 0.3427734375, 0.05072021484375, 0.11627197265625, 0.771484375, -0.8173828125, 0.034576416015625, 0.390869140625, -0.7041015625, 0.239501953125, 0.0589599609375, -1.0078125, 0.5322265625, -0.136962890625, 0.2064208984375, -0.365478515625, -1.001953125, 0.12225341796875, 0.31103515625, 0.050750732421875, -0.0292205810546875, 0.51318359375, 0.50341796875, 0.15869140625, -0.0288238525390625, 0.79150390625, -1.2958984375, 0.96337890625, 0.07952880859375, 0.5087890625, -0.591796875, -0.00539398193359375, -0.5888671875, -0.472900390625, -0.357666015625, -0.1966552734375, 0.8203125, 0.3779296875, -0.278564453125, 0.23583984375, 0.49462890625, -0.67041015625, 0.376220703125, 0.045623779296875, -0.354736328125, -0.3759765625, 0.8447265625, 1.05859375, -0.626953125, -0.5048828125, -0.328857421875, 0.468017578125, 0.41162109375, 0.5791015625, 0.338623046875, -0.53564453125, -0.65625 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: 1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si β‰  si + 1(1 ≀ i < n). 3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. Help him find such string or state that such string doesn't exist. String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes. Input A single line contains two positive integers n and k (1 ≀ n ≀ 106, 1 ≀ k ≀ 26) β€” the string's length and the number of distinct letters. Output In a single line print the required string. If there isn't such string, print "-1" (without the quotes). Examples Input 7 4 Output ababacd Input 4 7 Output -1 Submitted Solution: ``` n, t = map(int, input().split()) alphas = "abcdefghijklmnopqrstuvwxyz" if t > n: print(-1) elif n > 1 and t == 1: print(-1) elif n == 1 and t == 1: print("a") elif t == n: print(alphas[:n]) else: ans = '' if (n-(t-2)) % 2 == 1: ans += "ab"*((n-(t-2))//2) ans += "a" if t > 2: ans += alphas[2:(t-2) + 2] else: ans += "ab"*((n-(t-2))//2) if t > 2: ans += alphas[2:(t-2) + 2] print(ans) ``` Yes
107,316
[ 0.513671875, -0.103515625, 0.48486328125, 0.200927734375, -0.396484375, -0.330322265625, 0.000018298625946044922, 0.2020263671875, 0.291259765625, 0.7880859375, 0.6259765625, 0.0242462158203125, 0.057830810546875, -0.80126953125, -0.599609375, 0.07659912109375, -0.5703125, -0.397705078125, -0.283447265625, 0.1104736328125, -0.034210205078125, -0.2220458984375, -1.46484375, 0.04156494140625, -0.286865234375, 0.837890625, 0.36865234375, 0.0484619140625, 1.1396484375, 0.88330078125, -0.3583984375, -0.56689453125, 0.44140625, -0.8916015625, -0.47900390625, -0.435302734375, 0.65478515625, -1.009765625, -0.440185546875, -0.6328125, 0.06927490234375, -0.7021484375, 0.471435546875, -0.67333984375, -1.306640625, -0.08526611328125, -0.5341796875, -0.2861328125, -0.290283203125, -0.90185546875, 0.11956787109375, -0.28271484375, 0.451416015625, -0.66845703125, 0.033203125, 0.400390625, 0.1959228515625, -0.193603515625, -0.440673828125, 0.329345703125, -0.222412109375, 0.4326171875, 0.01055145263671875, -0.662109375, -0.2362060546875, 0.0447998046875, -0.08514404296875, -0.34912109375, 0.06640625, -0.4736328125, -0.2469482421875, 0.0465087890625, -0.60107421875, -0.2451171875, -0.3310546875, 0.1263427734375, 0.275146484375, 0.06756591796875, -0.66357421875, 0.79736328125, 0.361083984375, 1.4541015625, 0.51904296875, 0.38232421875, -0.035919189453125, -0.451904296875, 0.1446533203125, 0.5888671875, 0.291015625, -0.135986328125, 0.267578125, 0.389404296875, -0.87548828125, 0.057708740234375, 0.62890625, 0.3671875, 0.09576416015625, 0.4013671875, 0.302734375, -0.037506103515625, 0.921875, 0.89013671875, -0.1265869140625, 1.099609375, -0.6357421875, 0.28466796875, -0.09503173828125, -0.35546875, -0.1484375, -0.454345703125, -0.2020263671875, -0.1663818359375, 0.6875, 0.280517578125, -0.296630859375, 0.9296875, -0.127197265625, 0.343505859375, -0.84814453125, -0.06024169921875, 0.418212890625, 0.334716796875, 0.7392578125, 0.0897216796875, 0.01430511474609375, -0.2666015625, -0.66064453125, 0.87939453125, -0.60302734375, 0.161865234375, 0.42626953125, 0.08233642578125, -0.2000732421875, 0.06243896484375, 0.0853271484375, 0.5185546875, 0.0826416015625, 0.5283203125, 0.60107421875, -0.54345703125, 0.927734375, -0.22705078125, 0.056915283203125, 1.5537109375, 0.51953125, -0.33544921875, 0.6181640625, 0.1719970703125, -0.85302734375, 0.460205078125, -1.1376953125, 0.6640625, -0.1865234375, -0.0867919921875, -0.283935546875, 0.11566162109375, -0.2685546875, 0.260986328125, 0.5830078125, 0.194580078125, -0.38427734375, 0.207275390625, -0.37548828125, 0.58544921875, -0.29443359375, 0.65673828125, -0.53515625, -0.176513671875, 0.1605224609375, -0.309814453125, 0.1895751953125, -0.1494140625, -0.1483154296875, 0.9052734375, 0.77099609375, 1.2763671875, 0.9345703125, -0.27294921875, 0.224853515625, 0.44140625, -0.59814453125, -0.0264434814453125, 0.287109375, 0.5107421875, 0.032562255859375, 0.359619140625, 0.00021326541900634766, -0.5615234375, -0.7021484375, -0.7119140625, -0.051116943359375, 0.429443359375, -0.2276611328125, 0.447021484375, -0.12548828125, -0.0138092041015625, -0.7216796875, -0.2244873046875, -0.186767578125, -1.1005859375, -0.42578125, 0.58935546875, -0.11358642578125, 0.4462890625, -0.68212890625, -0.26513671875, 0.37255859375, 1.1181640625, -0.399658203125, 0.201904296875, 0.2357177734375, 0.2296142578125, -0.1806640625, 0.09124755859375, 0.320556640625, 0.25537109375, -0.76708984375, 0.7216796875, -0.245849609375, 0.061279296875, 0.1446533203125, 0.84423828125, 0.1612548828125, 0.3916015625, -0.330322265625, -0.11395263671875, 0.470703125, 0.9228515625, -0.07830810546875, 0.66796875, 0.48779296875, 1.177734375, 0.71728515625, 0.62353515625, 0.583984375, 0.59765625, 0.78955078125, 1.0537109375, -0.0716552734375, 0.2998046875, -0.2344970703125, 0.42431640625, 0.028076171875, 0.58984375, 0.2685546875, 0.3564453125, -0.04791259765625, 0.06671142578125, -0.2744140625, 0.304931640625, -0.09417724609375, 0.79052734375, 0.0024127960205078125, 0.4404296875, -0.5166015625, -0.429443359375, 0.1568603515625, 0.73388671875, -0.71484375, -0.59619140625, -0.1734619140625, 0.061431884765625, -0.06402587890625, -0.2291259765625, 0.040313720703125, 0.1123046875, 0.56396484375, 0.1556396484375, -0.360595703125, -0.2958984375, -1.1728515625, -0.70361328125, -1.3857421875, -0.2049560546875, -0.77392578125, 0.1650390625, 0.476806640625, -0.990234375, 0.1275634765625, -0.53857421875, -0.1834716796875, 0.054534912109375, -0.6533203125, 0.646484375, 0.09381103515625, 0.462158203125, -0.53955078125, 0.3935546875, 0.1474609375, 0.92431640625, -0.50927734375, -0.2218017578125, -0.10107421875, -0.37841796875, 0.327880859375, -0.284423828125, 0.53662109375, 0.034454345703125, -0.45849609375, -1.01953125, -0.422607421875, 0.04437255859375, -0.308349609375, -0.0293426513671875, -0.38720703125, 1.2333984375, 0.4013671875, -0.87451171875, 0.54736328125, 0.669921875, -0.78662109375, 0.54052734375, 0.458740234375, 0.201904296875, -0.83935546875, 1.51171875, 0.2880859375, 0.045440673828125, -0.58251953125, -0.5712890625, -0.29736328125, 0.2998046875, 0.140625, -0.52197265625, -0.109619140625, 0.53515625, 0.1474609375, -1.181640625, 0.81640625, -1.095703125, -0.433837890625, -0.48486328125, -0.368896484375, 0.64111328125, 0.58154296875, 0.3046875, -0.10791015625, -0.55322265625, -0.3701171875, 0.455078125, 0.379638671875, -0.87939453125, -0.204345703125, 0.5654296875, -0.3232421875, 0.33349609375, 0.054443359375, -0.2802734375, 0.0170440673828125, -0.12078857421875, 0.06915283203125, 0.9873046875, 0.255126953125, 0.1507568359375, 0.2308349609375, 1.0107421875, -0.7333984375, -0.378173828125, -0.6279296875, 0.6865234375, 0.2578125, 0.9296875, 0.436279296875, -0.046630859375, -0.38427734375, -1.341796875, 0.337158203125, -0.2373046875, 0.77294921875, -0.450927734375, 0.9609375, 0.424560546875, -0.66650390625, 0.61279296875, -0.52294921875, -0.133544921875, 1.2216796875, -0.05548095703125, 0.7734375, -0.496337890625, 0.343017578125, -0.11602783203125, -0.302734375, 0.58251953125, 0.13818359375, 0.92578125, -0.336669921875, -0.60302734375, -0.4482421875, -0.402099609375, -0.02056884765625, -0.4580078125, 0.1165771484375, -0.2880859375, -0.411865234375, -0.498291015625, 0.471435546875, 0.67626953125, 0.53515625, 0.1429443359375, 0.3681640625, -0.029754638671875, 0.1607666015625, 0.3564453125, -0.3701171875, 0.042938232421875, -0.384765625, 0.82080078125, 0.349609375, -0.267333984375, -0.76708984375, -0.42529296875, -0.0237274169921875, -0.254150390625, -0.050140380859375, -0.359130859375, -0.78271484375, 0.2578125, -0.1705322265625, 0.412353515625, -0.677734375, -0.47216796875, -0.33544921875, 0.466064453125, 0.53466796875, -1.0517578125, 0.148193359375, -0.58544921875, 0.343017578125, 0.485107421875, -0.2064208984375, -0.332275390625, -0.436767578125, -0.79931640625, -0.93115234375, 0.33447265625, 0.7314453125, 0.049591064453125, 0.1627197265625, -1.4736328125, 0.5615234375, 0.362060546875, -0.1663818359375, 0.0997314453125, -0.01324462890625, 0.2939453125, 0.2626953125, 0.8115234375, -0.439453125, -0.75634765625, 0.0273895263671875, -1.2890625, 0.456298828125, -0.6669921875, 0.2685546875, 0.0292510986328125, 0.095947265625, -0.10980224609375, 0.485107421875, -0.263916015625, 0.236083984375, -0.0330810546875, 0.4521484375, -1.025390625, -0.578125, 0.50634765625, -0.314208984375, -0.407958984375, 1.24609375, -0.1636962890625, -0.52978515625, 0.5478515625, 0.50830078125, -0.299560546875, 0.36474609375, -0.32275390625, 0.491943359375, -0.1881103515625, -0.2047119140625, -0.02691650390625, -0.388671875, 1.0498046875, -0.1817626953125, -0.8857421875, -0.427978515625, -1.1875, -0.0955810546875, -0.1627197265625, -0.365478515625, 0.359375, -0.10150146484375, 0.01056671142578125, -0.2139892578125, -0.490478515625, -0.529296875, -0.1478271484375, -0.152099609375, -0.42626953125, 0.1529541015625, 0.59033203125, 0.40771484375, 0.38720703125, -0.49658203125, 0.0159149169921875, -0.35986328125, -0.1580810546875, -0.393798828125, -0.15380859375, -0.177001953125, -0.2274169921875, -0.21630859375, 0.1441650390625, 0.273193359375, 0.6318359375, 0.38232421875, 0.455322265625, 0.7255859375, 0.41796875, -0.81640625, 0.984375, 0.1546630859375, -1.1728515625, -0.444091796875, 0.6611328125, 0.04351806640625, 0.53369140625, 0.356689453125, -0.73046875, -0.65576171875, -1.0390625, 0.187744140625, -0.416259765625, -0.3818359375, -0.8984375, 0.12298583984375, -0.2216796875, 0.64599609375, -0.230712890625, -0.5986328125, 0.085693359375, -1.3857421875, 0.131591796875, -0.71337890625, -0.36181640625, -0.62646484375, -0.24560546875, -0.06622314453125, 1.0107421875, 0.1019287109375, 0.19140625, -0.234375, -0.048553466796875, 0.300048828125, 0.04351806640625, -0.343505859375, -0.54248046875, -0.2081298828125, 0.30517578125, -0.2005615234375, 0.0134124755859375, -0.1832275390625, 0.62744140625, -0.70458984375, 0.11627197265625, -0.34326171875, -0.0928955078125, -0.288818359375, -0.2646484375, 1.0263671875, -0.374267578125, -0.265869140625, -0.08154296875, 0.156982421875, 0.76513671875, -0.44677734375, -0.21875, -0.6787109375, -0.268798828125, -0.76123046875, 0.53125, -0.257568359375, 0.0094146728515625, -0.763671875, -0.258544921875, 1.1591796875, -0.6416015625, 0.25146484375, 1.3271484375, 0.202392578125, 0.287353515625, -0.74658203125, 0.320556640625, 0.5732421875, -0.52978515625, -0.0853271484375, 0.1490478515625, -0.72607421875, 0.37841796875, -0.262451171875, -1.13671875, -0.55517578125, 0.389892578125, 1.4033203125, -0.254638671875, 0.76904296875, 0.2049560546875, -1.1630859375, -0.53515625, 0.720703125, -0.10321044921875, 0.2685546875, 1.0185546875, -0.139892578125, -0.241455078125, 0.055023193359375, -0.2646484375, -0.52099609375, -0.393310546875, 1.3974609375, -0.64306640625, -0.33544921875, 1.0869140625, 1.2587890625, -1.03125, -1.0283203125, -0.1319580078125, 0.06170654296875, -0.2978515625, -1.0986328125, 0.27197265625, 0.57177734375, -0.9345703125, -0.055145263671875, 0.12078857421875, -0.305908203125, 0.6767578125, 0.028411865234375, 0.336181640625, -0.57275390625, 0.1734619140625, 0.73681640625, -0.5341796875, -0.11505126953125, -0.55126953125, -0.10040283203125, -0.16455078125, 0.037567138671875, 0.62451171875, -0.450927734375, 0.16064453125, 0.43310546875, 0.0794677734375, 0.46923828125, -0.449951171875, -0.438232421875, 0.0201263427734375, -0.9560546875, -0.33447265625, 0.03369140625, 0.42333984375, -0.16455078125, 0.552734375, -0.91748046875, -0.06060791015625, 0.145263671875, 0.2347412109375, -0.395263671875, -0.54638671875, -0.34619140625, -1.1181640625, -0.58447265625, -0.4169921875, -0.8486328125, -0.435791015625, -0.1168212890625, 0.3310546875, -0.42529296875, 0.30224609375, 0.54736328125, -0.640625, 0.85009765625, -0.7646484375, 0.435546875, -0.81591796875, -0.128662109375, -0.54296875, -0.007671356201171875, -0.609375, 0.2333984375, -0.826171875, 0.15380859375, -0.01479339599609375, 0.434326171875, -0.428955078125, 0.332275390625, -0.1055908203125, -0.57177734375, 0.1943359375, 0.48095703125, -0.72509765625, 0.7734375, 0.1927490234375, 0.147216796875, -0.0273284912109375, -0.5791015625, -0.544921875, -0.1861572265625, 0.751953125, 0.361572265625, 0.1163330078125, 0.10064697265625, -0.4501953125, 0.033172607421875, -0.84326171875, 0.076416015625, -0.378662109375, 0.052734375, 0.160400390625, -0.51953125, 0.53662109375, 1.0810546875, -0.5029296875, 0.381103515625, -0.1925048828125, 0.047515869140625, 0.394775390625, 0.2386474609375, -0.319580078125, 0.284423828125, 0.340087890625, -0.12890625, 0.006809234619140625, 0.497314453125, 0.0667724609375, 0.341796875, -0.025238037109375, -0.81298828125, -0.9794921875, -0.1617431640625, -0.26025390625, 0.33349609375, 0.271728515625, -0.4541015625, -0.0966796875, -0.072998046875, -0.5478515625, 0.5146484375, -1.275390625, -0.90625, 0.38134765625, 0.193115234375, -0.615234375, 0.27880859375, -0.939453125, 0.0016870498657226562, 0.15380859375, 0.429443359375, -0.27783203125, 0.625, -0.1553955078125, 0.15478515625, -0.2257080078125, -0.220703125, 0.094482421875, 0.3974609375, -0.712890625, -0.461181640625, 0.09625244140625, 0.96337890625, 0.1639404296875, -0.25390625, -0.72314453125, 0.27587890625, 0.1357421875, -0.0231170654296875, -0.2509765625, 0.1387939453125, -0.34716796875, 0.6162109375, -0.80908203125, -0.0254669189453125, 0.08380126953125, 0.736328125, 0.2353515625, -0.430419921875, -0.47607421875, 0.7109375, 1.16796875, -0.22119140625, 0.5322265625, 0.25244140625, 0.58642578125, -0.07635498046875, -0.1585693359375, -0.42578125, 0.8740234375, 0.55078125, 0.537109375, 0.0214691162109375, 0.308349609375, 0.8056640625, 0.10723876953125, -0.23828125, 0.5693359375, -0.2301025390625, -0.038726806640625, -0.046966552734375, -0.2115478515625, -0.367431640625, 0.2279052734375, -0.720703125, 0.4912109375, -0.6220703125, -0.251953125, -0.2093505859375, -0.56005859375, 1.046875, -0.513671875, -0.0034027099609375, 0.1539306640625, -0.33349609375, 0.2314453125, 0.68359375, 0.191162109375, 0.1904296875, 0.99609375, 0.69580078125, 0.38623046875, 0.77685546875, 0.4052734375, 0.66748046875, -0.71728515625, -0.034942626953125, 0.1004638671875, -0.30908203125, -0.263671875, -0.53466796875, -1.2197265625, 0.734375, -0.10235595703125, -0.25048828125, 0.62646484375, -0.76611328125, 0.047149658203125, -0.276611328125, 0.84619140625, -0.4560546875, 0.33447265625, 0.0276031494140625, -0.33984375, -0.58740234375, 1, 0.09112548828125, 0.2744140625, 0.33056640625, 0.8759765625, -0.01531219482421875, 1.484375, 0.352294921875, 0.0797119140625, 0.18603515625, 0.5556640625, -0.5888671875, -0.759765625, -0.10028076171875, -0.377685546875, 0.1405029296875, -0.791015625, -0.384033203125, -0.260986328125, 0.888671875, 0.35595703125, -0.6875, -0.61767578125, 0.2403564453125, -0.93408203125, 0.436767578125, 0.29736328125, 0.2298583984375, 0.194091796875, -0.11114501953125, -0.352294921875, -0.75341796875, 0.126708984375, -0.5166015625, 0.225341796875, -0.61279296875, -0.40478515625, -0.276611328125, -0.359375, -0.3291015625, -0.3310546875, -0.1651611328125, -0.7734375, 0.8017578125, 0.404541015625, 0.359619140625, 0.39892578125, -0.16455078125, 0.30419921875, 0.9404296875, 0.69287109375, -0.28759765625, 0.6005859375, 0.260009765625, 0.0439453125, 0.2548828125, -0.51904296875, 0.477783203125, -0.0125885009765625, 0.435791015625, -0.58740234375, 0.5205078125, -0.8896484375, -1.109375, 0.07623291015625, 0.3232421875, 0.448486328125, -0.619140625, -0.93603515625, -0.30126953125, -0.91748046875, -0.01898193359375, -0.31787109375, 0.79443359375, -0.1531982421875, -0.09527587890625, -0.1610107421875, -1.021484375, 4.3828125, 1.0751953125, 0.60791015625, 0.214111328125, 0.2041015625, 0.60302734375, 0.34912109375, -0.865234375, -0.0567626953125, -0.30322265625, 0.60595703125, -0.1270751953125, 0.0404052734375, 1.0146484375, 0.4130859375, 0.6044921875, -0.46875, -0.376220703125, 0.1959228515625, -0.708984375, -0.85205078125, 0.26171875, 0.056243896484375, 0.3447265625, -0.0943603515625, 0.341552734375, 0.62939453125, -0.91455078125, -0.5908203125, -0.64111328125, 0.2054443359375, -0.2568359375, 1.083984375, -0.40087890625, -0.176513671875, 0.5947265625, 0.084228515625, -0.53857421875, -0.52685546875, 0.389404296875, 0.00878143310546875, 0.11224365234375, 0.76806640625, -0.8740234375, 0.0195159912109375, 0.46923828125, -0.66162109375, 0.222412109375, 0.1019287109375, -1.03515625, 0.4853515625, -0.152587890625, 0.22998046875, -0.384765625, -1.0302734375, 0.1566162109375, 0.354248046875, 0.058563232421875, -0.055999755859375, 0.51123046875, 0.448486328125, 0.09503173828125, 0.0259246826171875, 0.861328125, -1.361328125, 0.9775390625, 0.05316162109375, 0.5625, -0.6357421875, 0.0300140380859375, -0.6337890625, -0.4140625, -0.384033203125, -0.28955078125, 0.85107421875, 0.36767578125, -0.25634765625, 0.2281494140625, 0.449951171875, -0.59814453125, 0.427490234375, 0.0645751953125, -0.3671875, -0.438720703125, 0.84814453125, 1.0595703125, -0.60107421875, -0.5068359375, -0.3359375, 0.548828125, 0.435302734375, 0.54638671875, 0.279052734375, -0.5634765625, -0.7255859375 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: 1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si β‰  si + 1(1 ≀ i < n). 3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. Help him find such string or state that such string doesn't exist. String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes. Input A single line contains two positive integers n and k (1 ≀ n ≀ 106, 1 ≀ k ≀ 26) β€” the string's length and the number of distinct letters. Output In a single line print the required string. If there isn't such string, print "-1" (without the quotes). Examples Input 7 4 Output ababacd Input 4 7 Output -1 Submitted Solution: ``` def main(): n,m = [int(v) for v in input().split()] if m>n: print(-1) return if m==1 and n>1: print(-1) return p = "ab" prefix = p*((n-(m-2))//2) if (n-(m-2))%2!=0: prefix+="a" for i in range(2, 2+(m-2)): prefix+=chr(ord('a')+i) print(prefix[0:n]) if __name__ == "__main__": main() ``` Yes
107,317
[ 0.455078125, -0.185546875, 0.50732421875, 0.1751708984375, -0.337158203125, -0.33349609375, 0.0249176025390625, 0.12158203125, 0.272705078125, 0.7451171875, 0.6064453125, -0.003753662109375, -0.0106964111328125, -0.8369140625, -0.58984375, 0.065185546875, -0.55908203125, -0.453125, -0.3056640625, 0.04364013671875, -0.113525390625, -0.140625, -1.46484375, 0.0251007080078125, -0.28369140625, 0.87744140625, 0.361083984375, 0.016815185546875, 1.15234375, 0.837890625, -0.332763671875, -0.4970703125, 0.46337890625, -0.82861328125, -0.50048828125, -0.473876953125, 0.6591796875, -1.033203125, -0.396484375, -0.61279296875, 0.04962158203125, -0.65283203125, 0.42138671875, -0.64892578125, -1.3037109375, -0.0823974609375, -0.5419921875, -0.300048828125, -0.2335205078125, -0.92529296875, 0.0472412109375, -0.2412109375, 0.4091796875, -0.69091796875, 0.10296630859375, 0.365478515625, 0.25439453125, -0.1688232421875, -0.423095703125, 0.353759765625, -0.1666259765625, 0.434814453125, 0.017425537109375, -0.6259765625, -0.2353515625, 0.0240020751953125, -0.09112548828125, -0.371826171875, 0.04400634765625, -0.54052734375, -0.2459716796875, -0.01068878173828125, -0.5791015625, -0.229248046875, -0.34912109375, 0.2008056640625, 0.35986328125, 0.0731201171875, -0.677734375, 0.837890625, 0.367919921875, 1.4296875, 0.5517578125, 0.321044921875, -0.1334228515625, -0.43359375, 0.19921875, 0.52001953125, 0.233642578125, -0.164306640625, 0.274169921875, 0.39208984375, -0.8125, 0.11907958984375, 0.5322265625, 0.445556640625, 0.0047149658203125, 0.427001953125, 0.272216796875, -0.01849365234375, 0.8701171875, 0.87890625, -0.1375732421875, 1.0830078125, -0.65478515625, 0.292236328125, -0.13037109375, -0.345458984375, -0.223876953125, -0.386962890625, -0.1929931640625, -0.17138671875, 0.6064453125, 0.296630859375, -0.3408203125, 0.89208984375, -0.10589599609375, 0.34765625, -0.84228515625, -0.06719970703125, 0.46484375, 0.31103515625, 0.70849609375, 0.002490997314453125, 0.0256500244140625, -0.2320556640625, -0.744140625, 0.861328125, -0.59716796875, 0.1004638671875, 0.420166015625, 0.08740234375, -0.1416015625, 0.042144775390625, 0.1314697265625, 0.58837890625, 0.03155517578125, 0.55126953125, 0.6611328125, -0.473388671875, 0.94482421875, -0.2205810546875, 0.00238037109375, 1.4814453125, 0.5205078125, -0.321044921875, 0.59765625, 0.1845703125, -0.7568359375, 0.46875, -1.095703125, 0.57666015625, -0.1431884765625, -0.06805419921875, -0.181396484375, 0.2091064453125, -0.271240234375, 0.2548828125, 0.5712890625, 0.1744384765625, -0.415771484375, 0.2392578125, -0.2998046875, 0.56591796875, -0.352783203125, 0.6298828125, -0.5390625, -0.1966552734375, 0.08416748046875, -0.265380859375, 0.2109375, -0.0885009765625, -0.0926513671875, 0.90869140625, 0.74755859375, 1.20703125, 0.94482421875, -0.222900390625, 0.1356201171875, 0.43017578125, -0.56640625, -0.0170135498046875, 0.2958984375, 0.5654296875, 0.041595458984375, 0.337158203125, -0.02496337890625, -0.5107421875, -0.73046875, -0.71728515625, -0.05718994140625, 0.388916015625, -0.1610107421875, 0.452880859375, -0.08502197265625, -0.07525634765625, -0.69580078125, -0.31201171875, -0.200927734375, -1.046875, -0.406982421875, 0.60107421875, -0.1217041015625, 0.5244140625, -0.63916015625, -0.293212890625, 0.404052734375, 1.044921875, -0.387451171875, 0.11602783203125, 0.27734375, 0.19140625, -0.1571044921875, 0.056549072265625, 0.384765625, 0.2191162109375, -0.74755859375, 0.654296875, -0.2476806640625, 0.1256103515625, 0.0677490234375, 0.78662109375, 0.1815185546875, 0.3564453125, -0.355712890625, -0.08087158203125, 0.391357421875, 0.90673828125, -0.06451416015625, 0.67236328125, 0.443603515625, 1.1142578125, 0.74462890625, 0.5810546875, 0.61572265625, 0.54638671875, 0.75, 1.0048828125, -0.07708740234375, 0.3466796875, -0.25634765625, 0.490478515625, -0.0055084228515625, 0.58349609375, 0.307861328125, 0.361083984375, 0.005542755126953125, 0.1055908203125, -0.244873046875, 0.2276611328125, -0.08428955078125, 0.7451171875, -0.0289764404296875, 0.39990234375, -0.450927734375, -0.35009765625, 0.11663818359375, 0.74609375, -0.69287109375, -0.53076171875, -0.09698486328125, 0.1241455078125, -0.004543304443359375, -0.1802978515625, 0.0501708984375, 0.11090087890625, 0.59375, 0.1453857421875, -0.269775390625, -0.310546875, -1.1201171875, -0.6640625, -1.388671875, -0.1788330078125, -0.734375, 0.1343994140625, 0.402099609375, -0.9208984375, 0.148681640625, -0.49609375, -0.14794921875, 0.06951904296875, -0.640625, 0.666015625, 0.11346435546875, 0.412109375, -0.5712890625, 0.370361328125, 0.1300048828125, 0.8857421875, -0.47509765625, -0.2193603515625, 0.01678466796875, -0.34912109375, 0.261474609375, -0.305908203125, 0.53466796875, 0.113525390625, -0.36376953125, -0.97900390625, -0.49462890625, 0.03143310546875, -0.281982421875, -0.0355224609375, -0.406982421875, 1.2060546875, 0.369140625, -0.88720703125, 0.55908203125, 0.6064453125, -0.7470703125, 0.52978515625, 0.52490234375, 0.168212890625, -0.76123046875, 1.484375, 0.3291015625, -0.0189361572265625, -0.6015625, -0.54638671875, -0.298828125, 0.28515625, 0.1207275390625, -0.5703125, -0.1380615234375, 0.51123046875, 0.1260986328125, -1.158203125, 0.84765625, -1.0302734375, -0.484619140625, -0.53173828125, -0.35986328125, 0.63671875, 0.51708984375, 0.332275390625, -0.082763671875, -0.5546875, -0.405517578125, 0.422607421875, 0.40234375, -0.84228515625, -0.10272216796875, 0.50341796875, -0.373779296875, 0.31689453125, -0.020294189453125, -0.306396484375, 0.0245819091796875, -0.170166015625, 0.11981201171875, 0.99658203125, 0.253662109375, 0.1282958984375, 0.194091796875, 0.9794921875, -0.7255859375, -0.38720703125, -0.61279296875, 0.697265625, 0.29638671875, 0.90087890625, 0.452880859375, -0.07806396484375, -0.338623046875, -1.35546875, 0.269775390625, -0.2435302734375, 0.75830078125, -0.447265625, 0.9931640625, 0.416259765625, -0.6533203125, 0.634765625, -0.5791015625, -0.1300048828125, 1.22265625, -0.0044708251953125, 0.7626953125, -0.50341796875, 0.427734375, -0.1715087890625, -0.377685546875, 0.5380859375, 0.2314453125, 0.8779296875, -0.329833984375, -0.49365234375, -0.432373046875, -0.3642578125, -0.03839111328125, -0.38916015625, 0.213623046875, -0.313720703125, -0.403564453125, -0.453857421875, 0.431884765625, 0.72998046875, 0.498291015625, 0.25244140625, 0.46044921875, 0.00249481201171875, 0.1854248046875, 0.306396484375, -0.387939453125, 0.0040283203125, -0.418212890625, 0.82080078125, 0.269775390625, -0.244140625, -0.7919921875, -0.482421875, -0.022308349609375, -0.1678466796875, -0.0994873046875, -0.3798828125, -0.791015625, 0.1988525390625, -0.17236328125, 0.448974609375, -0.7421875, -0.466552734375, -0.32470703125, 0.422607421875, 0.4736328125, -1.013671875, 0.14404296875, -0.6123046875, 0.323486328125, 0.44970703125, -0.2091064453125, -0.348388671875, -0.46142578125, -0.83203125, -0.8681640625, 0.341796875, 0.68896484375, 0.0271148681640625, 0.152099609375, -1.3818359375, 0.55517578125, 0.3720703125, -0.1324462890625, 0.1077880859375, 0.046783447265625, 0.32861328125, 0.2490234375, 0.79296875, -0.4169921875, -0.7568359375, 0.1451416015625, -1.2578125, 0.392822265625, -0.5859375, 0.326171875, 0.1053466796875, 0.040618896484375, -0.1517333984375, 0.47705078125, -0.274658203125, 0.30419921875, -0.053924560546875, 0.405029296875, -0.98583984375, -0.5986328125, 0.54541015625, -0.318359375, -0.3798828125, 1.2578125, -0.1964111328125, -0.53564453125, 0.57177734375, 0.521484375, -0.232421875, 0.29052734375, -0.251220703125, 0.45947265625, -0.2091064453125, -0.1968994140625, -0.052490234375, -0.319091796875, 1.056640625, -0.177001953125, -0.7822265625, -0.40283203125, -1.1650390625, -0.11077880859375, -0.155517578125, -0.372802734375, 0.316162109375, -0.1717529296875, -0.045867919921875, -0.27783203125, -0.5029296875, -0.54541015625, -0.1942138671875, -0.043853759765625, -0.40966796875, 0.1875, 0.64990234375, 0.402587890625, 0.332275390625, -0.4560546875, -0.016815185546875, -0.275390625, -0.126220703125, -0.38330078125, -0.138671875, -0.1546630859375, -0.20654296875, -0.232421875, 0.14599609375, 0.2066650390625, 0.67724609375, 0.425537109375, 0.458984375, 0.66845703125, 0.423095703125, -0.78662109375, 0.93994140625, 0.1434326171875, -1.1220703125, -0.447021484375, 0.599609375, -0.0115814208984375, 0.487548828125, 0.275146484375, -0.69677734375, -0.62109375, -0.99267578125, 0.1895751953125, -0.3408203125, -0.376708984375, -0.90576171875, 0.0694580078125, -0.20166015625, 0.55712890625, -0.166259765625, -0.63037109375, 0.10833740234375, -1.353515625, 0.146728515625, -0.70849609375, -0.376220703125, -0.61474609375, -0.30029296875, -0.037322998046875, 0.97265625, 0.13330078125, 0.1680908203125, -0.1932373046875, -0.038330078125, 0.248046875, 0.081298828125, -0.342529296875, -0.44921875, -0.2379150390625, 0.21728515625, -0.149169921875, 0.036407470703125, -0.1871337890625, 0.6787109375, -0.67578125, 0.07879638671875, -0.37451171875, -0.165283203125, -0.315673828125, -0.1951904296875, 0.96240234375, -0.42138671875, -0.265869140625, -0.088134765625, 0.1927490234375, 0.67919921875, -0.465576171875, -0.1263427734375, -0.740234375, -0.2362060546875, -0.7841796875, 0.47021484375, -0.2880859375, -0.05828857421875, -0.8173828125, -0.295654296875, 1.1708984375, -0.60791015625, 0.2186279296875, 1.3173828125, 0.2349853515625, 0.31103515625, -0.7666015625, 0.3447265625, 0.5283203125, -0.54296875, -0.0943603515625, 0.1134033203125, -0.7265625, 0.339599609375, -0.29345703125, -1.1650390625, -0.580078125, 0.36328125, 1.3994140625, -0.21337890625, 0.73876953125, 0.2005615234375, -1.1474609375, -0.451904296875, 0.6669921875, -0.11505126953125, 0.27294921875, 0.98779296875, -0.1212158203125, -0.2406005859375, 0.10919189453125, -0.2452392578125, -0.51416015625, -0.357421875, 1.3125, -0.6201171875, -0.397216796875, 1.0625, 1.2763671875, -1.03125, -1.0576171875, -0.10736083984375, 0.055908203125, -0.3583984375, -1.017578125, 0.25390625, 0.58935546875, -0.9443359375, -0.0819091796875, 0.1505126953125, -0.342041015625, 0.689453125, -0.0692138671875, 0.3642578125, -0.5341796875, 0.138427734375, 0.73388671875, -0.5546875, -0.12451171875, -0.4638671875, -0.06903076171875, -0.164794921875, 0.00893402099609375, 0.53466796875, -0.449951171875, 0.1640625, 0.488037109375, 0.064697265625, 0.47119140625, -0.415283203125, -0.4658203125, 0.0035381317138671875, -0.9326171875, -0.34765625, 0.06671142578125, 0.425048828125, -0.17626953125, 0.53759765625, -0.91455078125, -0.074462890625, 0.129638671875, 0.2113037109375, -0.3642578125, -0.50634765625, -0.34521484375, -1.0849609375, -0.53271484375, -0.477783203125, -0.87646484375, -0.427734375, -0.10498046875, 0.322265625, -0.46826171875, 0.333984375, 0.5556640625, -0.67529296875, 0.8349609375, -0.708984375, 0.4580078125, -0.7646484375, -0.226806640625, -0.59326171875, 0.0185089111328125, -0.5, 0.1763916015625, -0.876953125, 0.1573486328125, -0.04339599609375, 0.413818359375, -0.4296875, 0.325927734375, -0.1494140625, -0.5859375, 0.1673583984375, 0.42529296875, -0.73486328125, 0.7880859375, 0.17919921875, 0.19970703125, 0.01213836669921875, -0.46875, -0.501953125, -0.213623046875, 0.69189453125, 0.33837890625, 0.056243896484375, 0.15966796875, -0.465087890625, -0.0074615478515625, -0.87548828125, 0.1409912109375, -0.435302734375, 0.12200927734375, 0.132080078125, -0.54345703125, 0.57275390625, 1.08984375, -0.46630859375, 0.40478515625, -0.13818359375, 0.10675048828125, 0.432861328125, 0.203125, -0.31982421875, 0.305908203125, 0.28759765625, -0.07794189453125, -0.042877197265625, 0.4921875, 0.047454833984375, 0.3291015625, -0.0109100341796875, -0.7099609375, -0.94775390625, -0.1900634765625, -0.3193359375, 0.369873046875, 0.224853515625, -0.505859375, -0.047119140625, -0.032928466796875, -0.55078125, 0.427978515625, -1.189453125, -0.8427734375, 0.32373046875, 0.07635498046875, -0.6064453125, 0.29150390625, -0.8955078125, 0.10333251953125, 0.173583984375, 0.43896484375, -0.277099609375, 0.634765625, -0.11407470703125, 0.115234375, -0.21142578125, -0.2117919921875, 0.0885009765625, 0.46142578125, -0.66943359375, -0.484375, 0.1751708984375, 0.90869140625, 0.219970703125, -0.202392578125, -0.66064453125, 0.301025390625, 0.1729736328125, -0.03009033203125, -0.29443359375, 0.1407470703125, -0.3798828125, 0.71044921875, -0.8203125, -0.040863037109375, 0.07879638671875, 0.75830078125, 0.1962890625, -0.379638671875, -0.48828125, 0.6865234375, 1.1494140625, -0.2230224609375, 0.513671875, 0.3212890625, 0.57177734375, -0.1466064453125, -0.168701171875, -0.411865234375, 0.84814453125, 0.55810546875, 0.58056640625, 0.0289154052734375, 0.34033203125, 0.779296875, 0.0738525390625, -0.263916015625, 0.56298828125, -0.2467041015625, -0.060302734375, 0.030853271484375, -0.2237548828125, -0.393310546875, 0.283447265625, -0.720703125, 0.51806640625, -0.59912109375, -0.319091796875, -0.2235107421875, -0.5576171875, 1.0234375, -0.47705078125, 0.000017583370208740234, 0.1502685546875, -0.344970703125, 0.296875, 0.68212890625, 0.2275390625, 0.1331787109375, 0.96044921875, 0.62451171875, 0.359375, 0.7421875, 0.346435546875, 0.59912109375, -0.6845703125, -0.0106048583984375, 0.1181640625, -0.27099609375, -0.1995849609375, -0.5224609375, -1.1982421875, 0.7666015625, -0.08367919921875, -0.274169921875, 0.5771484375, -0.6650390625, 0.0162506103515625, -0.25537109375, 0.85107421875, -0.480224609375, 0.321044921875, -0.036285400390625, -0.349609375, -0.607421875, 0.97802734375, 0.123291015625, 0.284423828125, 0.3310546875, 0.87255859375, -0.06805419921875, 1.48046875, 0.2264404296875, 0.08367919921875, 0.1768798828125, 0.5390625, -0.66796875, -0.67041015625, -0.10968017578125, -0.34814453125, 0.08056640625, -0.8271484375, -0.327392578125, -0.2208251953125, 0.84814453125, 0.444580078125, -0.7060546875, -0.5927734375, 0.2327880859375, -0.93505859375, 0.443115234375, 0.2880859375, 0.217041015625, 0.163818359375, -0.07403564453125, -0.369140625, -0.7294921875, 0.0970458984375, -0.60693359375, 0.299560546875, -0.58935546875, -0.39501953125, -0.283935546875, -0.336669921875, -0.26806640625, -0.32861328125, -0.192138671875, -0.7578125, 0.82275390625, 0.407470703125, 0.4013671875, 0.38671875, -0.10650634765625, 0.311279296875, 0.8876953125, 0.69482421875, -0.322998046875, 0.56640625, 0.2244873046875, 0.0865478515625, 0.216796875, -0.471435546875, 0.44384765625, -0.049163818359375, 0.4501953125, -0.6220703125, 0.479248046875, -0.9111328125, -1.109375, 0.151611328125, 0.273193359375, 0.4150390625, -0.5517578125, -0.97216796875, -0.347412109375, -0.93310546875, -0.0309906005859375, -0.37109375, 0.75439453125, -0.2406005859375, -0.11407470703125, -0.1546630859375, -0.978515625, 4.47265625, 1.0615234375, 0.5888671875, 0.261962890625, 0.2047119140625, 0.576171875, 0.2841796875, -0.85595703125, -0.035614013671875, -0.30859375, 0.63623046875, -0.1097412109375, 0.060882568359375, 0.97412109375, 0.3671875, 0.58740234375, -0.459228515625, -0.331298828125, 0.139404296875, -0.67578125, -0.8447265625, 0.2264404296875, 0.040496826171875, 0.341552734375, -0.13623046875, 0.31201171875, 0.57177734375, -0.89990234375, -0.51025390625, -0.6591796875, 0.2322998046875, -0.316650390625, 1.0869140625, -0.369873046875, -0.1942138671875, 0.65576171875, 0.05535888671875, -0.466552734375, -0.482666015625, 0.364990234375, 0.0404052734375, 0.1112060546875, 0.80224609375, -0.8662109375, 0.01544952392578125, 0.401123046875, -0.671875, 0.199462890625, 0.0178070068359375, -1.0263671875, 0.52734375, -0.1282958984375, 0.2130126953125, -0.365478515625, -0.9599609375, 0.1541748046875, 0.363037109375, 0.0682373046875, -0.053558349609375, 0.52197265625, 0.486572265625, 0.10992431640625, 0.01009368896484375, 0.77490234375, -1.26171875, 0.94921875, 0.1580810546875, 0.53955078125, -0.55224609375, 0.025726318359375, -0.60595703125, -0.457763671875, -0.35400390625, -0.257080078125, 0.81884765625, 0.332275390625, -0.259765625, 0.1737060546875, 0.4853515625, -0.625, 0.406005859375, -0.0244903564453125, -0.385009765625, -0.45556640625, 0.80224609375, 1.0595703125, -0.59765625, -0.481689453125, -0.338134765625, 0.4755859375, 0.3935546875, 0.56640625, 0.27685546875, -0.5673828125, -0.642578125 ]
0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: 1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si β‰  si + 1(1 ≀ i < n). 3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. Help him find such string or state that such string doesn't exist. String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes. Input A single line contains two positive integers n and k (1 ≀ n ≀ 106, 1 ≀ k ≀ 26) β€” the string's length and the number of distinct letters. Output In a single line print the required string. If there isn't such string, print "-1" (without the quotes). Examples Input 7 4 Output ababacd Input 4 7 Output -1 Submitted Solution: ``` n,m=input().split(" ") n=int(n) m=int(m) str="" list=[] for i in range(0,n): list.append("") list[0]="a" if(m==n and n==1): print("a") if(m>n or m==1): print("-1") else: d=ord("a") i=1 while(i<n-m+2): list[i]="b" i=i+2 j=2 while(j<=n-m+2): list[j]="a" j=j+2 j=2 i=n-m+2 while(i<n): list[i]=(chr(d+j)) j=j+1 i=i+1 c=str.join(list) print(c) ``` No
107,318
[ 0.43603515625, -0.193115234375, 0.491455078125, 0.2301025390625, -0.319580078125, -0.349853515625, 0.03265380859375, 0.1490478515625, 0.28369140625, 0.75537109375, 0.6396484375, -0.033538818359375, 0.015411376953125, -0.7890625, -0.59912109375, 0.062744140625, -0.56787109375, -0.431640625, -0.273193359375, 0.0626220703125, -0.056182861328125, -0.141357421875, -1.4814453125, 0.034027099609375, -0.333251953125, 0.85595703125, 0.352783203125, 0.07818603515625, 1.1142578125, 0.8779296875, -0.2861328125, -0.546875, 0.482666015625, -0.86572265625, -0.5341796875, -0.51416015625, 0.599609375, -1.009765625, -0.43310546875, -0.60693359375, 0.04833984375, -0.68994140625, 0.474365234375, -0.65478515625, -1.26171875, -0.11529541015625, -0.49755859375, -0.33349609375, -0.27001953125, -0.93994140625, 0.09234619140625, -0.218994140625, 0.423095703125, -0.69287109375, 0.11163330078125, 0.371337890625, 0.2049560546875, -0.2005615234375, -0.395751953125, 0.317626953125, -0.2174072265625, 0.4326171875, 0.04779052734375, -0.61376953125, -0.26513671875, 0.056304931640625, -0.063720703125, -0.367919921875, 0.0654296875, -0.52880859375, -0.2430419921875, 0.012451171875, -0.61669921875, -0.217041015625, -0.376953125, 0.1829833984375, 0.35009765625, 0.05792236328125, -0.61767578125, 0.85302734375, 0.381103515625, 1.40234375, 0.51416015625, 0.327880859375, -0.0975341796875, -0.446044921875, 0.197998046875, 0.5341796875, 0.28369140625, -0.17919921875, 0.31201171875, 0.3896484375, -0.82373046875, 0.1282958984375, 0.57568359375, 0.392578125, 0.0286712646484375, 0.42724609375, 0.279541015625, -0.031036376953125, 0.87353515625, 0.833984375, -0.154541015625, 1.0546875, -0.599609375, 0.301025390625, -0.12939453125, -0.35693359375, -0.1629638671875, -0.431640625, -0.2340087890625, -0.199951171875, 0.58642578125, 0.25537109375, -0.370361328125, 0.900390625, -0.1390380859375, 0.365966796875, -0.79296875, -0.096923828125, 0.498779296875, 0.31787109375, 0.6962890625, 0.04833984375, 0.02410888671875, -0.242431640625, -0.7236328125, 0.8857421875, -0.57470703125, 0.150634765625, 0.406494140625, 0.07476806640625, -0.1800537109375, 0.053802490234375, 0.1318359375, 0.57275390625, -0.00402069091796875, 0.53955078125, 0.6220703125, -0.50439453125, 0.921875, -0.245849609375, 0.0144500732421875, 1.501953125, 0.5087890625, -0.35400390625, 0.67578125, 0.195556640625, -0.78857421875, 0.489990234375, -1.1318359375, 0.6005859375, -0.1500244140625, -0.08062744140625, -0.167724609375, 0.233642578125, -0.275634765625, 0.2174072265625, 0.560546875, 0.2159423828125, -0.445068359375, 0.2166748046875, -0.298583984375, 0.55126953125, -0.30810546875, 0.62890625, -0.541015625, -0.1796875, 0.10467529296875, -0.2261962890625, 0.1588134765625, -0.092041015625, -0.09808349609375, 0.9140625, 0.7587890625, 1.298828125, 0.95947265625, -0.2115478515625, 0.16748046875, 0.410400390625, -0.6240234375, 0.0244293212890625, 0.27978515625, 0.5361328125, 0.10296630859375, 0.331787109375, -0.0106964111328125, -0.54833984375, -0.70654296875, -0.71484375, -0.04669189453125, 0.37646484375, -0.1524658203125, 0.4599609375, -0.1326904296875, -0.03765869140625, -0.70703125, -0.286376953125, -0.21630859375, -1.1103515625, -0.4013671875, 0.57080078125, -0.10394287109375, 0.5029296875, -0.61669921875, -0.291259765625, 0.435546875, 1.029296875, -0.368896484375, 0.150146484375, 0.197265625, 0.1595458984375, -0.1502685546875, 0.072509765625, 0.3759765625, 0.2783203125, -0.759765625, 0.61767578125, -0.28076171875, 0.0860595703125, 0.1011962890625, 0.84326171875, 0.109130859375, 0.367919921875, -0.3671875, -0.1019287109375, 0.422119140625, 0.90869140625, -0.0689697265625, 0.65576171875, 0.456298828125, 1.1630859375, 0.77490234375, 0.54638671875, 0.6083984375, 0.56884765625, 0.7490234375, 0.99462890625, -0.05377197265625, 0.34228515625, -0.27001953125, 0.483642578125, -0.01247406005859375, 0.6064453125, 0.292236328125, 0.384521484375, -0.04315185546875, 0.092041015625, -0.228271484375, 0.26318359375, -0.07366943359375, 0.73828125, -0.00679779052734375, 0.3994140625, -0.481201171875, -0.3642578125, 0.116455078125, 0.79638671875, -0.6875, -0.5810546875, -0.1063232421875, 0.1282958984375, -0.0010833740234375, -0.19189453125, 0.06048583984375, 0.1075439453125, 0.62548828125, 0.14599609375, -0.2978515625, -0.271728515625, -1.1669921875, -0.65185546875, -1.3642578125, -0.18896484375, -0.7197265625, 0.143310546875, 0.467041015625, -0.9501953125, 0.144775390625, -0.53173828125, -0.158203125, 0.0484619140625, -0.642578125, 0.646484375, 0.053436279296875, 0.418212890625, -0.51220703125, 0.388671875, 0.10565185546875, 0.90478515625, -0.49267578125, -0.211181640625, -0.00978851318359375, -0.366943359375, 0.30859375, -0.2822265625, 0.5146484375, 0.05865478515625, -0.36328125, -1.0234375, -0.475830078125, -0.0185546875, -0.26513671875, -0.05035400390625, -0.34130859375, 1.22265625, 0.387451171875, -0.904296875, 0.5458984375, 0.63037109375, -0.74072265625, 0.529296875, 0.546875, 0.191650390625, -0.78759765625, 1.4609375, 0.29541015625, 0.006893157958984375, -0.5693359375, -0.5126953125, -0.322998046875, 0.31396484375, 0.1119384765625, -0.51611328125, -0.09918212890625, 0.498779296875, 0.1385498046875, -1.1572265625, 0.81787109375, -1.041015625, -0.45458984375, -0.487060546875, -0.3349609375, 0.61279296875, 0.5546875, 0.36865234375, -0.072509765625, -0.5302734375, -0.41943359375, 0.403564453125, 0.3955078125, -0.90185546875, -0.16259765625, 0.52392578125, -0.4052734375, 0.302734375, 0.019073486328125, -0.228271484375, 0.056854248046875, -0.173583984375, 0.08563232421875, 1.017578125, 0.244140625, 0.125, 0.25390625, 0.9951171875, -0.6845703125, -0.397216796875, -0.642578125, 0.68310546875, 0.298095703125, 0.89306640625, 0.45947265625, -0.0673828125, -0.305419921875, -1.3544921875, 0.281494140625, -0.247314453125, 0.7412109375, -0.484375, 0.95947265625, 0.455078125, -0.62451171875, 0.6533203125, -0.5439453125, -0.11981201171875, 1.20703125, 0.0008244514465332031, 0.80322265625, -0.48828125, 0.385009765625, -0.163330078125, -0.3310546875, 0.560546875, 0.25634765625, 0.91552734375, -0.35107421875, -0.48974609375, -0.417236328125, -0.381103515625, -0.05389404296875, -0.4306640625, 0.1898193359375, -0.34326171875, -0.377685546875, -0.45751953125, 0.335693359375, 0.72802734375, 0.5029296875, 0.2646484375, 0.37939453125, 0.00595855712890625, 0.115966796875, 0.3349609375, -0.43896484375, 0.0105743408203125, -0.38330078125, 0.78857421875, 0.294189453125, -0.299560546875, -0.7802734375, -0.4853515625, -0.006977081298828125, -0.240234375, -0.07330322265625, -0.39111328125, -0.76025390625, 0.1802978515625, -0.17431640625, 0.415283203125, -0.7216796875, -0.4580078125, -0.31591796875, 0.43408203125, 0.498046875, -1.021484375, 0.11846923828125, -0.5771484375, 0.361083984375, 0.491455078125, -0.22802734375, -0.37158203125, -0.49853515625, -0.84423828125, -0.88916015625, 0.319091796875, 0.69580078125, -0.0185089111328125, 0.1434326171875, -1.42578125, 0.55419921875, 0.372314453125, -0.1500244140625, 0.154541015625, 0.02734375, 0.32958984375, 0.26513671875, 0.76611328125, -0.447265625, -0.79345703125, 0.108642578125, -1.2890625, 0.413330078125, -0.6455078125, 0.326904296875, 0.1329345703125, 0.074951171875, -0.1334228515625, 0.462646484375, -0.253662109375, 0.31298828125, -0.07989501953125, 0.455322265625, -1.05859375, -0.57666015625, 0.55908203125, -0.368896484375, -0.386474609375, 1.2802734375, -0.19873046875, -0.48291015625, 0.5703125, 0.48095703125, -0.253662109375, 0.314697265625, -0.265625, 0.48095703125, -0.2232666015625, -0.1943359375, -0.03228759765625, -0.378173828125, 1.0068359375, -0.15771484375, -0.85791015625, -0.3759765625, -1.18359375, -0.12127685546875, -0.12127685546875, -0.394287109375, 0.30078125, -0.1339111328125, -0.0877685546875, -0.270751953125, -0.50732421875, -0.55517578125, -0.182373046875, -0.08807373046875, -0.3984375, 0.162109375, 0.60205078125, 0.3359375, 0.388916015625, -0.491943359375, 0.0161285400390625, -0.294677734375, -0.10986328125, -0.392333984375, -0.1416015625, -0.1483154296875, -0.2071533203125, -0.1776123046875, 0.1390380859375, 0.267333984375, 0.68310546875, 0.38623046875, 0.453369140625, 0.658203125, 0.4482421875, -0.76220703125, 0.95947265625, 0.1439208984375, -1.142578125, -0.42041015625, 0.58447265625, 0.004730224609375, 0.4833984375, 0.26806640625, -0.68896484375, -0.62158203125, -1.017578125, 0.2191162109375, -0.333740234375, -0.34033203125, -0.90869140625, 0.131591796875, -0.1934814453125, 0.56640625, -0.166748046875, -0.5966796875, 0.09735107421875, -1.396484375, 0.1395263671875, -0.7275390625, -0.38134765625, -0.56396484375, -0.2666015625, -0.01495361328125, 0.9794921875, 0.07965087890625, 0.259033203125, -0.2003173828125, -0.1121826171875, 0.280517578125, 0.03521728515625, -0.329345703125, -0.498046875, -0.2481689453125, 0.21435546875, -0.17724609375, -0.0014677047729492188, -0.177490234375, 0.66650390625, -0.6982421875, 0.08843994140625, -0.38232421875, -0.1722412109375, -0.3095703125, -0.2236328125, 0.96484375, -0.39453125, -0.29296875, -0.0908203125, 0.1678466796875, 0.712890625, -0.462890625, -0.1260986328125, -0.67626953125, -0.20166015625, -0.736328125, 0.45703125, -0.282470703125, -0.0014905929565429688, -0.798828125, -0.25, 1.16796875, -0.64599609375, 0.2054443359375, 1.2880859375, 0.2286376953125, 0.36865234375, -0.73974609375, 0.2469482421875, 0.556640625, -0.53857421875, -0.134765625, 0.1259765625, -0.77978515625, 0.372802734375, -0.260498046875, -1.1416015625, -0.591796875, 0.314697265625, 1.3505859375, -0.2227783203125, 0.7119140625, 0.2066650390625, -1.1806640625, -0.461669921875, 0.7138671875, -0.11859130859375, 0.2440185546875, 1.013671875, -0.1478271484375, -0.259521484375, 0.048095703125, -0.2081298828125, -0.50537109375, -0.316162109375, 1.349609375, -0.59326171875, -0.374755859375, 1.0703125, 1.2822265625, -0.98681640625, -1.0400390625, -0.1632080078125, 0.0865478515625, -0.35595703125, -1.021484375, 0.275390625, 0.56787109375, -0.95703125, -0.0931396484375, 0.188232421875, -0.369140625, 0.73046875, -0.07281494140625, 0.3388671875, -0.53369140625, 0.1651611328125, 0.71728515625, -0.56201171875, -0.07196044921875, -0.51025390625, -0.08154296875, -0.1865234375, -0.002780914306640625, 0.54833984375, -0.491943359375, 0.1815185546875, 0.51025390625, 0.07708740234375, 0.456787109375, -0.434326171875, -0.52685546875, 0.0070343017578125, -0.89208984375, -0.322509765625, 0.047027587890625, 0.413818359375, -0.1597900390625, 0.5234375, -0.93994140625, -0.0740966796875, 0.1717529296875, 0.26318359375, -0.366455078125, -0.52197265625, -0.31005859375, -1.07421875, -0.50537109375, -0.482666015625, -0.83154296875, -0.462646484375, -0.07232666015625, 0.300048828125, -0.420166015625, 0.28173828125, 0.537109375, -0.69775390625, 0.828125, -0.7412109375, 0.484130859375, -0.775390625, -0.1767578125, -0.5791015625, 0.069580078125, -0.5771484375, 0.150390625, -0.87109375, 0.1796875, -0.0457763671875, 0.443359375, -0.421630859375, 0.3046875, -0.150390625, -0.5595703125, 0.1619873046875, 0.420166015625, -0.71875, 0.76416015625, 0.168212890625, 0.20458984375, 0.035400390625, -0.5205078125, -0.52099609375, -0.1942138671875, 0.70166015625, 0.359619140625, 0.05255126953125, 0.10540771484375, -0.441162109375, -0.016845703125, -0.91259765625, 0.0985107421875, -0.35791015625, 0.11688232421875, 0.148193359375, -0.53369140625, 0.58740234375, 1.0498046875, -0.482177734375, 0.4384765625, -0.1298828125, 0.059967041015625, 0.420166015625, 0.2333984375, -0.256103515625, 0.282470703125, 0.28564453125, -0.07379150390625, -0.006587982177734375, 0.49609375, 0.0335693359375, 0.343505859375, -0.0205230712890625, -0.7177734375, -0.92333984375, -0.226318359375, -0.347900390625, 0.3408203125, 0.2227783203125, -0.4970703125, -0.08984375, -0.06292724609375, -0.48291015625, 0.40966796875, -1.2666015625, -0.865234375, 0.3818359375, 0.10479736328125, -0.60498046875, 0.25390625, -0.90673828125, 0.069580078125, 0.1494140625, 0.4345703125, -0.282470703125, 0.63134765625, -0.1396484375, 0.1431884765625, -0.2130126953125, -0.1832275390625, 0.11968994140625, 0.430419921875, -0.69970703125, -0.466064453125, 0.1907958984375, 0.9130859375, 0.1942138671875, -0.2005615234375, -0.6611328125, 0.27001953125, 0.131591796875, -0.057525634765625, -0.25244140625, 0.1336669921875, -0.41796875, 0.64453125, -0.8095703125, -0.03228759765625, 0.056396484375, 0.783203125, 0.227294921875, -0.374755859375, -0.51513671875, 0.681640625, 1.171875, -0.2369384765625, 0.54443359375, 0.318115234375, 0.609375, -0.129150390625, -0.2132568359375, -0.412841796875, 0.85791015625, 0.546875, 0.54345703125, 0.015960693359375, 0.39013671875, 0.79296875, 0.1292724609375, -0.26025390625, 0.62744140625, -0.27587890625, -0.050537109375, -0.035308837890625, -0.2099609375, -0.4091796875, 0.279541015625, -0.6845703125, 0.53173828125, -0.58935546875, -0.316162109375, -0.197509765625, -0.55322265625, 1.0361328125, -0.54052734375, 0.035064697265625, 0.11572265625, -0.357421875, 0.2139892578125, 0.681640625, 0.2059326171875, 0.1474609375, 0.939453125, 0.60791015625, 0.375732421875, 0.76611328125, 0.368408203125, 0.58740234375, -0.6875, 0.0191497802734375, 0.09356689453125, -0.248291015625, -0.2322998046875, -0.548828125, -1.2177734375, 0.7119140625, -0.09527587890625, -0.314453125, 0.654296875, -0.69140625, 0.0295867919921875, -0.2186279296875, 0.84716796875, -0.5048828125, 0.34814453125, -0.0263824462890625, -0.322509765625, -0.56689453125, 0.98779296875, 0.09393310546875, 0.263427734375, 0.357177734375, 0.87841796875, -0.06378173828125, 1.4833984375, 0.250244140625, 0.0562744140625, 0.1607666015625, 0.55029296875, -0.6064453125, -0.70654296875, -0.1103515625, -0.3349609375, 0.0736083984375, -0.81884765625, -0.345947265625, -0.2376708984375, 0.91015625, 0.373779296875, -0.70947265625, -0.61669921875, 0.2249755859375, -0.9765625, 0.451171875, 0.254638671875, 0.242919921875, 0.1964111328125, -0.038604736328125, -0.38232421875, -0.7724609375, 0.10418701171875, -0.61865234375, 0.29296875, -0.5888671875, -0.417236328125, -0.2322998046875, -0.35693359375, -0.275390625, -0.365966796875, -0.156494140625, -0.75537109375, 0.7822265625, 0.41064453125, 0.389404296875, 0.3759765625, -0.137451171875, 0.325439453125, 0.9091796875, 0.67822265625, -0.337646484375, 0.5498046875, 0.197265625, 0.1357421875, 0.26171875, -0.4541015625, 0.414306640625, -0.053619384765625, 0.46337890625, -0.60400390625, 0.52197265625, -0.8447265625, -1.1015625, 0.08477783203125, 0.2978515625, 0.369140625, -0.57421875, -0.91943359375, -0.337646484375, -0.93798828125, -0.01454925537109375, -0.3544921875, 0.775390625, -0.1912841796875, -0.0955810546875, -0.1658935546875, -1.0224609375, 4.4453125, 1.0390625, 0.58154296875, 0.254150390625, 0.21240234375, 0.630859375, 0.294677734375, -0.8515625, -0.060394287109375, -0.3115234375, 0.67041015625, -0.0975341796875, 0.062164306640625, 1.0234375, 0.44091796875, 0.619140625, -0.470947265625, -0.332763671875, 0.1685791015625, -0.65380859375, -0.8447265625, 0.233154296875, 0.038970947265625, 0.33984375, -0.1295166015625, 0.30419921875, 0.56787109375, -0.8876953125, -0.58154296875, -0.63720703125, 0.2113037109375, -0.356689453125, 1.0732421875, -0.407958984375, -0.160888671875, 0.60888671875, 0.085205078125, -0.482177734375, -0.492431640625, 0.4013671875, 0.0245819091796875, 0.06085205078125, 0.81982421875, -0.89697265625, 0.01139068603515625, 0.408447265625, -0.6865234375, 0.267333984375, 0.0246124267578125, -1.037109375, 0.5107421875, -0.12646484375, 0.26416015625, -0.408447265625, -0.97900390625, 0.174072265625, 0.336669921875, 0.06427001953125, -0.0693359375, 0.47509765625, 0.5146484375, 0.1046142578125, -0.02752685546875, 0.83984375, -1.3251953125, 0.97802734375, 0.114990234375, 0.5263671875, -0.6162109375, 0.033935546875, -0.5576171875, -0.481201171875, -0.3466796875, -0.18701171875, 0.853515625, 0.381103515625, -0.2327880859375, 0.1968994140625, 0.478515625, -0.61865234375, 0.39892578125, 0.04620361328125, -0.378173828125, -0.41650390625, 0.8408203125, 1.0654296875, -0.63037109375, -0.47216796875, -0.298095703125, 0.47705078125, 0.3876953125, 0.59375, 0.288330078125, -0.55322265625, -0.65966796875 ]
0