{"prob_desc_description":"You are given a string $$$s$$$ consisting of lowercase Latin letters. Let the length of $$$s$$$ be $$$|s|$$$. You may perform several operations on this string.In one operation, you can choose some index $$$i$$$ and remove the $$$i$$$-th character of $$$s$$$ ($$$s_i$$$) if at least one of its adjacent characters is the previous letter in the Latin alphabet for $$$s_i$$$. For example, the previous letter for b is a, the previous letter for s is r, the letter a has no previous letters. Note that after each removal the length of the string decreases by one. So, the index $$$i$$$ should satisfy the condition $$$1 \\le i \\le |s|$$$ during each operation.For the character $$$s_i$$$ adjacent characters are $$$s_{i-1}$$$ and $$$s_{i+1}$$$. The first and the last characters of $$$s$$$ both have only one adjacent character (unless $$$|s| = 1$$$).Consider the following example. Let $$$s=$$$ bacabcab.  During the first move, you can remove the first character $$$s_1=$$$ b because $$$s_2=$$$ a. Then the string becomes $$$s=$$$ acabcab.  During the second move, you can remove the fifth character $$$s_5=$$$ c because $$$s_4=$$$ b. Then the string becomes $$$s=$$$ acabab.  During the third move, you can remove the sixth character $$$s_6=$$$'b' because $$$s_5=$$$ a. Then the string becomes $$$s=$$$ acaba.  During the fourth move, the only character you can remove is $$$s_4=$$$ b, because $$$s_3=$$$ a (or $$$s_5=$$$ a). The string becomes $$$s=$$$ acaa and you cannot do anything with it. Your task is to find the maximum possible number of characters you can remove if you choose the sequence of operations optimally.","prob_desc_output_spec":"Print one integer \u2014 the maximum possible number of characters you can remove if you choose the sequence of moves optimally.","lang_cluster":"","src_uid":"9ce37bc2d361f5bb8a0568fb479b8a38","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","constructive algorithms","strings","greedy"],"prob_desc_created_at":"1583057400","prob_desc_sample_inputs":"[\"8\\nbacabcab\", \"4\\nbcda\", \"6\\nabbbbb\"]","prob_desc_notes":"NoteThe first example is described in the problem statement. Note that the sequence of moves provided in the statement is not the only, but it can be shown that the maximum possible answer to this test is $$$4$$$.In the second example, you can remove all but one character of $$$s$$$. The only possible answer follows.  During the first move, remove the third character $$$s_3=$$$ d, $$$s$$$ becomes bca.  During the second move, remove the second character $$$s_2=$$$ c, $$$s$$$ becomes ba.  And during the third move, remove the first character $$$s_1=$$$ b, $$$s$$$ becomes a. ","exec_outcome":"","difficulty":1600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The only line of the input contains one integer $$$|s|$$$ ($$$1 \\le |s| \\le 100$$$) \u2014 the length of $$$s$$$. The second line of the input contains one string $$$s$$$ consisting of $$$|s|$$$ lowercase Latin letters.","prob_desc_sample_outputs":"[\"4\", \"3\", \"5\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"8\\r\\nbacabcab\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"4\\r\\nbcda\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"6\\r\\nabbbbb\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"1\\r\\na\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1\\r\\nt\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100\\r\\nciftajmzqbfkvbhnyugneialytrkwjlhzwltylptheadmypbjxdzkxnqovimgmzkwpuelzbbhciinfiyspfatgoexeezolulnliu\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100\\r\\nyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"100\\r\\naaaaaabbcccccccddffffhhhhhhhhiiiiiikkkkkkkkmmmmmmooooooopppprrrrrrrrrttttttvvvvvvvvvvvvxxxxxxxzzzzzz\\r\\n\", \"output\": [\"21\"]}, {\"input\": \"100\\r\\nbabaababbaabbabababbabbbababababbaabababaaababaababbbaaababbaabbababababbababbabaabbaabaaaaabbababba\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"100\\r\\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"100\\r\\nacdfijmnorszzyyzzzzzzyzzyzzzzxwzzzzzyzzzzzzyzzzzzzzyzzzzzyzzzzzzyxzzzyzzzzzyzzzzzyzzyzzzzvutqplkhgeb\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"100\\r\\nabcdeghfgefedeefcabaaabcedfefedacbbcaaabehhjlkjikjloqrtuyzxwvspnmnlkjgfdcbacdcghfedfebaacbcbcdbccaaa\\r\\n\", \"output\": [\"85\"]}, {\"input\": \"100\\r\\nababaaaabaabaaaaaaabaaaaaaaaaaaaacbaaaabaaaaaabaabaaaababaaaabaehijkmnpqvxzywutsrolgfdcbaaaabaabaaaa\\r\\n\", \"output\": [\"40\"]}, {\"input\": \"100\\r\\naaaaaaabaaaaaabcaaaaaaaaaaaaaaaaaaaabbbaaaaaaabefhklmnopsuxzywvtrqjigdcaaaaaaaaaaaaaaaaaaaaaaaabaaaa\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"100\\r\\naaaaabcjkprsvxyzwutqonmlihgfedaaaaaaaaaaaaaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"100\\r\\nyltrygcqmgjzsxoahbvovspancmoaltdrxgjnxwxbrehubvradguoqgiodzanljxtszdutuzgcnihmwevoloceyidyvoopnqbtlb\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"100\\r\\naaaabbbcccccccdddddeeeeeffgggghhhiijjjjkkkllmmnnnoooppqqqrrrrssssssttttuuuuuuuuvvvvvwwwwxxxxyyyyzzzz\\r\\n\", \"output\": [\"96\"]}, {\"input\": \"100\\r\\nrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100\\r\\nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100\\r\\njupemetthxolktvhbmzdwlrekwmcugngajdgifwseksjlibsdgmegmqtmeeeqszqjxjhjenjxofvkesfjugbzephryjqqkxatrvl\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"100\\r\\nmxjrojjwtrauhhccftvjsyfyfsnbdnwjfltyjetsylbddrkoqjxbmientcowknrecfqcvxfgsbymwyvakmbulhvrxzvzbygajtgc\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"100\\r\\nbldubjepvkwhjbxrueydtpparjszjgwpxjlqlpsmdrjoaagfnrohfcabchmdwaoctmilfbpztwjrfdgdioqggokdftcniqywmvjd\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"100\\r\\nzbzevxgewibujtbyvhzohoobudkghaivlbpaywiesizahkdxmcpdoqzsxqglezenmsgvsmxcrzcntauvarpakddglhrjmzylfuyq\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"100\\r\\nwhkbjjjrpcgsfaxgcmktmwypyfhbzvvowkvxltbmnyndqkswixxqxriopddrygymbcvadjjheugxgikrlirnhhsmnjmzpizyltau\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"1\\r\\nz\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5\\r\\nbabaa\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5\\r\\nabbdd\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"6\\r\\naaaaaa\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"6\\r\\nbbbbab\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"6\\r\\nbaabbb\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"6\\r\\ndacbab\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"7\\r\\naaaaaaa\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7\\r\\nbaaabab\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"7\\r\\nccababa\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"7\\r\\ncddcbcb\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"8\\r\\naaaaaaaa\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"8\\r\\naaabbaab\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"8\\r\\nabababbc\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"8\\r\\nbdaacddc\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"9\\r\\naaaaaaaaa\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"9\\r\\naabaaabab\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"9\\r\\nbaccbbaca\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"9\\r\\nacacaabaa\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10\\r\\naaaaaaaaaa\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"10\\r\\nbbaabaabbb\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"10\\r\\ncbbbbcaaca\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"10\\r\\ncadbcdddda\\r\\n\", \"output\": [\"6\"]}]"}
{"prob_desc_description":"You can not just take the file and send it. When Polycarp trying to send a file in the social network \"Codehorses\", he encountered an unexpected problem. If the name of the file contains three or more \"x\" (lowercase Latin letters \"x\") in a row, the system considers that the file content does not correspond to the social network topic. In this case, the file is not sent and an error message is displayed.Determine the minimum number of characters to remove from the file name so after that the name does not contain \"xxx\" as a substring. Print 0 if the file name does not initially contain a forbidden substring \"xxx\".You can delete characters in arbitrary positions (not necessarily consecutive). If you delete a character, then the length of a string is reduced by $$$1$$$. For example, if you delete the character in the position $$$2$$$ from the string \"exxxii\", then the resulting string is \"exxii\".","prob_desc_output_spec":"Print the minimum number of characters to remove from the file name so after that the name does not contain \"xxx\" as a substring. If initially the file name dost not contain a forbidden substring \"xxx\", print 0.","lang_cluster":"","src_uid":"8de14db41d0acee116bd5d8079cb2b02","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["strings","greedy"],"prob_desc_created_at":"1582202100","prob_desc_sample_inputs":"[\"6\\nxxxiii\", \"5\\nxxoxx\", \"10\\nxxxxxxxxxx\"]","prob_desc_notes":"NoteIn the first example Polycarp tried to send a file with name contains number $$$33$$$, written in Roman numerals. But he can not just send the file, because it name contains three letters \"x\" in a row. To send the file he needs to remove any one of this letters.","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains integer $$$n$$$ $$$(3 \\le n \\le 100)$$$ \u2014 the length of the file name. The second line contains a string of length $$$n$$$ consisting of lowercase Latin letters only \u2014 the file name.","prob_desc_sample_outputs":"[\"1\", \"0\", \"8\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"6\\r\\nxxxiii\\r\\n\", \"output\": [\"1\\r\\n\", \"1\", \"1\\n\"]}, {\"input\": \"5\\r\\nxxoxx\\r\\n\", \"output\": [\"0\\r\\n\", \"0\\n\", \"0\"]}, {\"input\": \"10\\r\\nxxxxxxxxxx\\r\\n\", \"output\": [\"8\\n\", \"8\", \"8\\r\\n\"]}, {\"input\": \"100\\r\\nxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\\r\\n\", \"output\": [\"98\", \"98\\n\", \"98\\r\\n\"]}, {\"input\": \"99\\r\\nxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxaxxa\\r\\n\", \"output\": [\"0\\r\\n\", \"0\\n\", \"0\"]}, {\"input\": \"3\\r\\nxxx\\r\\n\", \"output\": [\"1\\r\\n\", \"1\", \"1\\n\"]}, {\"input\": \"77\\r\\naaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxyyyzzz\\r\\n\", \"output\": [\"0\\r\\n\", \"0\\n\", \"0\"]}, {\"input\": \"100\\r\\nuxxxxxlmexxxxxxxwnxxexxxxxcxxfydxxxxxxvmdxxxxxxisxxxxxxxxidkxxxpxxxxxxxxmnuxxxxjxxxqcxxwmxxxxxxxxmrx\\r\\n\", \"output\": [\"41\", \"41\\r\\n\", \"41\\n\"]}, {\"input\": \"100\\r\\nxxxxxxxxxxxjtxxxxxxxxcxxxxxxcfxxxxzxxxxxxgxxxxxbxxxxbxxxxxxxxdycxxxxokixxxkizxxgcxxxxxxxxexxxxxfxxxc\\r\\n\", \"output\": [\"49\", \"49\\n\", \"49\\r\\n\"]}, {\"input\": \"100\\r\\nuxxxxxlmexxxxxxxwnxxexxxxxcxxfydxxxxxxvmdxxxxxxisxxxxxxxxidkxxxpxxxxxxxxmnuxxxxjxxxqcxxwmxxxxxwxxxxx\\r\\n\", \"output\": [\"41\", \"41\\r\\n\", \"41\\n\"]}, {\"input\": \"34\\r\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\r\\n\", \"output\": [\"0\\r\\n\", \"0\\n\", \"0\"]}, {\"input\": \"5\\r\\nfcyju\\r\\n\", \"output\": [\"0\\r\\n\", \"0\\n\", \"0\"]}, {\"input\": \"100\\r\\nihygyvdvyeifomhxhkhdkimquvgallbqharcyriyqkidnwykozuhvkwdldlztpabgyuflikychqpdenwzgtlzotyumjgdsrbxxxx\\r\\n\", \"output\": [\"2\", \"2\\n\", \"2\\r\\n\"]}]"}
{"prob_desc_description":"Pak Chanek plans to build a garage. He wants the garage to consist of a square and a right triangle that are arranged like the following illustration.  Define $$$a$$$ and $$$b$$$ as the lengths of two of the sides in the right triangle as shown in the illustration. An integer $$$x$$$ is suitable if and only if we can construct a garage with assigning positive integer values for the lengths $$$a$$$ and $$$b$$$ ($$$a<b$$$) so that the area of the square at the bottom is exactly $$$x$$$. As a good friend of Pak Chanek, you are asked to help him find the $$$N$$$-th smallest suitable number.","prob_desc_output_spec":"An integer that represents the $$$N$$$-th smallest suitable number.","lang_cluster":"","src_uid":"d0a8604b78ba19ab769fd1ec90a72e4e","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"128 megabytes","file_name":"prog_syn_val.jsonl","tags":["geometry","math","binary search"],"prob_desc_created_at":"1662298500","prob_desc_sample_inputs":"[\"3\"]","prob_desc_notes":"NoteThe $$$3$$$-rd smallest suitable number is $$$7$$$. A square area of $$$7$$$ can be obtained by assigning $$$a=3$$$ and $$$b=4$$$.","exec_outcome":"","difficulty":1500.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The only line contains a single integer $$$N$$$ ($$$1 \\leq N \\leq 10^9$$$).","prob_desc_sample_outputs":"[\"7\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3\\n\", \"output\": [\"7\\n\\n\", \"7\", \"7\\n\", \" 7 \\n\", \"7 \", \"\\n7\", \"7\\n\"]}, {\"input\": \"6\\n\", \"output\": [\"11\\n\", \"11\\n\", \"11\", \"11\\n\\n\", \"\\n11\", \"11 \"]}, {\"input\": \"5\\n\", \"output\": [\"\\n9\", \"9\\n\\n\", \"9\\n\", \"9 \", \"9\", \"9\\n\"]}, {\"input\": \"8\\n\", \"output\": [\"13 \", \"13\\n\\n\", \"13\\n\", \"13\\n\", \"\\n13\", \"13\"]}, {\"input\": \"4\\n\", \"output\": [\"8\\n\\n\", \"\\n8\", \"8 \", \"8\\n\", \"8\", \"8\\n\"]}, {\"input\": \"10\\n\", \"output\": [\"16 \", \"\\n16\", \"16\", \"16\\n\", \"16\\n\\n\", \"16\\n\"]}, {\"input\": \"18\\n\", \"output\": [\"27\", \"27\\n\", \"27 \", \"\\n27\", \"27\\n\", \"27\\n\\n\"]}, {\"input\": \"589284012\\n\", \"output\": [\"785712019\\n\", \"785712019\\n\", \"785712019\\n\\n\", \"785712019\"]}, {\"input\": \"636562060\\n\", \"output\": [\"848749416\\n\", \"848749416\\n\\n\", \"848749416 \", \"848749416\", \"848749416\\n\"]}, {\"input\": \"200000\\n\", \"output\": [\"266669\\n\", \"266669\", \"266669\\n\", \"266669\\n\\n\"]}, {\"input\": \"1000000000\\n\", \"output\": [\"1333333336\\n\", \"1333333336\", \"1333333336\\n\\n\", \"1333333336\\n\", \"1333333336 \"]}, {\"input\": \"999999999\\n\", \"output\": [\"1333333335\\n\", \"1333333335\", \"1333333335\\n\", \"1333333335\\n\\n\"]}, {\"input\": \"999999998\\n\", \"output\": [\"1333333333\", \"1333333333\\n\", \"1333333333\\n\\n\", \"1333333333\\n\"]}, {\"input\": \"999999997\\n\", \"output\": [\"1333333332 \", \"1333333332\\n\", \"1333333332\\n\\n\", \"1333333332\", \"1333333332\\n\"]}, {\"input\": \"1000005\\n\", \"output\": [\"1333343\\n\", \"1333343\\n\", \"1333343\\n\\n\", \"1333343\"]}, {\"input\": \"1000\\n\", \"output\": [\"1336\\n\\n\", \"1336\", \"1336\\n\", \"1336\\n\", \"1336 \"]}, {\"input\": \"2\\n\", \"output\": [\"5\\n\", \"5\", \" 5 \\n\", \"5\\n\\n\", \"5\\n\"]}, {\"input\": \"1\\n\", \"output\": [\"3\\n\\n\", \"3\\n\", \"3\\n\", \"3\", \" 3 \\n\"]}, {\"input\": \"767928734\\n\", \"output\": [\"1023904981\", \"1023904981\\n\", \"1023904981\\n\", \"1023904981\\n\\n\"]}, {\"input\": \"20400000\\n\", \"output\": [\"27200003\\n\", \"27200003\", \"27200003\\n\\n\", \"27200003\\n\"]}, {\"input\": \"999993999\\n\", \"output\": [\"1333325335\\n\\n\", \"1333325335\", \"1333325335\\n\", \"1333325335\\n\"]}, {\"input\": \"383964368\\n\", \"output\": [\"511952493\\n\", \"511952493\", \"511952493\\n\", \"511952493\\n\\n\"]}]"}
{"prob_desc_description":"A chainword is a special type of crossword. As most of the crosswords do, it has cells that you put the letters in and some sort of hints to what these letters should be.The letter cells in a chainword are put in a single row. We will consider chainwords of length $$$m$$$ in this task.A hint to a chainword is a sequence of segments such that the segments don't intersect with each other and cover all $$$m$$$ letter cells. Each segment contains a description of the word in the corresponding cells.The twist is that there are actually two hints: one sequence is the row above the letter cells and the other sequence is the row below the letter cells. When the sequences are different, they provide a way to resolve the ambiguity in the answers.You are provided with a dictionary of $$$n$$$ words, each word consists of lowercase Latin letters. All words are pairwise distinct.An instance of a chainword is the following triple:   a string of $$$m$$$ lowercase Latin letters;  the first hint: a sequence of segments such that the letters that correspond to each segment spell a word from the dictionary;  the second hint: another sequence of segments such that the letters that correspond to each segment spell a word from the dictionary. Note that the sequences of segments don't necessarily have to be distinct.Two instances of chainwords are considered different if they have different strings, different first hints or different second hints.Count the number of different instances of chainwords. Since the number might be pretty large, output it modulo $$$998\\,244\\,353$$$.","prob_desc_output_spec":"Print a single integer\u00a0\u2014 the number of different instances of chainwords of length $$$m$$$ for the given dictionary modulo $$$998\\,244\\,353$$$.","lang_cluster":"","src_uid":"711d15e11016d0164fb2b0c3756e4857","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["strings","string suffix structures","matrices","data structures","brute force","dp"],"prob_desc_created_at":"1618238100","prob_desc_sample_inputs":"[\"3 5\\nababa\\nab\\na\", \"2 4\\nab\\ncd\", \"5 100\\na\\naa\\naaa\\naaaa\\naaaaa\"]","prob_desc_notes":"NoteHere are all the instances of the valid chainwords for the first example:   The red lines above the letters denote the segments of the first hint, the blue lines below the letters denote the segments of the second hint.In the second example the possible strings are: \"abab\", \"abcd\", \"cdab\" and \"cdcd\". All the hints are segments that cover the first two letters and the last two letters.","exec_outcome":"","difficulty":2700.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"3 seconds","prob_desc_input_spec":"The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 8$$$, $$$1 \\le m \\le 10^9$$$)\u00a0\u2014 the number of words in the dictionary and the number of letter cells. Each of the next $$$n$$$ lines contains a word\u00a0\u2014 a non-empty string of no more than $$$5$$$ lowercase Latin letters. All words are pairwise distinct. ","prob_desc_sample_outputs":"[\"11\", \"4\", \"142528942\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3 5\\r\\nababa\\r\\nab\\r\\na\\r\\n\", \"output\": [\"11\\r\\n\", \"11\\n\"]}, {\"input\": \"2 4\\r\\nab\\r\\ncd\\r\\n\", \"output\": [\"4\\r\\n\", \"4\\n\"]}, {\"input\": \"5 100\\r\\na\\r\\naa\\r\\naaa\\r\\naaaa\\r\\naaaaa\\r\\n\", \"output\": [\"142528942\\n\", \"142528942\\r\\n\"]}, {\"input\": \"8 3\\r\\nba\\r\\nbbb\\r\\nbb\\r\\naba\\r\\naab\\r\\nbaa\\r\\nb\\r\\na\\r\\n\", \"output\": [\"56\\n\", \"56\\r\\n\"]}, {\"input\": \"8 5\\r\\nabb\\r\\nbaa\\r\\na\\r\\naba\\r\\naa\\r\\nb\\r\\nba\\r\\nbb\\r\\n\", \"output\": [\"1824\\r\\n\", \"1824\\n\"]}, {\"input\": \"8 10\\r\\naa\\r\\nba\\r\\na\\r\\naaa\\r\\nbb\\r\\naab\\r\\naba\\r\\nb\\r\\n\", \"output\": [\"7610511\\n\", \"7610511\\r\\n\"]}, {\"input\": \"8 10\\r\\nbac\\r\\naa\\r\\nbbac\\r\\nbcc\\r\\nbbca\\r\\naac\\r\\nabba\\r\\nbbba\\r\\n\", \"output\": [\"227\\r\\n\", \"227\\n\"]}, {\"input\": \"8 100\\r\\naabab\\r\\naaa\\r\\naba\\r\\nbbaba\\r\\na\\r\\naa\\r\\nbabba\\r\\nbba\\r\\n\", \"output\": [\"452563662\\n\", \"452563662\\r\\n\"]}, {\"input\": \"8 100\\r\\ncbb\\r\\nbaaba\\r\\ncc\\r\\nacb\\r\\nabbba\\r\\nbb\\r\\nbcc\\r\\ncbccc\\r\\n\", \"output\": [\"85330586\\r\\n\", \"85330586\\n\"]}, {\"input\": \"8 10000\\r\\nbb\\r\\nbbb\\r\\nbaa\\r\\nbbaaa\\r\\nbbabb\\r\\nbaabb\\r\\nab\\r\\nb\\r\\n\", \"output\": [\"921272334\\r\\n\", \"921272334\\n\"]}, {\"input\": \"8 10000\\r\\ncc\\r\\nbcbac\\r\\nc\\r\\nbbbca\\r\\nbab\\r\\nbcb\\r\\naab\\r\\nacbc\\r\\n\", \"output\": [\"62834015\\r\\n\", \"62834015\\n\"]}, {\"input\": \"8 1000000\\r\\nba\\r\\nbaab\\r\\nab\\r\\nbabaa\\r\\na\\r\\nb\\r\\naaa\\r\\nabb\\r\\n\", \"output\": [\"109599579\\n\", \"109599579\\r\\n\"]}, {\"input\": \"8 1000000\\r\\nabbca\\r\\nabcbc\\r\\nbc\\r\\ncb\\r\\nbcbc\\r\\nc\\r\\nb\\r\\nabc\\r\\n\", \"output\": [\"431249243\\n\", \"431249243\\r\\n\"]}, {\"input\": \"8 1000000\\r\\na\\r\\nccdc\\r\\ndac\\r\\nb\\r\\nbdad\\r\\nc\\r\\nadbdd\\r\\nbadbd\\r\\n\", \"output\": [\"467270984\\r\\n\", \"467270984\\n\"]}, {\"input\": \"8 1000000\\r\\nks\\r\\nmbha\\r\\nbyn\\r\\ncz\\r\\ng\\r\\nmv\\r\\nnct\\r\\nbty\\r\\n\", \"output\": [\"206210322\\r\\n\", \"206210322\\n\"]}, {\"input\": \"8 1000000000\\r\\nbbba\\r\\nb\\r\\naab\\r\\naabb\\r\\naba\\r\\nbaabb\\r\\nab\\r\\na\\r\\n\", \"output\": [\"108439359\\r\\n\", \"108439359\\n\"]}, {\"input\": \"8 1000000000\\r\\na\\r\\nacbca\\r\\nabcab\\r\\naabcb\\r\\nb\\r\\ncbb\\r\\nba\\r\\nbaaca\\r\\n\", \"output\": [\"678704568\\r\\n\", \"678704568\\n\"]}, {\"input\": \"8 1000000000\\r\\ndcaab\\r\\ndacdd\\r\\nddbdd\\r\\nbcca\\r\\ndcacd\\r\\nb\\r\\nccbba\\r\\nabdd\\r\\n\", \"output\": [\"458353495\\n\", \"458353495\\r\\n\"]}, {\"input\": \"8 1000000000\\r\\num\\r\\nmruk\\r\\nif\\r\\nsnyg\\r\\njts\\r\\np\\r\\nr\\r\\niwq\\r\\n\", \"output\": [\"108201875\\n\", \"108201875\\r\\n\"]}, {\"input\": \"8 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\"output\": [\"834686688\\n\", \"834686688\", \"834686688\\n\"]}, {\"input\": \"8 671088639\\naaaaa\\naaaa\\nbbbbb\\nbbbb\\nccccc\\ncccc\\nddddd\\ndddd\\n\", \"output\": [\"840688293\", \"840688293\\n\", \"840688293\\n\"]}, {\"input\": \"8 671088639\\naaaaa\\naaaa\\nbbbbb\\nbbbb\\naaabb\\nbbbaa\\naabbb\\nbbaaa\\n\", \"output\": [\"376573480\\n\", \"376573480\\n\", \"376573480\"]}, {\"input\": \"8 671088639\\naaaaa\\naaaa\\nbbbbb\\nbbbb\\naaaab\\nbbbba\\naaabb\\nbbbaa\\n\", \"output\": [\"775296008\\n\", \"775296008\", \"775296008\\n\"]}, {\"input\": \"8 805306367\\naaaaa\\naaaab\\naaabb\\naabbb\\nabbbb\\nbbbbb\\naaaa\\nbbbb\\n\", \"output\": [\"233390545\", \"233390545\\n\", \"233390545\\n\"]}, {\"input\": \"8 805306367\\nbbbb\\nabbaa\\nababa\\naabba\\nbbaab\\nbabab\\nbaabb\\nbbbbb\\n\", \"output\": [\"40171194\\n\", \"40171194\\n\", \"40171194\"]}, {\"input\": \"8 805306367\\naaaaa\\nbbbbb\\nccccc\\nddddd\\neeeee\\nfffff\\nggggg\\nhhhhh\\n\", \"output\": [\"0\\n\", \"0\", \"0\\n\"]}, {\"input\": \"8 805306367\\naeifj\\ncaeif\\neifjg\\nfjgc\\nfjgca\\ngcaei\\nifjgc\\njgcae\\n\", \"output\": [\"223759404\", \"223759404\\n\", \"223759404\\n\"]}, {\"input\": \"8 805306367\\nbidek\\ndekhj\\nekhjb\\nhjbid\\nidekh\\njbide\\nkhjbi\\nbide\\n\", \"output\": [\"223759404\", \"223759404\\n\", \"223759404\\n\"]}, {\"input\": \"8 805306365\\ncefdj\\ndjhic\\nefdjh\\nfdjhi\\nhicef\\nicefd\\njhice\\ndjhi\\n\", \"output\": [\"275348811\\n\", \"275348811\", \"275348811\\n\"]}]"}
{"prob_desc_description":"Little Johnny Bubbles enjoys spending hours in front of his computer playing video games. His favorite game is Bubble Strike, fast-paced bubble shooting online game for two players.Each game is set in one of the N maps, each having different terrain configuration. First phase of each game decides on which map the game will be played. The game system randomly selects three maps and shows them to the players. Each player must pick one of those three maps to be discarded. The game system then randomly selects one of the maps that were not picked by any of the players and starts the game.Johnny is deeply enthusiastic about the game and wants to spend some time studying maps, thus increasing chances to win games played on those maps. However, he also needs to do his homework, so he does not have time to study all the maps. That is why he asked himself the following question: \"What is the minimum number of maps I have to study, so that the probability to play one of those maps is at least $$$P$$$\"?Can you help Johnny find the answer for this question? You can assume Johnny's opponents do not know him, and they will randomly pick maps.","prob_desc_output_spec":"Output contains one integer number \u2013 minimum number of maps Johnny has to study.","lang_cluster":"","src_uid":"788ed59a964264bd0e755e155a37e14d","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["combinatorics","binary search","ternary search","probabilities","math"],"prob_desc_created_at":"1633770300","prob_desc_sample_inputs":"[\"7 1.0000\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":2000.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"0.5 seconds","prob_desc_input_spec":"The first line contains two integers $$$N$$$ ($$$3$$$ $$$\\leq$$$ $$$N$$$ $$$\\leq$$$ $$$10^{3}$$$) and $$$P$$$ ($$$0$$$ $$$\\leq$$$ $$$P$$$ $$$\\leq$$$ $$$1$$$) \u2013 total number of maps in the game and probability to play map Johnny has studied. $$$P$$$ will have at most four digits after the decimal point.","prob_desc_sample_outputs":"[\"6\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"7 1.0000\\n\", \"output\": [\"6\", \"6\\n\", \"6 \\n\", \"6\\n\\n\"]}, {\"input\": \"3 0.0000\\n\", \"output\": [\"0\\n\\n\", \"0\\n\", \"0\", \"0 \\n\"]}, {\"input\": \"3 1.0000\\n\", \"output\": [\"2\\n\", \"2\\n\\n\", \"2\", \"2 \\n\"]}, {\"input\": \"1000 0.0000\\n\", \"output\": [\"0\\n\\n\", \"0\\n\", \"0\", \"0 \\n\"]}, {\"input\": \"1000 1.0000\\n\", \"output\": [\"999\\n\\n\", \"999\\n\", \"999\", \"999 \\n\"]}, {\"input\": \"999 1.0000\\n\", \"output\": [\"998\\n\", \"998 \\n\", \"998\", \"998\\n\\n\"]}, {\"input\": \"38 0.2356\\n\", \"output\": [\"6\", \"6\\n\", \"6 \\n\", \"6\\n\\n\"]}, {\"input\": \"217 0.0744\\n\", \"output\": [\"11\", \"11\\n\", \"11 \\n\", \"11\\n\\n\"]}, {\"input\": \"847 0.3600\\n\", \"output\": [\"208 \\n\", \"208\", \"208\\n\\n\", \"208\\n\"]}, {\"input\": \"357 0.9853\\n\", \"output\": [\"321\", \"321\\n\", \"321 \\n\", \"321\\n\\n\"]}, {\"input\": \"440 0.9342\\n\", \"output\": [\"344 \\n\", \"344\\n\\n\", \"344\", \"344\\n\"]}, {\"input\": \"848 0.8576\\n\", \"output\": [\"571 \\n\", \"571\\n\\n\", \"571\", \"571\\n\"]}, {\"input\": \"141 0.0086\\n\", \"output\": [\"1\\n\\n\", \"1\", \"1\\n\", \"1 \\n\"]}, {\"input\": \"517 0.4859\\n\", \"output\": [\"174\\n\", \"174\\n\\n\", \"174\", \"174 \\n\"]}, {\"input\": \"937 0.8022\\n\", \"output\": [\"573\", \"573\\n\", \"573\\n\\n\", \"573 \\n\"]}, {\"input\": \"995 0.4480\\n\", \"output\": [\"307\\n\", \"307\", \"307\\n\\n\", \"307 \\n\"]}, {\"input\": \"956 0.9733\\n\", \"output\": [\"826\", \"826\\n\\n\", \"826\\n\", \"826 \\n\"]}, {\"input\": \"634 0.7906\\n\", \"output\": [\"380\\n\\n\", \"380\\n\", \"380\", \"380 \\n\"]}, {\"input\": \"439 0.0404\\n\", \"output\": [\"12\\n\\n\", \"12\", \"12\\n\", \"12 \\n\"]}, {\"input\": \"853 0.0684\\n\", \"output\": [\"39 \\n\", \"39\", \"39\\n\", \"39\\n\\n\"]}, {\"input\": \"716 0.9851\\n\", \"output\": [\"643 \\n\", \"643\\n\\n\", \"643\", \"643\\n\"]}, {\"input\": \"444 0.0180\\n\", \"output\": [\"6\", \"6\\n\", \"6 \\n\", \"6\\n\\n\"]}, {\"input\": \"840 0.5672\\n\", \"output\": [\"336\", \"336 \\n\", \"336\\n\\n\", \"336\\n\"]}, {\"input\": \"891 0.6481\\n\", \"output\": [\"415\\n\", \"415 \\n\", \"415\", \"415\\n\\n\"]}, {\"input\": \"588 0.3851\\n\", \"output\": [\"155 \\n\", \"155\", \"155\\n\", \"155\\n\\n\"]}, {\"input\": \"444 0.0265\\n\", \"output\": [\"8\", \"8\\n\", \"8 \\n\", \"8\\n\\n\"]}, {\"input\": \"504 0.2099\\n\", \"output\": [\"71\", \"71\\n\", \"71\\n\\n\", \"71 \\n\"]}, {\"input\": \"195 0.5459\\n\", \"output\": [\"75\", \"75\\n\\n\", \"75 \\n\", \"75\\n\"]}, {\"input\": \"566 0.6282\\n\", \"output\": [\"254\\n\", \"254\", \"254 \\n\", \"254\\n\\n\"]}, {\"input\": \"200 0.9495\\n\", \"output\": [\"162\", \"162\\n\\n\", \"162\\n\", \"162 \\n\"]}, {\"input\": \"571 0.5208\\n\", \"output\": [\"208 \\n\", \"208\", \"208\\n\\n\", \"208\\n\"]}, {\"input\": \"622 0.8974\\n\", \"output\": [\"452\\n\", \"452 \\n\", \"452\", \"452\\n\\n\"]}, {\"input\": \"267 0.4122\\n\", \"output\": [\"76\", \"76 \\n\", \"76\\n\", \"76\\n\\n\"]}, {\"input\": \"364 0.3555\\n\", \"output\": [\"88\\n\\n\", \"88 \\n\", \"88\\n\", \"88\"]}, {\"input\": \"317 0.2190\\n\", \"output\": [\"47\", \"47\\n\\n\", \"47\\n\", \"47 \\n\"]}, {\"input\": \"329 0.5879\\n\", \"output\": [\"137\\n\", \"137 \\n\", \"137\\n\\n\", \"137\"]}]"}
{"prob_desc_description":"You are given an undirected graph consisting of $$$n$$$ vertices and $$$m$$$ edges. Initially there is a single integer written on every vertex: the vertex $$$i$$$ has $$$p_i$$$ written on it. All $$$p_i$$$ are distinct integers from $$$1$$$ to $$$n$$$.You have to process $$$q$$$ queries of two types:  $$$1$$$ $$$v$$$ \u2014 among all vertices reachable from the vertex $$$v$$$ using the edges of the graph (including the vertex $$$v$$$ itself), find a vertex $$$u$$$ with the largest number $$$p_u$$$ written on it, print $$$p_u$$$ and replace $$$p_u$$$ with $$$0$$$;  $$$2$$$ $$$i$$$ \u2014 delete the $$$i$$$-th edge from the graph.  Note that, in a query of the first type, it is possible that all vertices reachable from $$$v$$$ have $$$0$$$ written on them. In this case, $$$u$$$ is not explicitly defined, but since the selection of $$$u$$$ does not affect anything, you can choose any vertex reachable from $$$v$$$ and print its value (which is $$$0$$$). ","prob_desc_output_spec":"For every query of the first type, print the value of $$$p_u$$$ written on the chosen vertex $$$u$$$.","lang_cluster":"","src_uid":"ad014bde729222db14f38caa521e4167","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["trees","data structures","graphs","dsu","implementation"],"prob_desc_created_at":"1601219100","prob_desc_sample_inputs":"[\"5 4 6\\n1 2 5 4 3\\n1 2\\n2 3\\n1 3\\n4 5\\n1 1\\n2 1\\n2 3\\n1 1\\n1 2\\n1 2\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":2600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1.5 seconds","prob_desc_input_spec":"The first line contains three integers $$$n$$$, $$$m$$$ and $$$q$$$ ($$$1 \\le n \\le 2 \\cdot 10^5$$$; $$$1 \\le m \\le 3 \\cdot 10^5$$$; $$$1 \\le q \\le 5 \\cdot 10^5$$$). The second line contains $$$n$$$ distinct integers $$$p_1$$$, $$$p_2$$$, ..., $$$p_n$$$, where $$$p_i$$$ is the number initially written on vertex $$$i$$$ ($$$1 \\le p_i \\le n$$$). Then $$$m$$$ lines follow, the $$$i$$$-th of them contains two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \\le a_i, b_i \\le n$$$, $$$a_i \\ne b_i$$$) and means that the $$$i$$$-th edge connects vertices $$$a_i$$$ and $$$b_i$$$. It is guaranteed that the graph does not contain multi-edges. Then $$$q$$$ lines follow, which describe the queries. Each line is given by one of the following formats:   $$$1$$$ $$$v$$$ \u2014 denotes a query of the first type with a vertex $$$v$$$ ($$$1 \\le v \\le n$$$).  $$$2$$$ $$$i$$$ \u2014 denotes a query of the second type with an edge $$$i$$$ ($$$1 \\le i \\le m$$$). For each query of the second type, it is guaranteed that the corresponding edge is not deleted from the graph yet. ","prob_desc_sample_outputs":"[\"5\\n1\\n2\\n0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"5 4 6\\r\\n1 2 5 4 3\\r\\n1 2\\r\\n2 3\\r\\n1 3\\r\\n4 5\\r\\n1 1\\r\\n2 1\\r\\n2 3\\r\\n1 1\\r\\n1 2\\r\\n1 2\\r\\n\", \"output\": [\"5\\r\\n1\\r\\n2\\r\\n0\"]}, {\"input\": \"6 5 8\\r\\n1 2 6 3 4 5\\r\\n2 4\\r\\n1 3\\r\\n1 6\\r\\n3 5\\r\\n2 5\\r\\n1 1\\r\\n1 4\\r\\n1 1\\r\\n2 1\\r\\n2 5\\r\\n2 2\\r\\n2 3\\r\\n1 4\\r\\n\", \"output\": [\"6\\r\\n5\\r\\n4\\r\\n3\"]}, {\"input\": \"9 5 14\\r\\n7 1 4 8 5 2 6 9 3\\r\\n2 8\\r\\n1 6\\r\\n5 7\\r\\n1 3\\r\\n3 9\\r\\n1 5\\r\\n1 8\\r\\n1 5\\r\\n1 4\\r\\n1 8\\r\\n1 3\\r\\n1 5\\r\\n1 5\\r\\n1 7\\r\\n1 7\\r\\n2 3\\r\\n1 2\\r\\n1 1\\r\\n1 2\\r\\n\", \"output\": [\"6\\r\\n9\\r\\n5\\r\\n8\\r\\n1\\r\\n7\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n4\\r\\n0\"]}, {\"input\": \"96 141 151\\r\\n94 95 96 15 36 76 48 59 46 34 6 39 43 2 54 64 71 91 18 3 79 50 89 61 40 88 51 67 37 52 41 30 29 8 55 26 9 14 82 17 63 19 56 74 87 31 5 38 60 10 66 83 35 62 1 77 90 68 24 70 23 22 13 7 45 4 20 53 32 78 73 86 11 85 72 21 28 42 44 57 93 75 92 80 47 12 33 16 84 58 69 25 81 65 27 49\\r\\n18 43\\r\\n31 68\\r\\n12 47\\r\\n41 46\\r\\n18 29\\r\\n7 70\\r\\n72 86\\r\\n46 90\\r\\n84 93\\r\\n26 69\\r\\n54 68\\r\\n48 61\\r\\n49 80\\r\\n10 46\\r\\n14 85\\r\\n77 88\\r\\n10 28\\r\\n20 56\\r\\n49 57\\r\\n7 40\\r\\n4 54\\r\\n35 80\\r\\n32 67\\r\\n16 61\\r\\n24 83\\r\\n20 94\\r\\n58 66\\r\\n67 72\\r\\n3 35\\r\\n70 85\\r\\n39 78\\r\\n63 79\\r...\", \"output\": [\"96\\r\\n95\\r\\n94\\r\\n93\\r\\n92\\r\\n91\\r\\n90\\r\\n89\\r\\n88\\r\\n87\\r\\n86\\r\\n85\\r\\n84\\r\\n83\\r\\n82\\r\\n81\\r\\n80\\r\\n79\\r\\n78\\r\\n77\\r\\n75\\r\\n74\\r\\n73\\r\\n72\\r\\n71\\r\\n70\\r\\n69\\r\\n68\\r\\n67\\r\\n66\\r\\n65\\r\\n64\\r\\n40\\r\\n63\\r\\n62\\r\\n60\\r\\n59\\r\\n58\\r\\n57\\r\\n56\\r\\n55\\r\\n54\\r\\n53\\r\\n51\\r\\n50\\r\\n61\\r\\n49\\r\\n48\\r\\n47\\r\\n46\\r\\n45\\r\\n44\\r\\n43\\r\\n42\\r\\n41\\r\\n39\\r\\n38\\r\\n37\\r\\n36\\r\\n35\\r\\n34\\r\\n33\\r\\n32\\r\\n31\\r\\n30\\r\\n0\\r\\n29\\r\\n28\\r\\n0\\r\\n26\\r\\n25\\r\\n17\\r\\n52\\r\\n0\\r\\n24\\r\\n20\\r\\n18\\r\\n16\\r\\n15\\r\\n14\\r\\n10\"]}, {\"input\": \"95 135 175\\r\\n65 40 61 17 58 55 77 84 79 27 35 54 87 36 25 2 45 43 63 34 89 15 49 60 42 20 10 9 7 38 5 74 52 16 56 14 6 29 53 57 46 78 28 95 8 72 32 50 85 66 62 4 13 3 19 39 48 41 33 31 70 37 1 64 44 51 18 94 83 82 11 23 21 47 22 30 24 75 92 93 88 76 80 59 91 67 12 69 81 71 68 90 26 73 86\\r\\n39 74\\r\\n6 32\\r\\n78 81\\r\\n43 93\\r\\n71 79\\r\\n59 77\\r\\n31 49\\r\\n29 88\\r\\n22 56\\r\\n5 70\\r\\n39 46\\r\\n53 58\\r\\n17 19\\r\\n18 64\\r\\n11 67\\r\\n14 69\\r\\n72 80\\r\\n18 40\\r\\n5 60\\r\\n6 80\\r\\n5 45\\r\\n63 83\\r\\n8 55\\r\\n79 93\\r\\n65 91\\r\\n15 67\\r\\n6 23\\r\\n21 68\\r\\n57 84\\r\\n24 85\\r\\n19 85\\r\\n51 67\\r\\n11 69...\", \"output\": [\"95\\r\\n94\\r\\n93\\r\\n92\\r\\n91\\r\\n90\\r\\n89\\r\\n88\\r\\n87\\r\\n86\\r\\n85\\r\\n84\\r\\n83\\r\\n82\\r\\n81\\r\\n80\\r\\n61\\r\\n79\\r\\n78\\r\\n77\\r\\n75\\r\\n74\\r\\n73\\r\\n72\\r\\n71\\r\\n70\\r\\n69\\r\\n68\\r\\n67\\r\\n76\\r\\n66\\r\\n65\\r\\n64\\r\\n63\\r\\n62\\r\\n59\\r\\n58\\r\\n0\\r\\n57\\r\\n56\\r\\n0\\r\\n55\\r\\n54\\r\\n53\\r\\n52\\r\\n51\\r\\n50\\r\\n49\\r\\n4\\r\\n41\\r\\n60\\r\\n3\\r\\n48\\r\\n47\\r\\n46\\r\\n45\\r\\n0\\r\\n0\\r\\n44\\r\\n15\\r\\n8\\r\\n0\\r\\n43\\r\\n42\\r\\n25\\r\\n40\\r\\n36\\r\\n34\\r\\n0\\r\\n35\\r\\n5\\r\\n39\\r\\n33\\r\\n0\\r\\n32\\r\\n0\\r\\n30\\r\\n0\\r\\n28\\r\\n29\\r\\n0\\r\\n27\\r\\n26\\r\\n24\\r\\n0\\r\\n20\\r\\n0\\r\\n0\\r\\n16\\r\\n9\\r\\n0\\r\\n0\\r\\n12\\r\\n0\"]}, {\"input\": \"95 136 190\\r\\n43 38 21 83 75 16 90 31 17 2 30 50 11 9 19 48 32 88 58 60 62 53 85 82 78 12 79 47 94 63 33 7 95 35 52 69 40 64 74 10 1 56 3 71 37 92 27 67 13 29 6 46 51 65 39 61 23 72 14 87 20 91 93 84 73 57 68 8 41 42 80 26 54 70 18 66 45 86 5 4 55 89 15 49 59 81 24 34 44 36 25 76 77 22 28\\r\\n35 48\\r\\n30 55\\r\\n57 64\\r\\n35 95\\r\\n60 90\\r\\n47 74\\r\\n7 28\\r\\n26 85\\r\\n37 91\\r\\n26 42\\r\\n12 83\\r\\n33 36\\r\\n24 88\\r\\n54 78\\r\\n62 86\\r\\n2 39\\r\\n62 93\\r\\n33 48\\r\\n41 80\\r\\n40 88\\r\\n91 94\\r\\n60 94\\r\\n55 87\\r\\n51 69\\r\\n48 93\\r\\n48 78\\r\\n13 79\\r\\n22 78\\r\\n38 91\\r\\n69 74\\r\\n64 90\\r\\n19 81\\r\\n...\", \"output\": [\"95\\r\\n94\\r\\n93\\r\\n92\\r\\n91\\r\\n90\\r\\n89\\r\\n88\\r\\n87\\r\\n78\\r\\n86\\r\\n85\\r\\n75\\r\\n84\\r\\n83\\r\\n82\\r\\n81\\r\\n80\\r\\n79\\r\\n77\\r\\n76\\r\\n74\\r\\n73\\r\\n48\\r\\n72\\r\\n71\\r\\n70\\r\\n68\\r\\n67\\r\\n66\\r\\n65\\r\\n64\\r\\n4\\r\\n63\\r\\n62\\r\\n61\\r\\n60\\r\\n58\\r\\n57\\r\\n56\\r\\n0\\r\\n69\\r\\n1\\r\\n55\\r\\n54\\r\\n53\\r\\n52\\r\\n51\\r\\n42\\r\\n50\\r\\n44\\r\\n49\\r\\n47\\r\\n45\\r\\n43\\r\\n0\\r\\n41\\r\\n46\\r\\n0\\r\\n40\\r\\n39\\r\\n37\\r\\n36\\r\\n0\\r\\n17\\r\\n14\\r\\n7\\r\\n34\\r\\n32\\r\\n6\\r\\n25\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n30\\r\\n2\\r\\n27\\r\\n38\\r\\n22\\r\\n20\\r\\n0\\r\\n0\\r\\n18\\r\\n0\\r\\n11\\r\\n29\\r\\n21\\r\\n3\\r\\n28\\r\\n0\\r\\n0\"]}, {\"input\": \"199998 299995 500000\\r\\n153412 35198 17343 46228 6928 75192 114464 157343 77601 124480 35526 8250 159607 117598 127301 14907 142148 113646 9279 13964 100293 191098 67767 174884 195356 172276 148583 67937 76083 62111 74204 157877 6258 199948 110132 73279 133863 66457 141633 37349 102702 136082 172280 171155 107690 146380 79248 79444 90312 12813 111262 18340 130380 22636 47489 123750 92754 120437 132649 184554 120382 8761 70744 7602 161965 191117 148929 165312 41648 33800 30457 185926 175425 90428 162843 62284...\", \"output\": [\"199998\\r\\n199997\\r\\n199996\\r\\n199995\\r\\n199994\\r\\n199993\\r\\n199992\\r\\n199991\\r\\n199990\\r\\n199989\\r\\n199988\\r\\n199987\\r\\n199986\\r\\n199985\\r\\n199984\\r\\n199983\\r\\n199982\\r\\n199981\\r\\n199980\\r\\n199979\\r\\n199978\\r\\n199977\\r\\n199976\\r\\n199975\\r\\n199974\\r\\n199973\\r\\n199972\\r\\n199971\\r\\n199970\\r\\n199969\\r\\n199968\\r\\n199967\\r\\n199966\\r\\n199965\\r\\n199964\\r\\n199963\\r\\n199962\\r\\n199961\\r\\n199960\\r\\n199959\\r\\n199958\\r\\n199957\\r\\n199956\\r\\n199955\\r\\n199954\\r\\n199953\\r\\n199952\\r\\n199951\\r\\n199950\\r\\n199949\\r\\n199948\\r\\n199947\\r\\n199946\\r\\n199945\\r\\n199944\\r\\n199943\\r\\n199942\\r\\n199941\\r\\n199940\\r\\n199939\\r\\n199938\\r\\n199937\\r\\n199936\\r\\n199935\\r...\"]}, {\"input\": \"199996 299992 500000\\r\\n134969 119070 62268 75542 161097 173429 45635 151168 19946 135122 74875 134424 31874 37302 79901 81696 42708 90725 196628 129748 21626 87953 174792 7460 158323 25320 68197 47874 14595 3536 14822 189176 199180 69986 20660 66406 31439 93214 26489 119279 158389 102844 118926 25739 118514 167586 111517 57976 166780 197301 88273 39379 137688 76319 110925 23009 54749 142749 137334 179650 188691 154104 59776 71041 164658 111663 167798 66632 13396 119714 175605 19059 63569 50549 84981 113073 ...\", \"output\": [\"199996\\r\\n199995\\r\\n199994\\r\\n199993\\r\\n199992\\r\\n199991\\r\\n199990\\r\\n199989\\r\\n199988\\r\\n199987\\r\\n199986\\r\\n199985\\r\\n199984\\r\\n199983\\r\\n199982\\r\\n199981\\r\\n199980\\r\\n199979\\r\\n199978\\r\\n199977\\r\\n199976\\r\\n199975\\r\\n199974\\r\\n199973\\r\\n199972\\r\\n199971\\r\\n199970\\r\\n199969\\r\\n199968\\r\\n199967\\r\\n199966\\r\\n199965\\r\\n199964\\r\\n199963\\r\\n199962\\r\\n199961\\r\\n199960\\r\\n199959\\r\\n199958\\r\\n199957\\r\\n199956\\r\\n199955\\r\\n199954\\r\\n199953\\r\\n199952\\r\\n199951\\r\\n199950\\r\\n199949\\r\\n199948\\r\\n199947\\r\\n199946\\r\\n199945\\r\\n199944\\r\\n199943\\r\\n199942\\r\\n199941\\r\\n199940\\r\\n199939\\r\\n199938\\r\\n199937\\r\\n199936\\r\\n199935\\r\\n199934\\r\\n199933\\r...\"]}, {\"input\": \"200000 299998 500000\\r\\n63954 186266 141361 37431 119610 97083 85069 51029 71720 199562 148270 183111 93287 197272 132986 184628 76678 9926 112644 103293 26006 181326 94392 74861 7606 154319 81537 92058 167401 118222 60803 160416 97000 89617 128732 168038 98960 100507 31036 143779 400 182663 119262 45751 79146 87393 41734 105835 160167 168566 161531 94869 60050 54311 196202 98422 78561 168636 107719 154079 115735 44228 42704 151318 58277 191724 76745 93644 117287 4387 41455 178742 194641 151300 171235 131516...\", \"output\": [\"200000\\r\\n199999\\r\\n199998\\r\\n199997\\r\\n199996\\r\\n199995\\r\\n199994\\r\\n199993\\r\\n199992\\r\\n199991\\r\\n199990\\r\\n199989\\r\\n199988\\r\\n199987\\r\\n199986\\r\\n199985\\r\\n199984\\r\\n199983\\r\\n199982\\r\\n199981\\r\\n199980\\r\\n199979\\r\\n199978\\r\\n199977\\r\\n199976\\r\\n199975\\r\\n199974\\r\\n199973\\r\\n199972\\r\\n199971\\r\\n199970\\r\\n199969\\r\\n199968\\r\\n199967\\r\\n199966\\r\\n199965\\r\\n199964\\r\\n199963\\r\\n199962\\r\\n199961\\r\\n199960\\r\\n199959\\r\\n199958\\r\\n199957\\r\\n199956\\r\\n199955\\r\\n199954\\r\\n199953\\r\\n199952\\r\\n199951\\r\\n199950\\r\\n199949\\r\\n199948\\r\\n199947\\r\\n199946\\r\\n199945\\r\\n199944\\r\\n199943\\r\\n199942\\r\\n199941\\r\\n199940\\r\\n199939\\r\\n199938\\r\\n199937\\r...\"]}, {\"input\": \"199998 299996 500000\\r\\n181007 145459 43706 122329 124404 59328 176095 51696 41499 43811 45123 82905 195328 80344 20782 102980 158516 166155 38254 6195 9192 21696 168146 166868 93724 127345 21765 81568 173820 158620 52734 168654 44342 80483 184804 79826 79596 144292 87781 155604 188568 20602 81604 101679 128809 27347 124214 194856 47065 54059 40486 79412 95100 93384 59132 156771 186347 187589 17444 35503 44710 176266 63308 159420 48713 151645 79239 191000 28002 112544 63362 50622 6545 153038 120370 80215 190...\", \"output\": 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{"prob_desc_description":"Andrey thinks he is truly a successful developer, but in reality he didn't know about the binary search algorithm until recently. After reading some literature Andrey understood that this algorithm allows to quickly find a certain number $$$x$$$ in an array. For an array $$$a$$$ indexed from zero, and an integer $$$x$$$ the pseudocode of the algorithm is as follows:  Note that the elements of the array are indexed from zero, and the division is done in integers (rounding down).Andrey read that the algorithm only works if the array is sorted. However, he found this statement untrue, because there certainly exist unsorted arrays for which the algorithm find $$$x$$$!Andrey wants to write a letter to the book authors, but before doing that he must consider the permutations of size $$$n$$$ such that the algorithm finds $$$x$$$ in them. A permutation of size $$$n$$$ is an array consisting of $$$n$$$ distinct integers between $$$1$$$ and $$$n$$$ in arbitrary order.Help Andrey and find the number of permutations of size $$$n$$$ which contain $$$x$$$ at position $$$pos$$$ and for which the given implementation of the binary search algorithm finds $$$x$$$ (returns true). As the result may be extremely large, print the remainder of its division by $$$10^9+7$$$.","prob_desc_output_spec":"Print a single number\u00a0\u2014 the remainder of the division of the number of valid permutations by $$$10^9+7$$$.","lang_cluster":"","src_uid":"24e2f10463f440affccc2755f4462d8a","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["combinatorics","binary search"],"prob_desc_created_at":"1603548300","prob_desc_sample_inputs":"[\"4 1 2\", \"123 42 24\"]","prob_desc_notes":"NoteAll possible permutations in the first test case: $$$(2, 3, 1, 4)$$$, $$$(2, 4, 1, 3)$$$, $$$(3, 2, 1, 4)$$$, $$$(3, 4, 1, 2)$$$, $$$(4, 2, 1, 3)$$$, $$$(4, 3, 1, 2)$$$.","exec_outcome":"","difficulty":1500.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The only line of input contains integers $$$n$$$, $$$x$$$ and $$$pos$$$ ($$$1 \\le x \\le n \\le 1000$$$, $$$0 \\le pos \\le n - 1$$$) \u2014 the required length of the permutation, the number to search, and the required position of that number, respectively.","prob_desc_sample_outputs":"[\"6\", \"824071958\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4 1 2\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"123 42 24\\r\\n\", \"output\": [\"824071958\"]}, {\"input\": \"1 1 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1000 501 501\\r\\n\", \"output\": [\"646597996\"]}, {\"input\": \"1000 999 799\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 2 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 1 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 2 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 3 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 2 0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 3 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 4 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"7 1 1\\r\\n\", \"output\": [\"720\"]}, {\"input\": \"7 7 6\\r\\n\", \"output\": [\"720\"]}, {\"input\": \"7 2 4\\r\\n\", \"output\": [\"120\"]}, {\"input\": \"7 4 4\\r\\n\", \"output\": [\"216\"]}, {\"input\": \"8 4 1\\r\\n\", \"output\": [\"1440\"]}, {\"input\": \"8 1 5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"8 8 7\\r\\n\", \"output\": [\"5040\"]}, {\"input\": \"8 7 6\\r\\n\", \"output\": [\"720\"]}, {\"input\": \"8 3 0\\r\\n\", \"output\": [\"1440\"]}, {\"input\": \"9 1 7\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"9 9 5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"9 5 5\\r\\n\", \"output\": [\"5760\"]}, {\"input\": \"9 4 4\\r\\n\", \"output\": [\"7200\"]}, {\"input\": \"9 3 3\\r\\n\", \"output\": [\"8640\"]}, {\"input\": \"10 1 1\\r\\n\", \"output\": [\"362880\"]}, {\"input\": \"10 10 9\\r\\n\", \"output\": [\"362880\"]}, {\"input\": \"10 5 5\\r\\n\", \"output\": [\"43200\"]}, {\"input\": \"10 3 7\\r\\n\", \"output\": [\"70560\"]}, {\"input\": \"10 4 4\\r\\n\", \"output\": [\"90720\"]}, {\"input\": \"10 6 6\\r\\n\", \"output\": [\"43200\"]}, {\"input\": \"10 7 7\\r\\n\", \"output\": [\"90720\"]}, {\"input\": \"10 9 5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"74 16 54\\r\\n\", \"output\": [\"625981152\"]}, {\"input\": \"63 15 45\\r\\n\", \"output\": [\"581829795\"]}, {\"input\": \"54 4 47\\r\\n\", \"output\": [\"911648281\"]}, {\"input\": \"92 22 62\\r\\n\", \"output\": [\"628152721\"]}, {\"input\": \"82 15 14\\r\\n\", \"output\": [\"187724629\"]}, {\"input\": \"91 60 48\\r\\n\", \"output\": [\"233776714\"]}, {\"input\": \"91 51 5\\r\\n\", \"output\": [\"660447677\"]}, {\"input\": \"70 45 16\\r\\n\", \"output\": [\"578976138\"]}, {\"input\": \"61 21 16\\r\\n\", \"output\": [\"516359078\"]}, {\"input\": \"61 29 15\\r\\n\", \"output\": [\"252758304\"]}, {\"input\": \"69 67 68\\r\\n\", \"output\": [\"736622722\"]}, {\"input\": \"59 40 1\\r\\n\", \"output\": [\"384105577\"]}, {\"input\": \"98 86 39\\r\\n\", \"output\": [\"132656801\"]}, {\"input\": \"97 89 29\\r\\n\", \"output\": [\"673334741\"]}, {\"input\": \"78 66 16\\r\\n\", \"output\": [\"703501645\"]}, {\"input\": \"777 254 720\\r\\n\", \"output\": [\"57449468\"]}, {\"input\": \"908 216 521\\r\\n\", \"output\": [\"601940707\"]}, {\"input\": \"749 158 165\\r\\n\", \"output\": [\"849211382\"]}, {\"input\": \"535 101 250\\r\\n\", \"output\": [\"111877808\"]}, {\"input\": \"665 5 305\\r\\n\", \"output\": [\"400272219\"]}, {\"input\": \"856 406 675\\r\\n\", \"output\": [\"663368144\"]}, {\"input\": \"697 390 118\\r\\n\", \"output\": [\"844062514\"]}, {\"input\": \"539 246 0\\r\\n\", \"output\": [\"410139856\"]}, {\"input\": \"669 380 461\\r\\n\", \"output\": [\"921432102\"]}, {\"input\": \"954 325 163\\r\\n\", \"output\": [\"917113541\"]}, {\"input\": \"646 467 58\\r\\n\", \"output\": [\"214437899\"]}, {\"input\": \"542 427 258\\r\\n\", \"output\": [\"830066531\"]}, {\"input\": \"562 388 191\\r\\n\", \"output\": [\"935998075\"]}, {\"input\": \"958 817 269\\r\\n\", \"output\": [\"513948977\"]}, {\"input\": \"1000 888 888\\r\\n\", \"output\": [\"644649893\"]}, {\"input\": \"1000 2 2\\r\\n\", \"output\": [\"22779421\"]}, {\"input\": \"534 376 180\\r\\n\", \"output\": [\"984450056\"]}, {\"input\": \"1000 1 1\\r\\n\", \"output\": [\"756641425\"]}, {\"input\": \"1000 3 3\\r\\n\", \"output\": [\"606772288\"]}, {\"input\": \"1000 500 500\\r\\n\", \"output\": [\"646597996\"]}, {\"input\": \"1000 1000 999\\r\\n\", \"output\": [\"756641425\"]}, {\"input\": \"1000 501 50\\r\\n\", \"output\": [\"636821580\"]}, {\"input\": \"6 4 3\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"3 2 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"100 5 50\\r\\n\", \"output\": [\"469732450\"]}, {\"input\": \"999 490 499\\r\\n\", \"output\": [\"998308393\"]}, {\"input\": \"7 3 3\\r\\n\", \"output\": [\"288\"]}, {\"input\": \"10 7 5\\r\\n\", \"output\": [\"4320\"]}, {\"input\": \"123 1 24\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5 5 2\\r\\n\", \"output\": [\"0\"]}]"}
{"prob_desc_description":"Today is the final contest of INOI (Iranian National Olympiad in Informatics). The contest room is a row with $$$n$$$ computers. All computers are numbered with integers from $$$1$$$ to $$$n$$$ from left to right. There are $$$m$$$ participants, numbered with integers from $$$1$$$ to $$$m$$$.We have an array $$$a$$$ of length $$$m$$$ where $$$a_{i}$$$ ($$$1 \\leq a_i \\leq n$$$) is the computer behind which the $$$i$$$-th participant wants to sit.Also, we have another array $$$b$$$ of length $$$m$$$ consisting of characters 'L' and 'R'. $$$b_i$$$ is the side from which the $$$i$$$-th participant enters the room. 'L' means the participant enters from the left of computer $$$1$$$ and goes from left to right, and 'R' means the participant enters from the right of computer $$$n$$$ and goes from right to left.The participants in the order from $$$1$$$ to $$$m$$$ enter the room one by one. The $$$i$$$-th of them enters the contest room in the direction $$$b_i$$$ and goes to sit behind the $$$a_i$$$-th computer. If it is occupied he keeps walking in his direction until he reaches the first unoccupied computer. After that, he sits behind it. If he doesn't find any computer he gets upset and gives up on the contest.The madness of the $$$i$$$-th participant is the distance between his assigned computer ($$$a_i$$$) and the computer he ends up sitting behind. The distance between computers $$$i$$$ and $$$j$$$ is equal to $$$|i - j|$$$.The values in the array $$$a$$$ can be equal. There exist $$$n^m \\cdot 2^m$$$ possible pairs of arrays $$$(a, b)$$$.Consider all pairs of arrays $$$(a, b)$$$ such that no person becomes upset. For each of them let's calculate the sum of participants madnesses. Find the sum of all these values.You will be given some prime modulo $$$p$$$. Find this sum by modulo $$$p$$$.","prob_desc_output_spec":"Print only one integer\u00a0\u2014 the required sum by modulo $$$p$$$.","lang_cluster":"","src_uid":"9812de5f2d272511a63ead8765b23190","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["fft","dp","combinatorics"],"prob_desc_created_at":"1605623700","prob_desc_sample_inputs":"[\"3 1 1000000007\", \"2 2 1000000009\", \"3 2 998244353\", \"20 10 1000000009\"]","prob_desc_notes":"NoteIn the first test, there are three possible arrays $$$a$$$: $$$\\{1\\}$$$, $$$\\{2\\}$$$, and $$$ \\{3\\}$$$ and two possible arrays $$$b$$$: $$$\\{\\mathtt{L}\\}$$$ and $$$\\{\\mathtt{R}\\}$$$. For all six pairs of arrays $$$(a, b)$$$, the only participant will sit behind the computer $$$a_1$$$, so his madness will be $$$0$$$. So the total sum of madnesses will be $$$0$$$.In the second test, all possible pairs of arrays $$$(a, b)$$$, such that no person becomes upset are:  $$$(\\{1, 1\\}, \\{\\mathtt{L}, \\mathtt{L}\\})$$$, the sum of madnesses is $$$1$$$;  $$$(\\{1, 1\\}, \\{\\mathtt{R}, \\mathtt{L}\\})$$$, the sum of madnesses is $$$1$$$;  $$$(\\{2, 2\\}, \\{\\mathtt{R}, \\mathtt{R}\\})$$$, the sum of madnesses is $$$1$$$;  $$$(\\{2, 2\\}, \\{\\mathtt{L}, \\mathtt{R}\\})$$$, the sum of madnesses is $$$1$$$;  all possible pairs of $$$a \\in \\{\\{1, 2\\}, \\{2, 1\\}\\}$$$ and $$$b \\in \\{\\{\\mathtt{L}, \\mathtt{L}\\}, \\{\\mathtt{R}, \\mathtt{L}\\}, \\{\\mathtt{L}, \\mathtt{R}\\}, \\{\\mathtt{R}, \\mathtt{R}\\}\\}$$$, the sum of madnesses is $$$0$$$. So, the answer is $$$1 + 1 + 1 + 1 + 0 \\ldots = 4$$$.","exec_outcome":"","difficulty":3100.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"3 seconds","prob_desc_input_spec":"The only line contains three integers $$$n$$$, $$$m$$$, $$$p$$$ ($$$1 \\leq m \\leq n \\leq 500, 10^8 \\leq p \\leq 10 ^ 9 + 9$$$). It is guaranteed, that the number $$$p$$$ is prime.","prob_desc_sample_outputs":"[\"0\", \"4\", \"8\", \"352081045\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3 1 1000000007\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 2 1000000009\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"3 2 998244353\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"20 10 1000000009\\r\\n\", \"output\": [\"352081045\"]}, {\"input\": \"5 2 1000000007\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"500 498 1000000007\\r\\n\", \"output\": [\"497900737\"]}, {\"input\": \"10 9 1000000007\\r\\n\", \"output\": [\"904119416\"]}, {\"input\": \"7 4 1000000009\\r\\n\", \"output\": [\"31488\"]}, {\"input\": \"8 8 700001153\\r\\n\", \"output\": [\"247497204\"]}, {\"input\": \"6 3 999999487\\r\\n\", \"output\": [\"768\"]}, {\"input\": \"310 228 998244799\\r\\n\", \"output\": [\"861313351\"]}, {\"input\": \"385 76 998244353\\r\\n\", \"output\": [\"750286580\"]}, {\"input\": \"259 76 998244353\\r\\n\", \"output\": [\"41310904\"]}, {\"input\": \"459 14 200003077\\r\\n\", \"output\": [\"142997933\"]}, {\"input\": \"1 1 1000000007\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"498 155 998244799\\r\\n\", \"output\": [\"673213318\"]}, {\"input\": \"372 309 1000000009\\r\\n\", \"output\": [\"698627891\"]}, {\"input\": \"44 19 998244799\\r\\n\", \"output\": [\"81944049\"]}, {\"input\": \"70 39 700001153\\r\\n\", \"output\": [\"401935379\"]}, {\"input\": \"282 190 300001657\\r\\n\", \"output\": [\"210852530\"]}, {\"input\": \"370 100 1000000007\\r\\n\", \"output\": [\"112411341\"]}, {\"input\": \"234 21 200003077\\r\\n\", \"output\": [\"137641479\"]}, {\"input\": \"194 184 200003077\\r\\n\", \"output\": [\"76845836\"]}, {\"input\": \"499 497 998244799\\r\\n\", \"output\": [\"514945258\"]}, {\"input\": \"500 117 1000000007\\r\\n\", \"output\": [\"234794832\"]}, {\"input\": \"45 41 200003077\\r\\n\", \"output\": [\"176259818\"]}, {\"input\": \"2 1 1000000007\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 2 1000000007\\r\\n\", \"output\": [\"4\"]}]"}
{"prob_desc_description":"The map of Bertown can be represented as a set of $$$n$$$ intersections, numbered from $$$1$$$ to $$$n$$$ and connected by $$$m$$$ one-way roads. It is possible to move along the roads from any intersection to any other intersection. The length of some path from one intersection to another is the number of roads that one has to traverse along the path. The shortest path from one intersection $$$v$$$ to another intersection $$$u$$$ is the path that starts in $$$v$$$, ends in $$$u$$$ and has the minimum length among all such paths.Polycarp lives near the intersection $$$s$$$ and works in a building near the intersection $$$t$$$. Every day he gets from $$$s$$$ to $$$t$$$ by car. Today he has chosen the following path to his workplace: $$$p_1$$$, $$$p_2$$$, ..., $$$p_k$$$, where $$$p_1 = s$$$, $$$p_k = t$$$, and all other elements of this sequence are the intermediate intersections, listed in the order Polycarp arrived at them. Polycarp never arrived at the same intersection twice, so all elements of this sequence are pairwise distinct. Note that you know Polycarp's path beforehand (it is fixed), and it is not necessarily one of the shortest paths from $$$s$$$ to $$$t$$$.Polycarp's car has a complex navigation system installed in it. Let's describe how it works. When Polycarp starts his journey at the intersection $$$s$$$, the system chooses some shortest path from $$$s$$$ to $$$t$$$ and shows it to Polycarp. Let's denote the next intersection in the chosen path as $$$v$$$. If Polycarp chooses to drive along the road from $$$s$$$ to $$$v$$$, then the navigator shows him the same shortest path (obviously, starting from $$$v$$$ as soon as he arrives at this intersection). However, if Polycarp chooses to drive to another intersection $$$w$$$ instead, the navigator rebuilds the path: as soon as Polycarp arrives at $$$w$$$, the navigation system chooses some shortest path from $$$w$$$ to $$$t$$$ and shows it to Polycarp. The same process continues until Polycarp arrives at $$$t$$$: if Polycarp moves along the road recommended by the system, it maintains the shortest path it has already built; but if Polycarp chooses some other path, the system rebuilds the path by the same rules.Here is an example. Suppose the map of Bertown looks as follows, and Polycarp drives along the path $$$[1, 2, 3, 4]$$$ ($$$s = 1$$$, $$$t = 4$$$): Check the picture by the link http:\/\/tk.codeforces.com\/a.png   When Polycarp starts at $$$1$$$, the system chooses some shortest path from $$$1$$$ to $$$4$$$. There is only one such path, it is $$$[1, 5, 4]$$$;  Polycarp chooses to drive to $$$2$$$, which is not along the path chosen by the system. When Polycarp arrives at $$$2$$$, the navigator rebuilds the path by choosing some shortest path from $$$2$$$ to $$$4$$$, for example, $$$[2, 6, 4]$$$ (note that it could choose $$$[2, 3, 4]$$$);  Polycarp chooses to drive to $$$3$$$, which is not along the path chosen by the system. When Polycarp arrives at $$$3$$$, the navigator rebuilds the path by choosing the only shortest path from $$$3$$$ to $$$4$$$, which is $$$[3, 4]$$$;  Polycarp arrives at $$$4$$$ along the road chosen by the navigator, so the system does not have to rebuild anything. Overall, we get $$$2$$$ rebuilds in this scenario. Note that if the system chose $$$[2, 3, 4]$$$ instead of $$$[2, 6, 4]$$$ during the second step, there would be only $$$1$$$ rebuild (since Polycarp goes along the path, so the system maintains the path $$$[3, 4]$$$ during the third step).The example shows us that the number of rebuilds can differ even if the map of Bertown and the path chosen by Polycarp stays the same. Given this information (the map and Polycarp's path), can you determine the minimum and the maximum number of rebuilds that could have happened during the journey?","prob_desc_output_spec":"Print two integers: the minimum and the maximum number of rebuilds that could have happened during the journey.","lang_cluster":"","src_uid":"19a0c05eb2d1559ccfe60e210c6fcd6a","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"512 megabytes","file_name":"prog_syn_val.jsonl","tags":["shortest paths","graphs"],"prob_desc_created_at":"1583068500","prob_desc_sample_inputs":"[\"6 9\\n1 5\\n5 4\\n1 2\\n2 3\\n3 4\\n4 1\\n2 6\\n6 4\\n4 2\\n4\\n1 2 3 4\", \"7 7\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 1\\n7\\n1 2 3 4 5 6 7\", \"8 13\\n8 7\\n8 6\\n7 5\\n7 4\\n6 5\\n6 4\\n5 3\\n5 2\\n4 3\\n4 2\\n3 1\\n2 1\\n1 8\\n5\\n8 7 5 2 1\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":null,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \\le n \\le m \\le 2 \\cdot 10^5$$$) \u2014 the number of intersections and one-way roads in Bertown, respectively. Then $$$m$$$ lines follow, each describing a road. Each line contains two integers $$$u$$$ and $$$v$$$ ($$$1 \\le u, v \\le n$$$, $$$u \\ne v$$$) denoting a road from intersection $$$u$$$ to intersection $$$v$$$. All roads in Bertown are pairwise distinct, which means that each ordered pair $$$(u, v)$$$ appears at most once in these $$$m$$$ lines (but if there is a road $$$(u, v)$$$, the road $$$(v, u)$$$ can also appear). The following line contains one integer $$$k$$$ ($$$2 \\le k \\le n$$$) \u2014 the number of intersections in Polycarp's path from home to his workplace. The last line contains $$$k$$$ integers $$$p_1$$$, $$$p_2$$$, ..., $$$p_k$$$ ($$$1 \\le p_i \\le n$$$, all these integers are pairwise distinct) \u2014 the intersections along Polycarp's path in the order he arrived at them. $$$p_1$$$ is the intersection where Polycarp lives ($$$s = p_1$$$), and $$$p_k$$$ is the intersection where Polycarp's workplace is situated ($$$t = p_k$$$). It is guaranteed that for every $$$i \\in [1, k - 1]$$$ the road from $$$p_i$$$ to $$$p_{i + 1}$$$ exists, so the path goes along the roads of Bertown. ","prob_desc_sample_outputs":"[\"1 2\", \"0 0\", \"0 3\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"6 9\\r\\n1 5\\r\\n5 4\\r\\n1 2\\r\\n2 3\\r\\n3 4\\r\\n4 1\\r\\n2 6\\r\\n6 4\\r\\n4 2\\r\\n4\\r\\n1 2 3 4\\r\\n\", \"output\": [\"1 2\"]}, {\"input\": \"7 7\\r\\n1 2\\r\\n2 3\\r\\n3 4\\r\\n4 5\\r\\n5 6\\r\\n6 7\\r\\n7 1\\r\\n7\\r\\n1 2 3 4 5 6 7\\r\\n\", \"output\": [\"0 0\"]}, {\"input\": \"8 13\\r\\n8 7\\r\\n8 6\\r\\n7 5\\r\\n7 4\\r\\n6 5\\r\\n6 4\\r\\n5 3\\r\\n5 2\\r\\n4 3\\r\\n4 2\\r\\n3 1\\r\\n2 1\\r\\n1 8\\r\\n5\\r\\n8 7 5 2 1\\r\\n\", \"output\": [\"0 3\"]}, {\"input\": \"20 50\\r\\n2 3\\r\\n18 10\\r\\n11 6\\r\\n11 1\\r\\n18 17\\r\\n18 7\\r\\n15 20\\r\\n6 11\\r\\n11 2\\r\\n8 2\\r\\n14 2\\r\\n20 1\\r\\n1 19\\r\\n17 2\\r\\n5 17\\r\\n15 17\\r\\n19 12\\r\\n16 9\\r\\n12 4\\r\\n19 2\\r\\n2 19\\r\\n14 3\\r\\n6 5\\r\\n20 19\\r\\n2 16\\r\\n1 12\\r\\n2 12\\r\\n9 2\\r\\n13 18\\r\\n2 13\\r\\n10 4\\r\\n12 8\\r\\n12 3\\r\\n17 5\\r\\n18 12\\r\\n18 11\\r\\n2 17\\r\\n6 20\\r\\n19 20\\r\\n7 9\\r\\n3 2\\r\\n19 15\\r\\n10 20\\r\\n13 12\\r\\n4 3\\r\\n18 15\\r\\n13 9\\r\\n2 11\\r\\n19 14\\r\\n16 11\\r\\n8\\r\\n18 10 4 3 2 19 12 8\\r\\n\", \"output\": [\"3 3\"]}, {\"input\": \"20 50\\r\\n20 3\\r\\n5 16\\r\\n1 3\\r\\n10 11\\r\\n10 15\\r\\n15 9\\r\\n20 9\\r\\n14 6\\r\\n16 5\\r\\n13 4\\r\\n11 5\\r\\n3 20\\r\\n13 17\\r\\n11 8\\r\\n11 6\\r\\n12 14\\r\\n16 18\\r\\n17 13\\r\\n18 7\\r\\n3 1\\r\\n8 10\\r\\n17 15\\r\\n7 2\\r\\n9 13\\r\\n5 11\\r\\n6 1\\r\\n2 16\\r\\n8 18\\r\\n10 8\\r\\n4 13\\r\\n9 15\\r\\n14 12\\r\\n1 6\\r\\n9 20\\r\\n7 18\\r\\n6 14\\r\\n7 6\\r\\n18 16\\r\\n2 7\\r\\n3 11\\r\\n15 17\\r\\n3 12\\r\\n14 10\\r\\n4 14\\r\\n19 4\\r\\n11 10\\r\\n4 19\\r\\n8 12\\r\\n17 8\\r\\n12 8\\r\\n16\\r\\n7 2 16 5 11 8 10 15 9 13 4 14 6 1 3 20\\r\\n\", \"output\": [\"5 8\"]}, {\"input\": \"200000 200000\\r\\n136681 174056\\r\\n15423 127122\\r\\n137672 18542\\r\\n61006 42559\\r\\n100993 75825\\r\\n127154 78864\\r\\n45846 107290\\r\\n90566 138733\\r\\n14816 162076\\r\\n103420 129914\\r\\n114282 76956\\r\\n84055 109451\\r\\n60410 98835\\r\\n87450 128443\\r\\n88089 53597\\r\\n17504 29650\\r\\n191714 90663\\r\\n123767 131600\\r\\n159335 5416\\r\\n50211 165717\\r\\n155480 122795\\r\\n114778 79131\\r\\n160130 30508\\r\\n122082 161582\\r\\n84675 57923\\r\\n160533 123470\\r\\n104475 154615\\r\\n71811 66321\\r\\n146618 29051\\r\\n9884 148531\\r\\n174343 136606\\r\\n12006 184589\\r\\n90277 132097\\r\\n36794 103218\\r\\n2543 158399\\r\\n31228 8...\", \"output\": [\"0 0\"]}, {\"input\": \"100000 200000\\r\\n99425 19372\\r\\n65894 49823\\r\\n46049 81197\\r\\n47047 88322\\r\\n27333 52675\\r\\n17577 47048\\r\\n37090 87556\\r\\n57515 38881\\r\\n68912 15728\\r\\n87086 45332\\r\\n96140 96168\\r\\n91687 85568\\r\\n35009 99210\\r\\n70897 52531\\r\\n1665 83360\\r\\n43728 59264\\r\\n4310 31016\\r\\n12521 45397\\r\\n88644 57610\\r\\n89520 60896\\r\\n74367 87421\\r\\n40373 75625\\r\\n4086 28966\\r\\n89659 97328\\r\\n11690 28936\\r\\n63889 64887\\r\\n65444 78523\\r\\n4094 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{"prob_desc_description":"Makoto has a big blackboard with a positive integer $$$n$$$ written on it. He will perform the following action exactly $$$k$$$ times:Suppose the number currently written on the blackboard is $$$v$$$. He will randomly pick one of the divisors of $$$v$$$ (possibly $$$1$$$ and $$$v$$$) and replace $$$v$$$ with this divisor. As Makoto uses his famous random number generator (RNG) and as he always uses $$$58$$$ as his generator seed, each divisor is guaranteed to be chosen with equal probability.He now wonders what is the expected value of the number written on the blackboard after $$$k$$$ steps.It can be shown that this value can be represented as $$$\\frac{P}{Q}$$$ where $$$P$$$ and $$$Q$$$ are coprime integers and $$$Q \\not\\equiv 0 \\pmod{10^9+7}$$$. Print the value of $$$P \\cdot Q^{-1}$$$ modulo $$$10^9+7$$$.","prob_desc_output_spec":"Print a single integer \u2014 the expected value of the number on the blackboard after $$$k$$$ steps as $$$P \\cdot Q^{-1} \\pmod{10^9+7}$$$ for $$$P$$$, $$$Q$$$ defined above.","lang_cluster":"","src_uid":"dc466d9c24b7dcb37c0e99337b4124d2","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","number theory","probabilities","dp"],"prob_desc_created_at":"1546613100","prob_desc_sample_inputs":"[\"6 1\", \"6 2\", \"60 5\"]","prob_desc_notes":"NoteIn the first example, after one step, the number written on the blackboard is $$$1$$$, $$$2$$$, $$$3$$$ or $$$6$$$ \u2014 each occurring with equal probability. Hence, the answer is $$$\\frac{1+2+3+6}{4}=3$$$.In the second example, the answer is equal to $$$1 \\cdot \\frac{9}{16}+2 \\cdot \\frac{3}{16}+3 \\cdot \\frac{3}{16}+6 \\cdot \\frac{1}{16}=\\frac{15}{8}$$$.","exec_outcome":"","difficulty":2200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The only line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\leq n \\leq 10^{15}$$$, $$$1 \\leq k \\leq 10^4$$$).","prob_desc_sample_outputs":"[\"3\", \"875000008\", \"237178099\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"6 1\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"6 2\\r\\n\", \"output\": [\"875000008\"]}, {\"input\": \"60 5\\r\\n\", \"output\": [\"237178099\"]}, {\"input\": \"2 4\\r\\n\", \"output\": [\"562500005\"]}, {\"input\": \"12 3\\r\\n\", \"output\": [\"775462970\"]}, {\"input\": \"55 5\\r\\n\", \"output\": [\"789062507\"]}, {\"input\": \"935 9\\r\\n\", \"output\": [\"658825880\"]}, {\"input\": \"1 10000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"120 1\\r\\n\", \"output\": [\"500000026\"]}, {\"input\": \"1000000000000000 10000\\r\\n\", \"output\": [\"215514159\"]}, {\"input\": \"671058194037157 8673\\r\\n\", \"output\": [\"298638658\"]}, {\"input\": \"900018062553298 4801\\r\\n\", \"output\": [\"345432320\"]}, {\"input\": \"128973636102142 5521\\r\\n\", \"output\": [\"99152648\"]}, {\"input\": \"999999999999993 8123\\r\\n\", \"output\": [\"868053217\"]}, {\"input\": \"260858031033600 9696\\r\\n\", \"output\": [\"692221824\"]}, {\"input\": \"562949953421312 9779\\r\\n\", \"output\": [\"98057767\"]}, {\"input\": \"357933504618282 1649\\r\\n\", \"output\": [\"197730476\"]}, {\"input\": \"586884783199831 5073\\r\\n\", \"output\": [\"883678085\"]}, {\"input\": \"187877211524483 8497\\r\\n\", \"output\": [\"562808746\"]}, {\"input\": \"866421317361600 10000\\r\\n\", \"output\": [\"82212846\"]}, {\"input\": \"782574093100800 9999\\r\\n\", \"output\": [\"293217028\"]}, {\"input\": \"577614211574400 9998\\r\\n\", \"output\": [\"681915605\"]}, {\"input\": \"65214507758400 9997\\r\\n\", \"output\": [\"677959603\"]}, {\"input\": \"963761198400 9996\\r\\n\", \"output\": [\"669401143\"]}, {\"input\": \"5587021440 9995\\r\\n\", \"output\": [\"360750834\"]}, {\"input\": \"17297280 9994\\r\\n\", \"output\": [\"94383698\"]}, {\"input\": \"7560 9993\\r\\n\", \"output\": [\"412712546\"]}, {\"input\": \"120 9992\\r\\n\", \"output\": [\"167656619\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"609359740010496 1337\\r\\n\", \"output\": [\"263703037\"]}, {\"input\": \"912750790581630 9876\\r\\n\", \"output\": [\"291557094\"]}, {\"input\": \"617673396283947 7777\\r\\n\", \"output\": [\"488769014\"]}, {\"input\": \"890604418498560 9119\\r\\n\", \"output\": [\"185509970\"]}, {\"input\": \"524288004718592 8888\\r\\n\", \"output\": [\"851726115\"]}, {\"input\": \"999999999999989 8998\\r\\n\", \"output\": [\"391873310\"]}, {\"input\": \"999999999999999 8123\\r\\n\", \"output\": [\"41003922\"]}, {\"input\": \"817237005720659 4233\\r\\n\", \"output\": [\"533017938\"]}, {\"input\": \"1000000007 1\\r\\n\", \"output\": [\"500000004\"]}, {\"input\": \"1000000007 2\\r\\n\", \"output\": [\"750000006\"]}, {\"input\": \"999999999999970 8998\\r\\n\", \"output\": [\"939941657\"]}, {\"input\": \"900000060000001 8123\\r\\n\", \"output\": [\"865356488\"]}, {\"input\": \"999011322032079 4233\\r\\n\", \"output\": [\"546309400\"]}, {\"input\": \"999005327998113 9119\\r\\n\", \"output\": [\"106270540\"]}, {\"input\": \"900000720000023 9876\\r\\n\", \"output\": [\"511266473\"]}]"}
{"prob_desc_description":"Let's introduce some definitions that will be needed later.Let $$$prime(x)$$$ be the set of prime divisors of $$$x$$$. For example, $$$prime(140) = \\{ 2, 5, 7 \\}$$$, $$$prime(169) = \\{ 13 \\}$$$.Let $$$g(x, p)$$$ be the maximum possible integer $$$p^k$$$ where $$$k$$$ is an integer such that $$$x$$$ is divisible by $$$p^k$$$. For example:  $$$g(45, 3) = 9$$$ ($$$45$$$ is divisible by $$$3^2=9$$$ but not divisible by $$$3^3=27$$$),  $$$g(63, 7) = 7$$$ ($$$63$$$ is divisible by $$$7^1=7$$$ but not divisible by $$$7^2=49$$$). Let $$$f(x, y)$$$ be the product of $$$g(y, p)$$$ for all $$$p$$$ in $$$prime(x)$$$. For example:  $$$f(30, 70) = g(70, 2) \\cdot g(70, 3) \\cdot g(70, 5) = 2^1 \\cdot 3^0 \\cdot 5^1 = 10$$$,  $$$f(525, 63) = g(63, 3) \\cdot g(63, 5) \\cdot g(63, 7) = 3^2 \\cdot 5^0 \\cdot 7^1 = 63$$$. You have integers $$$x$$$ and $$$n$$$. Calculate $$$f(x, 1) \\cdot f(x, 2) \\cdot \\ldots \\cdot f(x, n) \\bmod{(10^{9} + 7)}$$$.","prob_desc_output_spec":"Print the answer.","lang_cluster":"","src_uid":"04610fbaa746c083dda30e21fa6e1a0c","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","number theory"],"prob_desc_created_at":"1569762300","prob_desc_sample_inputs":"[\"10 2\", \"20190929 1605\", \"947 987654321987654321\"]","prob_desc_notes":"NoteIn the first example, $$$f(10, 1) = g(1, 2) \\cdot g(1, 5) = 1$$$, $$$f(10, 2) = g(2, 2) \\cdot g(2, 5) = 2$$$.In the second example, actual value of formula is approximately $$$1.597 \\cdot 10^{171}$$$. Make sure you print the answer modulo $$$(10^{9} + 7)$$$.In the third example, be careful about overflow issue.","exec_outcome":"","difficulty":1700.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The only line contains integers $$$x$$$ and $$$n$$$ ($$$2 \\le x \\le 10^{9}$$$, $$$1 \\le n \\le 10^{18}$$$)\u00a0\u2014 the numbers used in formula.","prob_desc_sample_outputs":"[\"2\", \"363165664\", \"593574252\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"10 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"20190929 1605\\r\\n\", \"output\": [\"363165664\"]}, {\"input\": \"947 987654321987654321\\r\\n\", \"output\": [\"593574252\"]}, {\"input\": \"2 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1000000000 1000000000000000000\\r\\n\", \"output\": [\"997440007\"]}, {\"input\": \"688829161 296569860304026304\\r\\n\", \"output\": [\"388155331\"]}, {\"input\": \"666010979 443570624148538441\\r\\n\", \"output\": [\"886507301\"]}, {\"input\": \"62459 243660471368579\\r\\n\", \"output\": [\"842535934\"]}, {\"input\": \"7946761 48034259999420806\\r\\n\", \"output\": [\"286862630\"]}, {\"input\": \"651423529 424352614134813841\\r\\n\", \"output\": [\"408736200\"]}, {\"input\": \"9 188\\r\\n\", \"output\": [\"954137859\"]}, {\"input\": \"670514203 852730801385798525\\r\\n\", \"output\": [\"355832385\"]}, {\"input\": \"610455946 416624575433175279\\r\\n\", \"output\": [\"338494046\"]}, {\"input\": \"49 79792266297612001\\r\\n\", \"output\": [\"444608448\"]}, {\"input\": \"3 450283905890997363\\r\\n\", \"output\": [\"137055211\"]}, {\"input\": \"46957 103538299629493\\r\\n\", \"output\": [\"516798047\"]}, {\"input\": \"732253291 788822690846812980\\r\\n\", \"output\": [\"73304767\"]}, {\"input\": \"97073 914735122128017\\r\\n\", \"output\": [\"829607048\"]}, {\"input\": \"17282811 699905460125739623\\r\\n\", \"output\": [\"59360995\"]}, {\"input\": \"181 6364290927201661\\r\\n\", \"output\": [\"475029602\"]}, {\"input\": \"858913688 891530069762947837\\r\\n\", \"output\": [\"647838042\"]}, {\"input\": \"967354019 885482785588887131\\r\\n\", \"output\": [\"808625396\"]}, {\"input\": \"266771957 238077331412324150\\r\\n\", \"output\": [\"739449215\"]}, {\"input\": \"830311913 317759021041529386\\r\\n\", \"output\": [\"693455621\"]}, {\"input\": \"848817679 656378982730193530\\r\\n\", \"output\": [\"62821476\"]}, {\"input\": \"195871858 768946182432660488\\r\\n\", \"output\": [\"392505530\"]}, {\"input\": \"711775563 733987980910045529\\r\\n\", \"output\": [\"162577667\"]}, {\"input\": \"525248617 82607938303742375\\r\\n\", \"output\": [\"23639347\"]}, {\"input\": \"143742939 719404683072701713\\r\\n\", \"output\": [\"302790025\"]}, {\"input\": \"28436 878968615689292495\\r\\n\", \"output\": [\"214265329\"]}, {\"input\": \"84649 916822936406978638\\r\\n\", \"output\": [\"246601699\"]}, {\"input\": \"87620 877857688202236881\\r\\n\", \"output\": [\"744263233\"]}, {\"input\": \"593239213 160216936483594374\\r\\n\", \"output\": [\"304167038\"]}, {\"input\": \"701679551 498836898172258517\\r\\n\", \"output\": [\"430076831\"]}, {\"input\": \"570117590 448352800956119696\\r\\n\", \"output\": [\"137534751\"]}, {\"input\": \"955489921 180523632657788226\\r\\n\", \"output\": [\"983910063\"]}, {\"input\": \"292681 817149800101377878\\r\\n\", \"output\": [\"608820127\"]}, {\"input\": \"1369 886139189349580965\\r\\n\", \"output\": [\"84873742\"]}, {\"input\": \"354907921 125959632388542241\\r\\n\", \"output\": [\"911890209\"]}, {\"input\": \"844561 602411242538130481\\r\\n\", \"output\": [\"731875446\"]}, {\"input\": \"841 353814783205469041\\r\\n\", \"output\": [\"865189676\"]}, {\"input\": \"602555209 363072779893033681\\r\\n\", \"output\": [\"506211588\"]}, {\"input\": \"822649 556728843703025449\\r\\n\", \"output\": [\"339554911\"]}, {\"input\": \"307371493 799006685782884121\\r\\n\", \"output\": [\"29424494\"]}, {\"input\": \"2 576460752303423488\\r\\n\", \"output\": [\"222384588\"]}, {\"input\": \"5 298023223876953125\\r\\n\", \"output\": [\"570366926\"]}, {\"input\": \"31891 32434291280971\\r\\n\", \"output\": [\"947227318\"]}, {\"input\": \"2 576460752303423487\\r\\n\", \"output\": [\"198832797\"]}, {\"input\": \"183 183\\r\\n\", \"output\": [\"387952563\"]}, {\"input\": \"139 1000000000000000000\\r\\n\", \"output\": [\"141180258\"]}]"}
{"prob_desc_description":"Anadi has a set of dominoes. Every domino has two parts, and each part contains some dots. For every $$$a$$$ and $$$b$$$ such that $$$1 \\leq a \\leq b \\leq 6$$$, there is exactly one domino with $$$a$$$ dots on one half and $$$b$$$ dots on the other half. The set contains exactly $$$21$$$ dominoes. Here is an exact illustration of his set:  Also, Anadi has an undirected graph without self-loops and multiple edges. He wants to choose some dominoes and place them on the edges of this graph. He can use at most one domino of each type. Each edge can fit at most one domino. It's not necessary to place a domino on each edge of the graph.When placing a domino on an edge, he also chooses its direction. In other words, one half of any placed domino must be directed toward one of the endpoints of the edge and the other half must be directed toward the other endpoint. There's a catch: if there are multiple halves of dominoes directed toward the same vertex, each of these halves must contain the same number of dots.How many dominoes at most can Anadi place on the edges of his graph?","prob_desc_output_spec":"Output one integer which denotes the maximum number of dominoes which Anadi can place on the edges of the graph.","lang_cluster":"","src_uid":"11e6559cfb71b8f6ca88242094b17a2b","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","graphs"],"prob_desc_created_at":"1569143100","prob_desc_sample_inputs":"[\"4 4\\n1 2\\n2 3\\n3 4\\n4 1\", \"7 0\", \"3 1\\n1 3\", \"7 21\\n1 2\\n1 3\\n1 4\\n1 5\\n1 6\\n1 7\\n2 3\\n2 4\\n2 5\\n2 6\\n2 7\\n3 4\\n3 5\\n3 6\\n3 7\\n4 5\\n4 6\\n4 7\\n5 6\\n5 7\\n6 7\"]","prob_desc_notes":"NoteHere is an illustration of Anadi's graph from the first sample test:  And here is one of the ways to place a domino on each of its edges:  Note that each vertex is faced by the halves of dominoes with the same number of dots. For instance, all halves directed toward vertex $$$1$$$ have three dots.","exec_outcome":"","difficulty":1700.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\leq n \\leq 7$$$, $$$0 \\leq m \\leq \\frac{n\\cdot(n-1)}{2}$$$) \u2014 the number of vertices and the number of edges in the graph. The next $$$m$$$ lines contain two integers each. Integers in the $$$i$$$-th line are $$$a_i$$$ and $$$b_i$$$ ($$$1 \\leq a, b \\leq n$$$, $$$a \\neq b$$$) and denote that there is an edge which connects vertices $$$a_i$$$ and $$$b_i$$$. The graph might be disconnected. It's however guaranteed that the graph doesn't contain any self-loops, and that there is at most one edge between any pair of vertices.","prob_desc_sample_outputs":"[\"4\", \"0\", \"1\", \"16\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4 4\\r\\n1 2\\r\\n2 3\\r\\n3 4\\r\\n4 1\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"7 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 1\\r\\n1 3\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7 21\\r\\n1 2\\r\\n1 3\\r\\n1 4\\r\\n1 5\\r\\n1 6\\r\\n1 7\\r\\n2 3\\r\\n2 4\\r\\n2 5\\r\\n2 6\\r\\n2 7\\r\\n3 4\\r\\n3 5\\r\\n3 6\\r\\n3 7\\r\\n4 5\\r\\n4 6\\r\\n4 7\\r\\n5 6\\r\\n5 7\\r\\n6 7\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"4 4\\r\\n4 2\\r\\n2 3\\r\\n3 4\\r\\n2 1\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"5 7\\r\\n4 3\\r\\n3 2\\r\\n1 4\\r\\n5 3\\r\\n5 2\\r\\n4 5\\r\\n1 5\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"6 9\\r\\n2 5\\r\\n3 6\\r\\n1 2\\r\\n1 4\\r\\n2 6\\r\\n6 1\\r\\n3 4\\r\\n1 3\\r\\n5 3\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"7 5\\r\\n5 6\\r\\n3 7\\r\\n7 2\\r\\n4 2\\r\\n1 4\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"7 14\\r\\n7 3\\r\\n2 4\\r\\n2 1\\r\\n2 5\\r\\n5 3\\r\\n6 7\\r\\n4 7\\r\\n5 4\\r\\n7 5\\r\\n4 3\\r\\n4 1\\r\\n6 1\\r\\n6 3\\r\\n3 1\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"7 15\\r\\n4 6\\r\\n7 3\\r\\n3 1\\r\\n6 5\\r\\n2 7\\r\\n3 6\\r\\n7 6\\r\\n2 6\\r\\n7 5\\r\\n3 5\\r\\n5 4\\r\\n4 7\\r\\n2 1\\r\\n2 4\\r\\n2 3\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"7 18\\r\\n1 5\\r\\n5 7\\r\\n1 3\\r\\n1 6\\r\\n4 5\\r\\n3 7\\r\\n6 7\\r\\n4 7\\r\\n2 7\\r\\n1 2\\r\\n7 1\\r\\n5 6\\r\\n6 2\\r\\n4 2\\r\\n5 3\\r\\n3 6\\r\\n4 6\\r\\n4 3\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"7 14\\r\\n2 7\\r\\n5 7\\r\\n3 4\\r\\n4 2\\r\\n2 3\\r\\n4 1\\r\\n6 5\\r\\n4 7\\r\\n6 2\\r\\n6 1\\r\\n5 3\\r\\n5 1\\r\\n7 6\\r\\n3 1\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"7 11\\r\\n4 7\\r\\n6 4\\r\\n5 1\\r\\n1 4\\r\\n5 4\\r\\n1 2\\r\\n3 4\\r\\n4 2\\r\\n6 1\\r\\n3 1\\r\\n7 1\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"7 18\\r\\n3 2\\r\\n5 3\\r\\n6 7\\r\\n7 3\\r\\n5 4\\r\\n4 6\\r\\n2 4\\r\\n7 1\\r\\n5 6\\r\\n5 2\\r\\n5 1\\r\\n3 4\\r\\n7 4\\r\\n6 1\\r\\n3 6\\r\\n7 2\\r\\n1 3\\r\\n1 2\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"7 17\\r\\n1 7\\r\\n5 6\\r\\n6 3\\r\\n1 2\\r\\n1 6\\r\\n3 4\\r\\n6 7\\r\\n4 5\\r\\n1 3\\r\\n1 5\\r\\n4 1\\r\\n5 2\\r\\n3 5\\r\\n4 6\\r\\n7 5\\r\\n7 2\\r\\n6 2\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"7 10\\r\\n3 6\\r\\n6 1\\r\\n4 6\\r\\n1 7\\r\\n7 4\\r\\n5 3\\r\\n5 6\\r\\n6 7\\r\\n7 5\\r\\n5 1\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"1 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 1\\r\\n2 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 2\\r\\n2 3\\r\\n1 3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3 3\\r\\n1 2\\r\\n2 3\\r\\n1 3\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"4 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 2\\r\\n2 4\\r\\n1 3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 6\\r\\n2 1\\r\\n1 4\\r\\n2 4\\r\\n3 1\\r\\n3 2\\r\\n3 4\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"5 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5 3\\r\\n5 1\\r\\n1 4\\r\\n5 4\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"5 10\\r\\n1 2\\r\\n3 4\\r\\n1 3\\r\\n2 3\\r\\n5 4\\r\\n5 1\\r\\n4 1\\r\\n5 3\\r\\n5 2\\r\\n2 4\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"6 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"6 3\\r\\n4 2\\r\\n5 4\\r\\n4 3\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"6 6\\r\\n4 3\\r\\n4 6\\r\\n1 2\\r\\n4 5\\r\\n6 3\\r\\n3 2\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"6 15\\r\\n4 3\\r\\n2 1\\r\\n3 6\\r\\n1 3\\r\\n4 1\\r\\n2 3\\r\\n3 5\\r\\n4 5\\r\\n6 1\\r\\n2 5\\r\\n1 5\\r\\n2 6\\r\\n6 4\\r\\n5 6\\r\\n4 2\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"6 12\\r\\n2 1\\r\\n4 3\\r\\n1 5\\r\\n6 4\\r\\n6 2\\r\\n3 6\\r\\n1 6\\r\\n2 4\\r\\n1 4\\r\\n2 5\\r\\n5 4\\r\\n1 3\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"7 1\\r\\n5 3\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7 2\\r\\n5 1\\r\\n3 5\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"7 3\\r\\n1 5\\r\\n5 7\\r\\n2 7\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"7 4\\r\\n3 7\\r\\n7 5\\r\\n1 3\\r\\n1 6\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"7 6\\r\\n3 5\\r\\n7 1\\r\\n3 7\\r\\n5 4\\r\\n7 4\\r\\n3 6\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"7 7\\r\\n2 5\\r\\n6 1\\r\\n5 4\\r\\n7 2\\r\\n3 2\\r\\n4 1\\r\\n7 3\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"7 8\\r\\n4 1\\r\\n5 7\\r\\n6 4\\r\\n7 1\\r\\n6 3\\r\\n3 4\\r\\n3 1\\r\\n6 7\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"7 9\\r\\n2 6\\r\\n7 4\\r\\n2 5\\r\\n2 7\\r\\n4 2\\r\\n3 5\\r\\n5 6\\r\\n6 7\\r\\n7 3\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"7 11\\r\\n2 4\\r\\n1 3\\r\\n5 2\\r\\n2 7\\r\\n1 4\\r\\n4 3\\r\\n2 1\\r\\n7 6\\r\\n3 2\\r\\n7 4\\r\\n4 5\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"7 12\\r\\n6 3\\r\\n3 5\\r\\n7 5\\r\\n1 5\\r\\n1 7\\r\\n7 6\\r\\n4 1\\r\\n2 1\\r\\n1 6\\r\\n5 6\\r\\n3 4\\r\\n4 2\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"7 13\\r\\n6 5\\r\\n5 7\\r\\n4 2\\r\\n7 2\\r\\n4 1\\r\\n6 7\\r\\n4 3\\r\\n1 6\\r\\n2 5\\r\\n5 4\\r\\n2 1\\r\\n6 4\\r\\n6 2\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"7 16\\r\\n3 5\\r\\n1 3\\r\\n3 7\\r\\n4 2\\r\\n1 4\\r\\n1 6\\r\\n7 6\\r\\n5 1\\r\\n7 2\\r\\n4 3\\r\\n3 6\\r\\n2 3\\r\\n2 5\\r\\n4 5\\r\\n2 6\\r\\n5 7\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"7 17\\r\\n4 6\\r\\n1 7\\r\\n7 5\\r\\n3 7\\r\\n7 2\\r\\n2 5\\r\\n6 7\\r\\n1 3\\r\\n5 1\\r\\n6 2\\r\\n4 2\\r\\n3 2\\r\\n1 2\\r\\n5 3\\r\\n4 5\\r\\n3 4\\r\\n1 6\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"7 19\\r\\n6 1\\r\\n6 4\\r\\n6 5\\r\\n1 7\\r\\n2 7\\r\\n3 5\\r\\n7 6\\r\\n2 4\\r\\n5 7\\r\\n3 4\\r\\n6 2\\r\\n4 1\\r\\n5 1\\r\\n4 7\\r\\n3 2\\r\\n4 5\\r\\n3 1\\r\\n2 5\\r\\n6 3\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"7 20\\r\\n4 7\\r\\n1 4\\r\\n2 3\\r\\n4 3\\r\\n3 7\\r\\n7 5\\r\\n4 5\\r\\n1 2\\r\\n6 7\\r\\n3 1\\r\\n3 5\\r\\n1 5\\r\\n1 7\\r\\n2 6\\r\\n6 4\\r\\n5 2\\r\\n5 6\\r\\n6 3\\r\\n1 6\\r\\n2 7\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"7 21\\r\\n3 5\\r\\n7 2\\r\\n2 3\\r\\n6 5\\r\\n5 2\\r\\n4 7\\r\\n2 6\\r\\n2 4\\r\\n6 7\\r\\n5 1\\r\\n1 4\\r\\n4 5\\r\\n5 7\\r\\n4 6\\r\\n3 1\\r\\n1 2\\r\\n3 4\\r\\n7 1\\r\\n3 7\\r\\n6 1\\r\\n3 6\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"7 12\\r\\n3 4\\r\\n5 4\\r\\n1 7\\r\\n7 3\\r\\n2 5\\r\\n3 2\\r\\n1 4\\r\\n5 6\\r\\n6 1\\r\\n6 3\\r\\n2 1\\r\\n5 7\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"7 7\\r\\n7 6\\r\\n4 2\\r\\n3 1\\r\\n4 7\\r\\n6 3\\r\\n2 5\\r\\n1 5\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"7 6\\r\\n7 5\\r\\n5 2\\r\\n1 5\\r\\n5 4\\r\\n3 5\\r\\n6 5\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"7 15\\r\\n5 1\\r\\n3 2\\r\\n2 5\\r\\n3 5\\r\\n6 1\\r\\n4 3\\r\\n6 2\\r\\n4 5\\r\\n7 5\\r\\n3 6\\r\\n3 1\\r\\n7 3\\r\\n4 6\\r\\n6 5\\r\\n6 7\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"7 18\\r\\n3 7\\r\\n3 2\\r\\n2 1\\r\\n1 7\\r\\n5 1\\r\\n3 4\\r\\n5 6\\r\\n4 2\\r\\n6 2\\r\\n1 4\\r\\n2 5\\r\\n6 3\\r\\n3 1\\r\\n6 7\\r\\n6 1\\r\\n7 2\\r\\n6 4\\r\\n3 5\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"7 19\\r\\n1 2\\r\\n7 3\\r\\n3 4\\r\\n4 7\\r\\n3 6\\r\\n7 5\\r\\n6 2\\r\\n4 6\\r\\n6 7\\r\\n5 2\\r\\n3 2\\r\\n6 5\\r\\n4 1\\r\\n2 4\\r\\n4 5\\r\\n6 1\\r\\n3 1\\r\\n1 7\\r\\n5 1\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"7 16\\r\\n3 2\\r\\n6 3\\r\\n6 1\\r\\n5 6\\r\\n7 5\\r\\n5 2\\r\\n6 2\\r\\n2 1\\r\\n5 4\\r\\n4 1\\r\\n7 2\\r\\n1 5\\r\\n2 4\\r\\n7 3\\r\\n1 7\\r\\n6 7\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"7 12\\r\\n4 1\\r\\n6 4\\r\\n3 4\\r\\n3 1\\r\\n2 4\\r\\n7 5\\r\\n5 4\\r\\n2 1\\r\\n6 7\\r\\n2 3\\r\\n7 4\\r\\n6 5\\r\\n\", \"output\": [\"11\"]}]"}
{"prob_desc_description":"Melody Pond was stolen from her parents as a newborn baby by Madame Kovarian, to become a weapon of the Silence in their crusade against the Doctor. Madame Kovarian changed Melody's name to River Song, giving her a new identity that allowed her to kill the Eleventh Doctor.Heidi figured out that Madame Kovarian uses a very complicated hashing function in order to change the names of the babies she steals. In order to prevent this from happening to future Doctors, Heidi decided to prepare herself by learning some basic hashing techniques.The first hashing function she designed is as follows.Given two positive integers $$$(x, y)$$$ she defines $$$H(x,y):=x^2+2xy+x+1$$$.Now, Heidi wonders if the function is reversible. That is, given a positive integer $$$r$$$, can you find a pair $$$(x, y)$$$ (of positive integers) such that $$$H(x, y) = r$$$?If multiple such pairs exist, output the one with smallest possible $$$x$$$. If there is no such pair, output \"NO\".","prob_desc_output_spec":"Output integers $$$x, y$$$ such that $$$H(x,y) = r$$$ and $$$x$$$ is smallest possible, or \"NO\" if no such pair exists.","lang_cluster":"","src_uid":"3ff1c25a1026c90aeb14d148d7fb96ba","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","math","number theory"],"prob_desc_created_at":"1562483100","prob_desc_sample_inputs":"[\"19\", \"16\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first and only line contains an integer $$$r$$$ ($$$1 \\le r \\le 10^{12}$$$).","prob_desc_sample_outputs":"[\"1 8\", \"NO\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"19\\r\\n\", \"output\": [\"1 8\"]}, {\"input\": \"16\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"1 1\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"1 2\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"1 3\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"11\\r\\n\", \"output\": [\"1 4\"]}, {\"input\": \"12\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"13\\r\\n\", \"output\": [\"1 5\"]}, {\"input\": \"14\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"15\\r\\n\", \"output\": [\"1 6\"]}, {\"input\": \"17\\r\\n\", \"output\": [\"1 7\"]}, {\"input\": \"18\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"20\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"21\\r\\n\", \"output\": [\"1 9\"]}, {\"input\": \"260158260522\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"250877914575\\r\\n\", \"output\": [\"1 125438957286\"]}, {\"input\": \"116602436426\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"540024979445\\r\\n\", \"output\": [\"1 270012489721\"]}, {\"input\": \"917861648772\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"962623690081\\r\\n\", \"output\": [\"1 481311845039\"]}, {\"input\": \"54433933447\\r\\n\", \"output\": [\"1 27216966722\"]}, {\"input\": \"16476190629\\r\\n\", \"output\": [\"1 8238095313\"]}, {\"input\": \"426262703497\\r\\n\", \"output\": [\"1 213131351747\"]}, {\"input\": \"723211047202\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"652509336151\\r\\n\", \"output\": [\"1 326254668074\"]}, {\"input\": \"215283472163\\r\\n\", \"output\": [\"1 107641736080\"]}, {\"input\": \"29617919\\r\\n\", \"output\": [\"1 14808958\"]}, {\"input\": \"7505295085\\r\\n\", \"output\": [\"1 3752647541\"]}, {\"input\": \"149890929717\\r\\n\", \"output\": [\"1 74945464857\"]}, {\"input\": \"185589070745\\r\\n\", \"output\": [\"1 92794535371\"]}, {\"input\": \"419450839\\r\\n\", \"output\": [\"1 209725418\"]}, {\"input\": \"519397679401\\r\\n\", \"output\": [\"1 259698839699\"]}, {\"input\": \"943447972637\\r\\n\", \"output\": [\"1 471723986317\"]}, {\"input\": \"54336309171\\r\\n\", \"output\": [\"1 27168154584\"]}, {\"input\": \"688373050717\\r\\n\", \"output\": [\"1 344186525357\"]}, {\"input\": \"156231653273\\r\\n\", \"output\": [\"1 78115826635\"]}, {\"input\": \"23744498401\\r\\n\", \"output\": [\"1 11872249199\"]}, {\"input\": \"768407398177\\r\\n\", \"output\": [\"1 384203699087\"]}, {\"input\": \"963761198401\\r\\n\", \"output\": [\"1 481880599199\"]}, {\"input\": \"240940299601\\r\\n\", \"output\": [\"1 120470149799\"]}]"}
{"prob_desc_description":"You are given a regular polygon with $$$n$$$ vertices labeled from $$$1$$$ to $$$n$$$ in counter-clockwise order. The triangulation of a given polygon is a set of triangles such that each vertex of each triangle is a vertex of the initial polygon, there is no pair of triangles such that their intersection has non-zero area, and the total area of all triangles is equal to the area of the given polygon. The weight of a triangulation is the sum of weigths of triangles it consists of, where the weight of a triagle is denoted as the product of labels of its vertices.Calculate the minimum weight among all triangulations of the polygon.","prob_desc_output_spec":"Print one integer \u2014 the minimum weight among all triangulations of the given polygon.","lang_cluster":"","src_uid":"1bd29d7a8793c22e81a1f6fd3991307a","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp","greedy","math"],"prob_desc_created_at":"1553267100","prob_desc_sample_inputs":"[\"3\", \"4\"]","prob_desc_notes":"NoteAccording to Wiki: polygon triangulation is the decomposition of a polygonal area (simple polygon) $$$P$$$ into a set of triangles, i.\u2009e., finding a set of triangles with pairwise non-intersecting interiors whose union is $$$P$$$.In the first example the polygon is a triangle, so we don't need to cut it further, so the answer is $$$1 \\cdot 2 \\cdot 3 = 6$$$.In the second example the polygon is a rectangle, so it should be divided into two triangles. It's optimal to cut it using diagonal $$$1-3$$$ so answer is $$$1 \\cdot 2 \\cdot 3 + 1 \\cdot 3 \\cdot 4 = 6 + 12 = 18$$$.","exec_outcome":"","difficulty":1200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains single integer $$$n$$$ ($$$3 \\le n \\le 500$$$) \u2014 the number of vertices in the regular polygon.","prob_desc_sample_outputs":"[\"6\", \"18\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"38\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"68\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"110\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"166\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"238\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"328\"]}, {\"input\": \"100\\r\\n\", \"output\": [\"333298\"]}, {\"input\": \"101\\r\\n\", \"output\": [\"343398\"]}, {\"input\": \"102\\r\\n\", \"output\": [\"353700\"]}, {\"input\": \"103\\r\\n\", \"output\": [\"364206\"]}, {\"input\": \"104\\r\\n\", \"output\": [\"374918\"]}, {\"input\": \"105\\r\\n\", \"output\": [\"385838\"]}, {\"input\": \"106\\r\\n\", \"output\": [\"396968\"]}, {\"input\": \"107\\r\\n\", \"output\": [\"408310\"]}, {\"input\": \"108\\r\\n\", \"output\": [\"419866\"]}, {\"input\": \"109\\r\\n\", \"output\": [\"431638\"]}, {\"input\": \"110\\r\\n\", \"output\": [\"443628\"]}, {\"input\": \"500\\r\\n\", \"output\": [\"41666498\"]}, {\"input\": \"497\\r\\n\", \"output\": [\"40920990\"]}, {\"input\": \"494\\r\\n\", \"output\": [\"40184428\"]}, {\"input\": \"491\\r\\n\", \"output\": [\"39456758\"]}, {\"input\": \"488\\r\\n\", \"output\": [\"38737926\"]}, {\"input\": \"485\\r\\n\", \"output\": [\"38027878\"]}, {\"input\": \"482\\r\\n\", \"output\": [\"37326560\"]}, {\"input\": \"479\\r\\n\", \"output\": [\"36633918\"]}, {\"input\": \"476\\r\\n\", \"output\": [\"35949898\"]}, {\"input\": \"473\\r\\n\", \"output\": [\"35274446\"]}, {\"input\": \"470\\r\\n\", \"output\": [\"34607508\"]}, {\"input\": \"467\\r\\n\", \"output\": [\"33949030\"]}, {\"input\": \"464\\r\\n\", \"output\": [\"33298958\"]}, {\"input\": \"461\\r\\n\", \"output\": [\"32657238\"]}, {\"input\": \"458\\r\\n\", \"output\": [\"32023816\"]}, {\"input\": \"455\\r\\n\", \"output\": [\"31398638\"]}, {\"input\": \"452\\r\\n\", \"output\": [\"30781650\"]}, {\"input\": \"449\\r\\n\", \"output\": [\"30172798\"]}, {\"input\": \"446\\r\\n\", \"output\": [\"29572028\"]}, {\"input\": \"42\\r\\n\", \"output\": [\"24680\"]}, {\"input\": \"69\\r\\n\", \"output\": [\"109478\"]}, {\"input\": \"228\\r\\n\", \"output\": [\"3950706\"]}, {\"input\": \"233\\r\\n\", \"output\": [\"4216366\"]}, {\"input\": \"420\\r\\n\", \"output\": [\"24695858\"]}, {\"input\": \"368\\r\\n\", \"output\": [\"16611886\"]}, {\"input\": \"225\\r\\n\", \"output\": [\"3796798\"]}, {\"input\": \"11\\r\\n\", \"output\": [\"438\"]}, {\"input\": \"12\\r\\n\", \"output\": [\"570\"]}, {\"input\": \"13\\r\\n\", \"output\": [\"726\"]}, {\"input\": \"14\\r\\n\", \"output\": [\"908\"]}, {\"input\": \"135\\r\\n\", \"output\": [\"820078\"]}, {\"input\": \"199\\r\\n\", \"output\": [\"2626798\"]}, {\"input\": \"137\\r\\n\", \"output\": [\"857070\"]}, {\"input\": \"131\\r\\n\", \"output\": [\"749318\"]}, {\"input\": \"130\\r\\n\", \"output\": [\"732288\"]}, {\"input\": \"139\\r\\n\", \"output\": [\"895158\"]}]"}
{"prob_desc_description":"Welcome to Codeforces Stock Exchange! We're pretty limited now as we currently allow trading on one stock, Codeforces Ltd. We hope you'll still be able to make profit from the market!In the morning, there are $$$n$$$ opportunities to buy shares. The $$$i$$$-th of them allows to buy as many shares as you want, each at the price of $$$s_i$$$ bourles.In the evening, there are $$$m$$$ opportunities to sell shares. The $$$i$$$-th of them allows to sell as many shares as you want, each at the price of $$$b_i$$$ bourles. You can't sell more shares than you have.It's morning now and you possess $$$r$$$ bourles and no shares.What is the maximum number of bourles you can hold after the evening?","prob_desc_output_spec":"Output a single integer \u2014 the maximum number of bourles you can hold after the evening.","lang_cluster":"","src_uid":"42f25d492bddc12d3d89d39315d63cb9","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["greedy","implementation"],"prob_desc_created_at":"1556548500","prob_desc_sample_inputs":"[\"3 4 11\\n4 2 5\\n4 4 5 4\", \"2 2 50\\n5 7\\n4 2\"]","prob_desc_notes":"NoteIn the first example test, you have $$$11$$$ bourles in the morning. It's optimal to buy $$$5$$$ shares of a stock at the price of $$$2$$$ bourles in the morning, and then to sell all of them at the price of $$$5$$$ bourles in the evening. It's easy to verify that you'll have $$$26$$$ bourles after the evening.In the second example test, it's optimal not to take any action.","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line of the input contains three integers $$$n, m, r$$$ ($$$1 \\leq n \\leq 30$$$, $$$1 \\leq m \\leq 30$$$, $$$1 \\leq r \\leq 1000$$$) \u2014 the number of ways to buy the shares on the market, the number of ways to sell the shares on the market, and the number of bourles you hold now. The next line contains $$$n$$$ integers $$$s_1, s_2, \\dots, s_n$$$ ($$$1 \\leq s_i \\leq 1000$$$); $$$s_i$$$ indicates the opportunity to buy shares at the price of $$$s_i$$$ bourles. The following line contains $$$m$$$ integers $$$b_1, b_2, \\dots, b_m$$$ ($$$1 \\leq b_i \\leq 1000$$$); $$$b_i$$$ indicates the opportunity to sell shares at the price of $$$b_i$$$ bourles.","prob_desc_sample_outputs":"[\"26\", \"50\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3 4 11\\r\\n4 2 5\\r\\n4 4 5 4\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"2 2 50\\r\\n5 7\\r\\n4 2\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"1 1 1\\r\\n1\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1 35\\r\\n5\\r\\n7\\r\\n\", \"output\": [\"49\"]}, {\"input\": \"1 1 36\\r\\n5\\r\\n7\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"3 5 20\\r\\n1000 4 6\\r\\n1 2 7 6 5\\r\\n\", \"output\": [\"35\"]}, {\"input\": \"5 3 20\\r\\n5 4 3 2 1\\r\\n6 7 1000\\r\\n\", \"output\": [\"20000\"]}, {\"input\": \"30 30 987\\r\\n413 937 166 77 749 925 792 353 773 88 218 863 71 186 753 306 952 966 236 501 84 163 767 99 887 380 435 888 589 761\\r\\n68 501 323 916 506 952 411 813 664 49 860 151 120 543 168 944 302 521 245 517 464 734 205 235 173 893 109 655 346 837\\r\\n\", \"output\": [\"12440\"]}, {\"input\": \"30 22 1000\\r\\n999 953 947 883 859 857 775 766 723 713 696 691 659 650 597 474 472 456 455 374 367 354 347 215 111 89 76 76 59 55\\r\\n172 188 223 247 404 445 449 489 493 554 558 587 588 627 686 714 720 744 747 786 830 953\\r\\n\", \"output\": [\"17164\"]}, {\"input\": \"28 29 1000\\r\\n555 962 781 562 856 700 628 591 797 873 950 607 526 513 552 954 768 823 863 650 984 653 741 548 676 577 625 902\\r\\n185 39 223 383 221 84 165 492 79 53 475 410 314 489 59 138 395 346 91 258 14 354 410 25 41 394 463 432 325\\r\\n\", \"output\": [\"1000\"]}, {\"input\": \"30 29 999\\r\\n993 982 996 992 988 984 981 982 981 981 992 997 982 996 995 981 995 982 994 996 988 986 990 991 987 993 1000 989 998 991\\r\\n19 12 14 5 20 11 15 11 7 14 12 8 1 9 7 15 6 20 15 20 17 15 20 1 4 13 2 2 17\\r\\n\", \"output\": [\"999\"]}, {\"input\": \"30 30 999\\r\\n19 8 6 1 4 12 14 12 8 14 14 2 13 11 10 15 13 14 2 5 15 17 18 16 9 4 2 14 12 9\\r\\n993 987 993 998 998 987 980 986 995 987 998 989 981 982 983 981 997 991 989 989 993 990 984 997 995 984 982 994 990 984\\r\\n\", \"output\": [\"997002\"]}, {\"input\": \"28 30 1000\\r\\n185 184 177 171 165 162 162 154 150 136 133 127 118 111 106 106 95 92 86 85 77 66 65 40 28 10 10 4\\r\\n305 309 311 313 319 321 323 338 349 349 349 351 359 373 378 386 405 409 420 445 457 462 463 466 466 471 473 479 479 482\\r\\n\", \"output\": [\"120500\"]}, {\"input\": \"1 1 10\\r\\n11\\r\\n1000\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"29 30 989\\r\\n450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450 450\\r\\n451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451 451\\r\\n\", \"output\": [\"991\"]}, {\"input\": \"25 30 989\\r\\n153 153 153 153 153 153 153 153 153 153 153 153 153 153 153 153 153 153 153 153 153 153 153 153 153\\r\\n153 153 153 153 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[\"20\"]}, {\"input\": \"1 2 19\\r\\n10\\r\\n1 11\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"1 3 4\\r\\n1\\r\\n1 5 2\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"1 2 100\\r\\n2\\r\\n1 10\\r\\n\", \"output\": [\"500\"]}, {\"input\": \"1 1 12\\r\\n9\\r\\n10\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"3 4 11\\r\\n4 2 5\\r\\n4 4 4 5\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"1 1 8\\r\\n6\\r\\n7\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"1 1 7\\r\\n4\\r\\n5\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"1 5 10\\r\\n1\\r\\n5 5 5 5 10\\r\\n\", \"output\": [\"100\"]}, {\"input\": \"1 2 10\\r\\n1\\r\\n1 20\\r\\n\", \"output\": [\"200\"]}, {\"input\": \"1 2 5\\r\\n1\\r\\n2 3\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"1 3 100\\r\\n5\\r\\n1 1 1000\\r\\n\", \"output\": [\"20000\"]}, {\"input\": \"2 1 11\\r\\n5 4\\r\\n5\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"4 3 11\\r\\n1 2 3 4\\r\\n1 2 3\\r\\n\", \"output\": [\"33\"]}, {\"input\": \"1 2 5\\r\\n2\\r\\n2 100\\r\\n\", \"output\": [\"201\"]}, {\"input\": \"1 5 10\\r\\n2\\r\\n1 1 1 1 100\\r\\n\", \"output\": [\"500\"]}, {\"input\": \"3 3 11\\r\\n4 5 6\\r\\n1 2 5\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"2 3 5\\r\\n1 1\\r\\n2 2 5\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"3 4 10\\r\\n5 3 1\\r\\n10 10 10 1000\\r\\n\", \"output\": [\"10000\"]}, {\"input\": \"1 1 13\\r\\n5\\r\\n6\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"1 1 1000\\r\\n51\\r\\n52\\r\\n\", \"output\": [\"1019\"]}, {\"input\": \"1 2 10\\r\\n1\\r\\n3 10\\r\\n\", \"output\": [\"100\"]}, {\"input\": \"3 4 2\\r\\n5 3 5\\r\\n10 10 10 1000\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 1 11\\r\\n8\\r\\n9\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"1 2 5\\r\\n5\\r\\n5 10\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"1 5 10\\r\\n1\\r\\n2 2 2 2 5\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"1 2 1\\r\\n1\\r\\n1 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3 5 100\\r\\n1 1 1\\r\\n2 2 2 2 7\\r\\n\", \"output\": [\"700\"]}, {\"input\": \"1 2 10\\r\\n2\\r\\n2 10\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"3 9 15\\r\\n1 2 3\\r\\n1 2 3 4 4 6 5 5 4\\r\\n\", \"output\": [\"90\"]}]"}
{"prob_desc_description":"Getting closer and closer to a mathematician, Serval becomes a university student on math major in Japari University. On the Calculus class, his teacher taught him how to calculate the expected length of a random subsegment of a given segment. Then he left a bonus problem as homework, with the award of a garage kit from IOI. The bonus is to extend this problem to the general case as follows.You are given a segment with length $$$l$$$. We randomly choose $$$n$$$ segments by choosing two points (maybe with non-integer coordinates) from the given segment equiprobably and the interval between the two points forms a segment. You are given the number of random segments $$$n$$$, and another integer $$$k$$$. The $$$2n$$$ endpoints of the chosen segments split the segment into $$$(2n+1)$$$ intervals. Your task is to calculate the expected total length of those intervals that are covered by at least $$$k$$$ segments of the $$$n$$$ random segments.You should find the answer modulo $$$998244353$$$.","prob_desc_output_spec":"Output one integer\u00a0\u2014 the expected total length of all the intervals covered by at least $$$k$$$ segments of the $$$n$$$ random segments modulo $$$998244353$$$. Formally, let $$$M = 998244353$$$. It can be shown that the answer can be expressed as an irreducible fraction $$$\\frac{p}{q}$$$, where $$$p$$$ and $$$q$$$ are integers and $$$q \\not \\equiv 0 \\pmod{M}$$$. Output the integer equal to $$$p \\cdot q^{-1} \\bmod M$$$. In other words, output such an integer $$$x$$$ that $$$0 \\le x < M$$$ and $$$x \\cdot q \\equiv p \\pmod{M}$$$.","lang_cluster":"","src_uid":"c9e79e83928d5d034123ebc3b2f5e064","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","probabilities","combinatorics","dp"],"prob_desc_created_at":"1555164300","prob_desc_sample_inputs":"[\"1 1 1\", \"6 2 1\", \"7 5 3\", \"97 31 9984524\"]","prob_desc_notes":"NoteIn the first example, the expected total length is $$$\\int_0^1 \\int_0^1 |x-y| \\,\\mathrm{d}x\\,\\mathrm{d}y = {1\\over 3}$$$, and $$$3^{-1}$$$ modulo $$$998244353$$$ is $$$332748118$$$.","exec_outcome":"","difficulty":2600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"First line contains three space-separated positive integers $$$n$$$, $$$k$$$ and $$$l$$$ ($$$1\\leq k \\leq n \\leq 2000$$$, $$$1\\leq l\\leq 10^9$$$).","prob_desc_sample_outputs":"[\"332748118\", \"760234711\", \"223383352\", \"267137618\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1 1 1\\r\\n\", \"output\": [\"332748118\"]}, {\"input\": \"6 2 1\\r\\n\", \"output\": [\"760234711\"]}, {\"input\": \"7 5 3\\r\\n\", \"output\": [\"223383352\"]}, {\"input\": \"97 31 9984524\\r\\n\", \"output\": [\"267137618\"]}, {\"input\": \"2000 1 772197283\\r\\n\", \"output\": [\"905584809\"]}, {\"input\": \"2000 2 76039754\\r\\n\", \"output\": [\"855496918\"]}, {\"input\": \"2000 3 40337285\\r\\n\", \"output\": [\"782495326\"]}, {\"input\": \"2000 2000 773356966\\r\\n\", \"output\": [\"104351589\"]}, {\"input\": \"2000 1999 239479112\\r\\n\", \"output\": [\"620815507\"]}, {\"input\": \"2000 1998 334042678\\r\\n\", \"output\": [\"322694394\"]}, {\"input\": \"2000 976 671942688\\r\\n\", \"output\": [\"767696001\"]}, {\"input\": \"2000 1415 40371690\\r\\n\", \"output\": [\"171032298\"]}, {\"input\": \"2000 1000 1000000000\\r\\n\", \"output\": [\"491672258\"]}, {\"input\": \"1998 1001 998244353\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2000 4 136878315\\r\\n\", \"output\": [\"880870575\"]}, {\"input\": \"2000 5 558837462\\r\\n\", \"output\": [\"18859862\"]}, {\"input\": \"2000 1997 525997660\\r\\n\", \"output\": [\"843278067\"]}, {\"input\": \"2000 1996 45458693\\r\\n\", \"output\": [\"772786701\"]}, {\"input\": \"2000 1947 62604662\\r\\n\", \"output\": [\"540795249\"]}, {\"input\": \"2000 1728 63723796\\r\\n\", \"output\": [\"421421553\"]}, {\"input\": \"1961 206 931072038\\r\\n\", \"output\": [\"794464980\"]}, {\"input\": \"1948 978 501529426\\r\\n\", \"output\": [\"50139353\"]}, {\"input\": \"1878 1529 66841298\\r\\n\", \"output\": [\"880727658\"]}, {\"input\": \"1900 1 495084177\\r\\n\", \"output\": [\"338668438\"]}, {\"input\": \"1885 2 286102770\\r\\n\", \"output\": [\"443099162\"]}, {\"input\": \"1928 3 200575371\\r\\n\", \"output\": [\"291241927\"]}, {\"input\": \"1978 4 436588015\\r\\n\", \"output\": [\"282947523\"]}, {\"input\": \"1987 1987 191667504\\r\\n\", \"output\": [\"627381301\"]}, {\"input\": \"1821 1820 866603455\\r\\n\", \"output\": [\"318623064\"]}, {\"input\": \"1824 1822 151884700\\r\\n\", \"output\": [\"462069981\"]}, {\"input\": \"1486 1 170331068\\r\\n\", \"output\": [\"692176218\"]}, {\"input\": \"1424 1 217388653\\r\\n\", \"output\": [\"56808622\"]}, {\"input\": \"1703 1 803103605\\r\\n\", \"output\": [\"660333930\"]}, {\"input\": \"1555 1 700556118\\r\\n\", \"output\": [\"615656029\"]}, {\"input\": \"1224 1 71403225\\r\\n\", \"output\": [\"128242924\"]}, {\"input\": \"1492 1 599215694\\r\\n\", \"output\": [\"195441337\"]}, {\"input\": \"1281 1 415457117\\r\\n\", \"output\": [\"111407914\"]}, {\"input\": \"1664 1 517151944\\r\\n\", \"output\": [\"126430274\"]}, {\"input\": \"1771 1 555450393\\r\\n\", \"output\": [\"280416119\"]}, {\"input\": \"1045 1 375567139\\r\\n\", \"output\": [\"983012429\"]}, {\"input\": \"1025 1025 871316577\\r\\n\", \"output\": [\"266993477\"]}, {\"input\": \"1243 1243 296556443\\r\\n\", \"output\": [\"209836419\"]}, {\"input\": \"1240 1240 846679367\\r\\n\", \"output\": [\"744376915\"]}, {\"input\": \"1946 1946 432053608\\r\\n\", \"output\": [\"329055332\"]}, {\"input\": \"1806 1806 174417450\\r\\n\", \"output\": [\"287857698\"]}, {\"input\": \"1321 1321 774237640\\r\\n\", \"output\": [\"573916469\"]}, {\"input\": \"1205 1205 972407779\\r\\n\", \"output\": [\"970505824\"]}, {\"input\": \"1063 1063 497812546\\r\\n\", \"output\": [\"203394740\"]}, {\"input\": \"1443 1443 784034214\\r\\n\", \"output\": [\"489871338\"]}, {\"input\": \"1099 1099 548018740\\r\\n\", \"output\": [\"530449224\"]}, {\"input\": \"1334 667 998244356\\r\\n\", \"output\": [\"123570327\"]}, {\"input\": \"1621 810 998244355\\r\\n\", \"output\": [\"334476739\"]}, {\"input\": \"1253 626 998244353\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1217 608 998244355\\r\\n\", \"output\": [\"465345479\"]}, {\"input\": \"1966 983 998244357\\r\\n\", \"output\": [\"81898103\"]}, {\"input\": \"1471 735 998244354\\r\\n\", \"output\": [\"399941190\"]}, {\"input\": \"1496 748 998244357\\r\\n\", \"output\": [\"419593982\"]}, {\"input\": \"1307 653 998244355\\r\\n\", \"output\": [\"823060783\"]}, {\"input\": \"1706 853 998244357\\r\\n\", \"output\": [\"627644358\"]}, {\"input\": \"1025 512 998244357\\r\\n\", \"output\": [\"120622427\"]}]"}
{"prob_desc_description":"Young Teodor enjoys drawing. His favourite hobby is drawing segments with integer borders inside his huge [1;m] segment. One day Teodor noticed that picture he just drawn has one interesting feature: there doesn't exist an integer point, that belongs each of segments in the picture. Having discovered this fact, Teodor decided to share it with Sasha.Sasha knows that Teodor likes to show off so he never trusts him. Teodor wants to prove that he can be trusted sometimes, so he decided to convince Sasha that there is no such integer point in his picture, which belongs to each segment. However Teodor is lazy person and neither wills to tell Sasha all coordinates of segments' ends nor wills to tell him their amount, so he suggested Sasha to ask him series of questions 'Given the integer point xi, how many segments in Fedya's picture contain that point?', promising to tell correct answers for this questions.Both boys are very busy studying and don't have much time, so they ask you to find out how many questions can Sasha ask Teodor, that having only answers on his questions, Sasha can't be sure that Teodor isn't lying to him. Note that Sasha doesn't know amount of segments in Teodor's picture. Sure, Sasha is smart person and never asks about same point twice.","prob_desc_output_spec":"Single line of output should contain one integer number k \u2013 size of largest set (xi,\u2009cnt(xi)) where all xi are different, 1\u2009\u2264\u2009xi\u2009\u2264\u2009m, and cnt(xi) is amount of segments, containing point with coordinate xi, such that one can't be sure that there doesn't exist point, belonging to all of segments in initial picture, if he knows only this set(and doesn't know n).","lang_cluster":"","src_uid":"ce8350be138ce2061349d7f9224a5aaf","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["data structures","dp","binary search"],"prob_desc_created_at":"1520177700","prob_desc_sample_inputs":"[\"2 4\\n1 2\\n3 4\", \"4 6\\n1 3\\n2 3\\n4 6\\n5 6\"]","prob_desc_notes":"NoteFirst example shows situation where Sasha can never be sure that Teodor isn't lying to him, because even if one knows cnt(xi) for each point in segment [1;4], he can't distinguish this case from situation Teodor has drawn whole [1;4] segment.In second example Sasha can ask about 5 points e.g. 1,\u20092,\u20093,\u20095,\u20096, still not being sure if Teodor haven't lied to him. But once he knows information about all points in [1;6] segment, Sasha can be sure that Teodor haven't lied to him.","exec_outcome":"","difficulty":1900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"First line of input contains two integer numbers: n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009100\u2009000)\u00a0\u2014 amount of segments of Teodor's picture and maximal coordinate of point that Sasha can ask about. ith of next n lines contains two integer numbers li and ri (1\u2009\u2264\u2009li\u2009\u2264\u2009ri\u2009\u2264\u2009m)\u00a0\u2014 left and right ends of ith segment in the picture. Note that that left and right ends of segment can be the same point. It is guaranteed that there is no integer point, that belongs to all segments.","prob_desc_sample_outputs":"[\"4\", \"5\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 4\\r\\n1 2\\r\\n3 4\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"4 6\\r\\n1 3\\r\\n2 3\\r\\n4 6\\r\\n5 6\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"70 1495\\r\\n148 339\\r\\n470 596\\r\\n859 1322\\r\\n214 443\\r\\n74 1320\\r\\n995 1246\\r\\n266 1261\\r\\n147 1240\\r\\n690 1439\\r\\n1178 1455\\r\\n789 1478\\r\\n563 1206\\r\\n68 1490\\r\\n339 467\\r\\n1324 1471\\r\\n681 1289\\r\\n346 822\\r\\n72 1080\\r\\n126 1326\\r\\n382 910\\r\\n267 1168\\r\\n101 119\\r\\n382 666\\r\\n79 1176\\r\\n358 1185\\r\\n958 1426\\r\\n590 989\\r\\n80 539\\r\\n273 617\\r\\n1129 1343\\r\\n210 1071\\r\\n144 1484\\r\\n210 609\\r\\n397 1077\\r\\n950 1112\\r\\n523 1343\\r\\n396 888\\r\\n640 1281\\r\\n491 729\\r\\n704 761\\r\\n1208 1276\\r\\n357 1139\\r\\n341 772\\r\\n1111 1453\\r\\n893 1482\\r\\n718 1200\\r\\n67 547\\r\\n302 494\\r\\n98 949\\r\\n17 69\\r\\n353 1146\\r\\n346 534\\r\\n997 132...\", \"output\": [\"1108\"]}, {\"input\": \"85 1596\\r\\n125 264\\r\\n823 1193\\r\\n811 1042\\r\\n278 1556\\r\\n257 1311\\r\\n273 586\\r\\n210 576\\r\\n443 1082\\r\\n16 639\\r\\n460 1206\\r\\n580 1521\\r\\n636 1128\\r\\n729 1299\\r\\n1257 1387\\r\\n428 1577\\r\\n838 979\\r\\n1019 1422\\r\\n342 344\\r\\n1222 1316\\r\\n1045 1352\\r\\n136 463\\r\\n280 1558\\r\\n199 763\\r\\n126 1248\\r\\n281 713\\r\\n803 1476\\r\\n1230 1493\\r\\n190 693\\r\\n1137 1417\\r\\n383 615\\r\\n236 1243\\r\\n271 1500\\r\\n174 488\\r\\n316 1500\\r\\n132 1199\\r\\n298 1251\\r\\n47 336\\r\\n117 1310\\r\\n619 668\\r\\n272 1239\\r\\n11 870\\r\\n501 1535\\r\\n1041 1105\\r\\n906 1119\\r\\n251 525\\r\\n578 1393\\r\\n820 1182\\r\\n854 1141\\r\\n77 610\\r\\n566 1210\\r\\n320 969\\r\\n114 312...\", \"output\": [\"1249\"]}, {\"input\": \"458 1408\\r\\n530 595\\r\\n182 831\\r\\n180 1002\\r\\n874 1012\\r\\n135 990\\r\\n718 879\\r\\n618 778\\r\\n582 891\\r\\n630 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74969\\r\\n12382 61565\\r\\n19568 78762\\r\\n19579 55432\\r\\n1075 32213\\r\\n22741 38473\\r\\n9807 58754\\r\\n9324 80579\\r\\n9038 59462\\r\\n52566 77687\\r\\n56424 79294\\r\\n21091 32659\\r\\n39997 70527\\r\\n6678 28014\\r\\n49703 60460\\r\\n18666 42815\\r\\n24857 73974\\r\\n62242 77717\\r\\n56703 78265\\r\\n28039 36817\\r\\n6009 43436\\r\\n46938 73775\\r\\n6093 52041\\r\\n35928 72074\\r\\n46910 79583\\r\\n29901 64853\\r\\n31716 48370\\r\\n11571 65682\\r\\n64410 67222\\r\\n32144 43362\\r\\n8546 46547\\r\\n68661 80080\\r\\n36213 74307\\r\\n30667 60134\\r\\n11016 38318\\r...\", \"output\": [\"61566\"]}, {\"input\": \"59525 89384\\r\\n22351 37316\\r\\n65890 74214\\r\\n28398 69995\\r\\n7467 43872\\r\\n55064 76804\\r\\n17923 40495\\r\\n62371 74803\\r\\n4078 41237\\r\\n5070 74654\\r\\n38831 68938\\r\\n34960 50130\\r\\n6497 10295\\r\\n20711 72215\\r\\n358 62798\\r\\n20330 76559\\r\\n31787 44161\\r\\n58696 68851\\r\\n41746 60647\\r\\n862 24831\\r\\n6657 41239\\r\\n23616 39414\\r\\n63285 88377\\r\\n78268 81666\\r\\n77321 83615\\r\\n14826 49605\\r\\n17298 58135\\r\\n61310 66378\\r\\n41532 60393\\r\\n7443 42799\\r\\n10376 67040\\r\\n10755 23961\\r\\n27367 46089\\r\\n11675 88260\\r\\n16142 17354\\r\\n6602 42235\\r\\n37343 83132\\r\\n17087 49236\\r\\n33715 43589\\r\\n41925 85734\\r\\n25...\", \"output\": [\"67524\"]}, {\"input\": \"99143 93090\\r\\n50949 54195\\r\\n32798 34537\\r\\n17211 79559\\r\\n36749 92805\\r\\n13116 39671\\r\\n67088 71043\\r\\n22544 47957\\r\\n26386 35771\\r\\n37980 37987\\r\\n9822 61785\\r\\n8101 73845\\r\\n5149 8215\\r\\n47380 80113\\r\\n20561 86349\\r\\n52610 71366\\r\\n43269 57659\\r\\n41120 52324\\r\\n32491 73474\\r\\n35902 90128\\r\\n5725 71756\\r\\n27877 35227\\r\\n11910 90238\\r\\n32044 70574\\r\\n10722 72856\\r\\n15517 54617\\r\\n6547 8884\\r\\n47616 61104\\r\\n53770 57368\\r\\n16732 26101\\r\\n7105 64634\\r\\n61970 77705\\r\\n10903 29752\\r\\n18239 66216\\r\\n65594 66758\\r\\n82949 89760\\r\\n8633 48276\\r\\n77048 88335\\r\\n38243 65802\\r\\n10328 51408\\r\\n...\", \"output\": [\"72086\"]}, {\"input\": \"80038 95220\\r\\n27728 33168\\r\\n83975 94946\\r\\n76876 85129\\r\\n14236 79899\\r\\n6047 54365\\r\\n9883 68142\\r\\n31694 74447\\r\\n42889 94287\\r\\n2440 72173\\r\\n2946 6315\\r\\n25159 28719\\r\\n4559 66970\\r\\n28291 64140\\r\\n35011 46851\\r\\n54309 89457\\r\\n38510 40730\\r\\n39559 43176\\r\\n43629 62353\\r\\n30265 48534\\r\\n3953 63839\\r\\n30212 54534\\r\\n12094 63189\\r\\n51397 51837\\r\\n4583 37642\\r\\n89248 94413\\r\\n737 76815\\r\\n24524 72921\\r\\n10358 63341\\r\\n6131 26984\\r\\n25453 46820\\r\\n38211 46668\\r\\n44254 86369\\r\\n39007 84346\\r\\n10570 15013\\r\\n21086 64657\\r\\n53177 57118\\r\\n10582 23461\\r\\n28625 85735\\r\\n81544 90724\\r\\n28...\", \"output\": [\"73158\"]}, {\"input\": \"62566 97927\\r\\n68317 77647\\r\\n21653 94931\\r\\n7414 64175\\r\\n998 48021\\r\\n11329 57019\\r\\n4429 79689\\r\\n63794 85527\\r\\n62731 76214\\r\\n66545 79506\\r\\n18043 32928\\r\\n34373 56177\\r\\n61044 78810\\r\\n1286 95569\\r\\n30285 63149\\r\\n43609 48993\\r\\n3798 75012\\r\\n18286 52430\\r\\n45974 66319\\r\\n65151 65727\\r\\n91617 97765\\r\\n14752 17033\\r\\n4498 87772\\r\\n6188 27320\\r\\n85342 86948\\r\\n27865 65647\\r\\n27855 49251\\r\\n14868 58888\\r\\n33808 43690\\r\\n43321 86031\\r\\n32626 95314\\r\\n63421 94544\\r\\n262 50279\\r\\n4267 88940\\r\\n27526 71711\\r\\n20509 61941\\r\\n17617 93054\\r\\n35039 57388\\r\\n24592 65582\\r\\n7713 41455\\r\\n393...\", \"output\": [\"74433\"]}, {\"input\": \"65563 90360\\r\\n5917 72615\\r\\n1527 10076\\r\\n21803 22289\\r\\n36217 75333\\r\\n17621 20343\\r\\n71805 85391\\r\\n1295 50612\\r\\n49982 90286\\r\\n53712 69340\\r\\n32990 41756\\r\\n59756 68713\\r\\n38135 39485\\r\\n31019 50729\\r\\n59732 65657\\r\\n56770 61017\\r\\n1089 58646\\r\\n423 72757\\r\\n795 16334\\r\\n8304 58577\\r\\n82708 87667\\r\\n61234 77087\\r\\n9132 62236\\r\\n44889 49543\\r\\n16031 21015\\r\\n14643 54441\\r\\n1804 88183\\r\\n26959 86411\\r\\n15435 83636\\r\\n21892 24019\\r\\n56029 69807\\r\\n4552 38176\\r\\n19898 23801\\r\\n62208 88196\\r\\n2744 14470\\r\\n44354 45484\\r\\n54899 68475\\r\\n10739 46722\\r\\n3359 64876\\r\\n41128 53716\\r\\n69030...\", \"output\": [\"68828\"]}, {\"input\": \"58242 95875\\r\\n50628 88159\\r\\n10216 42194\\r\\n24797 75311\\r\\n35327 94418\\r\\n10294 41016\\r\\n74579 81427\\r\\n2681 20988\\r\\n43652 85835\\r\\n22030 87583\\r\\n15623 83335\\r\\n7167 41731\\r\\n39891 82405\\r\\n13018 95058\\r\\n29503 89074\\r\\n16348 84112\\r\\n44981 46647\\r\\n44355 74204\\r\\n47555 60988\\r\\n3502 77623\\r\\n30152 42128\\r\\n11686 87903\\r\\n4261 9361\\r\\n8147 29496\\r\\n10263 87608\\r\\n36553 62806\\r\\n14753 27358\\r\\n31756 60790\\r\\n13952 69174\\r\\n4623 54241\\r\\n36090 92900\\r\\n84953 89229\\r\\n40187 53301\\r\\n41345 83109\\r\\n17296 92667\\r\\n7741 57946\\r\\n61708 93175\\r\\n27516 86322\\r\\n36765 90186\\r\\n6476 9807\\r\\n3...\", \"output\": [\"72658\"]}, {\"input\": \"58571 94052\\r\\n18089 88936\\r\\n2964 47107\\r\\n300 70501\\r\\n51871 89730\\r\\n43263 84195\\r\\n63464 64360\\r\\n41784 57811\\r\\n13956 49997\\r\\n45205 67429\\r\\n14439 59561\\r\\n8396 89897\\r\\n15925 25159\\r\\n7612 54254\\r\\n25352 55548\\r\\n37823 88837\\r\\n65531 85460\\r\\n24387 77030\\r\\n8884 16625\\r\\n18167 36805\\r\\n54449 55664\\r\\n80274 86111\\r\\n42838 44052\\r\\n49963 79598\\r\\n5276 46778\\r\\n43604 53916\\r\\n71609 83318\\r\\n5997 17697\\r\\n14843 26608\\r\\n46229 80954\\r\\n2081 81328\\r\\n22502 59827\\r\\n3741 87969\\r\\n80446 80495\\r\\n74921 79210\\r\\n65941 81086\\r\\n68241 86906\\r\\n22428 91169\\r\\n38976 44477\\r\\n560 33035\\r\\n136...\", \"output\": [\"70990\"]}, {\"input\": \"11 3\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n2 2\\r\\n2 2\\r\\n2 2\\r\\n3 3\\r\\n3 3\\r\\n3 3\\r\\n3 3\\r\\n\", \"output\": [\"2\"]}]"}
{"prob_desc_description":"You are given an integer N. Consider all possible segments on the coordinate axis with endpoints at integer points with coordinates between 0 and N, inclusive; there will be  of them.You want to draw these segments in several layers so that in each layer the segments don't overlap (they might touch at the endpoints though). You can not move the segments to a different location on the coordinate axis. Find the minimal number of layers you have to use for the given N.","prob_desc_output_spec":"Output a single integer - the minimal number of layers required to draw the segments for the given N.","lang_cluster":"","src_uid":"f8af5dfcf841a7f105ac4c144eb51319","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","constructive algorithms"],"prob_desc_created_at":"1514392500","prob_desc_sample_inputs":"[\"2\", \"3\", \"4\"]","prob_desc_notes":"NoteAs an example, here are the segments and their optimal arrangement into layers for N\u2009=\u20094.  ","exec_outcome":"","difficulty":1300.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The only input line contains a single integer N (1\u2009\u2264\u2009N\u2009\u2264\u2009100).","prob_desc_sample_outputs":"[\"2\", \"4\", \"6\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"21\\r\\n\", \"output\": [\"121\"]}, {\"input\": \"100\\r\\n\", \"output\": [\"2550\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"11\\r\\n\", \"output\": [\"36\"]}, {\"input\": \"12\\r\\n\", \"output\": [\"42\"]}, {\"input\": \"13\\r\\n\", \"output\": [\"49\"]}, {\"input\": \"14\\r\\n\", \"output\": [\"56\"]}, {\"input\": \"15\\r\\n\", \"output\": [\"64\"]}, {\"input\": \"16\\r\\n\", \"output\": [\"72\"]}, {\"input\": \"17\\r\\n\", \"output\": [\"81\"]}, {\"input\": \"18\\r\\n\", \"output\": [\"90\"]}, {\"input\": \"19\\r\\n\", \"output\": [\"100\"]}, {\"input\": \"20\\r\\n\", \"output\": [\"110\"]}, {\"input\": \"22\\r\\n\", \"output\": [\"132\"]}, {\"input\": \"23\\r\\n\", \"output\": [\"144\"]}, {\"input\": \"24\\r\\n\", \"output\": [\"156\"]}, {\"input\": \"25\\r\\n\", \"output\": [\"169\"]}, {\"input\": \"26\\r\\n\", \"output\": [\"182\"]}, {\"input\": \"27\\r\\n\", \"output\": [\"196\"]}, {\"input\": \"28\\r\\n\", \"output\": [\"210\"]}, {\"input\": \"29\\r\\n\", \"output\": [\"225\"]}, {\"input\": \"30\\r\\n\", \"output\": [\"240\"]}, {\"input\": \"31\\r\\n\", \"output\": [\"256\"]}, {\"input\": \"32\\r\\n\", \"output\": [\"272\"]}, {\"input\": \"33\\r\\n\", \"output\": [\"289\"]}, {\"input\": \"34\\r\\n\", \"output\": [\"306\"]}, {\"input\": \"35\\r\\n\", \"output\": [\"324\"]}, {\"input\": \"36\\r\\n\", \"output\": [\"342\"]}, {\"input\": \"37\\r\\n\", \"output\": [\"361\"]}, {\"input\": \"38\\r\\n\", \"output\": [\"380\"]}, {\"input\": \"39\\r\\n\", \"output\": [\"400\"]}, {\"input\": \"40\\r\\n\", \"output\": [\"420\"]}, {\"input\": \"41\\r\\n\", \"output\": [\"441\"]}, {\"input\": \"42\\r\\n\", \"output\": [\"462\"]}, {\"input\": \"43\\r\\n\", \"output\": [\"484\"]}, {\"input\": \"44\\r\\n\", \"output\": [\"506\"]}, {\"input\": \"45\\r\\n\", \"output\": [\"529\"]}, {\"input\": \"46\\r\\n\", \"output\": [\"552\"]}, {\"input\": \"47\\r\\n\", \"output\": [\"576\"]}, {\"input\": \"48\\r\\n\", \"output\": [\"600\"]}, {\"input\": \"49\\r\\n\", \"output\": [\"625\"]}, {\"input\": \"50\\r\\n\", \"output\": [\"650\"]}, {\"input\": \"51\\r\\n\", \"output\": [\"676\"]}, {\"input\": \"52\\r\\n\", \"output\": [\"702\"]}, {\"input\": \"53\\r\\n\", \"output\": [\"729\"]}, {\"input\": \"54\\r\\n\", \"output\": [\"756\"]}, {\"input\": \"55\\r\\n\", \"output\": [\"784\"]}, {\"input\": \"56\\r\\n\", \"output\": [\"812\"]}, {\"input\": \"57\\r\\n\", \"output\": [\"841\"]}, {\"input\": \"58\\r\\n\", \"output\": [\"870\"]}, {\"input\": \"59\\r\\n\", \"output\": [\"900\"]}, {\"input\": \"60\\r\\n\", \"output\": [\"930\"]}, {\"input\": \"61\\r\\n\", \"output\": [\"961\"]}, {\"input\": \"62\\r\\n\", \"output\": [\"992\"]}, {\"input\": \"63\\r\\n\", \"output\": [\"1024\"]}, {\"input\": \"64\\r\\n\", \"output\": [\"1056\"]}, {\"input\": \"65\\r\\n\", \"output\": [\"1089\"]}, {\"input\": \"66\\r\\n\", \"output\": [\"1122\"]}, {\"input\": \"67\\r\\n\", \"output\": [\"1156\"]}, {\"input\": \"68\\r\\n\", \"output\": [\"1190\"]}, {\"input\": \"69\\r\\n\", \"output\": [\"1225\"]}, {\"input\": \"70\\r\\n\", \"output\": [\"1260\"]}, {\"input\": \"71\\r\\n\", \"output\": [\"1296\"]}, {\"input\": \"72\\r\\n\", \"output\": [\"1332\"]}, {\"input\": \"73\\r\\n\", \"output\": [\"1369\"]}, {\"input\": \"74\\r\\n\", \"output\": [\"1406\"]}, {\"input\": \"75\\r\\n\", \"output\": [\"1444\"]}, {\"input\": \"76\\r\\n\", \"output\": [\"1482\"]}, {\"input\": \"77\\r\\n\", \"output\": [\"1521\"]}, {\"input\": \"78\\r\\n\", \"output\": [\"1560\"]}, {\"input\": \"79\\r\\n\", \"output\": [\"1600\"]}, {\"input\": \"80\\r\\n\", \"output\": [\"1640\"]}, {\"input\": \"81\\r\\n\", \"output\": [\"1681\"]}, {\"input\": \"82\\r\\n\", \"output\": [\"1722\"]}, {\"input\": \"83\\r\\n\", \"output\": [\"1764\"]}, {\"input\": \"84\\r\\n\", \"output\": [\"1806\"]}, {\"input\": \"85\\r\\n\", \"output\": [\"1849\"]}, {\"input\": \"86\\r\\n\", \"output\": [\"1892\"]}, {\"input\": \"87\\r\\n\", \"output\": [\"1936\"]}, {\"input\": \"88\\r\\n\", \"output\": [\"1980\"]}, {\"input\": \"89\\r\\n\", \"output\": [\"2025\"]}, {\"input\": \"90\\r\\n\", \"output\": [\"2070\"]}, {\"input\": \"91\\r\\n\", \"output\": [\"2116\"]}, {\"input\": \"92\\r\\n\", \"output\": [\"2162\"]}, {\"input\": \"93\\r\\n\", \"output\": [\"2209\"]}, {\"input\": \"94\\r\\n\", \"output\": [\"2256\"]}, {\"input\": \"95\\r\\n\", \"output\": [\"2304\"]}, {\"input\": \"96\\r\\n\", \"output\": [\"2352\"]}, {\"input\": \"97\\r\\n\", \"output\": [\"2401\"]}, {\"input\": \"98\\r\\n\", \"output\": [\"2450\"]}, {\"input\": \"99\\r\\n\", \"output\": [\"2500\"]}]"}
{"prob_desc_description":"Given an integer $$$x$$$. Your task is to find out how many positive integers $$$n$$$ ($$$1 \\leq n \\leq x$$$) satisfy $$$$$$n \\cdot a^n \\equiv b \\quad (\\textrm{mod}\\;p),$$$$$$ where $$$a, b, p$$$ are all known constants.","prob_desc_output_spec":"Print a single integer: the number of possible answers $$$n$$$.","lang_cluster":"","src_uid":"4b9f470e5889da29affae6376f6c9f6a","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","chinese remainder theorem","number theory"],"prob_desc_created_at":"1517403900","prob_desc_sample_inputs":"[\"2 3 5 8\", \"4 6 7 13\", \"233 233 10007 1\"]","prob_desc_notes":"NoteIn the first sample, we can see that $$$n=2$$$ and $$$n=8$$$ are possible answers.","exec_outcome":"","difficulty":2100.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"3 seconds","prob_desc_input_spec":"The only line contains four integers $$$a,b,p,x$$$ ($$$2 \\leq p \\leq 10^6+3$$$, $$$1 \\leq a,b < p$$$, $$$1 \\leq x \\leq 10^{12}$$$). It is guaranteed that $$$p$$$ is a prime.","prob_desc_sample_outputs":"[\"2\", \"1\", \"1\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 3 5 8\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 6 7 13\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"233 233 10007 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"338792 190248 339821 152634074578\\r\\n\", \"output\": [\"449263\"]}, {\"input\": \"629260 663548 739463 321804928248\\r\\n\", \"output\": [\"434818\"]}, {\"input\": \"656229 20757 818339 523535590429\\r\\n\", \"output\": [\"639482\"]}, {\"input\": \"1000002 1000002 1000003 1000000000000\\r\\n\", \"output\": [\"999998\"]}, {\"input\": \"345 2746 1000003 5000000\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"802942 824238 836833 605503824329\\r\\n\", \"output\": [\"723664\"]}, {\"input\": \"1 1 2 880336470888\\r\\n\", \"output\": [\"440168235444\"]}, {\"input\": \"2 2 3 291982585081\\r\\n\", \"output\": [\"97327528361\"]}, {\"input\": \"699601 39672 1000003 391631540387\\r\\n\", \"output\": [\"391905\"]}, {\"input\": \"9 1 11 792412106895\\r\\n\", \"output\": [\"72037464262\"]}, {\"input\": \"85 535 541 680776274925\\r\\n\", \"output\": [\"1258366493\"]}, {\"input\": \"3153 4504 7919 903755230811\\r\\n\", \"output\": [\"114124839\"]}, {\"input\": \"10021 18448 20719 509684975746\\r\\n\", \"output\": [\"24599907\"]}, {\"input\": \"66634 64950 66889 215112576953\\r\\n\", \"output\": [\"3215965\"]}, {\"input\": \"585128 179390 836839 556227387547\\r\\n\", \"output\": [\"664796\"]}, {\"input\": \"299973 381004 1000003 140225320941\\r\\n\", \"output\": [\"140481\"]}, {\"input\": \"941641 359143 1000003 851964325687\\r\\n\", \"output\": [\"851984\"]}, {\"input\": \"500719 741769 1000003 596263138944\\r\\n\", \"output\": [\"596056\"]}, {\"input\": \"142385 83099 1000003 308002143690\\r\\n\", \"output\": [\"307937\"]}, {\"input\": \"891986 300056 999983 445202944465\\r\\n\", \"output\": [\"445451\"]}, {\"input\": \"620328 378284 999983 189501757723\\r\\n\", \"output\": [\"189574\"]}, {\"input\": \"524578 993938 999979 535629124351\\r\\n\", \"output\": [\"535377\"]}, {\"input\": \"419620 683571 999979 243073161801\\r\\n\", \"output\": [\"243611\"]}, {\"input\": \"339138 549930 999883 962863668031\\r\\n\", \"output\": [\"962803\"]}, {\"input\": \"981603 635385 999233 143056117417\\r\\n\", \"output\": [\"143126\"]}, {\"input\": \"416133 340425 998561 195227456237\\r\\n\", \"output\": [\"195090\"]}, {\"input\": \"603835 578057 996323 932597132292\\r\\n\", \"output\": [\"936103\"]}, {\"input\": \"997998 999323 1000003 999968459613\\r\\n\", \"output\": [\"999964\"]}, {\"input\": \"997642 996418 999983 999997055535\\r\\n\", \"output\": [\"1000007\"]}, {\"input\": \"812415 818711 820231 999990437063\\r\\n\", \"output\": [\"1219017\"]}, {\"input\": \"994574 993183 1000003 999974679059\\r\\n\", \"output\": [\"999965\"]}, {\"input\": \"999183 998981 999979 999970875649\\r\\n\", \"output\": [\"999996\"]}, {\"input\": \"1 1 2 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"699601 39672 1000003 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 1 5 15\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"912896 91931 999983 236754\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"154814 35966 269041 1234567\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"1 2 5 470854713201\\r\\n\", \"output\": [\"94170942640\"]}, {\"input\": \"3 27 29 968042258975\\r\\n\", \"output\": [\"33380767549\"]}, {\"input\": \"473 392 541 108827666667\\r\\n\", \"output\": [\"201160200\"]}, {\"input\": \"8 27 29 193012366642\\r\\n\", \"output\": [\"6655598851\"]}, {\"input\": \"1302 504 1987 842777827450\\r\\n\", \"output\": [\"424145863\"]}, {\"input\": \"693528 398514 1000003 1000000000000\\r\\n\", \"output\": [\"999995\"]}, {\"input\": \"533806 514846 1000003 999999999999\\r\\n\", \"output\": [\"999997\"]}, {\"input\": \"812509 699256 1000003 999999999999\\r\\n\", \"output\": [\"999997\"]}, {\"input\": \"28361 465012 1000003 1000000000000\\r\\n\", \"output\": [\"999996\"]}, {\"input\": \"28361 465012 1000003 12693229\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"28361 465012 1000003 13271836\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"28361 465012 1000003 13271835\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"28361 465012 1000003 13421000\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"28361 465012 1000003 19609900\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"28361 465012 1000003 12693228\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1 2 1000000000000\\r\\n\", \"output\": [\"500000000000\"]}, {\"input\": \"1 1000002 1000003 1000000000000\\r\\n\", \"output\": [\"999997\"]}, {\"input\": \"1 44444 1000003 999999999998\\r\\n\", \"output\": [\"999997\"]}, {\"input\": \"2 1000002 1000003 1000000000000\\r\\n\", \"output\": [\"1000001\"]}, {\"input\": \"2 23333 1000003 1000000000000\\r\\n\", \"output\": [\"999999\"]}]"}
{"prob_desc_description":"Imp is in a magic forest, where xorangles grow (wut?)  A xorangle of order n is such a non-degenerate triangle, that lengths of its sides are integers not exceeding n, and the xor-sum of the lengths is equal to zero. Imp has to count the number of distinct xorangles of order n to get out of the forest. Formally, for a given integer n you have to find the number of such triples (a,\u2009b,\u2009c), that:  1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u2009c\u2009\u2264\u2009n;  , where  denotes the bitwise xor of integers x and y.  (a,\u2009b,\u2009c) form a non-degenerate (with strictly positive area) triangle. ","prob_desc_output_spec":"Print the number of xorangles of order n.","lang_cluster":"","src_uid":"838f2e75fdff0f13f002c0dfff0b2e8d","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force"],"prob_desc_created_at":"1518023700","prob_desc_sample_inputs":"[\"6\", \"10\"]","prob_desc_notes":"NoteThe only xorangle in the first sample is (3,\u20095,\u20096).","exec_outcome":"","difficulty":1300.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The only line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u20092500).","prob_desc_sample_outputs":"[\"1\", \"2\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"6\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2500\\r\\n\", \"output\": [\"700393\"]}, {\"input\": \"952\\r\\n\", \"output\": [\"118547\"]}, {\"input\": \"88\\r\\n\", \"output\": [\"536\"]}, {\"input\": \"1216\\r\\n\", \"output\": [\"160822\"]}, {\"input\": \"2140\\r\\n\", \"output\": [\"614785\"]}, {\"input\": \"564\\r\\n\", \"output\": [\"35087\"]}, {\"input\": \"1488\\r\\n\", \"output\": [\"239580\"]}, {\"input\": \"116\\r\\n\", \"output\": [\"1332\"]}, {\"input\": \"1040\\r\\n\", \"output\": [\"145820\"]}, {\"input\": \"1965\\r\\n\", \"output\": [\"545494\"]}, {\"input\": \"593\\r\\n\", \"output\": [\"36605\"]}, {\"input\": \"779\\r\\n\", \"output\": [\"63500\"]}, {\"input\": \"1703\\r\\n\", \"output\": [\"352045\"]}, {\"input\": \"331\\r\\n\", \"output\": [\"9877\"]}, {\"input\": \"1051\\r\\n\", \"output\": [\"145985\"]}, {\"input\": \"2179\\r\\n\", \"output\": [\"618074\"]}, {\"input\": \"603\\r\\n\", \"output\": [\"37312\"]}, {\"input\": \"1731\\r\\n\", \"output\": [\"369691\"]}, {\"input\": \"2451\\r\\n\", \"output\": [\"681980\"]}, {\"input\": \"1079\\r\\n\", \"output\": [\"146833\"]}, {\"input\": \"2207\\r\\n\", \"output\": [\"621708\"]}, {\"input\": \"2394\\r\\n\", \"output\": [\"663240\"]}, {\"input\": \"818\\r\\n\", \"output\": [\"73972\"]}, {\"input\": \"1946\\r\\n\", \"output\": [\"529383\"]}, {\"input\": \"166\\r\\n\", \"output\": [\"2200\"]}, {\"input\": \"1294\\r\\n\", \"output\": [\"175915\"]}, {\"input\": \"2218\\r\\n\", \"output\": [\"623386\"]}, {\"input\": \"846\\r\\n\", \"output\": [\"82106\"]}, {\"input\": \"1566\\r\\n\", \"output\": [\"273341\"]}, {\"input\": \"194\\r\\n\", \"output\": [\"3240\"]}, {\"input\": \"1322\\r\\n\", \"output\": [\"183405\"]}, {\"input\": \"1508\\r\\n\", \"output\": [\"247634\"]}, {\"input\": \"2433\\r\\n\", \"output\": [\"675245\"]}, {\"input\": \"857\\r\\n\", \"output\": [\"85529\"]}, {\"input\": \"1781\\r\\n\", \"output\": [\"402718\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2444\\r\\n\", \"output\": [\"679373\"]}, {\"input\": \"2498\\r\\n\", \"output\": [\"699536\"]}]"}
{"prob_desc_description":"Mahmoud and Ehab play a game called the even-odd game. Ehab chooses his favorite integer n and then they take turns, starting from Mahmoud. In each player's turn, he has to choose an integer a and subtract it from n such that:  1\u2009\u2264\u2009a\u2009\u2264\u2009n.  If it's Mahmoud's turn, a has to be even, but if it's Ehab's turn, a has to be odd. If the current player can't choose any number satisfying the conditions, he loses. Can you determine the winner if they both play optimally?","prob_desc_output_spec":"Output \"Mahmoud\" (without quotes) if Mahmoud wins and \"Ehab\" (without quotes) otherwise.","lang_cluster":"","src_uid":"5e74750f44142624e6da41d4b35beb9a","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["games","math"],"prob_desc_created_at":"1522771500","prob_desc_sample_inputs":"[\"1\", \"2\"]","prob_desc_notes":"NoteIn the first sample, Mahmoud can't choose any integer a initially because there is no positive even integer less than or equal to 1 so Ehab wins.In the second sample, Mahmoud has to choose a\u2009=\u20092 and subtract it from n. It's Ehab's turn and n\u2009=\u20090. There is no positive odd integer less than or equal to 0 so Mahmoud wins.","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The only line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009109), the number at the beginning of the game.","prob_desc_sample_outputs":"[\"Ehab\", \"Mahmoud\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1\\r\\n\", \"output\": [\"Ehab\"]}, {\"input\": \"2\\r\\n\", \"output\": [\"Mahmoud\"]}, {\"input\": \"10000\\r\\n\", \"output\": [\"Mahmoud\"]}, {\"input\": \"33333\\r\\n\", \"output\": [\"Ehab\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"Ehab\"]}, {\"input\": \"1000000000\\r\\n\", \"output\": [\"Mahmoud\"]}, {\"input\": \"999999999\\r\\n\", \"output\": [\"Ehab\"]}, {\"input\": \"123123123\\r\\n\", \"output\": [\"Ehab\"]}, {\"input\": \"22222221\\r\\n\", \"output\": [\"Ehab\"]}, {\"input\": \"22222220\\r\\n\", \"output\": [\"Mahmoud\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"Ehab\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"Mahmoud\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"Mahmoud\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"Ehab\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"Mahmoud\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"Ehab\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"Mahmoud\"]}, {\"input\": \"536870912\\r\\n\", \"output\": [\"Mahmoud\"]}, {\"input\": \"536870913\\r\\n\", \"output\": [\"Ehab\"]}, {\"input\": \"536870911\\r\\n\", \"output\": [\"Ehab\"]}]"}
{"prob_desc_description":"Katie, Kuro and Shiro are best friends. They have known each other since kindergarten. That's why they often share everything with each other and work together on some very hard problems.Today is Shiro's birthday. She really loves pizza so she wants to invite her friends to the pizza restaurant near her house to celebrate her birthday, including her best friends Katie and Kuro.She has ordered a very big round pizza, in order to serve her many friends. Exactly $$$n$$$ of Shiro's friends are here. That's why she has to divide the pizza into $$$n + 1$$$ slices (Shiro also needs to eat). She wants the slices to be exactly the same size and shape. If not, some of her friends will get mad and go home early, and the party will be over.Shiro is now hungry. She wants to cut the pizza with minimum of straight cuts. A cut is a straight segment, it might have ends inside or outside the pizza. But she is too lazy to pick up the calculator.As usual, she will ask Katie and Kuro for help. But they haven't come yet. Could you help Shiro with this problem?","prob_desc_output_spec":"A single integer\u00a0\u2014 the number of straight cuts Shiro needs.","lang_cluster":"","src_uid":"236177ff30dafe68295b5d33dc501828","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"128 megabytes","file_name":"prog_syn_val.jsonl","tags":["math"],"prob_desc_created_at":"1526308500","prob_desc_sample_inputs":"[\"3\", \"4\"]","prob_desc_notes":"NoteTo cut the round pizza into quarters one has to make two cuts through the center with angle $$$90^{\\circ}$$$ between them.To cut the round pizza into five equal parts one has to make five cuts.","exec_outcome":"","difficulty":1000.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"A single line contains one non-negative integer $$$n$$$ ($$$0 \\le n \\leq 10^{18}$$$)\u00a0\u2014 the number of Shiro's friends. The circular pizza has to be sliced into $$$n + 1$$$ pieces.","prob_desc_sample_outputs":"[\"2\", \"5\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"10000000000\\r\\n\", \"output\": [\"10000000001\"]}, {\"input\": \"1234567891\\r\\n\", \"output\": [\"617283946\"]}, {\"input\": \"7509213957\\r\\n\", \"output\": [\"3754606979\"]}, {\"input\": \"99999999999999999\\r\\n\", \"output\": [\"50000000000000000\"]}, {\"input\": \"21\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"712394453192\\r\\n\", \"output\": [\"712394453193\"]}, {\"input\": \"172212168\\r\\n\", \"output\": [\"172212169\"]}, {\"input\": \"822981260158260519\\r\\n\", \"output\": [\"411490630079130260\"]}, {\"input\": \"28316250877914571\\r\\n\", \"output\": [\"14158125438957286\"]}, {\"input\": \"779547116602436424\\r\\n\", \"output\": [\"779547116602436425\"]}, {\"input\": \"578223540024979436\\r\\n\", \"output\": [\"578223540024979437\"]}, {\"input\": \"335408917861648766\\r\\n\", \"output\": [\"335408917861648767\"]}, {\"input\": \"74859962623690078\\r\\n\", \"output\": [\"74859962623690079\"]}, {\"input\": \"252509054433933439\\r\\n\", \"output\": [\"126254527216966720\"]}, {\"input\": \"760713016476190622\\r\\n\", \"output\": [\"760713016476190623\"]}, {\"input\": \"919845426262703496\\r\\n\", \"output\": [\"919845426262703497\"]}, {\"input\": \"585335723211047194\\r\\n\", \"output\": [\"585335723211047195\"]}, {\"input\": \"522842184971407769\\r\\n\", \"output\": [\"261421092485703885\"]}, {\"input\": \"148049062628894320\\r\\n\", \"output\": [\"148049062628894321\"]}, {\"input\": \"84324828731963974\\r\\n\", \"output\": [\"84324828731963975\"]}, {\"input\": \"354979173822804781\\r\\n\", \"output\": [\"177489586911402391\"]}, {\"input\": \"1312150450968413\\r\\n\", \"output\": [\"656075225484207\"]}, {\"input\": \"269587449430302150\\r\\n\", \"output\": [\"269587449430302151\"]}, {\"input\": \"645762258982631926\\r\\n\", \"output\": [\"645762258982631927\"]}, {\"input\": \"615812229161735895\\r\\n\", \"output\": [\"307906114580867948\"]}, {\"input\": \"0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"349993004923078531\\r\\n\", \"output\": [\"174996502461539266\"]}, {\"input\": \"891351282707723851\\r\\n\", \"output\": [\"445675641353861926\"]}, {\"input\": \"563324731189330734\\r\\n\", \"output\": [\"563324731189330735\"]}, {\"input\": \"520974001910286909\\r\\n\", \"output\": [\"260487000955143455\"]}, {\"input\": \"666729339802329204\\r\\n\", \"output\": [\"666729339802329205\"]}, {\"input\": \"856674611404539671\\r\\n\", \"output\": [\"428337305702269836\"]}, {\"input\": \"791809296303238499\\r\\n\", \"output\": [\"395904648151619250\"]}, {\"input\": \"711066337317063338\\r\\n\", \"output\": [\"711066337317063339\"]}, {\"input\": \"931356503492686566\\r\\n\", \"output\": [\"931356503492686567\"]}, {\"input\": \"234122432773361866\\r\\n\", \"output\": [\"234122432773361867\"]}, {\"input\": \"1000000000000000000\\r\\n\", \"output\": [\"1000000000000000001\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"63\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"24\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"15\\r\\n\", \"output\": [\"8\"]}]"}
{"prob_desc_description":"Today on Informatics class Nastya learned about GCD and LCM (see links below). Nastya is very intelligent, so she solved all the tasks momentarily and now suggests you to solve one of them as well.We define a pair of integers (a,\u2009b) good, if GCD(a,\u2009b)\u2009=\u2009x and LCM(a,\u2009b)\u2009=\u2009y, where GCD(a,\u2009b) denotes the greatest common divisor of a and b, and LCM(a,\u2009b) denotes the least common multiple of a and b.You are given two integers x and y. You are to find the number of good pairs of integers (a,\u2009b) such that l\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009r. Note that pairs (a,\u2009b) and (b,\u2009a) are considered different if a\u2009\u2260\u2009b.","prob_desc_output_spec":"In the only line print the only integer\u00a0\u2014 the answer for the problem.","lang_cluster":"","src_uid":"d37dde5841116352c9b37538631d0b15","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","number theory"],"prob_desc_created_at":"1529339700","prob_desc_sample_inputs":"[\"1 2 1 2\", \"1 12 1 12\", \"50 100 3 30\"]","prob_desc_notes":"NoteIn the first example there are two suitable good pairs of integers (a,\u2009b): (1,\u20092) and (2,\u20091).In the second example there are four suitable good pairs of integers (a,\u2009b): (1,\u200912), (12,\u20091), (3,\u20094) and (4,\u20093).In the third example there are good pairs of integers, for example, (3,\u200930), but none of them fits the condition l\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009r.","exec_outcome":"","difficulty":1600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The only line contains four integers l,\u2009r,\u2009x,\u2009y (1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009109, 1\u2009\u2264\u2009x\u2009\u2264\u2009y\u2009\u2264\u2009109).","prob_desc_sample_outputs":"[\"2\", \"4\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1 2 1 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 12 1 12\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"50 100 3 30\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1000000000 1 1000000000\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"1 1000000000 158260522 200224287\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1000000000 2 755829150\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"1 1000000000 158260522 158260522\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1000000000 877914575 877914575\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"232 380232688 116 760465376\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"47259 3393570 267 600661890\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"1 1000000000 1 672672000\\r\\n\", \"output\": [\"64\"]}, {\"input\": \"1000000000 1000000000 1000000000 1000000000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1000000000 1 649209600\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"1 1000000000 1 682290000\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"1 1000000000 1 228614400\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"1 1000000000 1 800280000\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"1 1000000000 1 919987200\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"1 1000000000 1 456537870\\r\\n\", \"output\": [\"64\"]}, {\"input\": \"1 1000000000 1 7198102\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"1 1000000000 1 58986263\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"1 1000000000 1 316465536\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"1 1000000000 1 9558312\\r\\n\", 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6 1024\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 100 2 4\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 10000 2 455\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1000000000 250000000 1000000000\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3 3 1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1000000000 100000000 1000000000\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"5 10 3 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1000 5 13\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 2 3 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1000000000 499999993 999999986\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 1 1 10\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 10 10 100\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1000 4 36\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 1000000000 10000000 20000000\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"100 100 5 5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 3 3 9\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"36 200 24 144\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 100 3 10\\r\\n\", \"output\": [\"0\"]}]"}
{"prob_desc_description":"Vasya has got a tree consisting of $$$n$$$ vertices. He wants to delete some (possibly zero) edges in this tree such that the maximum matching in the resulting graph is unique. He asks you to calculate the number of ways to choose a set of edges to remove.A matching in the graph is a subset of its edges such that there is no vertex incident to two (or more) edges from the subset. A maximum matching is a matching such that the number of edges in the subset is maximum possible among all matchings in this graph.Since the answer may be large, output it modulo $$$998244353$$$.","prob_desc_output_spec":"Print one integer \u2014 the number of ways to delete some (possibly empty) subset of edges so that the maximum matching in the resulting graph is unique. Print the answer modulo $$$998244353$$$.","lang_cluster":"","src_uid":"a40e78a7144ac2fae1890ac7598990bf","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp","trees"],"prob_desc_created_at":"1542557100","prob_desc_sample_inputs":"[\"4\\n1 2\\n1 3\\n1 4\", \"4\\n1 2\\n2 3\\n3 4\", \"1\"]","prob_desc_notes":"NotePossible ways to delete edges in the first example:   delete $$$(1, 2)$$$ and $$$(1, 3)$$$.  delete $$$(1, 2)$$$ and $$$(1, 4)$$$.  delete $$$(1, 3)$$$ and $$$(1, 4)$$$.  delete all edges. Possible ways to delete edges in the second example:   delete no edges.  delete $$$(1, 2)$$$ and $$$(2, 3)$$$.  delete $$$(1, 2)$$$ and $$$(3, 4)$$$.  delete $$$(2, 3)$$$ and $$$(3, 4)$$$.  delete $$$(2, 3)$$$.  delete all edges. ","exec_outcome":"","difficulty":2400.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"3 seconds","prob_desc_input_spec":"The first line contains one integer $$$n$$$ ($$$1 \\le n \\le 3 \\cdot 10^5$$$) \u2014 the number of vertices in the tree. Each of the next $$$n \u2212 1$$$ lines contains two integers $$$u$$$ and $$$v$$$ ($$$1 \\le u, v \\le n, u \\neq v$$$) denoting an edge between vertex $$$u$$$ and vertex $$$v$$$. It is guaranteed that these edges form a tree.","prob_desc_sample_outputs":"[\"4\", \"6\", \"1\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4\\r\\n1 2\\r\\n1 3\\r\\n1 4\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"4\\r\\n1 2\\r\\n2 3\\r\\n3 4\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10\\r\\n7 4\\r\\n3 8\\r\\n7 8\\r\\n9 5\\r\\n10 8\\r\\n9 7\\r\\n2 4\\r\\n1 3\\r\\n6 9\\r\\n\", \"output\": [\"161\"]}, {\"input\": \"299600\\r\\n186599 238798\\r\\n125435 238798\\r\\n141148 238798\\r\\n120933 238798\\r\\n238798 197437\\r\\n39681 238798\\r\\n150685 238798\\r\\n238798 201653\\r\\n173007 238798\\r\\n238798 177497\\r\\n285789 238798\\r\\n238798 40789\\r\\n203051 238798\\r\\n283442 238798\\r\\n238798 1521\\r\\n238798 147196\\r\\n238798 36884\\r\\n238798 212334\\r\\n140653 238798\\r\\n238798 38375\\r\\n238798 224506\\r\\n238798 183809\\r\\n238798 31698\\r\\n238798 63074\\r\\n238798 147783\\r\\n238798 40988\\r\\n238798 16903\\r\\n238798 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197582\\r\\n25728 73901\\r\\n25728 254104\\r\\n25728 268816\\r\\n25728 294542\\r\\n25728 138861\\r\\n25728 30229\\r\\n25728 114007\\r\\n25728 36291\\r\\n25728 49699\\r\\n25728 11316\\r\\n25728 45245\\r\\n25728 125329\\r\\n25728 49730\\r\\n25728 60141\\r\\n25728 34216\\r\\n25728 11356\\r\\n25728 162631\\r\\n25728 88601\\r\\n25728 295915\\r\\n25728 103814\\r\\n25728 61356\\r\\n25728 199525\\r\\n25728 256497\\r\\n25728 12399\\r\\n25728 223819\\r\\n25728 206737\\r\\n25728 290583\\r\\n25728 152541\\r\\n25728 201950\\r\\n25728 31937\\r\\n25728 168983\\r\\n25728 88484\\r\\n257...\", \"output\": [\"490284571\"]}, {\"input\": \"300000\\r\\n230566 122042\\r\\n230566 66294\\r\\n230566 191268\\r\\n230566 196188\\r\\n230566 201806\\r\\n230566 123230\\r\\n230566 144329\\r\\n230566 94286\\r\\n230566 7406\\r\\n230566 290629\\r\\n230566 125323\\r\\n230566 98347\\r\\n230566 110586\\r\\n230566 77562\\r\\n230566 137733\\r\\n230566 107085\\r\\n230566 36623\\r\\n230566 250717\\r\\n230566 199261\\r\\n230566 65767\\r\\n230566 94341\\r\\n230566 7164\\r\\n230566 19106\\r\\n230566 118066\\r\\n230566 26436\\r\\n230566 228636\\r\\n230566 224566\\r\\n230566 155593\\r\\n230566 223789\\r\\n230566 189526\\r\\n230566 222331\\r\\n230566 62124\\r\\n230566 148393\\r\\n230566 110371\\r\\n230566 ...\", \"output\": [\"26114030\"]}]"}
{"prob_desc_description":"You are given a binary string $$$s$$$.Find the number of distinct cyclical binary strings of length $$$n$$$ which contain $$$s$$$ as a substring.The cyclical string $$$t$$$ contains $$$s$$$ as a substring if there is some cyclical shift of string $$$t$$$, such that $$$s$$$ is a substring of this cyclical shift of $$$t$$$.For example, the cyclical string \"000111\" contains substrings \"001\", \"01110\" and \"10\", but doesn't contain \"0110\" and \"10110\".Two cyclical strings are called different if they differ from each other as strings. For example, two different strings, which differ from each other by a cyclical shift, are still considered different cyclical strings.","prob_desc_output_spec":"Print the only integer\u00a0\u2014 the number of distinct cyclical binary strings $$$t$$$, which contain $$$s$$$ as a substring.","lang_cluster":"","src_uid":"0034806908c9794086736a2d07fc654c","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp","strings"],"prob_desc_created_at":"1536248100","prob_desc_sample_inputs":"[\"2\\n0\", \"4\\n1010\", \"20\\n10101010101010\"]","prob_desc_notes":"NoteIn the first example, there are three cyclical strings, which contain \"0\"\u00a0\u2014 \"00\", \"01\" and \"10\".In the second example, there are only two such strings\u00a0\u2014 \"1010\", \"0101\".","exec_outcome":"","difficulty":2900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 40$$$)\u00a0\u2014 the length of the target string $$$t$$$. The next line contains the string $$$s$$$ ($$$1 \\le |s| \\le n$$$)\u00a0\u2014 the string which must be a substring of cyclical string $$$t$$$. String $$$s$$$ contains only characters '0' and '1'.","prob_desc_sample_outputs":"[\"3\", \"2\", \"962\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2\\r\\n0\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"4\\r\\n1010\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"20\\r\\n10101010101010\\r\\n\", \"output\": [\"962\"]}, {\"input\": \"2\\r\\n11\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"5\\r\\n00101\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"10\\r\\n100101\\r\\n\", \"output\": [\"155\"]}, {\"input\": \"4\\r\\n0011\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"7\\r\\n1100\\r\\n\", \"output\": [\"56\"]}, {\"input\": \"8\\r\\n01010001\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"6\\r\\n10\\r\\n\", \"output\": [\"62\"]}, {\"input\": \"17\\r\\n011100101100110\\r\\n\", \"output\": [\"68\"]}, {\"input\": \"22\\r\\n1110011010100111\\r\\n\", \"output\": [\"1408\"]}, {\"input\": \"17\\r\\n1110110111010101\\r\\n\", \"output\": [\"34\"]}, {\"input\": \"11\\r\\n10100000100\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"20\\r\\n10100001011\\r\\n\", \"output\": [\"10230\"]}, {\"input\": \"16\\r\\n101011\\r\\n\", \"output\": [\"15248\"]}, {\"input\": \"33\\r\\n0001100010001100110000\\r\\n\", \"output\": [\"67584\"]}, {\"input\": \"30\\r\\n111001000100\\r\\n\", \"output\": [\"7857600\"]}, {\"input\": \"40\\r\\n1001\\r\\n\", \"output\": [\"1029761794578\"]}, {\"input\": \"31\\r\\n101\\r\\n\", \"output\": [\"2110188507\"]}, {\"input\": \"18\\r\\n001000011010000\\r\\n\", \"output\": [\"144\"]}, {\"input\": \"36\\r\\n110110010000\\r\\n\", \"output\": [\"603021324\"]}, {\"input\": \"40\\r\\n00000111111100110111000010000010101001\\r\\n\", \"output\": [\"160\"]}, {\"input\": \"39\\r\\n000000000000000000000000000000000000001\\r\\n\", \"output\": [\"39\"]}, {\"input\": \"37\\r\\n0101010101010101010101010101010101010\\r\\n\", \"output\": [\"37\"]}, {\"input\": \"31\\r\\n11011101110000011100\\r\\n\", \"output\": [\"63488\"]}, {\"input\": \"34\\r\\n110000100\\r\\n\", \"output\": [\"1121963008\"]}, {\"input\": \"35\\r\\n111111100100100\\r\\n\", \"output\": [\"36696800\"]}, {\"input\": \"20\\r\\n100010000\\r\\n\", \"output\": [\"40840\"]}, {\"input\": \"21\\r\\n01011101001010001\\r\\n\", \"output\": [\"336\"]}, {\"input\": \"11\\r\\n00010\\r\\n\", \"output\": [\"638\"]}, {\"input\": \"16\\r\\n10011000100001\\r\\n\", \"output\": [\"64\"]}, {\"input\": \"39\\r\\n11101001101111001011110111010010111001\\r\\n\", \"output\": [\"78\"]}, {\"input\": \"32\\r\\n10101100\\r\\n\", \"output\": [\"519167992\"]}, {\"input\": \"13\\r\\n111\\r\\n\", \"output\": [\"5435\"]}, {\"input\": \"4\\r\\n01\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"8\\r\\n100\\r\\n\", \"output\": [\"208\"]}, {\"input\": \"9\\r\\n1110\\r\\n\", \"output\": [\"270\"]}, {\"input\": \"1\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"20\\r\\n01100111000\\r\\n\", \"output\": [\"10230\"]}, {\"input\": \"5\\r\\n1\\r\\n\", \"output\": [\"31\"]}, {\"input\": \"38\\r\\n11111010100111100011\\r\\n\", \"output\": [\"9961415\"]}, {\"input\": \"24\\r\\n1101110111000111011\\r\\n\", \"output\": [\"768\"]}, {\"input\": \"6\\r\\n101111\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"39\\r\\n1010001010100100001\\r\\n\", \"output\": [\"40894230\"]}, {\"input\": \"34\\r\\n1111001001101011101101101\\r\\n\", \"output\": [\"17408\"]}, {\"input\": \"35\\r\\n11100110100\\r\\n\", \"output\": [\"585195800\"]}, {\"input\": \"7\\r\\n1111\\r\\n\", \"output\": [\"29\"]}, {\"input\": \"35\\r\\n010100010101011110110101000\\r\\n\", \"output\": [\"8960\"]}, {\"input\": \"18\\r\\n110101110001\\r\\n\", \"output\": [\"1152\"]}, {\"input\": \"10\\r\\n0110101\\r\\n\", \"output\": [\"75\"]}, {\"input\": \"38\\r\\n0111110111100000000000100\\r\\n\", \"output\": [\"311296\"]}, {\"input\": \"32\\r\\n101011001\\r\\n\", \"output\": [\"263480312\"]}, {\"input\": \"39\\r\\n111011011000100\\r\\n\", \"output\": [\"654211584\"]}, {\"input\": \"31\\r\\n00101010000\\r\\n\", \"output\": [\"32331574\"]}, {\"input\": \"35\\r\\n100011111010001011100001\\r\\n\", \"output\": [\"71680\"]}, {\"input\": \"39\\r\\n1010000110\\r\\n\", \"output\": [\"20653344998\"]}, {\"input\": \"34\\r\\n1011010111111001100011110111\\r\\n\", \"output\": [\"2176\"]}, {\"input\": \"37\\r\\n100110110011100100100010110000011\\r\\n\", \"output\": [\"592\"]}, {\"input\": \"40\\r\\n1010100001001010110011000110001\\r\\n\", \"output\": [\"20480\"]}, {\"input\": \"30\\r\\n11110010111010001010111\\r\\n\", \"output\": [\"3840\"]}, {\"input\": \"36\\r\\n100101110110110111100110010011001\\r\\n\", \"output\": [\"288\"]}, {\"input\": \"40\\r\\n01011011110\\r\\n\", \"output\": [\"21354424310\"]}, {\"input\": \"36\\r\\n00001010001000010101111010\\r\\n\", \"output\": [\"36864\"]}, {\"input\": \"40\\r\\n111101001000110000111001110111111110111\\r\\n\", \"output\": [\"80\"]}, {\"input\": \"37\\r\\n1000101000000000011101011111010011\\r\\n\", \"output\": [\"296\"]}, {\"input\": \"31\\r\\n0111111101001100\\r\\n\", \"output\": [\"1015777\"]}, {\"input\": \"35\\r\\n00010000111011\\r\\n\", \"output\": [\"73382400\"]}, {\"input\": \"38\\r\\n11111111111111111111111111111111100000\\r\\n\", \"output\": [\"38\"]}, {\"input\": \"39\\r\\n000000000000000111111111111111111111111\\r\\n\", \"output\": [\"39\"]}, {\"input\": \"36\\r\\n000000000011111111111111111111111111\\r\\n\", \"output\": [\"36\"]}, {\"input\": \"37\\r\\n1111110000000000000000000000000000000\\r\\n\", \"output\": [\"37\"]}, {\"input\": \"37\\r\\n0000000000000000011111111111111111111\\r\\n\", \"output\": [\"37\"]}, {\"input\": \"39\\r\\n101010101010101010101010101010101010101\\r\\n\", \"output\": [\"39\"]}, {\"input\": \"38\\r\\n10101010101010101010101010101010101010\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"37\\r\\n1010101010101010101010101010101010101\\r\\n\", \"output\": [\"37\"]}, {\"input\": \"40\\r\\n0101010101010101010101010101010101010101\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"38\\r\\n00000000000000000000000000000000000000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"37\\r\\n0011111111111011011111110111011111111\\r\\n\", \"output\": [\"37\"]}, {\"input\": \"35\\r\\n00001000110100100101101111110101111\\r\\n\", \"output\": [\"35\"]}, {\"input\": \"40\\r\\n0000000000100000100000000000000000000000\\r\\n\", \"output\": [\"40\"]}, {\"input\": \"37\\r\\n0000110000100100011101000100000001010\\r\\n\", \"output\": [\"37\"]}, {\"input\": \"40\\r\\n1111111111111011111111101111111111111111\\r\\n\", \"output\": [\"40\"]}, {\"input\": \"38\\r\\n10100000011100111001100101000100001000\\r\\n\", \"output\": [\"38\"]}, {\"input\": \"40\\r\\n1111110111111111111111011111111111111110\\r\\n\", \"output\": [\"40\"]}, {\"input\": \"40\\r\\n0000010010000000000001000110000001010100\\r\\n\", \"output\": [\"40\"]}, {\"input\": \"39\\r\\n100110001010001000000001010000000110100\\r\\n\", \"output\": [\"39\"]}, {\"input\": \"38\\r\\n01011110100111011\\r\\n\", \"output\": [\"79690256\"]}, {\"input\": \"37\\r\\n100110111000011010011010110011101\\r\\n\", \"output\": [\"592\"]}, {\"input\": \"30\\r\\n000000000110001011111011000\\r\\n\", \"output\": [\"240\"]}, {\"input\": \"33\\r\\n101110110010101\\r\\n\", \"output\": [\"8647584\"]}, {\"input\": \"34\\r\\n1101010100001111111\\r\\n\", \"output\": [\"1114095\"]}, {\"input\": \"32\\r\\n01100010110111100111110010\\r\\n\", \"output\": [\"2048\"]}, {\"input\": \"40\\r\\n000010101101010011111101011110010011\\r\\n\", \"output\": [\"640\"]}, {\"input\": \"32\\r\\n0111010100\\r\\n\", \"output\": [\"133105408\"]}, {\"input\": \"31\\r\\n0101100101100000111001\\r\\n\", \"output\": [\"15872\"]}, {\"input\": \"39\\r\\n00111\\r\\n\", \"output\": [\"419341377312\"]}, {\"input\": \"33\\r\\n00111101\\r\\n\", \"output\": [\"1068677566\"]}, {\"input\": \"37\\r\\n1010001011111100110101110\\r\\n\", \"output\": [\"151552\"]}, {\"input\": \"37\\r\\n111000011\\r\\n\", \"output\": [\"9626769261\"]}, {\"input\": \"37\\r\\n011111001111100010001011000001100111\\r\\n\", \"output\": [\"74\"]}, {\"input\": \"40\\r\\n0000\\r\\n\", \"output\": [\"848129718780\"]}, {\"input\": \"40\\r\\n1000\\r\\n\", \"output\": [\"1060965767804\"]}, {\"input\": \"40\\r\\n0100\\r\\n\", \"output\": [\"1029761794578\"]}, {\"input\": \"40\\r\\n1100\\r\\n\", \"output\": [\"1060965767804\"]}, {\"input\": \"40\\r\\n0010\\r\\n\", \"output\": [\"1029761794578\"]}, {\"input\": \"40\\r\\n1010\\r\\n\", \"output\": [\"1000453489698\"]}, {\"input\": \"40\\r\\n0110\\r\\n\", \"output\": [\"1029761794578\"]}, {\"input\": \"40\\r\\n1110\\r\\n\", \"output\": [\"1060965767804\"]}, {\"input\": \"40\\r\\n0001\\r\\n\", \"output\": [\"1060965767804\"]}, {\"input\": \"40\\r\\n0101\\r\\n\", \"output\": [\"1000453489698\"]}, {\"input\": \"40\\r\\n1101\\r\\n\", \"output\": [\"1029761794578\"]}, {\"input\": \"40\\r\\n0011\\r\\n\", \"output\": [\"1060965767804\"]}, {\"input\": \"40\\r\\n1011\\r\\n\", \"output\": [\"1029761794578\"]}, {\"input\": \"40\\r\\n0111\\r\\n\", \"output\": [\"1060965767804\"]}, {\"input\": \"40\\r\\n1111\\r\\n\", \"output\": [\"848129718780\"]}, {\"input\": \"40\\r\\n000\\r\\n\", \"output\": [\"1060965767805\"]}, {\"input\": \"40\\r\\n100\\r\\n\", \"output\": [\"1099282801648\"]}, {\"input\": \"40\\r\\n010\\r\\n\", \"output\": [\"1093624901051\"]}, {\"input\": \"40\\r\\n110\\r\\n\", \"output\": [\"1099282801648\"]}, {\"input\": \"40\\r\\n001\\r\\n\", \"output\": [\"1099282801648\"]}, {\"input\": \"40\\r\\n101\\r\\n\", \"output\": [\"1093624901051\"]}, {\"input\": \"40\\r\\n011\\r\\n\", \"output\": [\"1099282801648\"]}, {\"input\": \"40\\r\\n111\\r\\n\", \"output\": [\"1060965767805\"]}, {\"input\": \"40\\r\\n00\\r\\n\", \"output\": [\"1099282801649\"]}, {\"input\": \"40\\r\\n01\\r\\n\", \"output\": [\"1099511627774\"]}, {\"input\": \"40\\r\\n10\\r\\n\", \"output\": [\"1099511627774\"]}, {\"input\": \"40\\r\\n11\\r\\n\", \"output\": [\"1099282801649\"]}, {\"input\": \"40\\r\\n0\\r\\n\", \"output\": [\"1099511627775\"]}, {\"input\": \"40\\r\\n1\\r\\n\", \"output\": [\"1099511627775\"]}, {\"input\": \"1\\r\\n0\\r\\n\", \"output\": [\"1\"]}]"}
{"prob_desc_description":"Masha has three sticks of length $$$a$$$, $$$b$$$ and $$$c$$$ centimeters respectively. In one minute Masha can pick one arbitrary stick and increase its length by one centimeter. She is not allowed to break sticks.What is the minimum number of minutes she needs to spend increasing the stick's length in order to be able to assemble a triangle of positive area. Sticks should be used as triangle's sides (one stick for one side) and their endpoints should be located at triangle's vertices.","prob_desc_output_spec":"Print a single integer\u00a0\u2014 the minimum number of minutes that Masha needs to spend in order to be able to make the triangle of positive area from her sticks.","lang_cluster":"","src_uid":"3dc56bc08606a39dd9ca40a43c452f09","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["geometry","brute force","math"],"prob_desc_created_at":"1539511500","prob_desc_sample_inputs":"[\"3 4 5\", \"2 5 3\", \"100 10 10\"]","prob_desc_notes":"NoteIn the first example, Masha can make a triangle from the sticks without increasing the length of any of them.In the second example, Masha can't make a triangle of positive area from the sticks she has at the beginning, but she can spend one minute to increase the length $$$2$$$ centimeter stick by one and after that form a triangle with sides $$$3$$$, $$$3$$$ and $$$5$$$ centimeters.In the third example, Masha can take $$$33$$$ minutes to increase one of the $$$10$$$ centimeters sticks by $$$33$$$ centimeters, and after that take $$$48$$$ minutes to increase another $$$10$$$ centimeters stick by $$$48$$$ centimeters. This way she can form a triangle with lengths $$$43$$$, $$$58$$$ and $$$100$$$ centimeters in $$$81$$$ minutes. One can show that it is impossible to get a valid triangle faster.","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The only line contains tree integers $$$a$$$, $$$b$$$ and $$$c$$$ ($$$1 \\leq a, b, c \\leq 100$$$)\u00a0\u2014 the lengths of sticks Masha possesses.","prob_desc_sample_outputs":"[\"0\", \"1\", \"81\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3 4 5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 5 3\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"100 10 10\\r\\n\", \"output\": [\"81\"]}, {\"input\": \"1 1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100 100 100\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100 1 1\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"12 34 56\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"68 1 67\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"100 100 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100 1 99\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"23 56 33\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"98 12 23\\r\\n\", \"output\": [\"64\"]}, {\"input\": \"88 2 6\\r\\n\", \"output\": [\"81\"]}, {\"input\": \"1 50 87\\r\\n\", \"output\": [\"37\"]}, {\"input\": \"1 50 100\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"1 92 13\\r\\n\", \"output\": [\"79\"]}, {\"input\": \"56 42 87\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100 100 99\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 1 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"14 21 76\\r\\n\", \"output\": [\"42\"]}, {\"input\": \"1 7 35\\r\\n\", \"output\": [\"28\"]}, {\"input\": \"86 43 10\\r\\n\", \"output\": [\"34\"]}, {\"input\": \"2 10 2\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"32 99 10\\r\\n\", \"output\": [\"58\"]}, {\"input\": \"2 3 6\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 5 6\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 2 7\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2 5 2\\r\\n\", \"output\": [\"2\"]}]"}
{"prob_desc_description":"Hasan loves playing games and has recently discovered a game called TopScore. In this soccer-like game there are $$$p$$$ players doing penalty shoot-outs. Winner is the one who scores the most. In case of ties, one of the top-scorers will be declared as the winner randomly with equal probability.They have just finished the game and now are waiting for the result. But there's a tiny problem! The judges have lost the paper of scores! Fortunately they have calculated sum of the scores before they get lost and also for some of the players they have remembered a lower bound on how much they scored. However, the information about the bounds is private, so Hasan only got to know his bound.According to the available data, he knows that his score is at least $$$r$$$ and sum of the scores is $$$s$$$.Thus the final state of the game can be represented in form of sequence of $$$p$$$ integers $$$a_1, a_2, \\dots, a_p$$$ ($$$0 \\le a_i$$$) \u2014 player's scores. Hasan is player number $$$1$$$, so $$$a_1 \\ge r$$$. Also $$$a_1 + a_2 + \\dots + a_p = s$$$. Two states are considered different if there exists some position $$$i$$$ such that the value of $$$a_i$$$ differs in these states. Once again, Hasan doesn't know the exact scores (he doesn't know his exact score as well). So he considers each of the final states to be equally probable to achieve.Help Hasan find the probability of him winning.It can be shown that it is in the form of $$$\\frac{P}{Q}$$$ where $$$P$$$ and $$$Q$$$ are non-negative integers and $$$Q \\ne 0$$$, $$$P \\le Q$$$. Report the value of $$$P \\cdot Q^{-1} \\pmod {998244353}$$$.","prob_desc_output_spec":"Print a single integer \u2014 the probability of Hasan winning. It can be shown that it is in the form of $$$\\frac{P}{Q}$$$ where $$$P$$$ and $$$Q$$$ are non-negative integers and $$$Q \\ne 0$$$, $$$P \\le Q$$$. Report the value of $$$P \\cdot Q^{-1} \\pmod {998244353}$$$.","lang_cluster":"","src_uid":"609195ef4a970c62a8210dafe118580e","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","probabilities","combinatorics","dp"],"prob_desc_created_at":"1546007700","prob_desc_sample_inputs":"[\"2 6 3\", \"5 20 11\", \"10 30 10\"]","prob_desc_notes":"NoteIn the first example Hasan can score $$$3$$$, $$$4$$$, $$$5$$$ or $$$6$$$ goals. If he scores $$$4$$$ goals or more than he scores strictly more than his only opponent. If he scores $$$3$$$ then his opponent also scores $$$3$$$ and Hasan has a probability of $$$\\frac 1 2$$$ to win the game. Thus, overall he has the probability of $$$\\frac 7 8$$$ to win.In the second example even Hasan's lower bound on goal implies him scoring more than any of his opponents. Thus, the resulting probability is $$$1$$$.","exec_outcome":"","difficulty":2500.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"3 seconds","prob_desc_input_spec":"The only line contains three integers $$$p$$$, $$$s$$$ and $$$r$$$ ($$$1 \\le p \\le 100$$$, $$$0 \\le r \\le s \\le 5000$$$) \u2014 the number of players, the sum of scores of all players and Hasan's score, respectively.","prob_desc_sample_outputs":"[\"124780545\", \"1\", \"85932500\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 6 3\\r\\n\", \"output\": [\"124780545\"]}, {\"input\": \"5 20 11\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10 30 10\\r\\n\", \"output\": [\"85932500\"]}, {\"input\": \"100 0 0\\r\\n\", \"output\": [\"828542813\"]}, {\"input\": \"100 1 0\\r\\n\", \"output\": [\"828542813\"]}, {\"input\": \"1 5000 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 5000 4999\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 4999 0\\r\\n\", \"output\": [\"499122177\"]}, {\"input\": \"83 2813 123\\r\\n\", \"output\": [\"758958584\"]}, {\"input\": \"100 5000 5000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"100 5000 30\\r\\n\", \"output\": [\"860412292\"]}, {\"input\": \"100 5000 0\\r\\n\", \"output\": [\"828542813\"]}, {\"input\": \"1 0 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 1 0\\r\\n\", \"output\": [\"499122177\"]}, {\"input\": \"45 2315 860\\r\\n\", \"output\": [\"256332294\"]}, {\"input\": \"69 813 191\\r\\n\", \"output\": [\"367363860\"]}, {\"input\": \"93 2364 1182\\r\\n\", \"output\": [\"952630216\"]}, {\"input\": \"21 862 387\\r\\n\", \"output\": [\"910580465\"]}, {\"input\": \"45 886 245\\r\\n\", \"output\": [\"23345522\"]}, {\"input\": \"45 2315 2018\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"69 813 598\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"93 2364 2364\\r\\n\", \"output\": [\"1\"]}]"}
{"prob_desc_description":"Hongcow is learning to spell! One day, his teacher gives him a word that he needs to learn to spell. Being a dutiful student, he immediately learns how to spell the word.Hongcow has decided to try to make new words from this one. He starts by taking the word he just learned how to spell, and moves the last character of the word to the beginning of the word. He calls this a cyclic shift. He can apply cyclic shift many times. For example, consecutively applying cyclic shift operation to the word \"abracadabra\" Hongcow will get words \"aabracadabr\", \"raabracadab\" and so on.Hongcow is now wondering how many distinct words he can generate by doing the cyclic shift arbitrarily many times. The initial string is also counted.","prob_desc_output_spec":"Output a single integer equal to the number of distinct strings that Hongcow can obtain by applying the cyclic shift arbitrarily many times to the given string.","lang_cluster":"","src_uid":"8909ac99ed4ab2ee4d681ec864c7831e","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["strings","implementation"],"prob_desc_created_at":"1481992500","prob_desc_sample_inputs":"[\"abcd\", \"bbb\", \"yzyz\"]","prob_desc_notes":"NoteFor the first sample, the strings Hongcow can generate are \"abcd\", \"dabc\", \"cdab\", and \"bcda\".For the second sample, no matter how many times Hongcow does the cyclic shift, Hongcow can only generate \"bbb\".For the third sample, the two strings Hongcow can generate are \"yzyz\" and \"zyzy\".","exec_outcome":"","difficulty":900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line of input will be a single string s (1\u2009\u2264\u2009|s|\u2009\u2264\u200950), the word Hongcow initially learns how to spell. The string s consists only of lowercase English letters ('a'\u2013'z').","prob_desc_sample_outputs":"[\"4\", \"1\", \"2\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"abcd\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"bbb\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"yzyz\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"abcdefghijklmnopqrstuvwxyabcdefghijklmnopqrstuvwxy\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"zclkjadoprqronzclkjadoprqronzclkjadoprqron\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"xyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxy\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"y\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"ervbfotfedpozygoumbmxeaqegouaqqzqerlykhmvxvvlcaos\\r\\n\", \"output\": [\"49\"]}, {\"input\": \"zyzzzyyzyyyzyyzyzyzyzyzzzyyyzzyzyyzzzzzyyyzzzzyzyy\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"zzfyftdezzfyftdezzfyftdezzfyftdezzfyftdezzfyftde\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"yehcqdlllqpuxdsaicyjjxiylahgxbygmsopjbxhtimzkashs\\r\\n\", \"output\": [\"49\"]}, {\"input\": \"yyyyzzzyzzzyzyzyzyyyyyzzyzyzyyyyyzyzyyyzyzzyyzzzz\\r\\n\", \"output\": [\"49\"]}, {\"input\": \"zkqcrhzlzsnwzkqcrhzlzsnwzkqcrhzlzsnwzkqcrhzlzsnw\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"xxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxy\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"aaaaaaaaaaaaaaaaaaaaaaaabaaaaaaaaaaaaaaaaaaaaaaaab\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"aabaaabaaabaaabaaabaaabaaabaaabaaabaaabaaabaaaba\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"pqqpqqpqqpqqpqqpqqpqqpqqpqqpqqpqqppqppqppqppqppq\\r\\n\", \"output\": [\"48\"]}, {\"input\": \"zxkljaqzxkljaqzxkljaqzxkljaqzxrljaqzxkljaqzxkljaq\\r\\n\", \"output\": [\"49\"]}, {\"input\": \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwx\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaz\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"abcddcba\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"aabaabaabaacaabaabaabaacaabaabaabaacaabaabaabaac\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"aabaabcaabaabcdaabaabcaabaabcd\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"ababaababaaababaababaaaababaababaaababaababaaaa\\r\\n\", \"output\": [\"47\"]}, {\"input\": \"ababaababaaababaababaaaababaababaaababaababaaa\\r\\n\", \"output\": [\"23\"]}, {\"input\": \"aaababaab\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"aba\\r\\n\", \"output\": [\"3\"]}]"}
{"prob_desc_description":"One day Kefa found n baloons. For convenience, we denote color of i-th baloon as si \u2014 lowercase letter of the Latin alphabet. Also Kefa has k friends. Friend will be upset, If he get two baloons of the same color. Kefa want to give out all baloons to his friends. Help Kefa to find out, can he give out all his baloons, such that no one of his friens will be upset \u2014 print \u00abYES\u00bb, if he can, and \u00abNO\u00bb, otherwise. Note, that Kefa's friend will not upset, if he doesn't get baloons at all.","prob_desc_output_spec":"Answer to the task \u2014 \u00abYES\u00bb or \u00abNO\u00bb in a single line. You can choose the case (lower or upper) for each letter arbitrary.","lang_cluster":"","src_uid":"ceb3807aaffef60bcdbcc9a17a1391be","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","implementation"],"prob_desc_created_at":"1503068700","prob_desc_sample_inputs":"[\"4 2\\naabb\", \"6 3\\naacaab\"]","prob_desc_notes":"NoteIn the first sample Kefa can give 1-st and 3-rd baloon to the first friend, and 2-nd and 4-th to the second.In the second sample Kefa needs to give to all his friends baloons of color a, but one baloon will stay, thats why answer is \u00abNO\u00bb.","exec_outcome":"","difficulty":900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains two integers n and k (1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u2009100) \u2014 the number of baloons and friends. Next line contains string s \u2014 colors of baloons.","prob_desc_sample_outputs":"[\"YES\", \"NO\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4 2\\r\\naabb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"6 3\\r\\naacaab\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 2\\r\\nlu\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"5 3\\r\\novvoo\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"36 13\\r\\nbzbzcffczzcbcbzzfzbbfzfzzbfbbcbfccbf\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"81 3\\r\\nooycgmvvrophvcvpoupepqllqttwcocuilvyxbyumdmmfapvpnxhjhxfuagpnntonibicaqjvwfhwxhbv\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100 100\\r\\nxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 1\\r\\nnubcvvjvbjgnjsdkajimdcxvewbcytvfkihunycdrlconddlwgzjasjlsrttlrzsumzpyumpveglfqzmaofbshbojmwuwoxxvrod\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100 13\\r\\nvyldolgryldqrvoldvzvrdrgorlorszddtgqvrlisxxrxdxlqtvtgsrqlzixoyrozxzogqxlsgzdddzqrgitxxritoolzolgrtvl\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"18 6\\r\\njzwtnkvmscqhmdlsxy\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"21 2\\r\\nfscegcqgzesefghhwcexs\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"32 22\\r\\ncduamsptaklqtxlyoutlzepxgyfkvngc\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"49 27\\r\\noxyorfnkzwsfllnyvdhdanppuzrnbxehugvmlkgeymqjlmfxd\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"50 24\\r\\nxxutzjwbggcwvxztttkmzovtmuwttzcbwoztttohzzxghuuthv\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"57 35\\r\\nglxshztrqqfyxthqamagvtmrdparhelnzrqvcwqxjytkbuitovkdxueul\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"75 23\\r\\nittttiiuitutuiiuuututiuttiuiuutuuuiuiuuuuttuuttuutuiiuiuiiuiitttuututuiuuii\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"81 66\\r\\nfeqevfqfebhvubhuuvfuqheuqhbeeuebehuvhffvbqvqvfbqqvvhevqffbqqhvvqhfeehuhqeqhueuqqq\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"93 42\\r\\npqeiafraiavfcteumflpcbpozcomlvpovlzdbldvoopnhdoeqaopzthiuzbzmeieiatthdeqovaqfipqlddllmfcrrnhb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 53\\r\\nizszyqyndzwzyzgsdagdwdazadiawizinagqqgczaqqnawgijziziawzszdjdcqjdjqiwgadydcnqisaayjiqqsscwwzjzaycwwc\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 14\\r\\nvkrdcqbvkwuckpmnbydmczdxoagdsgtqxvhaxntdcxhjcrjyvukhugoglbmyoaqexgtcfdgemmizoniwtmisqqwcwfusmygollab\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 42\\r\\naaaaaiiiiaiiiaaiaiiaaiiiiiaaaaaiaiiiaiiiiaiiiaaaaaiiiaaaiiaaiiiaiiiaiaaaiaiiiiaaiiiaiiaiaiiaiiiaaaia\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100 89\\r\\ntjbkmydejporbqhcbztkcumxjjgsrvxpuulbhzeeckkbchpbxwhedrlhjsabcexcohgdzouvsgphjdthpuqrlkgzxvqbuhqxdsmf\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 100\\r\\njhpyiuuzizhubhhpxbbhpyxzhbpjphzppuhiahihiappbhuypyauhizpbibzixjbzxzpbphuiaypyujappuxiyuyaajaxjupbahb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 3\\r\\nsszoovvzysavsvzsozzvoozvysozsaszayaszasaysszzzysosyayyvzozovavzoyavsooaoyvoozvvozsaosvayyovazzszzssa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100 44\\r\\ndluthkxwnorabqsukgnxnvhmsmzilyulpursnxkdsavgemiuizbyzebhyjejgqrvuckhaqtuvdmpziesmpmewpvozdanjyvwcdgo\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 90\\r\\ntljonbnwnqounictqqctgonktiqoqlocgoblngijqokuquoolciqwnctgoggcbojtwjlculoikbggquqncittwnjbkgkgubnioib\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 79\\r\\nykxptzgvbqxlregvkvucewtydvnhqhuggdsyqlvcfiuaiddnrrnstityyehiamrggftsqyduwxpuldztyzgmfkehprrneyvtknmf\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 79\\r\\naagwekyovbviiqeuakbqbqifwavkfkutoriovgfmittulhwojaptacekdirgqoovlleeoqkkdukpadygfwavppohgdrmymmulgci\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 93\\r\\nearrehrehenaddhdnrdddhdahnadndheeennrearrhraharddreaeraddhehhhrdnredanndneheddrraaneerreedhnadnerhdn\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 48\\r\\nbmmaebaebmmmbbmxvmammbvvebvaemvbbaxvbvmaxvvmveaxmbbxaaemxmxvxxxvxbmmxaaaevvaxmvamvvmaxaxavexbmmbmmev\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 55\\r\\nhsavbkehaaesffaeeffakhkhfehbbvbeasahbbbvkesbfvkefeesesevbsvfkbffakvshsbkahfkfakebsvafkbvsskfhfvaasss\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 2\\r\\ncscffcffsccffsfsfffccssfsscfsfsssffcffsscfccssfffcfscfsscsccccfsssffffcfcfsfffcsfsccffscffcfccccfffs\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100 3\\r\\nzrgznxgdpgfoiifrrrsjfuhvtqxjlgochhyemismjnanfvvpzzvsgajcbsulxyeoepjfwvhkqogiiwqxjkrpsyaqdlwffoockxnc\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100 5\\r\\njbltyyfjakrjeodqepxpkjideulofbhqzxjwlarufwzwsoxhaexpydpqjvhybmvjvntuvhvflokhshpicbnfgsqsmrkrfzcrswwi\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100 1\\r\\nfnslnqktlbmxqpvcvnemxcutebdwepoxikifkzaaixzzydffpdxodmsxjribmxuqhueifdlwzytxkklwhljswqvlejedyrgguvah\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100 21\\r\\nddjenetwgwmdtjbpzssyoqrtirvoygkjlqhhdcjgeurqpunxpupwaepcqkbjjfhnvgpyqnozhhrmhfwararmlcvpgtnopvjqsrka\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 100\\r\\nnjrhiauqlgkkpkuvciwzivjbbplipvhslqgdkfnmqrxuxnycmpheenmnrglotzuyxycosfediqcuadklsnzjqzfxnbjwvfljnlvq\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 100\\r\\nbbbbbbbtbbttbtbbbttbttbtbbttttbbbtbttbbbtbttbtbbttttbbbbbtbbttbtbbtbttbbbtbtbtbtbtbtbbbttbbtbtbtbbtb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"14 5\\r\\nfssmmsfffmfmmm\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 1\\r\\nff\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 1\\r\\nhw\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"2 2\\r\\nss\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1 1\\r\\nl\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 50\\r\\nfffffttttttjjjuuuvvvvvdddxxxxwwwwgggbsssncccczzyyyyyhhhhhkrreeeeeeaaaaaiiillllllllooooqqqqqqmmpppppp\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 50\\r\\nbbbbbbbbgggggggggggaaaaaaaahhhhhhhhhhpppppppppsssssssrrrrrrrrllzzzzzzzeeeeeeekkkkkkkwwwwwwwwjjjjjjjj\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 50\\r\\nwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxxxxxzzzzzzzzzzzzzzzzzzbbbbbbbbbbbbbbbbbbbbjjjjjjjjjjjjjjjjjjjjjjjj\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 80\\r\\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 10\\r\\nbbttthhhhiiiiiiijjjjjvvvvpppssssseeeeeeewwwwgggkkkkkkkkmmmddddduuuzzzzllllnnnnnxxyyyffffccraaaaooooq\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"100 20\\r\\nssssssssssbbbbbbbhhhhhhhyyyyyyyzzzzzzzzzzzzcccccxxxxxxxxxxddddmmmmmmmeeeeeeejjjjjjjjjwwwwwwwtttttttt\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1 2\\r\\na\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"3 1\\r\\nabb\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 1\\r\\naa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 1\\r\\nab\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"6 2\\r\\naaaaaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"8 4\\r\\naaaaaaaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 2\\r\\naaaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 3\\r\\naaaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"1 3\\r\\na\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"4 3\\r\\nzzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 1\\r\\naaaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"3 4\\r\\nabc\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"2 5\\r\\nab\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"2 4\\r\\nab\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1 10\\r\\na\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"5 2\\r\\nzzzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"53 26\\r\\naaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbb\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 1\\r\\nabab\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 1\\r\\nabcb\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 2\\r\\nabbb\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"5 2\\r\\nabccc\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 3\\r\\nab\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"4 3\\r\\nbbbs\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"10 2\\r\\nazzzzzzzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"1 2\\r\\nb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1 3\\r\\nb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"4 5\\r\\nabcd\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"4 6\\r\\naabb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"5 2\\r\\naaaab\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"3 5\\r\\naaa\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"5 3\\r\\nazzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 100\\r\\naabb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"3 10\\r\\naaa\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"3 4\\r\\naaa\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"12 5\\r\\naaaaabbbbbbb\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"5 2\\r\\naabbb\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"10 5\\r\\nzzzzzzzzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 4\\r\\naa\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1 5\\r\\na\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"10 5\\r\\naaaaaaaaaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"6 3\\r\\naaaaaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"7 1\\r\\nabcdeee\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"18 3\\r\\naaaaaabbbbbbcccccc\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"8 2\\r\\naabbccdd\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"4 2\\r\\nzzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 2\\r\\nabaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"3 2\\r\\naaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"3 1\\r\\nzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"5 4\\r\\nzzzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"6 2\\r\\naabbbc\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"3 6\\r\\naaa\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"2 1\\r\\nzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"10 3\\r\\naaaeeeeeee\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 5\\r\\naabb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"3 1\\r\\naaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"5 2\\r\\naazzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"6 2\\r\\nabbbbc\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 2\\r\\nxxxx\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"6 3\\r\\nzzzzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"3 2\\r\\nabb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"3 2\\r\\nzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"6 5\\r\\nzzzzzz\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"6 3\\r\\nbcaaaa\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100 100\\r\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"3 6\\r\\nabc\\r\\n\", \"output\": [\"YES\"]}]"}
{"prob_desc_description":"The Floral Clock has been standing by the side of Mirror Lake for years. Though unable to keep time, it reminds people of the passage of time and the good old days.On the rim of the Floral Clock are 2n flowers, numbered from 1 to 2n clockwise, each of which has a colour among all n possible ones. For each colour, there are exactly two flowers with it, the distance between which either is less than or equal to 2, or equals n. Additionally, if flowers u and v are of the same colour, then flowers opposite to u and opposite to v should be of the same colour as well \u2014 symmetry is beautiful!Formally, the distance between two flowers is 1 plus the number of flowers on the minor arc (or semicircle) between them. Below is a possible arrangement with n\u2009=\u20096 that cover all possibilities.  The beauty of an arrangement is defined to be the product of the lengths of flower segments separated by all opposite flowers of the same colour. In other words, in order to compute the beauty, we remove from the circle all flowers that have the same colour as flowers opposite to them. Then, the beauty is the product of lengths of all remaining segments. Note that we include segments of length 0 in this product. If there are no flowers that have the same colour as flower opposite to them, the beauty equals 0. For instance, the beauty of the above arrangement equals 1\u2009\u00d7\u20093\u2009\u00d7\u20091\u2009\u00d7\u20093\u2009=\u20099 \u2014 the segments are {2}, {4,\u20095,\u20096}, {8} and {10,\u200911,\u200912}.While keeping the constraints satisfied, there may be lots of different arrangements. Find out the sum of beauty over all possible arrangements, modulo 998\u2009244\u2009353. Two arrangements are considered different, if a pair (u,\u2009v) (1\u2009\u2264\u2009u,\u2009v\u2009\u2264\u20092n) exists such that flowers u and v are of the same colour in one of them, but not in the other.","prob_desc_output_spec":"Output one integer \u2014 the sum of beauty over all possible arrangements of flowers, modulo 998\u2009244\u2009353.","lang_cluster":"","src_uid":"24fd5cd218f65d4ffb7c5b97b725293e","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["divide and conquer","combinatorics","fft","dp","math"],"prob_desc_created_at":"1504272900","prob_desc_sample_inputs":"[\"3\", \"4\", \"7\", \"15\"]","prob_desc_notes":"NoteWith n\u2009=\u20093, the following six arrangements each have a beauty of 2\u2009\u00d7\u20092\u2009=\u20094.  While many others, such as the left one in the figure below, have a beauty of 0. The right one is invalid, since it's asymmetric.  ","exec_outcome":"","difficulty":3400.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"7 seconds","prob_desc_input_spec":"The first and only line of input contains a lonely positive integer n (3\u2009\u2264\u2009n\u2009\u2264\u200950\u2009000)\u00a0\u2014 the number of colours present on the Floral Clock.","prob_desc_sample_outputs":"[\"24\", \"4\", \"1316\", \"3436404\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"1316\"]}, {\"input\": \"15\\r\\n\", \"output\": [\"3436404\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"26200\"]}, {\"input\": \"99\\r\\n\", \"output\": [\"620067986\"]}, {\"input\": \"1317\\r\\n\", \"output\": [\"414025\"]}, {\"input\": \"50000\\r\\n\", \"output\": [\"475800099\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"240\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"204\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"2988\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"6720\"]}, {\"input\": \"11\\r\\n\", \"output\": [\"50248\"]}, {\"input\": \"12\\r\\n\", \"output\": [\"174280\"]}, {\"input\": \"13\\r\\n\", \"output\": [\"436904\"]}, {\"input\": \"14\\r\\n\", \"output\": [\"1140888\"]}, {\"input\": \"16\\r\\n\", \"output\": [\"8348748\"]}, {\"input\": \"17\\r\\n\", \"output\": [\"24631232\"]}, {\"input\": \"18\\r\\n\", \"output\": [\"64575924\"]}, {\"input\": \"19\\r\\n\", \"output\": [\"174658944\"]}, {\"input\": \"20\\r\\n\", \"output\": [\"488230244\"]}, {\"input\": \"33\\r\\n\", \"output\": [\"823529776\"]}, {\"input\": \"39\\r\\n\", \"output\": [\"302870971\"]}, {\"input\": \"89\\r\\n\", \"output\": [\"530141864\"]}, {\"input\": \"144\\r\\n\", \"output\": [\"395837543\"]}, {\"input\": \"233\\r\\n\", \"output\": [\"422271260\"]}, {\"input\": \"396\\r\\n\", \"output\": [\"994574954\"]}, {\"input\": \"418\\r\\n\", \"output\": [\"57956054\"]}, {\"input\": \"431\\r\\n\", \"output\": [\"767293469\"]}, {\"input\": \"831\\r\\n\", \"output\": [\"418821250\"]}, {\"input\": \"985\\r\\n\", \"output\": [\"574051668\"]}, {\"input\": \"998\\r\\n\", \"output\": [\"452930999\"]}, {\"input\": \"1000\\r\\n\", \"output\": [\"945359814\"]}, {\"input\": \"2017\\r\\n\", \"output\": [\"222633425\"]}, {\"input\": \"3939\\r\\n\", \"output\": [\"582943734\"]}, {\"input\": \"5000\\r\\n\", \"output\": [\"148029988\"]}, {\"input\": \"8081\\r\\n\", \"output\": [\"473740780\"]}, {\"input\": \"10000\\r\\n\", \"output\": [\"938538566\"]}, {\"input\": \"10001\\r\\n\", \"output\": [\"552705744\"]}, {\"input\": \"10492\\r\\n\", \"output\": [\"914991759\"]}, {\"input\": \"20178\\r\\n\", \"output\": [\"207394683\"]}, {\"input\": \"23333\\r\\n\", \"output\": [\"259575428\"]}, {\"input\": \"25252\\r\\n\", \"output\": [\"306102706\"]}, {\"input\": \"30000\\r\\n\", \"output\": [\"583465411\"]}, {\"input\": \"35000\\r\\n\", \"output\": [\"520751787\"]}, {\"input\": \"39393\\r\\n\", \"output\": [\"929692433\"]}, {\"input\": \"40404\\r\\n\", \"output\": [\"618777849\"]}, {\"input\": \"45000\\r\\n\", \"output\": [\"672059275\"]}, {\"input\": \"49997\\r\\n\", \"output\": [\"645043850\"]}, {\"input\": \"49999\\r\\n\", \"output\": [\"791828238\"]}]"}
{"prob_desc_description":"Where do odds begin, and where do they end? Where does hope emerge, and will they ever break?Given an integer sequence a1,\u2009a2,\u2009...,\u2009an of length n. Decide whether it is possible to divide it into an odd number of non-empty subsegments, the each of which has an odd length and begins and ends with odd numbers.A subsegment is a contiguous slice of the whole sequence. For example, {3,\u20094,\u20095} and {1} are subsegments of sequence {1,\u20092,\u20093,\u20094,\u20095,\u20096}, while {1,\u20092,\u20094} and {7} are not.","prob_desc_output_spec":"Output \"Yes\" if it's possible to fulfill the requirements, and \"No\" otherwise. You can output each letter in any case (upper or lower).","lang_cluster":"","src_uid":"2b8c2deb5d7e49e8e3ededabfd4427db","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["implementation"],"prob_desc_created_at":"1504272900","prob_desc_sample_inputs":"[\"3\\n1 3 5\", \"5\\n1 0 1 5 1\", \"3\\n4 3 1\", \"4\\n3 9 9 3\"]","prob_desc_notes":"NoteIn the first example, divide the sequence into 1 subsegment: {1,\u20093,\u20095} and the requirements will be met.In the second example, divide the sequence into 3 subsegments: {1,\u20090,\u20091}, {5}, {1}.In the third example, one of the subsegments must start with 4 which is an even number, thus the requirements cannot be met.In the fourth example, the sequence can be divided into 2 subsegments: {3,\u20099,\u20099}, {3}, but this is not a valid solution because 2 is an even number.","exec_outcome":"","difficulty":1000.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line of input contains a non-negative integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the length of the sequence. The second line contains n space-separated non-negative integers a1,\u2009a2,\u2009...,\u2009an (0\u2009\u2264\u2009ai\u2009\u2264\u2009100) \u2014 the elements of the sequence.","prob_desc_sample_outputs":"[\"Yes\", \"Yes\", \"No\", \"No\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3\\r\\n1 3 5\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"5\\r\\n1 0 1 5 1\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n4 3 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n3 9 9 3\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"1\\r\\n1\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"5\\r\\n100 99 100 99 99\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"100\\r\\n100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"1\\r\\n0\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"2\\r\\n1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"2\\r\\n10 10\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"2\\r\\n54 21\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n0 0 0 0 0\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n67 92 0 26 43\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"15\\r\\n45 52 35 80 68 80 93 57 47 32 69 23 63 90 43\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"15\\r\\n81 28 0 82 71 64 63 89 87 92 38 30 76 72 36\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"50\\r\\n49 32 17 59 77 98 65 50 85 10 40 84 65 34 52 25 1 31 61 45 48 24 41 14 76 12 33 76 44 86 53 33 92 58 63 93 50 24 31 79 67 50 72 93 2 38 32 14 87 99\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"55\\r\\n65 69 53 66 11 100 68 44 43 17 6 66 24 2 6 6 61 72 91 53 93 61 52 96 56 42 6 8 79 49 76 36 83 58 8 43 2 90 71 49 80 21 75 13 76 54 95 61 58 82 40 33 73 61 46\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"99\\r\\n73 89 51 85 42 67 22 80 75 3 90 0 52 100 90 48 7 15 41 1 54 2 23 62 86 68 2 87 57 12 45 34 68 54 36 49 27 46 22 70 95 90 57 91 90 79 48 89 67 92 28 27 25 37 73 66 13 89 7 99 62 53 48 24 73 82 62 88 26 39 21 86 50 95 26 27 60 6 56 14 27 90 55 80 97 18 37 36 70 2 28 53 36 77 39 79 82 42 69\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"99\\r\\n99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"100\\r\\n61 63 34 45 20 91 31 28 40 27 94 1 73 5 69 10 56 94 80 23 79 99 59 58 13 56 91 59 77 78 88 72 80 72 70 71 63 60 41 41 41 27 83 10 43 14 35 48 0 78 69 29 63 33 42 67 1 74 51 46 79 41 37 61 16 29 82 28 22 14 64 49 86 92 82 55 54 24 75 58 95 31 3 34 26 23 78 91 49 6 30 57 27 69 29 54 42 0 61 83\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 2 2 2 2 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n1 2 1\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"4\\r\\n1 3 2 3\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 1 1 1 1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 1 0 0 1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n1 4 9 3\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n1 0 1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"10\\r\\n1 0 0 1 1 1 1 1 1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"10\\r\\n9 2 5 7 8 3 1 9 4 9\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"99\\r\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 2 1 2 2 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 0 1 0 0 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n1 3 4 7\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"8\\r\\n1 1 1 2 1 1 1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n1 1 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n1 2 1 2 1\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"5\\r\\n5 4 4 2 1\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"6\\r\\n1 3 3 3 3 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"7\\r\\n1 2 1 2 2 2 1\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"4\\r\\n1 2 2 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 2 3 4 6 5\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n1 1 2 2 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n1 0 0 1 1\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n1 2 4\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n1 0 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n1 1 1 0 1\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"4\\r\\n3 9 2 3\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 1 1 4 4 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 2 3 5 6 7\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 1 1 2 2 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 1 1 0 0 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n1 2 2 5 5\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"5\\r\\n1 3 2 4 5\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"8\\r\\n1 2 3 5 7 8 8 5\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"10\\r\\n1 1 1 2 1 1 1 1 1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n1 0 0 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"7\\r\\n1 0 1 1 0 0 1\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"7\\r\\n1 4 5 7 6 6 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"4\\r\\n2 2 2 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n2 3 4 5 6\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n1 1 2 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n1 2 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"6\\r\\n1 3 3 2 2 3\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n1 1 2 3\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n1 2 3 5\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n3 4 4 3 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"4\\r\\n3 2 2 3\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 1 1 1 2 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 1 2 2 1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"10\\r\\n3 4 2 4 3 2 2 4 4 3\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"7\\r\\n1 2 4 3 2 4 5\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"28\\r\\n75 51 25 52 13 7 34 29 5 59 68 56 13 2 9 37 59 83 18 32 36 30 20 43 92 76 78 67\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"79\\r\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 18\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"100\\r\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}]"}
{"prob_desc_description":"Nikolay has a lemons, b apples and c pears. He decided to cook a compote. According to the recipe the fruits should be in the ratio 1:\u20092:\u20094. It means that for each lemon in the compote should be exactly 2 apples and exactly 4 pears. You can't crumble up, break up or cut these fruits into pieces. These fruits\u00a0\u2014 lemons, apples and pears\u00a0\u2014 should be put in the compote as whole fruits.Your task is to determine the maximum total number of lemons, apples and pears from which Nikolay can cook the compote. It is possible that Nikolay can't use any fruits, in this case print 0. ","prob_desc_output_spec":"Print the maximum total number of lemons, apples and pears from which Nikolay can cook the compote.","lang_cluster":"","src_uid":"82a4a60eac90765fb62f2a77d2305c01","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","implementation"],"prob_desc_created_at":"1482057300","prob_desc_sample_inputs":"[\"2\\n5\\n7\", \"4\\n7\\n13\", \"2\\n3\\n2\"]","prob_desc_notes":"NoteIn the first example Nikolay can use 1 lemon, 2 apples and 4 pears, so the answer is 1\u2009+\u20092\u2009+\u20094\u2009=\u20097.In the second example Nikolay can use 3 lemons, 6 apples and 12 pears, so the answer is 3\u2009+\u20096\u2009+\u200912\u2009=\u200921.In the third example Nikolay don't have enough pears to cook any compote, so the answer is 0. ","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains the positive integer a (1\u2009\u2264\u2009a\u2009\u2264\u20091000)\u00a0\u2014 the number of lemons Nikolay has.  The second line contains the positive integer b (1\u2009\u2264\u2009b\u2009\u2264\u20091000)\u00a0\u2014 the number of apples Nikolay has.  The third line contains the positive integer c (1\u2009\u2264\u2009c\u2009\u2264\u20091000)\u00a0\u2014 the number of pears Nikolay has.","prob_desc_sample_outputs":"[\"7\", \"21\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2\\r\\n5\\r\\n7\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"4\\r\\n7\\r\\n13\\r\\n\", \"output\": [\"21\"]}, {\"input\": \"2\\r\\n3\\r\\n2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1\\r\\n1\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1\\r\\n2\\r\\n4\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1000\\r\\n1000\\r\\n1000\\r\\n\", \"output\": [\"1750\"]}, {\"input\": \"1\\r\\n1\\r\\n4\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1\\r\\n2\\r\\n3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1\\r\\n1000\\r\\n1000\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1000\\r\\n1\\r\\n1000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1000\\r\\n2\\r\\n1000\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1000\\r\\n500\\r\\n1000\\r\\n\", \"output\": [\"1750\"]}, {\"input\": \"1000\\r\\n1000\\r\\n4\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1000\\r\\n1000\\r\\n3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4\\r\\n8\\r\\n12\\r\\n\", \"output\": [\"21\"]}, {\"input\": \"10\\r\\n20\\r\\n40\\r\\n\", \"output\": [\"70\"]}, {\"input\": \"100\\r\\n200\\r\\n399\\r\\n\", \"output\": [\"693\"]}, {\"input\": \"200\\r\\n400\\r\\n800\\r\\n\", \"output\": [\"1400\"]}, {\"input\": \"199\\r\\n400\\r\\n800\\r\\n\", \"output\": [\"1393\"]}, {\"input\": \"201\\r\\n400\\r\\n800\\r\\n\", \"output\": [\"1400\"]}, {\"input\": \"200\\r\\n399\\r\\n800\\r\\n\", \"output\": [\"1393\"]}, {\"input\": \"200\\r\\n401\\r\\n800\\r\\n\", \"output\": [\"1400\"]}, {\"input\": \"200\\r\\n400\\r\\n799\\r\\n\", \"output\": [\"1393\"]}, {\"input\": \"200\\r\\n400\\r\\n801\\r\\n\", \"output\": [\"1400\"]}, {\"input\": \"139\\r\\n252\\r\\n871\\r\\n\", \"output\": [\"882\"]}, {\"input\": \"109\\r\\n346\\r\\n811\\r\\n\", \"output\": [\"763\"]}, {\"input\": \"237\\r\\n487\\r\\n517\\r\\n\", \"output\": [\"903\"]}, {\"input\": \"161\\r\\n331\\r\\n725\\r\\n\", \"output\": [\"1127\"]}, {\"input\": \"39\\r\\n471\\r\\n665\\r\\n\", \"output\": [\"273\"]}, {\"input\": \"9\\r\\n270\\r\\n879\\r\\n\", \"output\": [\"63\"]}, {\"input\": \"137\\r\\n422\\r\\n812\\r\\n\", \"output\": [\"959\"]}, {\"input\": \"15\\r\\n313\\r\\n525\\r\\n\", \"output\": [\"105\"]}, {\"input\": \"189\\r\\n407\\r\\n966\\r\\n\", \"output\": [\"1323\"]}, {\"input\": \"18\\r\\n268\\r\\n538\\r\\n\", \"output\": [\"126\"]}, {\"input\": \"146\\r\\n421\\r\\n978\\r\\n\", \"output\": [\"1022\"]}, {\"input\": \"70\\r\\n311\\r\\n685\\r\\n\", \"output\": [\"490\"]}, {\"input\": \"244\\r\\n405\\r\\n625\\r\\n\", \"output\": [\"1092\"]}, {\"input\": \"168\\r\\n454\\r\\n832\\r\\n\", \"output\": [\"1176\"]}, {\"input\": \"46\\r\\n344\\r\\n772\\r\\n\", \"output\": [\"322\"]}, {\"input\": \"174\\r\\n438\\r\\n987\\r\\n\", \"output\": [\"1218\"]}, {\"input\": \"144\\r\\n387\\r\\n693\\r\\n\", \"output\": [\"1008\"]}, {\"input\": \"22\\r\\n481\\r\\n633\\r\\n\", \"output\": [\"154\"]}, {\"input\": \"196\\r\\n280\\r\\n848\\r\\n\", \"output\": [\"980\"]}, {\"input\": \"190\\r\\n454\\r\\n699\\r\\n\", \"output\": [\"1218\"]}, {\"input\": \"231\\r\\n464\\r\\n928\\r\\n\", \"output\": [\"1617\"]}, {\"input\": \"151\\r\\n308\\r\\n616\\r\\n\", \"output\": [\"1057\"]}, {\"input\": \"88\\r\\n182\\r\\n364\\r\\n\", \"output\": [\"616\"]}, {\"input\": \"12\\r\\n26\\r\\n52\\r\\n\", \"output\": [\"84\"]}, {\"input\": \"204\\r\\n412\\r\\n824\\r\\n\", \"output\": [\"1428\"]}, {\"input\": \"127\\r\\n256\\r\\n512\\r\\n\", \"output\": [\"889\"]}, {\"input\": \"224\\r\\n446\\r\\n896\\r\\n\", \"output\": [\"1561\"]}, {\"input\": \"146\\r\\n291\\r\\n584\\r\\n\", \"output\": [\"1015\"]}, {\"input\": \"83\\r\\n164\\r\\n332\\r\\n\", \"output\": [\"574\"]}, {\"input\": \"20\\r\\n38\\r\\n80\\r\\n\", \"output\": [\"133\"]}, {\"input\": \"198\\r\\n393\\r\\n792\\r\\n\", \"output\": [\"1372\"]}, {\"input\": \"120\\r\\n239\\r\\n480\\r\\n\", \"output\": [\"833\"]}, {\"input\": \"208\\r\\n416\\r\\n831\\r\\n\", \"output\": [\"1449\"]}, {\"input\": \"130\\r\\n260\\r\\n517\\r\\n\", \"output\": [\"903\"]}, {\"input\": \"67\\r\\n134\\r\\n267\\r\\n\", \"output\": [\"462\"]}, {\"input\": \"245\\r\\n490\\r\\n979\\r\\n\", \"output\": [\"1708\"]}, {\"input\": \"182\\r\\n364\\r\\n727\\r\\n\", \"output\": [\"1267\"]}, {\"input\": \"104\\r\\n208\\r\\n413\\r\\n\", \"output\": [\"721\"]}, {\"input\": \"10\\r\\n2\\r\\n100\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"2\\r\\n100\\r\\n100\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"2\\r\\n3\\r\\n8\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1\\r\\n2\\r\\n8\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1\\r\\n2\\r\\n200\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"5\\r\\n4\\r\\n16\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"1\\r\\n10\\r\\n10\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1\\r\\n4\\r\\n8\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"100\\r\\n4\\r\\n1000\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"2\\r\\n6\\r\\n12\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"10\\r\\n7\\r\\n4\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"2\\r\\n10\\r\\n100\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"2\\r\\n3\\r\\n4\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1\\r\\n2\\r\\n999\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1\\r\\n10\\r\\n20\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"100\\r\\n18\\r\\n20\\r\\n\", \"output\": [\"35\"]}, {\"input\": \"100\\r\\n1\\r\\n100\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3\\r\\n7\\r\\n80\\r\\n\", \"output\": [\"21\"]}, {\"input\": \"2\\r\\n8\\r\\n24\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"1\\r\\n100\\r\\n100\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"2\\r\\n1\\r\\n8\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"10\\r\\n5\\r\\n23\\r\\n\", \"output\": [\"14\"]}]"}
{"prob_desc_description":"A big company decided to launch a new series of rectangular displays, and decided that the display must have exactly n pixels. Your task is to determine the size of the rectangular display \u2014 the number of lines (rows) of pixels a and the number of columns of pixels b, so that:  there are exactly n pixels on the display;  the number of rows does not exceed the number of columns, it means a\u2009\u2264\u2009b;  the difference b\u2009-\u2009a is as small as possible. ","prob_desc_output_spec":"Print two integers\u00a0\u2014 the number of rows and columns on the display. ","lang_cluster":"","src_uid":"f52af273954798a4ae38a1378bfbf77a","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","math"],"prob_desc_created_at":"1482113100","prob_desc_sample_inputs":"[\"8\", \"64\", \"5\", \"999999\"]","prob_desc_notes":"NoteIn the first example the minimum possible difference equals 2, so on the display should be 2 rows of 4 pixels.In the second example the minimum possible difference equals 0, so on the display should be 8 rows of 8 pixels.In the third example the minimum possible difference equals 4, so on the display should be 1 row of 5 pixels.","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains the positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009106)\u00a0\u2014 the number of pixels display should have.","prob_desc_sample_outputs":"[\"2 4\", \"8 8\", \"1 5\", \"999 1001\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"8\\r\\n\", \"output\": [\"2 4\"]}, {\"input\": \"64\\r\\n\", \"output\": [\"8 8\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"1 5\"]}, {\"input\": \"999999\\r\\n\", \"output\": [\"999 1001\"]}, {\"input\": \"716539\\r\\n\", \"output\": [\"97 7387\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"1 1\"]}, {\"input\": \"2\\r\\n\", \"output\": [\"1 2\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"1 3\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"2 2\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"2 3\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"1 7\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"3 3\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"2 5\"]}, {\"input\": \"11\\r\\n\", \"output\": [\"1 11\"]}, {\"input\": \"12\\r\\n\", \"output\": [\"3 4\"]}, {\"input\": \"15\\r\\n\", \"output\": [\"3 5\"]}, {\"input\": \"100\\r\\n\", \"output\": [\"10 10\"]}, {\"input\": \"101\\r\\n\", \"output\": [\"1 101\"]}, {\"input\": \"169\\r\\n\", \"output\": [\"13 13\"]}, {\"input\": \"179\\r\\n\", \"output\": [\"1 179\"]}, {\"input\": \"190\\r\\n\", \"output\": [\"10 19\"]}, {\"input\": \"1000\\r\\n\", \"output\": [\"25 40\"]}, {\"input\": \"10000\\r\\n\", \"output\": [\"100 100\"]}, {\"input\": \"10001\\r\\n\", \"output\": [\"73 137\"]}, {\"input\": \"100000\\r\\n\", \"output\": [\"250 400\"]}, {\"input\": \"100001\\r\\n\", \"output\": [\"11 9091\"]}, {\"input\": \"1000000\\r\\n\", \"output\": [\"1000 1000\"]}, {\"input\": \"999983\\r\\n\", \"output\": [\"1 999983\"]}, {\"input\": \"524288\\r\\n\", \"output\": [\"512 1024\"]}, {\"input\": \"954493\\r\\n\", \"output\": [\"971 983\"]}, {\"input\": \"966289\\r\\n\", \"output\": [\"983 983\"]}, {\"input\": \"944663\\r\\n\", \"output\": [\"961 983\"]}, {\"input\": \"912673\\r\\n\", \"output\": [\"97 9409\"]}, {\"input\": \"732641\\r\\n\", \"output\": [\"679 1079\"]}, {\"input\": \"232897\\r\\n\", \"output\": [\"343 679\"]}, {\"input\": \"16807\\r\\n\", \"output\": [\"49 343\"]}, {\"input\": \"999958\\r\\n\", \"output\": [\"2 499979\"]}, {\"input\": \"990151\\r\\n\", \"output\": [\"1 990151\"]}, {\"input\": \"997002\\r\\n\", \"output\": [\"998 999\"]}, {\"input\": \"20\\r\\n\", \"output\": [\"4 5\"]}, {\"input\": \"20261\\r\\n\", \"output\": [\"1 20261\"]}, {\"input\": \"999123\\r\\n\", \"output\": [\"3 333041\"]}, {\"input\": \"901841\\r\\n\", \"output\": [\"1 901841\"]}]"}
{"prob_desc_description":"Pupils decided to go to amusement park. Some of them were with parents. In total, n people came to the park and they all want to get to the most extreme attraction and roll on it exactly once.Tickets for group of x people are sold on the attraction, there should be at least one adult in each group (it is possible that the group consists of one adult). The ticket price for such group is c1\u2009+\u2009c2\u00b7(x\u2009-\u20091)2 (in particular, if the group consists of one person, then the price is c1). All pupils who came to the park and their parents decided to split into groups in such a way that each visitor join exactly one group, and the total price of visiting the most extreme attraction is as low as possible. You are to determine this minimum possible total price. There should be at least one adult in each group. ","prob_desc_output_spec":"Print the minimum price of visiting the most extreme attraction for all pupils and their parents. Each of them should roll on the attraction exactly once.","lang_cluster":"","src_uid":"78d013b01497053b8e321fe7b6ce3760","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["ternary search"],"prob_desc_created_at":"1491406500","prob_desc_sample_inputs":"[\"3 4 1\\n011\", \"4 7 2\\n1101\"]","prob_desc_notes":"NoteIn the first test one group of three people should go to the attraction. Then they have to pay 4\u2009+\u20091\u2009*\u2009(3\u2009-\u20091)2\u2009=\u20098.In the second test it is better to go to the attraction in two groups. The first group should consist of two adults (for example, the first and the second person), the second should consist of one pupil and one adult (the third and the fourth person). Then each group will have a size of two and for each the price of ticket is 7\u2009+\u20092\u2009*\u2009(2\u2009-\u20091)2\u2009=\u20099. Thus, the total price for two groups is 18.","exec_outcome":"","difficulty":2100.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains three integers n, c1 and c2 (1\u2009\u2264\u2009n\u2009\u2264\u2009200\u2009000, 1\u2009\u2264\u2009c1,\u2009c2\u2009\u2264\u2009107)\u00a0\u2014 the number of visitors and parameters for determining the ticket prices for a group. The second line contains the string of length n, which consists of zeros and ones. If the i-th symbol of the string is zero, then the i-th visitor is a pupil, otherwise the i-th person is an adult. It is guaranteed that there is at least one adult. It is possible that there are no pupils.","prob_desc_sample_outputs":"[\"8\", \"18\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3 4 1\\r\\n011\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"4 7 2\\r\\n1101\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"1 2 2\\r\\n1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2 3 10\\r\\n01\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"5 10 3\\r\\n11100\\r\\n\", \"output\": [\"35\"]}, {\"input\": \"10 2 2\\r\\n1111101111\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"20 3 13\\r\\n01111110011111010101\\r\\n\", \"output\": [\"120\"]}, {\"input\": \"50 13 44\\r\\n11101110100110111100010110001111001001110010111011\\r\\n\", \"output\": [\"1270\"]}, {\"input\": \"100 1000 1000\\r\\n0000010100101100110100101111001111111111100101111100111011110001011110110111111010000000101000111000\\r\\n\", \"output\": [\"100000\"]}, {\"input\": \"1000 10000 10000\\r\\n1111011110111111111111111111011111111001111111111111111111011111111101111111111111101011111111111011111111111111111101111111111011111111101111111111111111111111111111111110111110110111111111111101111110101111111101111111111111111111111110111111011001111011111111111110101101111111101111111101111111101111111111110101111111111111111111011011111101111101111111111111111111111111110111011100111111101111101111101101111111111111110111011111111111111111111111111111111111111111111111011111111011111...\", \"output\": [\"10000000\"]}, {\"input\": \"10000 100 1000000\\r\\n101111011011011111011111100110111001100110101111100100011101011011110110001011001101011010111110101011011101111111111010111101001110111111111010011100110111111110101101111111011010111111101111101100011000101010111101110111111101011110010100111010110011011011101111111111011011010110011010111110111101110010101011011100011110100011101100101010111100111111101111100011000110110001111111110111101110101010111110111101011111111110101001101001100111100110110000011111110001110010001011011101001110...\", \"output\": [\"3759624100\"]}, {\"input\": \"20001 1000 100\\r\\n000100010100111100011011010110111011110111110011000110010010010000110111001000010101111000110110111010101000100111100100101010101010000010111101011000010011111011110001110001110111001000110111110001011100010011001110110100010011101010001010101101000110001000001010011001100010011111001010001101111101110010001011011000101111110001111101010010101101000000100110011100100100001110111001010011110011000111100001011011111011100101100111110010011010111001001011011000111110101011000101010111000111110...\", \"output\": [\"9333800\"]}, {\"input\": \"50000 100 1000\\r\\n100001000000100000101110011001101100001101110010010001000101011000010000000000000000100111001000000100111010000110011011011011011101011100100010000010000001011010010000011100100100000010000000000001000011010011001000110110110100001001001010100011011000110010000011001000001110100100000000111110000110000010010011001111101000000000100001110001011001000011101010010100110110100011110001010000010101000111100001010110011100000100001000001010000000000100100000000110100010100010101111111010010000101...\", \"output\": [\"62539900\"]}, {\"input\": \"99999 10000 10000\\r\\n010010000000000000000001000000000001000100001000001000000010000000000110000000001000100000000000100000000000000000100010000000100000000001001010000000010000000000010110000000000000000001000010000000000000000000000000000001100000000000000100000000000000000000010010000000000000100010000100010000101001000001000001000000110000100000000000000000000000100000000000010000001000000000001000000000101000000000000000000000000000010000000001000010000100001000000100000000000000000000000100000001001000...\", \"output\": [\"6092190000\"]}, {\"input\": \"200000 1234 234123\\r\\n00000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000100000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000001000000000000000000...\", \"output\": [\"1612837280853\"]}, {\"input\": \"200000 123 1242\\r\\n00000010000000000000001000000000010000000000000000000000000000000000010000000000000000000000000000000000000000000000010000000000000000000001100000000000000000000000000000000000000000000000000000000000010000000000000000000000100000000000000000000000000000001000000000000000000000000000000000100000000000000000000010000000000000000100000000101000000000000000000000000000000000000000001000000000000000000000000100010000000100000000000000000000000000000000000100100000000010001001000001000000100000...\", \"output\": [\"4251434880\"]}, {\"input\": \"200000 10000000 10000000\\r\\n00000000000000000000001000000000000000000000001000001010000100100000000000000000001001000000000000000000000000000000000000000100000011010000000000010000000000000000000000000000000010000000000000000100000000000000000000000000000000000000000000010000000100000000000100000000000101000000000000000000100010001000001000000001010010000000000000000001000000000000000000000000000000000000000000000010000000000010000000000000000000000000000000000000000000010000000000000000000000000000000000000...\", \"output\": [\"31778720000000\"]}, {\"input\": \"200000 10000 10000\\r\\n11110111111111111111111111101111111111111111101111111111101111111110111111101111111111111111111111111110111101111111111111011111111111100111111111111101101111111111111111111111111111111111110111111111111111111111101111011011111111111111111111011011111110111110111111111111101111110111111111110111101111111111111111111111110101110111111111111111110111111111111111111011111111101111101111111101101101111111111111111111111111111111111110111111111111111111111111110111001111111111111011111110111...\", \"output\": [\"2000000000\"]}, {\"input\": \"200000 1000 10000000\\r\\n000100001100000000100001100000010011110000001000001000000100001100000100000101000100000001000010100001010000011010010100001001011010000000000000111000011100110001000100001000000000000000001000101110110001001100010101000000000011100110000110100001011100110110000001000010100100000101010000000000000010000000001000000011010101100000110000011110000000000001111011010001101011011011000000100000000000101011010001100001000000011001010000000100011011000001100000000000000100111010001010100010001...\", \"output\": [\"3897475478000\"]}, {\"input\": \"200000 10000000 3\\r\\n111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111...\", \"output\": [\"2189709470\"]}, {\"input\": \"200000 10000000 10000000\\r\\n10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...\", \"output\": [\"399996000020000000\"]}, {\"input\": \"200000 3 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44\\r\\n110111111011110111111110111110101110110010101010110111111011100011101111111111011011011101000010110111101110101001111101101110101111111100111100011111111111111111111100001101111011111110111011100110110011011111011101011111010101100111010001111110111111111111011011111111111111101101110011101010101101111011011011001110111100100111111111111001111110111101111111110111111001111111101100111011111111111000110000101111110111101111101111101111011111110010110111101101111111010111110000101111010110101101...\", \"output\": [\"2588662\"]}, {\"input\": \"200000 33 1212\\r\\n111111111111111111111111110110111111111111111111111111111111111111101111111111111111111111110111111111111111111101111111111111111111111111111111111111111111110111111011111111111111110111111111111111111111111101111111111111101111111101111111111111111111110110111111111111111111111111111011111111111111111101111111111101111111110111111111111111111111111111111111111101111111111111111111111111111111111111111111111111111101111111111111101111111111111110111111111111111111111111011111111111111111111...\", \"output\": [\"15754935\"]}, {\"input\": \"200000 123123 45345\\r\\n1111111011101111111111111111111111111111111111111111111111111111111010111111111110111111111111111111111111111111111111111111011111111111111111111111101111111111111111111111111111111111111111111111111111111111111111111111001111011111111111111111111111111110111111111111111111111111111111111011111111111111111111111111111111111111111111110011110111111111011111111111111111111111011111111111111111111101111111111111111111111111011110111111111111111111111111111111110111111111111101111111111111...\", \"output\": [\"16846800000\"]}, {\"input\": \"200000 234531 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123434\\r\\n0010111000100000111111000111011010010001100101001011100000001010111000101010110010011000100110001001101000000001110101000001101100000010111111010000001010000110011110100101000010001001100011001000000011100000000110010101010010001000101001110111001100100101001101111001001100100001111000011000110001000111000111101001011010000101011110100011000101100010011001011100101110110111111110010010101001110011011010000010000100110100101010010000000011110000011101001010001111101001001001101011001...\", \"output\": [\"397773019028\"]}, {\"input\": \"200000 10000000 234345\\r\\n0000000100000001000000000010000100000000000000000000000100000001010010000010000000100000000000100000000000100010000001100000100001000000000000101010000000000000000000010000000000000000000010000000000000001000100000000001000100000000000000000000010000000000000000001000000000100100000010000000000001000000000000000001100001000000000011000000000000000000000010000000000000000000001000100000000000000000000000000000100000001000000010000000000000000000001000000000000000000000010000000000000...\", \"output\": [\"552374355975\"]}, {\"input\": \"200000 1000 1203\\r\\n0001000111000000010000100010110000101111000001000100010100001010000000000001110000101000010000000101001000100000110001000001100011000000010010000110000000010001010011000000101000001110100100000101010100000110100000100000000000010100110110010000100000100001000000010000010100000100000101100000010000001011000101010000000000100010000010000000101001001000000000010100010000000000000100100010000001010100000110000100000001010101000100000011001101000001000100011010010010011010000000010010100001100...\", \"output\": [\"498073375\"]}, {\"input\": \"200000 1000000 1000000\\r\\n1110111111111111111111011110101111111111111110111110111111111111111111111111111111111111111111111111111111111111111111111111010111100111110111111011111111111111111111111111111111011011101111111111111111111011110110111111111111111111111111111111111111111111111111101111111111110111111111110111111111011111111110111111111111111111111100111111110111110111111111111111110111111111110111111111111111101111111111111111111111111111111111011111111100110011111111111111111111011111111011111111111...\", \"output\": [\"200000000000\"]}, {\"input\": \"200000 11200 100\\r\\n0000000010000100100100000000100100000000000000000000000000000010000000100000000000000000000000000000000000000000000011000000000000000000000001000101000001000000001110000000010000000100000001001000000000000000000000100000000000000100000010101010000000000000100100000000000001000010000000010010000000000010010000000000000000010110001010010010101010001001110000000000000000000100000110000000000000000000000010000000000010000000000000100001000101000000010000000000100000110000000000011001100001111...\", \"output\": [\"385454600\"]}]"}
{"prob_desc_description":"Bomboslav likes to look out of the window in his room and watch lads outside playing famous shell game. The game is played by two persons: operator and player. Operator takes three similar opaque shells and places a ball beneath one of them. Then he shuffles the shells by swapping some pairs and the player has to guess the current position of the ball.Bomboslav noticed that guys are not very inventive, so the operator always swaps the left shell with the middle one during odd moves (first, third, fifth, etc.) and always swaps the middle shell with the right one during even moves (second, fourth, etc.).Let's number shells from 0 to 2 from left to right. Thus the left shell is assigned number 0, the middle shell is 1 and the right shell is 2. Bomboslav has missed the moment when the ball was placed beneath the shell, but he knows that exactly n movements were made by the operator and the ball was under shell x at the end. Now he wonders, what was the initial position of the ball?","prob_desc_output_spec":"Print one integer from 0 to 2\u00a0\u2014 the index of the shell where the ball was initially placed.","lang_cluster":"","src_uid":"7853e03d520cd71571a6079cdfc4c4b0","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","constructive algorithms","implementation"],"prob_desc_created_at":"1487930700","prob_desc_sample_inputs":"[\"4\\n2\", \"1\\n1\"]","prob_desc_notes":"NoteIn the first sample, the ball was initially placed beneath the middle shell and the operator completed four movements.  During the first move operator swapped the left shell and the middle shell. The ball is now under the left shell.  During the second move operator swapped the middle shell and the right one. The ball is still under the left shell.  During the third move operator swapped the left shell and the middle shell again. The ball is again in the middle.  Finally, the operators swapped the middle shell and the right shell. The ball is now beneath the right shell. ","exec_outcome":"","difficulty":1000.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"0.5 seconds","prob_desc_input_spec":"The first line of the input contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u20092\u00b7109)\u00a0\u2014 the number of movements made by the operator. The second line contains a single integer x (0\u2009\u2264\u2009x\u2009\u2264\u20092)\u00a0\u2014 the index of the shell where the ball was found after n movements.","prob_desc_sample_outputs":"[\"1\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4\\r\\n2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2\\r\\n2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3\\r\\n2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3\\r\\n0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2000000000\\r\\n0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2\\r\\n0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2\\r\\n1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4\\r\\n0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5\\r\\n0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5\\r\\n1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5\\r\\n2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"6\\r\\n0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"6\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"6\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"7\\r\\n0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"100000\\r\\n0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"100000\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100000\\r\\n2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"99999\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"99998\\r\\n1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"99997\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"99996\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"99995\\r\\n1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1999999995\\r\\n0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1999999995\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1999999995\\r\\n2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1999999996\\r\\n0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1999999996\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1999999996\\r\\n2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1999999997\\r\\n0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1999999997\\r\\n1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1999999997\\r\\n2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1999999998\\r\\n0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1999999998\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1999999998\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1999999999\\r\\n0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1999999999\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1999999999\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2000000000\\r\\n1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2000000000\\r\\n2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1234567890\\r\\n0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1234567890\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1234567890\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"123456789\\r\\n0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"123456789\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"123456789\\r\\n2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"123456790\\r\\n0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"12\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"32\\r\\n1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"20\\r\\n2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"10\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1\\r\\n0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"76994383\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"25\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"12\\r\\n0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"150\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"15\\r\\n0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"21\\r\\n2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"18\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"8\\r\\n2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"10\\r\\n0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"16\\r\\n0\\r\\n\", \"output\": [\"2\"]}]"}
{"prob_desc_description":"Let quasi-palindromic number be such number that adding some leading zeros (possible none) to it produces a palindromic string. String t is called a palindrome, if it reads the same from left to right and from right to left.For example, numbers 131 and 2010200 are quasi-palindromic, they can be transformed to strings \"131\" and \"002010200\", respectively, which are palindromes.You are given some integer number x. Check if it's a quasi-palindromic number.","prob_desc_output_spec":"Print \"YES\" if number x is quasi-palindromic. Otherwise, print \"NO\" (without quotes).","lang_cluster":"","src_uid":"d82278932881e3aa997086c909f29051","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","implementation"],"prob_desc_created_at":"1506006300","prob_desc_sample_inputs":"[\"131\", \"320\", \"2010200\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains one integer number x (1\u2009\u2264\u2009x\u2009\u2264\u2009109). This number is given without any leading zeroes.","prob_desc_sample_outputs":"[\"YES\", \"NO\", \"YES\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"131\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"320\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"2010200\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"1000000000\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"999999999\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"999999998\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"102000\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"210000000\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"213443120\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"99\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"22002\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"1010\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"1201\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6460046\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"503435\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"21002\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"101001\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"200102\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"20010002\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"33003\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"100101\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"1021\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"1101\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"10101100\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"101\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"1011\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"11010\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"10110\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"110000\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"2011\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"10020001\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"12505021\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"12310\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"100501\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"11001\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"20020002\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"202002\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"1001\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"1020021\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"60660\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"98809\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"11000000\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"807008\\r\\n\", \"output\": [\"No\", \"NO\"]}]"}
{"prob_desc_description":"As you may know, MemSQL has American offices in both San Francisco and Seattle. Being a manager in the company, you travel a lot between the two cities, always by plane.You prefer flying from Seattle to San Francisco than in the other direction, because it's warmer in San Francisco. You are so busy that you don't remember the number of flights you have made in either direction. However, for each of the last n days you know whether you were in San Francisco office or in Seattle office. You always fly at nights, so you never were at both offices on the same day. Given this information, determine if you flew more times from Seattle to San Francisco during the last n days, or not.","prob_desc_output_spec":"Print \"YES\" if you flew more times from Seattle to San Francisco, and \"NO\" otherwise. You can print each letter in any case (upper or lower).","lang_cluster":"","src_uid":"ab8a2070ea758d118b3c09ee165d9517","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["implementation"],"prob_desc_created_at":"1506791100","prob_desc_sample_inputs":"[\"4\\nFSSF\", \"2\\nSF\", \"10\\nFFFFFFFFFF\", \"10\\nSSFFSFFSFF\"]","prob_desc_notes":"NoteIn the first example you were initially at San Francisco, then flew to Seattle, were there for two days and returned to San Francisco. You made one flight in each direction, so the answer is \"NO\".In the second example you just flew from Seattle to San Francisco, so the answer is \"YES\".In the third example you stayed the whole period in San Francisco, so the answer is \"NO\".In the fourth example if you replace 'S' with ones, and 'F' with zeros, you'll get the first few digits of \u03c0 in binary representation. Not very useful information though.","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line of input contains single integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the number of days. The second line contains a string of length n consisting of only capital 'S' and 'F' letters. If the i-th letter is 'S', then you were in Seattle office on that day. Otherwise you were in San Francisco. The days are given in chronological order, i.e. today is the last day in this sequence.","prob_desc_sample_outputs":"[\"NO\", \"YES\", \"NO\", \"YES\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4\\r\\nFSSF\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"2\\r\\nSF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"10\\r\\nFFFFFFFFFF\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"10\\r\\nSSFFSFFSFF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"20\\r\\nSFSFFFFSSFFFFSSSSFSS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"20\\r\\nSSFFFFFSFFFFFFFFFFFF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"20\\r\\nSSFSFSFSFSFSFSFSSFSF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"20\\r\\nSSSSFSFSSFSFSSSSSSFS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nFFFSFSFSFSSFSFFSSFFFFFSSSSFSSFFFFSFFFFFSFFFSSFSSSFFFFSSFFSSFSFFSSFSSSFSFFSFSFFSFSFFSSFFSFSSSSFSFSFSS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nFFFFFFFFFFFFFFFFFFFFFFFFFFSFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFSFFFFFFFFFFFFFFFFFSS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nFFFFFFFFFFFFFSFFFFFFFFFSFSSFFFFFFFFFFFFFFFFFFFFFFSFFSFFFFFSFFFFFFFFSFFFFFFFFFFFFFSFFFFFFFFSFFFFFFFSF\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nSFFSSFFFFFFSSFFFSSFSFFFFFSSFFFSFFFFFFSFSSSFSFSFFFFSFSSFFFFFFFFSFFFFFSFFFFFSSFFFSFFSFSFFFFSFFSFFFFFFF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nFFFFSSSSSFFSSSFFFSFFFFFSFSSFSFFSFFSSFFSSFSFFFFFSFSFSFSFFFFFFFFFSFSFFSFFFFSFSFFFFFFFFFFFFSFSSFFSSSSFF\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nFFFFFFFFFFFFSSFFFFSFSFFFSFSSSFSSSSSFSSSSFFSSFFFSFSFSSFFFSSSFFSFSFSSFSFSSFSFFFSFFFFFSSFSFFFSSSFSSSFFS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nFFFSSSFSFSSSSFSSFSFFSSSFFSSFSSFFSSFFSFSSSSFFFSFFFSFSFSSSFSSFSFSFSFFSSSSSFSSSFSFSFFSSFSFSSFFSSFSFFSFS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nFFSSSSFSSSFSSSSFSSSFFSFSSFFSSFSSSFSSSFFSFFSSSSSSSSSSSSFSSFSSSSFSFFFSSFFFFFFSFSFSSSSSSFSSSFSFSSFSSFSS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nSSSFFFSSSSFFSSSSSFSSSSFSSSFSSSSSFSSSSSSSSFSFFSSSFFSSFSSSSFFSSSSSSFFSSSSFSSSSSSFSSSFSSSSSSSFSSSSFSSSS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nFSSSSSSSSSSSFSSSSSSSSSSSSSSSSFSSSSSSFSSSSSSSSSSSSSFSSFSSSSSFSSFSSSSSSSSSFFSSSSSFSFSSSFFSSSSSSSSSSSSS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nSSSSSSSSSSSSSFSSSSSSSSSSSSFSSSFSSSSSSSSSSSSSSSSSSSSSSSSSSSSSFSSSSSSSSSSSSSSSSFSFSSSSSSSSSSSSSSSSSSFS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS\\r\\n\", \"output\": [\"NO\", \"no\"]}, {\"input\": \"100\\r\\nSFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFSFSFFFFFFFFFFFSFSFFFFFFFFFFFFFSFFFFFFFFFFFFFFFFFFFFFFFFF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSFFFFFFFFFFFFSSFFFFSFFFFFFFFFFFFFFFFFFFSFFFSSFFFFSFSFFFSFFFFFFFFFFFFFFFSSFFFFFFFFSSFFFFFFFFFFFFFFSFF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSFFSSSFFSFSFSFFFFSSFFFFSFFFFFFFFSFSFFFSFFFSFFFSFFFFSFSFFFFFFFSFFFFFFFFFFSFFSSSFFSSFFFFSFFFFSFFFFSFFF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSFFFSFFFFSFFFSSFFFSFSFFFSFFFSSFSFFFFFSFFFFFFFFSFSFSFFSFFFSFSSFSFFFSFSFFSSFSFSSSFFFFFFSSFSFFSFFFFFFFF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSSSSFFFFSFFFFFFFSFFFFSFSFFFFSSFFFFFFFFFSFFSSFFFFFFSFSFSSFSSSFFFFFFFSFSFFFSSSFFFFFFFSFFFSSFFFFSSFFFSF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSSSFSSFFFSFSSSSFSSFSSSSFSSFFFFFSFFSSSSFFSSSFSSSFSSSSFSSSSFSSSSSSSFSFSSFFFSSFFSFFSSSSFSSFFSFSSFSFFFSF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSFFSFSSSSSSSFFSSSFSSSSFSFSSFFFSSSSSSFSSSSFSSFSSSFSSSSSSSFSSFSFFFSSFSSFSFSFSSSSSSSSSSSSFFFFSSSSSFSFFF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSSSFSFFSFSFFSSSSSFSSSFSSSFFFSSSSSSSSSFSFSFSSSSFSFSSFFFFFSSSSSSSSSSSSSSSSSSSFFSSSSSFSFSSSSFFSSSSFSSSF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSSSFSSSSSSSSSSFSSSSFSSSSSSFSSSSSSFSSSSSSSSSSSSSSFSSSFSSSFSSSSSSSSSSSFSSSSSSFSFSSSSFSSSSSSFSSSSSSSSFF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSSSSSSSSSSSSSSSFSFSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSFFSSSSSSSSSFSSSSSSSSSSSSSSSSSF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"100\\r\\nSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSF\\r\\n\", \"output\": [\"YES\", \"yes\"]}, {\"input\": \"2\\r\\nSS\\r\\n\", \"output\": [\"NO\", \"no\"]}]"}
{"prob_desc_description":"You are given two lists of non-zero digits.Let's call an integer pretty if its (base 10) representation has at least one digit from the first list and at least one digit from the second list. What is the smallest positive pretty integer?","prob_desc_output_spec":"Print the smallest pretty integer.","lang_cluster":"","src_uid":"3a0c1b6d710fd8f0b6daf420255d76ee","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","implementation"],"prob_desc_created_at":"1508054700","prob_desc_sample_inputs":"[\"2 3\\n4 2\\n5 7 6\", \"8 8\\n1 2 3 4 5 6 7 8\\n8 7 6 5 4 3 2 1\"]","prob_desc_notes":"NoteIn the first example 25, 46, 24567 are pretty, as well as many other integers. The smallest among them is 25. 42 and 24 are not pretty because they don't have digits from the second list.In the second example all integers that have at least one digit different from 9 are pretty. It's obvious that the smallest among them is 1, because it's the smallest positive integer.","exec_outcome":"","difficulty":900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains two integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20099) \u2014 the lengths of the first and the second lists, respectively. The second line contains n distinct digits a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u20099) \u2014 the elements of the first list. The third line contains m distinct digits b1,\u2009b2,\u2009...,\u2009bm (1\u2009\u2264\u2009bi\u2009\u2264\u20099) \u2014 the elements of the second list.","prob_desc_sample_outputs":"[\"25\", \"1\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 3\\r\\n4 2\\r\\n5 7 6\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"8 8\\r\\n1 2 3 4 5 6 7 8\\r\\n8 7 6 5 4 3 2 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1\\r\\n9\\r\\n1\\r\\n\", \"output\": [\"19\"]}, {\"input\": \"9 1\\r\\n5 4 2 3 6 1 7 9 8\\r\\n9\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"5 3\\r\\n7 2 5 8 6\\r\\n3 1 9\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"4 5\\r\\n5 2 6 4\\r\\n8 9 1 3 7\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"5 9\\r\\n4 2 1 6 7\\r\\n2 3 4 5 6 7 8 9 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"9 9\\r\\n5 4 3 2 1 6 7 8 9\\r\\n3 2 1 5 4 7 8 9 6\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"9 5\\r\\n2 3 4 5 6 7 8 9 1\\r\\n4 2 1 6 7\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"9 9\\r\\n1 2 3 4 5 6 7 8 9\\r\\n1 2 3 4 5 6 7 8 9\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"9 9\\r\\n1 2 3 4 5 6 7 8 9\\r\\n9 8 7 6 5 4 3 2 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"9 9\\r\\n9 8 7 6 5 4 3 2 1\\r\\n1 2 3 4 5 6 7 8 9\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"9 9\\r\\n9 8 7 6 5 4 3 2 1\\r\\n9 8 7 6 5 4 3 2 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1\\r\\n8\\r\\n9\\r\\n\", \"output\": [\"89\"]}, {\"input\": \"1 1\\r\\n9\\r\\n8\\r\\n\", \"output\": [\"89\"]}, {\"input\": \"1 1\\r\\n1\\r\\n2\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"1 1\\r\\n2\\r\\n1\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"1 1\\r\\n9\\r\\n9\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"1 1\\r\\n1\\r\\n1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"4 5\\r\\n3 2 4 5\\r\\n1 6 5 9 8\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"3 2\\r\\n4 5 6\\r\\n1 5\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"5 4\\r\\n1 3 5 6 7\\r\\n2 4 3 9\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"5 5\\r\\n1 3 5 7 9\\r\\n2 4 6 8 9\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"2 2\\r\\n1 8\\r\\n2 8\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"5 5\\r\\n5 6 7 8 9\\r\\n1 2 3 4 5\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"5 5\\r\\n1 2 3 4 5\\r\\n1 2 3 4 5\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"5 5\\r\\n1 2 3 4 5\\r\\n2 3 4 5 6\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2 2\\r\\n1 5\\r\\n2 5\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"4 4\\r\\n1 3 5 8\\r\\n2 4 6 8\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"3 3\\r\\n1 5 3\\r\\n2 5 7\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"3 3\\r\\n3 6 8\\r\\n2 6 9\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"2 2\\r\\n1 4\\r\\n2 4\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"5 3\\r\\n3 4 5 6 7\\r\\n1 5 9\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"4 4\\r\\n1 2 3 4\\r\\n2 5 6 7\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5 5\\r\\n1 2 3 4 5\\r\\n9 2 1 7 5\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 2\\r\\n1 3\\r\\n2 3\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"3 3\\r\\n3 2 1\\r\\n3 2 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 3\\r\\n1 3 5\\r\\n2 3 6\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"3 3\\r\\n5 6 7\\r\\n5 6 7\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"1 2\\r\\n5\\r\\n2 5\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"3 3\\r\\n2 4 9\\r\\n7 8 9\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"3 3\\r\\n1 2 4\\r\\n3 4 5\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"3 2\\r\\n1 4 9\\r\\n2 4\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"3 3\\r\\n3 5 6\\r\\n1 5 9\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"3 2\\r\\n1 2 4\\r\\n3 4\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"2 4\\r\\n8 9\\r\\n1 2 3 9\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"1 2\\r\\n9\\r\\n8 9\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"3 2\\r\\n1 2 4\\r\\n4 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2 3\\r\\n4 5\\r\\n1 3 5\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"3 2\\r\\n1 2 3\\r\\n2 3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 3\\r\\n1 3 5 9\\r\\n2 8 9\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"2 2\\r\\n1 9\\r\\n9 2\\r\\n\", \"output\": [\"9\"]}]"}
{"prob_desc_description":"Unlucky year in Berland is such a year that its number n can be represented as n\u2009=\u2009xa\u2009+\u2009yb, where a and b are non-negative integer numbers. For example, if x\u2009=\u20092 and y\u2009=\u20093 then the years 4 and 17 are unlucky (4\u2009=\u200920\u2009+\u200931, 17\u2009=\u200923\u2009+\u200932\u2009=\u200924\u2009+\u200930) and year 18 isn't unlucky as there is no such representation for it.Such interval of years that there are no unlucky years in it is called The Golden Age.You should write a program which will find maximum length of The Golden Age which starts no earlier than the year l and ends no later than the year r. If all years in the interval [l,\u2009r] are unlucky then the answer is 0.","prob_desc_output_spec":"Print the maximum length of The Golden Age within the interval [l,\u2009r]. If all years in the interval [l,\u2009r] are unlucky then print 0.","lang_cluster":"","src_uid":"68ca8a8730db27ac2230f9fe9b120f5f","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","math"],"prob_desc_created_at":"1496675100","prob_desc_sample_inputs":"[\"2 3 1 10\", \"3 5 10 22\", \"2 3 3 5\"]","prob_desc_notes":"NoteIn the first example the unlucky years are 2, 3, 4, 5, 7, 9 and 10. So maximum length of The Golden Age is achived in the intervals [1,\u20091], [6,\u20096] and [8,\u20098].In the second example the longest Golden Age is the interval [15,\u200922].","exec_outcome":"","difficulty":1800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains four integer numbers x, y, l and r (2\u2009\u2264\u2009x,\u2009y\u2009\u2264\u20091018, 1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u20091018).","prob_desc_sample_outputs":"[\"1\", \"8\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 3 1 10\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 5 10 22\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"2 3 3 5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 2 1 10\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 2 1 1000000\\r\\n\", \"output\": [\"213568\"]}, {\"input\": \"2 2 1 1000000000000000000\\r\\n\", \"output\": [\"144115188075855871\"]}, {\"input\": \"2 3 1 1000000\\r\\n\", \"output\": [\"206415\"]}, {\"input\": \"2 3 1 1000000000000000000\\r\\n\", \"output\": [\"261485717957290893\"]}, {\"input\": \"12345 54321 1 1000000\\r\\n\", \"output\": [\"933334\"]}, {\"input\": \"54321 12345 1 1000000000000000000\\r\\n\", \"output\": [\"976614248345331214\"]}, {\"input\": \"2 3 100000000 1000000000000\\r\\n\", \"output\": [\"188286357653\"]}, {\"input\": \"2 14 732028847861235712 732028847861235712\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"14 2 732028847861235713 732028847861235713\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 2 6 7\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"16 5 821690667 821691481\\r\\n\", \"output\": [\"815\"]}, {\"input\": \"1000000000000000000 2 1 1000000000000000000\\r\\n\", \"output\": [\"423539247696576511\"]}, {\"input\": \"2 1000000000000000000 1000000000000000 1000000000000000000\\r\\n\", \"output\": [\"423539247696576511\"]}, {\"input\": \"2 2 1000000000000000000 1000000000000000000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 3 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 3 626492297402423196 726555387600422608\\r\\n\", \"output\": [\"100063090197999413\"]}, {\"input\": \"4 4 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"304279187938024110 126610724244348052 78460471576735729 451077737144268785\\r\\n\", \"output\": [\"177668463693676057\"]}, {\"input\": \"510000000000 510000000000 1 1000000000000000000\\r\\n\", \"output\": [\"999998980000000000\"]}, {\"input\": \"2 10000000000000000 1 1000000000000000000\\r\\n\", \"output\": [\"413539247696576512\"]}, {\"input\": \"84826654960259 220116531311479700 375314289098080160 890689132792406667\\r\\n\", \"output\": [\"515374843694326508\"]}, {\"input\": \"1001 9999 1 1000000000000000000\\r\\n\", \"output\": [\"988998989390034998\"]}, {\"input\": \"106561009498593483 3066011339919949 752858505287719337 958026822891358781\\r\\n\", \"output\": [\"205168317603639445\"]}, {\"input\": \"650233444262690661 556292951587380938 715689923804218376 898772439356652923\\r\\n\", \"output\": [\"183082515552434548\"]}, {\"input\": \"4294967297 4294967297 1 1000000000000000000\\r\\n\", \"output\": [\"999999991410065406\"]}, {\"input\": \"1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 2 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"73429332516742239 589598864615747534 555287238606698050 981268715519611449\\r\\n\", \"output\": [\"318240518387121676\"]}, {\"input\": \"282060925969693883 446418005951342865 709861829378794811 826972744183396568\\r\\n\", \"output\": [\"98493812262359820\"]}, {\"input\": \"97958277744315833 443452631396066615 33878596673318768 306383421710156519\\r\\n\", \"output\": [\"208425143965840685\"]}, {\"input\": \"40975442958818854 7397733549114401 299774870238987084 658001214206968260\\r\\n\", \"output\": [\"358226343967981177\"]}, {\"input\": \"699 700 1 1000\\r\\n\", \"output\": [\"697\"]}, {\"input\": \"483076744475822225 425097332543006422 404961220953110704 826152774360856248\\r\\n\", \"output\": [\"343076029885034022\"]}, {\"input\": \"4294967297 4294967297 1 999999999999999999\\r\\n\", \"output\": [\"999999991410065405\"]}, {\"input\": \"702012794 124925148 2623100012 1000000000000000000\\r\\n\", \"output\": [\"491571744457491660\"]}, {\"input\": \"433333986179614514 1000000000000000000 433333986179614515 726628630292055493\\r\\n\", \"output\": [\"293294644112440978\"]}, {\"input\": \"999999999999999999 364973116927770629 4 4\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"4 2 40 812\\r\\n\", \"output\": [\"191\"]}, {\"input\": \"2 3 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1556368728 1110129598 120230736 1258235681\\r\\n\", \"output\": [\"989898863\"]}, {\"input\": \"7 9 164249007852879073 459223650245359577\\r\\n\", \"output\": [\"229336748650748455\"]}, {\"input\": \"324693328712373699 541961409169732375 513851377473048715 873677521504257312\\r\\n\", \"output\": [\"324693328712373697\"]}, {\"input\": \"370083000139673112 230227213530985315 476750241623737312 746365058930029530\\r\\n\", \"output\": [\"146054845259371103\"]}, {\"input\": \"4 3 584 899\\r\\n\", \"output\": [\"146\"]}, {\"input\": \"4 3 286 581\\r\\n\", \"output\": [\"161\"]}, {\"input\": \"304045744870965151 464630021384225732 142628934177558000 844155070300317027\\r\\n\", \"output\": [\"304045744870965149\"]}, {\"input\": \"195627622825327857 666148746663834172 1 1000000000000000000\\r\\n\", \"output\": [\"470521123838506314\"]}, {\"input\": \"459168731438725410 459955118458373596 410157890472128901 669197645706452507\\r\\n\", \"output\": [\"209242527248078910\"]}, {\"input\": \"999999999999999999 999999999999999999 1 1000000000000000000\\r\\n\", \"output\": [\"999999999999999997\"]}, {\"input\": \"752299248283963354 680566564599126819 73681814274367577 960486443362068685\\r\\n\", \"output\": [\"606884750324759243\"]}, {\"input\": \"20373217421623606 233158243228114207 97091516440255589 395722640217125926\\r\\n\", \"output\": [\"142191179567388113\"]}, {\"input\": \"203004070900 20036005000 1 1000000000000000000\\r\\n\", \"output\": [\"999999776959924100\"]}, {\"input\": \"565269817339236857 318270460838647700 914534538271870694 956123707310168659\\r\\n\", \"output\": [\"41589169038297966\"]}, {\"input\": \"2 5 330 669\\r\\n\", \"output\": [\"131\"]}, {\"input\": \"9 9 91 547\\r\\n\", \"output\": [\"385\"]}, {\"input\": \"9 4 866389615074294253 992899492208527253\\r\\n\", \"output\": [\"126509877134233001\"]}, {\"input\": \"3037000500 3037000500 1 1000000000000000000\\r\\n\", \"output\": [\"999999993925999000\"]}, {\"input\": \"4294967297 4294967297 12 1000000000000000000\\r\\n\", \"output\": [\"999999991410065406\"]}, {\"input\": \"5 3 78510497842978003 917156799600023483\\r\\n\", \"output\": [\"238418579101562499\"]}, {\"input\": \"749206377024033575 287723056504284448 387669391392789697 931234393488075794\\r\\n\", \"output\": [\"361536985631243879\"]}, {\"input\": \"999999999999999999 454135 1000000000000000000 1000000000000000000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"759826429841877401 105086867783910112 667080043736858072 797465019478234768\\r\\n\", \"output\": [\"92746386105019330\"]}, {\"input\": \"1000000000000000000 1000000000000000000 5 7\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"440968000218771383 43378854522801881 169393324037146024 995429539593716237\\r\\n\", \"output\": [\"511082684852142973\"]}, {\"input\": \"15049917793417622 113425474361704411 87565655389309185 803955352361026671\\r\\n\", \"output\": [\"675479960205904638\"]}, {\"input\": \"4 6 264626841724745187 925995096479842591\\r\\n\", \"output\": [\"369878143059623936\"]}, {\"input\": \"4294967297 4294967297 13 1000000000000000000\\r\\n\", \"output\": [\"999999991410065406\"]}, {\"input\": \"315729630349763416 22614591055604717 66895291338255006 947444311481017774\\r\\n\", \"output\": [\"609100090075649641\"]}, {\"input\": \"3 10 173 739\\r\\n\", \"output\": [\"386\"]}, {\"input\": \"161309010783040325 128259041753158864 5843045875031294 854024306926137845\\r\\n\", \"output\": [\"564456254389938656\"]}, {\"input\": \"239838434825939759 805278168279318096 202337849919104640 672893754916863788\\r\\n\", \"output\": [\"433055320090924028\"]}, {\"input\": \"9 9 435779695685310822 697902619874412541\\r\\n\", \"output\": [\"262122924189101720\"]}, {\"input\": \"967302429573451368 723751675006196376 143219686319239751 266477897142546404\\r\\n\", \"output\": [\"123258210823306654\"]}, {\"input\": \"10 8 139979660652061677 941135332855173888\\r\\n\", \"output\": [\"697020144779318016\"]}, {\"input\": \"4294967297 1000000000000000000 4294967296 17179869184\\r\\n\", \"output\": [\"12884901886\"]}, {\"input\": \"100914030314340517 512922595840756536 812829791042966971 966156272123068006\\r\\n\", \"output\": [\"153326481080101036\"]}, {\"input\": \"288230376151711744 288230376151711744 1 1000000000000000000\\r\\n\", \"output\": [\"423539247696576512\"]}, {\"input\": \"6 9 681 750\\r\\n\", \"output\": [\"49\"]}, {\"input\": \"880356874212472951 178538501711453307 162918237570625233 224969951233811739\\r\\n\", \"output\": [\"46431449522358431\"]}, {\"input\": \"2 7 405373082004080437 771991379629433514\\r\\n\", \"output\": [\"153172782079203571\"]}, {\"input\": \"10 11 10 11\\r\\n\", \"output\": [\"1\"]}]"}
{"prob_desc_description":"Captain Bill the Hummingbird and his crew recieved an interesting challenge offer. Some stranger gave them a map, potion of teleportation and said that only this potion might help them to reach the treasure. Bottle with potion has two values x and y written on it. These values define four moves which can be performed using the potion:         Map shows that the position of Captain Bill the Hummingbird is (x1,\u2009y1) and the position of the treasure is (x2,\u2009y2).You task is to tell Captain Bill the Hummingbird whether he should accept this challenge or decline. If it is possible for Captain to reach the treasure using the potion then output \"YES\", otherwise \"NO\" (without quotes).The potion can be used infinite amount of times.","prob_desc_output_spec":"Print \"YES\" if it is possible for Captain to reach the treasure using the potion, otherwise print \"NO\" (without quotes).","lang_cluster":"","src_uid":"1c80040104e06c9f24abfcfe654a851f","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","number theory","implementation"],"prob_desc_created_at":"1497539100","prob_desc_sample_inputs":"[\"0 0 0 6\\n2 3\", \"1 1 3 6\\n1 5\"]","prob_desc_notes":"NoteIn the first example there exists such sequence of moves:   \u2014 the first type of move   \u2014 the third type of move ","exec_outcome":"","difficulty":1200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains four integer numbers x1,\u2009y1,\u2009x2,\u2009y2 (\u2009-\u2009105\u2009\u2264\u2009x1,\u2009y1,\u2009x2,\u2009y2\u2009\u2264\u2009105) \u2014 positions of Captain Bill the Hummingbird and treasure respectively. The second line contains two integer numbers x,\u2009y (1\u2009\u2264\u2009x,\u2009y\u2009\u2264\u2009105) \u2014 values on the potion bottle.","prob_desc_sample_outputs":"[\"YES\", \"NO\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"0 0 0 6\\r\\n2 3\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1 1 3 6\\r\\n1 5\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"5 4 6 -10\\r\\n1 1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"6 -3 -7 -7\\r\\n1 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 -5 -8 8\\r\\n2 1\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"70 -81 -17 80\\r\\n87 23\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"41 366 218 -240\\r\\n3456 1234\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-61972 -39646 -42371 -24854\\r\\n573 238\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-84870 -42042 94570 98028\\r\\n8972 23345\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"-58533 -50999 -1007 -59169\\r\\n8972 23345\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-100000 -100000 100000 100000\\r\\n100000 100000\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"-100000 -100000 100000 100000\\r\\n1 1\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"5 2 5 3\\r\\n1 1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"5 5 5 5\\r\\n5 5\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"0 0 1000 1000\\r\\n1 1\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"0 0 0 1\\r\\n1 1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"1 1 4 4\\r\\n2 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100000 100000 99999 99999\\r\\n100000 100000\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"1 1 1 6\\r\\n1 5\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 9 4 0\\r\\n2 3\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"0 0 0 9\\r\\n2 3\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"14 88 14 88\\r\\n100 500\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"-1 0 3 0\\r\\n4 4\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"0 0 8 9\\r\\n2 3\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-2 5 7 -6\\r\\n1 1\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"3 7 -8 8\\r\\n2 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-4 -8 -6 -1\\r\\n1 3\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"0 8 6 2\\r\\n1 1\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"-5 -2 -8 -2\\r\\n1 1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"1 4 -5 0\\r\\n1 1\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"8 -4 4 -7\\r\\n1 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"5 2 2 4\\r\\n2 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 0 -4 6\\r\\n1 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-2 6 -5 -4\\r\\n1 2\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"-6 5 10 6\\r\\n2 4\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"3 -7 1 -8\\r\\n1 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4 1 4 -4\\r\\n9 4\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"9 -3 -9 -3\\r\\n2 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-6 -6 -10 -5\\r\\n6 7\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-5 -2 2 2\\r\\n1 7\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"9 0 8 1\\r\\n7 10\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-1 6 -7 -6\\r\\n6 4\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"2 2 -3 -3\\r\\n3 1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2 -6 7 2\\r\\n2 1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-6 2 -7 -7\\r\\n1 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-5 -5 -1 -5\\r\\n2 2\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"0 5 3 -6\\r\\n2 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"0 -6 2 -1\\r\\n1 1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-6 6 -5 -4\\r\\n1 2\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"7 -7 1 -7\\r\\n2 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"99966 -99952 -99966 99923\\r\\n1 1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"99921 99980 -99956 -99907\\r\\n3 4\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"100000 100000 -100000 -100000\\r\\n1 1\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1 0 2 0\\r\\n5 1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-3 0 -8 0\\r\\n7 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-9 4 -5 -1\\r\\n8 2\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"-99999 -100000 100000 100000\\r\\n1 1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"0 0 -100 -100\\r\\n2 2\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"9 -5 -3 -2\\r\\n1 4\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"1 -10 -10 5\\r\\n7 5\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"6 -9 -1 -9\\r\\n1 9\\r\\n\", \"output\": [\"NO\"]}]"}
{"prob_desc_description":"Okabe needs bananas for one of his experiments for some strange reason. So he decides to go to the forest and cut banana trees.Consider the point (x,\u2009y) in the 2D plane such that x and y are integers and 0\u2009\u2264\u2009x,\u2009y. There is a tree in such a point, and it has x\u2009+\u2009y bananas. There are no trees nor bananas in other points. Now, Okabe draws a line with equation . Okabe can select a single rectangle with axis aligned sides with all points on or under the line and cut all the trees in all points that are inside or on the border of this rectangle and take their bananas. Okabe's rectangle can be degenerate; that is, it can be a line segment or even a point.Help Okabe and find the maximum number of bananas he can get if he chooses the rectangle wisely.Okabe is sure that the answer does not exceed 1018. You can trust him.","prob_desc_output_spec":"Print the maximum number of bananas Okabe can get from the trees he cuts.","lang_cluster":"","src_uid":"9300f1c07dd36e0cf7e6cb7911df4cf2","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","math"],"prob_desc_created_at":"1498401300","prob_desc_sample_inputs":"[\"1 5\", \"2 3\"]","prob_desc_notes":"Note  The graph above corresponds to sample test 1. The optimal rectangle is shown in red and has 30 bananas.","exec_outcome":"","difficulty":1300.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line of input contains two space-separated integers m and b (1\u2009\u2264\u2009m\u2009\u2264\u20091000, 1\u2009\u2264\u2009b\u2009\u2264\u200910000).","prob_desc_sample_outputs":"[\"30\", \"25\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1 5\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"2 3\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"4 6\\r\\n\", \"output\": [\"459\"]}, {\"input\": \"6 3\\r\\n\", \"output\": [\"171\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10 1\\r\\n\", \"output\": [\"55\"]}, {\"input\": \"20 10\\r\\n\", \"output\": [\"40326\"]}, {\"input\": \"1000 10000\\r\\n\", \"output\": [\"74133360011484445\"]}, {\"input\": \"139 9252\\r\\n\", \"output\": [\"1137907933561080\"]}, {\"input\": \"859 8096\\r\\n\", \"output\": [\"29032056230649780\"]}, {\"input\": \"987 4237\\r\\n\", \"output\": [\"5495451829240878\"]}, {\"input\": \"411 3081\\r\\n\", \"output\": [\"366755153481948\"]}, {\"input\": \"539 9221\\r\\n\", \"output\": [\"16893595018603386\"]}, {\"input\": \"259 770\\r\\n\", \"output\": [\"2281741798549\"]}, {\"input\": \"387 5422\\r\\n\", \"output\": [\"1771610559998400\"]}, {\"input\": \"515 1563\\r\\n\", \"output\": [\"75233740231341\"]}, {\"input\": \"939 407\\r\\n\", \"output\": [\"4438222781916\"]}, {\"input\": \"518 6518\\r\\n\", \"output\": [\"5511730799718825\"]}, {\"input\": \"646 1171\\r\\n\", \"output\": [\"49802404050106\"]}, {\"input\": \"70 7311\\r\\n\", \"output\": [\"142915220249910\"]}, {\"input\": \"494 6155\\r\\n\", \"output\": [\"4221391613846823\"]}, {\"input\": \"918 7704\\r\\n\", \"output\": [\"28569727339126165\"]}, {\"input\": \"46 3844\\r\\n\", \"output\": [\"9007500020760\"]}, {\"input\": \"174 2688\\r\\n\", \"output\": [\"43730657099581\"]}, {\"input\": \"894 4637\\r\\n\", \"output\": [\"5909849585253250\"]}, {\"input\": \"22 3481\\r\\n\", \"output\": [\"1548544125646\"]}, {\"input\": \"446 5030\\r\\n\", \"output\": [\"1878390629993745\"]}, {\"input\": \"440 8704\\r\\n\", \"output\": [\"9470470760118060\"]}, {\"input\": \"569 7548\\r\\n\", \"output\": [\"10326205017481606\"]}, {\"input\": \"289 6393\\r\\n\", \"output\": [\"1620061541812350\"]}, {\"input\": \"417 1045\\r\\n\", \"output\": [\"14758909519725\"]}, {\"input\": \"841 7185\\r\\n\", \"output\": [\"19452619774222875\"]}, {\"input\": \"969 6030\\r\\n\", \"output\": [\"15265318959845745\"]}, {\"input\": \"393 4874\\r\\n\", \"output\": [\"1327174123029975\"]}, {\"input\": \"817 3719\\r\\n\", \"output\": [\"2546859449982016\"]}, {\"input\": \"945 2563\\r\\n\", \"output\": [\"1115613396515835\"]}, {\"input\": \"369 4511\\r\\n\", \"output\": [\"927715710215505\"]}, {\"input\": \"555 3594\\r\\n\", \"output\": [\"1061060598862891\"]}]"}
{"prob_desc_description":"Holidays have finished. Thanks to the help of the hacker Leha, Noora managed to enter the university of her dreams which is located in a town Pavlopolis. It's well known that universities provide students with dormitory for the period of university studies. Consequently Noora had to leave Vi\u010dkopolis and move to Pavlopolis. Thus Leha was left completely alone in a quiet town Vi\u010dkopolis. He almost even fell into a depression from boredom!Leha came up with a task for himself to relax a little. He chooses two integers A and B and then calculates the greatest common divisor of integers \"A factorial\" and \"B factorial\". Formally the hacker wants to find out GCD(A!,\u2009B!). It's well known that the factorial of an integer x is a product of all positive integers less than or equal to x. Thus x!\u2009=\u20091\u00b72\u00b73\u00b7...\u00b7(x\u2009-\u20091)\u00b7x. For example 4!\u2009=\u20091\u00b72\u00b73\u00b74\u2009=\u200924. Recall that GCD(x,\u2009y) is the largest positive integer q that divides (without a remainder) both x and y.Leha has learned how to solve this task very effective. You are able to cope with it not worse, aren't you?","prob_desc_output_spec":"Print a single integer denoting the greatest common divisor of integers A! and B!.","lang_cluster":"","src_uid":"7bf30ceb24b66d91382e97767f9feeb6","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","number theory","implementation"],"prob_desc_created_at":"1499011500","prob_desc_sample_inputs":"[\"4 3\"]","prob_desc_notes":"NoteConsider the sample.4!\u2009=\u20091\u00b72\u00b73\u00b74\u2009=\u200924. 3!\u2009=\u20091\u00b72\u00b73\u2009=\u20096. The greatest common divisor of integers 24 and 6 is exactly 6.","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first and single line contains two integers A and B (1\u2009\u2264\u2009A,\u2009B\u2009\u2264\u2009109,\u2009min(A,\u2009B)\u2009\u2264\u200912).","prob_desc_sample_outputs":"[\"6\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"10 399603090\\r\\n\", \"output\": [\"3628800\"]}, {\"input\": \"6 973151934\\r\\n\", \"output\": [\"720\"]}, {\"input\": \"2 841668075\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"7 415216919\\r\\n\", \"output\": [\"5040\"]}, {\"input\": \"3 283733059\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"11 562314608\\r\\n\", \"output\": [\"39916800\"]}, {\"input\": \"3 990639260\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"11 859155400\\r\\n\", \"output\": [\"39916800\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"5 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"1 4\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"5 4\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"1 12\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"9 7\\r\\n\", \"output\": [\"5040\"]}, {\"input\": \"2 3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"6 11\\r\\n\", \"output\": [\"720\"]}, {\"input\": \"6 7\\r\\n\", \"output\": [\"720\"]}, {\"input\": \"11 11\\r\\n\", \"output\": [\"39916800\"]}, {\"input\": \"4 999832660\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"7 999228288\\r\\n\", \"output\": [\"5040\"]}, {\"input\": \"11 999257105\\r\\n\", \"output\": [\"39916800\"]}, {\"input\": \"11 999286606\\r\\n\", \"output\": [\"39916800\"]}, {\"input\": \"3 999279109\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"999632727 11\\r\\n\", \"output\": [\"39916800\"]}, {\"input\": \"999625230 7\\r\\n\", \"output\": [\"5040\"]}, {\"input\": \"999617047 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"999646548 7\\r\\n\", \"output\": [\"5040\"]}, {\"input\": \"999639051 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"12 12\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"12 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1213 5\\r\\n\", \"output\": [\"120\"]}, {\"input\": \"8 9\\r\\n\", \"output\": [\"40320\"]}, {\"input\": \"12 9\\r\\n\", \"output\": [\"362880\"]}, {\"input\": \"12 1000000000\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"1000000000 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"12 13\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"2 29845\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"10 21\\r\\n\", \"output\": [\"3628800\"]}, {\"input\": \"12 20\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"15 12\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"1000000000 12\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"11 30\\r\\n\", \"output\": [\"39916800\"]}, {\"input\": \"17 12\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"4 19\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"12 15\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"20 6\\r\\n\", \"output\": [\"720\"]}, {\"input\": \"10 20\\r\\n\", \"output\": [\"3628800\"]}, {\"input\": \"10 10\\r\\n\", \"output\": [\"3628800\"]}, {\"input\": \"22 12\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"20 12\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"12 23\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"12 22\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"18 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"14 10\\r\\n\", \"output\": [\"3628800\"]}, {\"input\": \"14 12\\r\\n\", \"output\": [\"479001600\"]}, {\"input\": \"8 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"5 5\\r\\n\", \"output\": [\"120\"]}]"}
{"prob_desc_description":"One day Petya was solving a very interesting problem. But although he used many optimization techniques, his solution still got Time limit exceeded verdict. Petya conducted a thorough analysis of his program and found out that his function for finding maximum element in an array of n positive integers was too slow. Desperate, Petya decided to use a somewhat unexpected optimization using parameter k, so now his function contains the following code:int fast_max(int n, int a[]) {     int ans = 0;    int offset = 0;    for (int i = 0; i < n; ++i)        if (ans < a[i]) {            ans = a[i];            offset = 0;        } else {            offset = offset + 1;            if (offset == k)                return ans;        }    return ans;}That way the function iteratively checks array elements, storing the intermediate maximum, and if after k consecutive iterations that maximum has not changed, it is returned as the answer.Now Petya is interested in fault rate of his function. He asked you to find the number of permutations of integers from 1 to n such that the return value of his function on those permutations is not equal to n. Since this number could be very big, output the answer modulo 109\u2009+\u20097.","prob_desc_output_spec":"Output the answer to the problem modulo 109\u2009+\u20097.","lang_cluster":"","src_uid":"0644605611a2cd10ab3a9f12f18d7ae4","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp","combinatorics","math"],"prob_desc_created_at":"1510502700","prob_desc_sample_inputs":"[\"5 2\", \"5 3\", \"6 3\"]","prob_desc_notes":"NotePermutations from second example: [4,\u20091,\u20092,\u20093,\u20095], [4,\u20091,\u20093,\u20092,\u20095], [4,\u20092,\u20091,\u20093,\u20095], [4,\u20092,\u20093,\u20091,\u20095], [4,\u20093,\u20091,\u20092,\u20095], [4,\u20093,\u20092,\u20091,\u20095].","exec_outcome":"","difficulty":2400.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The only line contains two integers n and k (1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u2009106), separated by a space\u00a0\u2014 the length of the permutations and the parameter k.","prob_desc_sample_outputs":"[\"22\", \"6\", \"84\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"5 2\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"5 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"6 3\\r\\n\", \"output\": [\"84\"]}, {\"input\": \"5 10\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 1\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"4 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5 1\\r\\n\", \"output\": [\"55\"]}, {\"input\": \"5 4\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5 5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1000000 500000\\r\\n\", \"output\": [\"900097839\"]}, {\"input\": \"1000000 1000000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1000000 1\\r\\n\", \"output\": [\"131797017\"]}, {\"input\": \"1 1000000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"959139 199252\\r\\n\", \"output\": [\"770937198\"]}, {\"input\": \"9859 748096\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"125987 264237\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"209411 813081\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"325539 329221\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"376259 910770\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"492387 235422\\r\\n\", \"output\": [\"249147139\"]}, {\"input\": \"608515 751563\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"691939 300407\\r\\n\", \"output\": [\"700547157\"]}, {\"input\": \"30518 196518\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"146646 521171\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"230070 37311\\r\\n\", \"output\": [\"993306535\"]}, {\"input\": \"313494 586155\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"396918 167704\\r\\n\", \"output\": [\"943821934\"]}, {\"input\": \"513046 683844\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"629174 232688\\r\\n\", \"output\": [\"831745227\"]}, {\"input\": \"679894 524637\\r\\n\", \"output\": [\"655418678\"]}, {\"input\": \"796022 73481\\r\\n\", \"output\": [\"883548575\"]}, {\"input\": \"879446 655030\\r\\n\", \"output\": [\"563982505\"]}, {\"input\": \"405440 588704\\r\\n\", \"output\": [\"0\"]}]"}
{"prob_desc_description":"Ivan has a robot which is situated on an infinite grid. Initially the robot is standing in the starting cell (0,\u20090). The robot can process commands. There are four types of commands it can perform:  U \u2014 move from the cell (x,\u2009y) to (x,\u2009y\u2009+\u20091);  D \u2014 move from (x,\u2009y) to (x,\u2009y\u2009-\u20091);  L \u2014 move from (x,\u2009y) to (x\u2009-\u20091,\u2009y);  R \u2014 move from (x,\u2009y) to (x\u2009+\u20091,\u2009y). Ivan entered a sequence of n commands, and the robot processed it. After this sequence the robot ended up in the starting cell (0,\u20090), but Ivan doubts that the sequence is such that after performing it correctly the robot ends up in the same cell. He thinks that some commands were ignored by robot. To acknowledge whether the robot is severely bugged, he needs to calculate the maximum possible number of commands that were performed correctly. Help Ivan to do the calculations!","prob_desc_output_spec":"Print the maximum possible number of commands from the sequence the robot could perform to end up in the starting cell.","lang_cluster":"","src_uid":"b9fa2bb8001bd064ede531a5281cfd8a","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["greedy"],"prob_desc_created_at":"1510239900","prob_desc_sample_inputs":"[\"4\\nLDUR\", \"5\\nRRRUU\", \"6\\nLLRRRR\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1000.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains one number n \u2014 the length of sequence of commands entered by Ivan (1\u2009\u2264\u2009n\u2009\u2264\u2009100). The second line contains the sequence itself \u2014 a string consisting of n characters. Each character can be U, D, L or R.","prob_desc_sample_outputs":"[\"4\", \"0\", \"4\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4\\r\\nLDUR\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"5\\r\\nRRRUU\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"6\\r\\nLLRRRR\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"88\\r\\nLLUUULRDRRURDDLURRLRDRLLRULRUUDDLLLLRRDDURDURRLDURRLDRRRUULDDLRRRDDRRLUULLURDURUDDDDDLDR\\r\\n\", \"output\": [\"76\"]}, {\"input\": \"89\\r\\nLDLLLDRDUDURRRRRUDULDDDLLUDLRLRLRLDLDUULRDUDLRRDLUDLURRDDRRDLDUDUUURUUUDRLUDUDLURDLDLLDDU\\r\\n\", \"output\": [\"80\"]}, {\"input\": \"90\\r\\nRRRDUULLLRDUUDDRLDLRLUDURDRDUUURUURDDRRRURLDDDUUDRLLLULURDRDRURLDRRRRUULDULDDLLLRRLRDLLLLR\\r\\n\", \"output\": [\"84\"]}, {\"input\": \"91\\r\\nRLDRLRRLLDLULULLURULLRRULUDUULLUDULDUULURUDRUDUURDULDUDDUUUDRRUUDLLRULRULURLDRDLDRURLLLRDDD\\r\\n\", \"output\": [\"76\"]}, {\"input\": \"92\\r\\nRLRDDLULRLLUURRDDDLDDDLDDUURRRULLRDULDULLLUUULDUDLRLRRDRDRDDULDRLUDRDULDRURUDUULLRDRRLLDRLRR\\r\\n\", \"output\": [\"86\"]}, {\"input\": \"93\\r\\nRLLURLULRURDDLUURLUDDRDLUURLRDLRRRDUULLRDRRLRLDURRDLLRDDLLLDDDLDRRURLLDRUDULDDRRULRRULRLDRDLR\\r\\n\", \"output\": [\"84\"]}, {\"input\": \"94\\r\\nRDULDDDLULRDRUDRUUDUUDRRRULDRRUDURUULRDUUDLULLLUDURRDRDLUDRULRRRULUURUDDDDDUDLLRDLDRLLRUUURLUL\\r\\n\", \"output\": [\"86\"]}, {\"input\": \"95\\r\\nRDLUUULLUURDDRLDLLRRRULRLRDULULRULRUDURLULDDDRLURLDRULDUDUUULLRDDURUULULLDDLDRDRLLLURLRDLLDDDDU\\r\\n\", \"output\": [\"86\"]}, {\"input\": \"96\\r\\nRDDRLRLLDDULRLRURUDLRLDUDRURLLUUDLLURDLRRUURDRRUDRURLLDLLRDURDURLRLUDURULLLRDUURULUUULRRURRDLURL\\r\\n\", \"output\": [\"84\"]}, {\"input\": \"97\\r\\nRURDDLRLLRULUDURDLRLLUUDURRLLUDLLLDUDRUULDRUUURURULRDLDRRLLUUUDLLLDDLLLLRLLDUDRRDLLUDLRURUDULRLUR\\r\\n\", \"output\": [\"82\"]}, {\"input\": \"98\\r\\nRUDURLULLDDLLRDLLRDDLLLLRLDDDDRRRDDRRURLDRLLRUUUDLUUUDDDUDRUURLURUUDUUDRULRRULLRRLRULLULDLUURLULRD\\r\\n\", \"output\": [\"92\"]}, {\"input\": \"99\\r\\nRRULLDULRRDRULLDUDRUDDDRLLUUDRDDUDURLDDRUUDRRUUURRRURDDLDUURDLRLURRDDLUDDLUDURDRUDDURLURURLRUDRURLD\\r\\n\", \"output\": [\"86\"]}, {\"input\": \"100\\r\\nUDRLRRLLRRLRRRDDLLDDDLULLDDLURUURUULUDDDRDDLLRDLLUURLRDRLRRLRLLLULDUDDUURRLRDULDRDURRRRRRULDRRDLDRRL\\r\\n\", \"output\": [\"88\"]}, {\"input\": \"1\\r\\nU\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5\\r\\nUUULD\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1\\r\\nD\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5\\r\\nURLUL\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5\\r\\nDDDRU\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2\\r\\nLR\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"8\\r\\nDDRDLDUR\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"6\\r\\nLLLLUD\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"13\\r\\nRRRLLLLLLLLLL\\r\\n\", \"output\": [\"6\"]}]"}
{"prob_desc_description":"You are given an array a consisting of n integers, and additionally an integer m. You have to choose some sequence of indices b1,\u2009b2,\u2009...,\u2009bk (1\u2009\u2264\u2009b1\u2009<\u2009b2\u2009<\u2009...\u2009<\u2009bk\u2009\u2264\u2009n) in such a way that the value of  is maximized. Chosen sequence can be empty.Print the maximum possible value of .","prob_desc_output_spec":"Print the maximum possible value of .","lang_cluster":"","src_uid":"d3a8a3e69a55936ee33aedd66e5b7f4a","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["bitmasks","meet-in-the-middle","divide and conquer"],"prob_desc_created_at":"1510239900","prob_desc_sample_inputs":"[\"4 4\\n5 2 4 1\", \"3 20\\n199 41 299\"]","prob_desc_notes":"NoteIn the first example you can choose a sequence b\u2009=\u2009{1,\u20092}, so the sum  is equal to 7 (and that's 3 after taking it modulo 4).In the second example you can choose a sequence b\u2009=\u2009{3}.","exec_outcome":"","difficulty":1800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains two integers n and m (1\u2009\u2264\u2009n\u2009\u2264\u200935, 1\u2009\u2264\u2009m\u2009\u2264\u2009109). The second line contains n integers a1, a2, ..., an (1\u2009\u2264\u2009ai\u2009\u2264\u2009109).","prob_desc_sample_outputs":"[\"3\", \"19\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4 4\\r\\n5 2 4 1\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"3 20\\r\\n199 41 299\\r\\n\", \"output\": [\"19\"]}, {\"input\": \"5 10\\r\\n47 100 49 2 56\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"5 1000\\r\\n38361 75847 14913 11499 8297\\r\\n\", \"output\": [\"917\"]}, {\"input\": \"10 10\\r\\n48 33 96 77 67 59 35 15 14 86\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"10 1000\\r\\n16140 63909 7177 99953 35627 40994 29288 7324 44476 36738\\r\\n\", \"output\": [\"999\"]}, {\"input\": \"30 10\\r\\n99 44 42 36 43 82 99 99 10 79 97 84 5 78 37 45 87 87 11 11 79 66 47 100 8 50 27 98 32 27\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"30 1000\\r\\n81021 18939 94456 90340 76840 78808 27921 71826 99382 1237 93435 35153 71691 25508 96732 23778 49073 60025 95231 88719 61650 50925 34416 73600 7295 14654 78340 72871 17324 77484\\r\\n\", \"output\": [\"999\"]}, {\"input\": \"35 10\\r\\n86 66 98 91 61 71 14 58 49 92 13 97 13 22 98 83 85 29 85 41 51 16 76 17 75 25 71 10 87 11 9 34 3 6 4\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"35 1000\\r\\n33689 27239 14396 26525 30455 13710 37039 80789 26268 1236 89916 87557 90571 13710 59152 99417 39577 40675 25931 14900 86611 46223 7105 64074 41238 59169 81308 70534 99894 10332 72983 85414 73848 68378 98404\\r\\n\", \"output\": [\"999\"]}, {\"input\": \"35 1000000000\\r\\n723631245 190720106 931659134 503095294 874181352 712517040 800614682 904895364 256863800 39366772 763190862 770183843 774794919 55669976 329106527 513566505 207828535 258356470 816288168 657823769 5223226 865258331 655737365 278677545 880429272 718852999 810522025 229560899 544602508 195068526 878937336 739178504 474601895 54057210 432282541\\r\\n\", \"output\": [\"999999999\"]}, {\"input\": \"35 982451653\\r\\n27540278 680344696 757828533 487257472 581415866 897315944 104006244 109795853 24393319 840585536 643747159 864374693 675946278 27492061 172462571 484550119 801174500 94160579 818984382 53253720 966692115 811281559 154162995 890236127 799613478 611617443 787587569 606421577 91876376 464150101 671199076 108388038 342311910 974681791 862530363\\r\\n\", \"output\": [\"982451652\"]}, {\"input\": \"15 982451653\\r\\n384052103 7482105 882228352 582828798 992251028 892163214 687253903 951043841 277531875 402248542 499362766 919046434 350763964 288775999 982610665\\r\\n\", \"output\": [\"982368704\"]}, {\"input\": \"35 1000000000\\r\\n513 9778 5859 8149 297 7965 7152 917 243 4353 7248 4913 9403 6199 2930 7461 3888 1898 3222 9424 3960 1902 2933 5268 2650 1687 5319 5065 8450 141 4219 2586 2176 1118 9635\\r\\n\", \"output\": [\"158921\"]}, {\"input\": \"35 982451653\\r\\n5253 7912 3641 7428 6138 9613 9059 6352 9070 89 9030 1686 3098 7852 3316 8158 7497 5804 130 6201 235 64 3451 6104 4148 3446 6059 6802 7466 8781 1636 8291 8874 8924 5997\\r\\n\", \"output\": [\"197605\"]}, {\"input\": \"15 982451653\\r\\n7975 7526 1213 2318 209 7815 4153 1853 6651 2880 4535 587 8022 3365 5491\\r\\n\", \"output\": [\"64593\"]}, {\"input\": \"35 1730970\\r\\n141538 131452 93552 3046 119468 8282 166088 33782 36462 25246 178798 81434 180900 15102 175898 157782 155254 166352 60772 75162 102326 104854 181138 58618 123800 54458 157516 20658 25084 155276 194920 16680 15148 188292 88802\\r\\n\", \"output\": [\"1730968\"]}, {\"input\": \"35 346194136\\r\\n89792 283104 58936 184528 194768 253076 304368 140216 220836 69196 274604 68988 300412 242588 25328 183488 81712 374964 377696 317872 146208 147400 346276 14356 90432 347556 35452 119348 311320 126112 113200 98936 189500 363424 320164\\r\\n\", \"output\": [\"6816156\"]}, {\"input\": \"35 129822795\\r\\n379185 168630 1047420 892020 180690 1438200 168330 1328610 933930 936360 1065225 351990 1079190 681510 1336020 814590 365820 1493580 495825 809745 309585 190320 1148640 146790 1008900 365655 947265 1314060 1048770 1463535 1233420 969330 1324530 944130 1457160\\r\\n\", \"output\": [\"29838960\"]}, {\"input\": \"35 106920170\\r\\n36941450 53002950 90488020 66086895 77577045 16147985 26130825 84977690 87374560 59007480 61416705 100977415 43291920 56833000 12676230 50531950 5325005 54745005 105536410 76922230 9031505 121004870 104634495 16271535 55819890 47603815 85830185 65938635 33074335 40289655 889560 19829775 31653510 120671285 37843365\\r\\n\", \"output\": [\"106907815\"]}, {\"input\": \"35 200000000\\r\\n75420000 93400000 70560000 93860000 183600000 143600000 61780000 145000000 99360000 14560000 109280000 22040000 141220000 14360000 55140000 78580000 96940000 62400000 173220000 40420000 139600000 30100000 141640000 64780000 186080000 159220000 137780000 133640000 83560000 51280000 139100000 133020000 99460000 35900000 78980000\\r\\n\", \"output\": [\"199980000\"]}, {\"input\": \"4 1\\r\\n435 124 324 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 12\\r\\n13\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1000000000\\r\\n1000000000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7 19\\r\\n8 1 4 8 8 7 3\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"6 7\\r\\n1 1 1 1 1 6\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"3 5\\r\\n1 2 3\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"4 36\\r\\n22 9 24 27\\r\\n\", \"output\": [\"33\"]}, {\"input\": \"2 8\\r\\n7 1\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"2 12\\r\\n8 7\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"4 10\\r\\n11 31 12 3\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"2 8\\r\\n2 7\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"4 19\\r\\n16 20 19 21\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"3 4\\r\\n9 16 11\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"2 3\\r\\n3 7\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 20\\r\\n4 3\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"3 299\\r\\n100 100 200\\r\\n\", \"output\": [\"200\"]}]"}
{"prob_desc_description":"Amr loves Geometry. One day he came up with a very interesting problem.Amr has a circle of radius r and center in point (x,\u2009y). He wants the circle center to be in new position (x',\u2009y').In one step Amr can put a pin to the border of the circle in a certain point, then rotate the circle around that pin by any angle and finally remove the pin.Help Amr to achieve his goal in minimum number of steps.","prob_desc_output_spec":"Output a single integer \u2014 minimum number of steps required to move the center of the circle to the destination point.","lang_cluster":"","src_uid":"698da80c7d24252b57cca4e4f0ca7031","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["geometry","math"],"prob_desc_created_at":"1422028800","prob_desc_sample_inputs":"[\"2 0 0 0 4\", \"1 1 1 4 4\", \"4 5 6 5 6\"]","prob_desc_notes":"NoteIn the first sample test the optimal way is to put a pin at point (0,\u20092) and rotate the circle by 180 degrees counter-clockwise (or clockwise, no matter).","exec_outcome":"","difficulty":1400.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"Input consists of 5 space-separated integers r, x, y, x' y' (1\u2009\u2264\u2009r\u2009\u2264\u2009105, \u2009-\u2009105\u2009\u2264\u2009x,\u2009y,\u2009x',\u2009y'\u2009\u2264\u2009105), circle radius, coordinates of original center of the circle and coordinates of destination center of the circle respectively.","prob_desc_sample_outputs":"[\"1\", \"3\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 0 0 0 4\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1 1 4 4\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"4 5 6 5 6\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"10 20 0 40 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"9 20 0 40 0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5 -1 -6 -5 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"99125 26876 -21414 14176 17443\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"8066 7339 19155 -90534 -60666\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"100000 -100000 -100000 100000 100000\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"10 20 0 41 0\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"25 -64 -6 -56 64\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"125 455 450 439 721\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5 6 3 7 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"24 130 14786 3147 2140\\r\\n\", \"output\": [\"271\"]}, {\"input\": \"125 -363 176 93 330\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 14 30 30 14\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"25 96 13 7 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 100000 -100000 100000 -100000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 3 4 2 5\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 -3 3 2 6\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"2 7 20 13 -5\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1 1 1 1 4\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"249 -54242 -30537 -45023 -89682\\r\\n\", \"output\": [\"121\"]}, {\"input\": \"4 100000 -100000 100000 -99999\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"97741 23818 78751 97583 26933\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"56767 -29030 51625 79823 -56297\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"98260 13729 74998 23701 9253\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"67377 -80131 -90254 -57320 14102\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 100000 100000 100000 -100000\\r\\n\", \"output\": [\"100000\"]}, {\"input\": \"19312 19470 82059 58064 62231\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"67398 -68747 -79056 -34193 29400\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"91099 37184 -71137 75650 -3655\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"46456 -2621 -23623 -98302 -99305\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"100 100000 -100000 100000 -99999\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 100000 -100000 100000 -100000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"8 0 0 0 32\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"100000 100000 1 -100000 0\\r\\n\", \"output\": [\"2\"]}]"}
{"prob_desc_description":"Drazil is playing a math game with Varda.Let's define  for positive integer x as a product of factorials of its digits. For example, .First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:1. x doesn't contain neither digit 0 nor digit 1.2.  = .Help friends find such number.","prob_desc_output_spec":"Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.","lang_cluster":"","src_uid":"60dbfc7a65702ae8bd4a587db1e06398","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["greedy","math","sortings","dp","implementation"],"prob_desc_created_at":"1424190900","prob_desc_sample_inputs":"[\"4\\n1234\", \"3\\n555\"]","prob_desc_notes":"NoteIn the first case, ","exec_outcome":"","difficulty":1400.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u200915) \u2014 the number of digits in a. The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.","prob_desc_sample_outputs":"[\"33222\", \"555\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4\\r\\n1234\\r\\n\", \"output\": [\"33222\"]}, {\"input\": \"3\\r\\n555\\r\\n\", \"output\": [\"555\"]}, {\"input\": \"15\\r\\n012345781234578\\r\\n\", \"output\": [\"7777553333222222222222\"]}, {\"input\": \"1\\r\\n8\\r\\n\", \"output\": [\"7222\"]}, {\"input\": \"10\\r\\n1413472614\\r\\n\", \"output\": [\"75333332222222\"]}, {\"input\": \"8\\r\\n68931246\\r\\n\", \"output\": [\"77553333332222222\"]}, {\"input\": \"7\\r\\n4424368\\r\\n\", \"output\": [\"75333332222222222\"]}, {\"input\": \"6\\r\\n576825\\r\\n\", \"output\": [\"7755532222\"]}, {\"input\": \"5\\r\\n97715\\r\\n\", \"output\": [\"7775332\"]}, {\"input\": \"3\\r\\n915\\r\\n\", \"output\": [\"75332\"]}, {\"input\": \"2\\r\\n26\\r\\n\", \"output\": [\"532\"]}, {\"input\": \"1\\r\\n4\\r\\n\", \"output\": [\"322\"]}, {\"input\": \"15\\r\\n028745260720699\\r\\n\", \"output\": [\"7777755533333332222222222\"]}, {\"input\": \"13\\r\\n5761790121605\\r\\n\", \"output\": [\"7775555333322\"]}, {\"input\": \"10\\r\\n3312667105\\r\\n\", \"output\": [\"755533332\"]}, {\"input\": \"1\\r\\n7\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"15\\r\\n989898989898989\\r\\n\", \"output\": [\"777777777777777333333333333333322222222222222222222222222222\"]}, {\"input\": \"15\\r\\n000000000000007\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"15\\r\\n999999999999990\\r\\n\", \"output\": [\"77777777777777333333333333333333333333333322222222222222\"]}, {\"input\": \"1\\r\\n2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1\\r\\n3\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"1\\r\\n5\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"1\\r\\n6\\r\\n\", \"output\": [\"53\"]}, {\"input\": \"1\\r\\n9\\r\\n\", \"output\": [\"7332\"]}, {\"input\": \"2\\r\\n09\\r\\n\", \"output\": [\"7332\"]}, {\"input\": \"13\\r\\n1337251172966\\r\\n\", \"output\": [\"777555333333222\"]}, {\"input\": \"15\\r\\n987654329876543\\r\\n\", \"output\": [\"777777555533333333332222222222222\"]}, {\"input\": \"9\\r\\n234567899\\r\\n\", \"output\": [\"777755333333322222222\"]}, {\"input\": \"2\\r\\n99\\r\\n\", \"output\": [\"77333322\"]}, {\"input\": \"2\\r\\n66\\r\\n\", \"output\": [\"5533\"]}, {\"input\": \"3\\r\\n999\\r\\n\", \"output\": [\"777333333222\"]}, {\"input\": \"5\\r\\n99999\\r\\n\", \"output\": [\"77777333333333322222\"]}, {\"input\": \"9\\r\\n123456789\\r\\n\", \"output\": [\"77755333332222222\"]}, {\"input\": \"9\\r\\n987654321\\r\\n\", \"output\": [\"77755333332222222\"]}, {\"input\": \"3\\r\\n666\\r\\n\", \"output\": [\"555333\"]}, {\"input\": \"6\\r\\n555777\\r\\n\", \"output\": [\"777555\"]}, {\"input\": \"10\\r\\n1234567899\\r\\n\", \"output\": [\"777755333333322222222\"]}, {\"input\": \"4\\r\\n6666\\r\\n\", \"output\": [\"55553333\"]}, {\"input\": \"4\\r\\n9754\\r\\n\", \"output\": [\"775333222\"]}, {\"input\": \"2\\r\\n95\\r\\n\", \"output\": [\"75332\"]}, {\"input\": \"14\\r\\n11122233344455\\r\\n\", \"output\": [\"55333333222222222\"]}, {\"input\": \"12\\r\\n836544897832\\r\\n\", \"output\": [\"77777553333333222222222222222\"]}]"}
{"prob_desc_description":"Let's define the permutation of length n as an array p\u2009=\u2009[p1,\u2009p2,\u2009...,\u2009pn] consisting of n distinct integers from range from 1 to n. We say that this permutation maps value 1 into the value p1, value 2 into the value p2 and so on.Kyota Ootori has just learned about cyclic representation of a permutation. A cycle is a sequence of numbers such that each element of this sequence is being mapped into the next element of this sequence (and the last element of the cycle is being mapped into the first element of the cycle). The cyclic representation is a representation of p as a collection of cycles forming p. For example, permutation p\u2009=\u2009[4,\u20091,\u20096,\u20092,\u20095,\u20093] has a cyclic representation that looks like (142)(36)(5) because 1 is replaced by 4, 4 is replaced by 2, 2 is replaced by 1, 3 and 6 are swapped, and 5 remains in place. Permutation may have several cyclic representations, so Kyoya defines the standard cyclic representation of a permutation as follows. First, reorder the elements within each cycle so the largest element is first. Then, reorder all of the cycles so they are sorted by their first element. For our example above, the standard cyclic representation of [4,\u20091,\u20096,\u20092,\u20095,\u20093] is (421)(5)(63).Now, Kyoya notices that if we drop the parenthesis in the standard cyclic representation, we get another permutation! For instance, [4,\u20091,\u20096,\u20092,\u20095,\u20093] will become [4,\u20092,\u20091,\u20095,\u20096,\u20093].Kyoya notices that some permutations don't change after applying operation described above at all. He wrote all permutations of length n that do not change in a list in lexicographic order. Unfortunately, his friend Tamaki Suoh lost this list. Kyoya wishes to reproduce the list and he needs your help. Given the integers n and k, print the permutation that was k-th on Kyoya's list.","prob_desc_output_spec":"Print n space-separated integers, representing the permutation that is the answer for the question. ","lang_cluster":"","src_uid":"e03c6d3bb8cf9119530668765691a346","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["greedy","combinatorics","binary search","constructive algorithms","math","implementation"],"prob_desc_created_at":"1435163400","prob_desc_sample_inputs":"[\"4 3\", \"10 1\"]","prob_desc_notes":"NoteThe standard cycle representation is (1)(32)(4), which after removing parenthesis gives us the original permutation. The first permutation on the list would be [1,\u20092,\u20093,\u20094], while the second permutation would be [1,\u20092,\u20094,\u20093].","exec_outcome":"","difficulty":1900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line will contain two integers n, k (1\u2009\u2264\u2009n\u2009\u2264\u200950, 1\u2009\u2264\u2009k\u2009\u2264\u2009min{1018,\u2009l} where l is the length of the Kyoya's list).","prob_desc_sample_outputs":"[\"1 3 2 4\", \"1 2 3 4 5 6 7 8 9 10\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4 3\\r\\n\", \"output\": [\"1 3 2 4\"]}, {\"input\": \"10 1\\r\\n\", \"output\": [\"1 2 3 4 5 6 7 8 9 10\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"50 1\\r\\n\", \"output\": [\"1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50\"]}, {\"input\": \"10 57\\r\\n\", \"output\": [\"2 1 3 4 5 6 7 8 10 9\"]}, {\"input\": \"50 20365011074\\r\\n\", \"output\": [\"2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49\"]}, {\"input\": \"20 9999\\r\\n\", \"output\": [\"2 1 4 3 5 7 6 8 9 10 11 13 12 14 15 17 16 18 19 20\"]}, {\"input\": \"49 12586269025\\r\\n\", \"output\": [\"2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 49\"]}, {\"input\": \"49 1\\r\\n\", \"output\": [\"1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49\"]}, {\"input\": \"10 89\\r\\n\", \"output\": [\"2 1 4 3 6 5 8 7 10 9\"]}, {\"input\": \"10 1\\r\\n\", \"output\": [\"1 2 3 4 5 6 7 8 9 10\"]}, {\"input\": \"5 8\\r\\n\", \"output\": [\"2 1 4 3 5\"]}, {\"input\": \"5 1\\r\\n\", \"output\": [\"1 2 3 4 5\"]}, {\"input\": \"25 121393\\r\\n\", \"output\": [\"2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 25\"]}, {\"input\": \"25 1\\r\\n\", \"output\": [\"1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"2 1\"]}, {\"input\": \"3 3\\r\\n\", \"output\": [\"2 1 3\"]}, {\"input\": \"4 2\\r\\n\", \"output\": [\"1 2 4 3\"]}, {\"input\": \"5 8\\r\\n\", \"output\": [\"2 1 4 3 5\"]}, {\"input\": \"6 10\\r\\n\", \"output\": [\"2 1 3 4 6 5\"]}, {\"input\": \"7 20\\r\\n\", \"output\": [\"2 1 4 3 5 7 6\"]}, {\"input\": \"8 24\\r\\n\", \"output\": [\"2 1 3 4 5 7 6 8\"]}, {\"input\": \"9 1\\r\\n\", \"output\": [\"1 2 3 4 5 6 7 8 9\"]}, {\"input\": \"10 24\\r\\n\", \"output\": [\"1 2 4 3 5 6 7 9 8 10\"]}, {\"input\": \"11 77\\r\\n\", \"output\": [\"1 3 2 5 4 6 7 8 9 10 11\"]}, {\"input\": \"12 101\\r\\n\", \"output\": [\"1 3 2 4 5 6 8 7 10 9 11 12\"]}, {\"input\": \"13 240\\r\\n\", \"output\": [\"2 1 3 4 5 6 7 8 10 9 11 13 12\"]}, {\"input\": \"14 356\\r\\n\", \"output\": [\"1 3 2 5 4 6 8 7 10 9 12 11 14 13\"]}, {\"input\": \"15 463\\r\\n\", \"output\": [\"1 3 2 4 5 7 6 9 8 11 10 12 13 15 14\"]}, {\"input\": \"16 747\\r\\n\", \"output\": [\"1 3 2 4 5 7 6 9 8 11 10 12 13 14 15 16\"]}, {\"input\": \"17 734\\r\\n\", \"output\": [\"1 2 4 3 5 6 8 7 10 9 11 12 13 14 15 16 17\"]}, {\"input\": \"18 1809\\r\\n\", \"output\": [\"1 3 2 4 5 6 8 7 10 9 11 12 14 13 16 15 18 17\"]}, {\"input\": \"19 859\\r\\n\", \"output\": [\"1 2 3 4 6 5 8 7 9 10 11 12 14 13 15 16 18 17 19\"]}, {\"input\": \"20 491\\r\\n\", \"output\": [\"1 2 3 4 5 6 8 7 9 11 10 12 14 13 15 16 18 17 19 20\"]}, {\"input\": \"21 14921\\r\\n\", \"output\": [\"2 1 3 5 4 7 6 9 8 10 11 12 13 15 14 16 18 17 19 20 21\"]}, {\"input\": \"22 731\\r\\n\", \"output\": [\"1 2 3 4 5 6 7 9 8 10 11 13 12 14 16 15 18 17 19 21 20 22\"]}, {\"input\": \"23 45599\\r\\n\", \"output\": [\"2 1 4 3 6 5 8 7 9 10 11 13 12 15 14 16 18 17 20 19 21 22 23\"]}, {\"input\": \"24 47430\\r\\n\", \"output\": [\"2 1 3 4 5 6 7 8 10 9 11 12 13 14 16 15 17 19 18 21 20 22 24 23\"]}, {\"input\": \"25 58467\\r\\n\", \"output\": [\"1 3 2 4 6 5 7 8 9 11 10 12 13 15 14 16 17 19 18 20 21 22 23 24 25\"]}, {\"input\": \"26 168988\\r\\n\", \"output\": [\"2 1 4 3 5 6 7 8 9 10 12 11 13 15 14 16 17 18 19 20 21 23 22 24 26 25\"]}, {\"input\": \"27 298209\\r\\n\", \"output\": [\"2 1 4 3 5 7 6 9 8 10 12 11 14 13 15 16 17 19 18 21 20 22 24 23 25 27 26\"]}, {\"input\": \"28 77078\\r\\n\", \"output\": [\"1 2 3 5 4 6 7 8 9 10 11 13 12 14 16 15 17 18 20 19 22 21 23 24 25 27 26 28\"]}, {\"input\": \"29 668648\\r\\n\", \"output\": [\"2 1 3 5 4 6 8 7 9 10 12 11 13 14 15 16 17 19 18 20 22 21 23 25 24 26 27 29 28\"]}, {\"input\": \"30 582773\\r\\n\", \"output\": [\"1 3 2 4 5 6 8 7 10 9 11 13 12 14 15 16 17 19 18 20 21 23 22 25 24 26 28 27 29 30\"]}, {\"input\": \"31 1899100\\r\\n\", \"output\": [\"2 1 4 3 5 6 7 8 10 9 11 13 12 15 14 16 17 19 18 21 20 23 22 24 26 25 28 27 29 31 30\"]}, {\"input\": \"32 1314567\\r\\n\", \"output\": [\"1 2 4 3 6 5 8 7 9 11 10 13 12 14 16 15 18 17 19 20 22 21 23 24 25 26 27 28 30 29 32 31\"]}, {\"input\": \"33 1811927\\r\\n\", \"output\": [\"1 2 4 3 5 7 6 9 8 10 11 13 12 15 14 16 18 17 19 21 20 22 23 24 25 26 27 28 29 31 30 32 33\"]}, {\"input\": \"34 2412850\\r\\n\", \"output\": [\"1 2 4 3 5 6 7 9 8 10 11 13 12 14 16 15 18 17 19 20 21 22 23 25 24 26 28 27 29 31 30 32 34 33\"]}, {\"input\": \"35 706065\\r\\n\", \"output\": [\"1 2 3 4 5 6 8 7 9 11 10 13 12 15 14 16 18 17 20 19 21 23 22 25 24 27 26 28 29 31 30 32 33 35 34\"]}, {\"input\": \"36 7074882\\r\\n\", \"output\": [\"1 2 4 3 5 7 6 8 9 10 11 12 13 14 16 15 18 17 19 20 22 21 23 25 24 26 27 28 30 29 32 31 33 34 35 36\"]}, {\"input\": \"37 27668397\\r\\n\", \"output\": [\"2 1 3 4 5 7 6 9 8 11 10 13 12 15 14 16 18 17 19 21 20 23 22 24 25 26 28 27 30 29 32 31 34 33 35 36 37\"]}, {\"input\": \"38 23790805\\r\\n\", \"output\": [\"1 2 4 3 6 5 8 7 10 9 11 12 14 13 15 16 18 17 20 19 21 22 24 23 25 27 26 29 28 31 30 32 33 34 36 35 38 37\"]}, {\"input\": \"39 68773650\\r\\n\", \"output\": [\"2 1 3 4 5 6 8 7 10 9 12 11 13 15 14 16 17 19 18 20 21 23 22 24 26 25 28 27 29 31 30 32 33 34 35 36 37 39 38\"]}, {\"input\": \"40 43782404\\r\\n\", \"output\": [\"1 2 4 3 5 6 7 9 8 10 12 11 14 13 15 16 17 18 20 19 21 22 23 25 24 26 28 27 29 31 30 32 34 33 36 35 37 39 38 40\"]}, {\"input\": \"41 130268954\\r\\n\", \"output\": [\"1 3 2 4 6 5 7 8 10 9 11 12 13 14 16 15 17 19 18 20 21 23 22 25 24 26 27 28 30 29 31 32 34 33 35 36 37 38 39 41 40\"]}, {\"input\": \"42 40985206\\r\\n\", \"output\": [\"1 2 3 4 6 5 7 8 9 10 11 13 12 15 14 16 17 18 19 21 20 22 24 23 25 26 28 27 29 30 31 33 32 35 34 36 37 39 38 40 42 41\"]}, {\"input\": \"43 193787781\\r\\n\", \"output\": [\"1 2 4 3 5 6 8 7 9 10 12 11 13 14 16 15 17 18 19 20 21 22 24 23 25 26 27 28 29 30 31 32 33 35 34 36 38 37 39 40 41 43 42\"]}, {\"input\": \"44 863791309\\r\\n\", \"output\": [\"2 1 3 4 6 5 8 7 10 9 12 11 13 14 15 16 18 17 19 20 21 22 23 24 26 25 27 29 28 31 30 32 34 33 36 35 38 37 40 39 41 42 44 43\"]}, {\"input\": \"45 1817653076\\r\\n\", \"output\": [\"2 1 4 3 6 5 8 7 9 11 10 12 14 13 16 15 18 17 19 20 22 21 24 23 25 27 26 29 28 30 32 31 34 33 35 36 38 37 39 40 42 41 43 44 45\"]}, {\"input\": \"46 1176411936\\r\\n\", \"output\": [\"1 3 2 4 5 6 7 8 10 9 11 12 13 14 16 15 17 18 19 21 20 22 23 25 24 27 26 29 28 31 30 32 34 33 35 37 36 38 40 39 41 42 43 44 46 45\"]}, {\"input\": \"47 4199125763\\r\\n\", \"output\": [\"2 1 4 3 5 6 7 8 10 9 12 11 13 14 16 15 18 17 20 19 22 21 23 24 25 27 26 28 30 29 31 32 33 34 36 35 38 37 39 40 41 43 42 44 45 46 47\"]}, {\"input\": \"48 4534695914\\r\\n\", \"output\": [\"1 3 2 5 4 6 8 7 10 9 12 11 14 13 15 17 16 18 19 21 20 23 22 25 24 26 27 28 29 30 31 32 33 34 36 35 37 38 40 39 41 43 42 44 46 45 47 48\"]}, {\"input\": \"49 3790978105\\r\\n\", \"output\": [\"1 2 4 3 5 7 6 8 9 11 10 12 13 15 14 16 17 18 19 21 20 22 24 23 25 27 26 28 30 29 31 33 32 35 34 37 36 38 39 41 40 42 44 43 45 47 46 48 49\"]}, {\"input\": \"50 5608642004\\r\\n\", \"output\": [\"1 2 4 3 5 6 8 7 9 10 11 13 12 15 14 17 16 18 20 19 22 21 23 24 25 26 28 27 30 29 31 32 33 34 35 36 38 37 40 39 42 41 44 43 45 46 47 48 50 49\"]}]"}
{"prob_desc_description":"You are given three sticks with positive integer lengths of a,\u2009b, and c centimeters. You can increase length of some of them by some positive integer number of centimeters (different sticks can be increased by a different length), but in total by at most l centimeters. In particular, it is allowed not to increase the length of any stick.Determine the number of ways to increase the lengths of some sticks so that you can form from them a non-degenerate (that is, having a positive area) triangle. Two ways are considered different, if the length of some stick is increased by different number of centimeters in them.","prob_desc_output_spec":"Print a single integer \u2014 the number of ways to increase the sizes of the sticks by the total of at most l centimeters, so that you can make a non-degenerate triangle from it.","lang_cluster":"","src_uid":"185ff90a8b0ae0e2b75605f772589410","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","combinatorics","brute force","dp","implementation"],"prob_desc_created_at":"1440261000","prob_desc_sample_inputs":"[\"1 1 1 2\", \"1 2 3 1\", \"10 2 1 7\"]","prob_desc_notes":"NoteIn the first sample test you can either not increase any stick or increase any two sticks by 1 centimeter.In the second sample test you can increase either the first or the second stick by one centimeter. Note that the triangle made from the initial sticks is degenerate and thus, doesn't meet the conditions.","exec_outcome":"","difficulty":2100.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The single line contains 4 integers a,\u2009b,\u2009c,\u2009l (1\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u20093\u00b7105, 0\u2009\u2264\u2009l\u2009\u2264\u20093\u00b7105).","prob_desc_sample_outputs":"[\"4\", \"2\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1 1 1 2\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"1 2 3 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"10 2 1 7\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 2 1 5\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"10 15 17 10\\r\\n\", \"output\": [\"281\"]}, {\"input\": \"5 5 5 10000\\r\\n\", \"output\": [\"41841675001\"]}, {\"input\": \"5 7 30 100\\r\\n\", \"output\": [\"71696\"]}, {\"input\": \"5 5 5 300000\\r\\n\", \"output\": [\"1125157500250001\"]}, {\"input\": \"4 2 5 28\\r\\n\", \"output\": [\"1893\"]}, {\"input\": \"2 7 8 4\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"85 50 17 89\\r\\n\", \"output\": [\"68620\"]}, {\"input\": \"17 28 19 5558\\r\\n\", \"output\": [\"7396315389\"]}, {\"input\": \"5276 8562 1074 8453\\r\\n\", \"output\": [\"49093268246\"]}, {\"input\": \"9133 7818 3682 82004\\r\\n\", \"output\": [\"38306048676255\"]}, {\"input\": \"81780 54799 231699 808\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"53553 262850 271957 182759\\r\\n\", \"output\": [\"834977070873802\"]}, {\"input\": \"300000 300000 300000 300000\\r\\n\", \"output\": [\"4500090000549998\"]}, {\"input\": \"1 1 300000 300000\\r\\n\", \"output\": [\"599999\"]}, {\"input\": \"300000 300000 1 300000\\r\\n\", \"output\": [\"2250045000350001\"]}, {\"input\": \"300000 300000 1 24234\\r\\n\", \"output\": [\"1186319275394\"]}, {\"input\": \"1 1 1 300000\\r\\n\", \"output\": [\"1125022500250001\"]}, {\"input\": \"3 5 7 300000\\r\\n\", \"output\": [\"1125157499050009\"]}, {\"input\": \"63 5 52 78\\r\\n\", \"output\": [\"46502\"]}, {\"input\": \"2 42 49 93\\r\\n\", \"output\": [\"72542\"]}, {\"input\": \"61 100 3 8502\\r\\n\", \"output\": [\"27050809786\"]}, {\"input\": \"30 918 702 591\\r\\n\", \"output\": [\"14315560\"]}, {\"input\": \"98406 37723 3 257918\\r\\n\", \"output\": [\"1154347569149860\"]}, {\"input\": \"552 250082 77579 278985\\r\\n\", \"output\": [\"596240712378446\"]}, {\"input\": \"183808 8 8 294771\\r\\n\", \"output\": [\"622921327009564\"]}, {\"input\": \"2958 4133 233463 259655\\r\\n\", \"output\": [\"65797591388150\"]}, {\"input\": \"300000 200000 100000 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"300000 200000 100000 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100000 300000 100000 100000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100000 300000 100000 100001\\r\\n\", \"output\": [\"100002\"]}, {\"input\": \"100000 300000 100000 100002\\r\\n\", \"output\": [\"200005\"]}, {\"input\": \"100000 300000 100000 100003\\r\\n\", \"output\": [\"400012\"]}, {\"input\": \"100000 300000 100000 100010\\r\\n\", \"output\": [\"3000195\"]}, {\"input\": \"100000 300000 100000 100100\\r\\n\", \"output\": [\"255131325\"]}, {\"input\": \"100000 300000 199999 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100000 300000 200001 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 1 29 1\\r\\n\", \"output\": [\"0\"]}]"}
{"prob_desc_description":"One day Vasya the Hipster decided to count how many socks he had. It turned out that he had a red socks and b blue socks.According to the latest fashion, hipsters should wear the socks of different colors: a red one on the left foot, a blue one on the right foot.Every day Vasya puts on new socks in the morning and throws them away before going to bed as he doesn't want to wash them.Vasya wonders, what is the maximum number of days when he can dress fashionable and wear different socks, and after that, for how many days he can then wear the same socks until he either runs out of socks or cannot make a single pair from the socks he's got.Can you help him?","prob_desc_output_spec":"Print two space-separated integers \u2014 the maximum number of days when Vasya can wear different socks and the number of days when he can wear the same socks until he either runs out of socks or cannot make a single pair from the socks he's got. Keep in mind that at the end of the day Vasya throws away the socks that he's been wearing on that day.","lang_cluster":"","src_uid":"775766790e91e539c1cfaa5030e5b955","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","implementation"],"prob_desc_created_at":"1443430800","prob_desc_sample_inputs":"[\"3 1\", \"2 3\", \"7 3\"]","prob_desc_notes":"NoteIn the first sample Vasya can first put on one pair of different socks, after that he has two red socks left to wear on the second day.","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The single line of the input contains two positive integers a and b (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009100) \u2014 the number of red and blue socks that Vasya's got.","prob_desc_sample_outputs":"[\"1 1\", \"2 0\", \"3 2\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3 1\\r\\n\", \"output\": [\"1 1\", \"1  1\", \"1\\r\\n1\"]}, {\"input\": \"2 3\\r\\n\", \"output\": [\"2  0\", \"2 0\", \"2\\r\\n0\"]}, {\"input\": \"7 3\\r\\n\", \"output\": [\"3\\r\\n2\", \"3  2\", \"3 2\"]}, {\"input\": \"100 100\\r\\n\", \"output\": [\"100 0\", \"100  0\", \"100\\r\\n0\"]}, {\"input\": \"4 10\\r\\n\", \"output\": [\"4\\r\\n3\", \"4  3\", \"4 3\"]}, {\"input\": \"6 10\\r\\n\", \"output\": [\"6\\r\\n2\", \"6 2\", \"6  2\"]}, {\"input\": \"6 11\\r\\n\", \"output\": [\"6\\r\\n2\", \"6 2\", \"6  2\"]}, {\"input\": \"10 40\\r\\n\", \"output\": [\"10\\r\\n15\", \"10 15\", \"10  15\"]}, {\"input\": \"11 56\\r\\n\", \"output\": [\"11 22\", \"11\\r\\n22\", \"11  22\"]}, {\"input\": \"34 30\\r\\n\", \"output\": [\"30\\r\\n2\", \"30 2\", \"30  2\"]}, {\"input\": \"33 33\\r\\n\", \"output\": [\"33  0\", \"33\\r\\n0\", \"33 0\"]}, {\"input\": \"100 45\\r\\n\", \"output\": [\"45\\r\\n27\", \"45  27\", \"45 27\"]}, {\"input\": \"100 23\\r\\n\", \"output\": [\"23  38\", \"23\\r\\n38\", \"23 38\"]}, {\"input\": \"45 12\\r\\n\", \"output\": [\"12  16\", \"12 16\", \"12\\r\\n16\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"1  0\", \"1\\r\\n0\", \"1 0\"]}, {\"input\": \"1 100\\r\\n\", \"output\": [\"1  49\", \"1 49\", \"1\\r\\n49\"]}, {\"input\": \"100 1\\r\\n\", \"output\": [\"1  49\", \"1 49\", \"1\\r\\n49\"]}, {\"input\": \"68 59\\r\\n\", \"output\": [\"59  4\", \"59\\r\\n4\", \"59 4\"]}, {\"input\": \"45 99\\r\\n\", \"output\": [\"45\\r\\n27\", \"45  27\", \"45 27\"]}, {\"input\": \"99 100\\r\\n\", \"output\": [\"99  0\", \"99 0\", \"99\\r\\n0\"]}, {\"input\": \"100 98\\r\\n\", \"output\": [\"98 1\", \"98\\r\\n1\", \"98  1\"]}, {\"input\": \"59 12\\r\\n\", \"output\": [\"12 23\", \"12  23\", \"12\\r\\n23\"]}, {\"input\": \"86 4\\r\\n\", \"output\": [\"4  41\", \"4\\r\\n41\", \"4 41\"]}, {\"input\": \"68 21\\r\\n\", \"output\": [\"21 23\", \"21  23\", \"21\\r\\n23\"]}, {\"input\": \"100 11\\r\\n\", \"output\": [\"11  44\", \"11\\r\\n44\", \"11 44\"]}, {\"input\": \"100 10\\r\\n\", \"output\": [\"10 45\", \"10\\r\\n45\", \"10  45\"]}, {\"input\": \"15 45\\r\\n\", \"output\": [\"15\\r\\n15\", \"15  15\", \"15 15\"]}, {\"input\": \"11 32\\r\\n\", \"output\": [\"11\\r\\n10\", \"11 10\", \"11  10\"]}, {\"input\": \"34 96\\r\\n\", \"output\": [\"34\\r\\n31\", \"34  31\", \"34 31\"]}, {\"input\": \"89 89\\r\\n\", \"output\": [\"89  0\", \"89 0\", \"89\\r\\n0\"]}]"}
{"prob_desc_description":"A monster is attacking the Cyberland!Master Yang, a braver, is going to beat the monster. Yang and the monster each have 3 attributes: hitpoints (HP), offensive power (ATK) and defensive power (DEF).During the battle, every second the monster's HP decrease by max(0,\u2009ATKY\u2009-\u2009DEFM), while Yang's HP decreases by max(0,\u2009ATKM\u2009-\u2009DEFY), where index Y denotes Master Yang and index M denotes monster. Both decreases happen simultaneously Once monster's HP\u2009\u2264\u20090 and the same time Master Yang's HP\u2009>\u20090, Master Yang wins.Master Yang can buy attributes from the magic shop of Cyberland: h bitcoins per HP, a bitcoins per ATK, and d bitcoins per DEF.Now Master Yang wants to know the minimum number of bitcoins he can spend in order to win.","prob_desc_output_spec":"The only output line should contain an integer, denoting the minimum bitcoins Master Yang should spend in order to win.","lang_cluster":"","src_uid":"bf8a133154745e64a547de6f31ddc884","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","binary search","implementation"],"prob_desc_created_at":"1416590400","prob_desc_sample_inputs":"[\"1 2 1\\n1 100 1\\n1 100 100\", \"100 100 100\\n1 1 1\\n1 1 1\"]","prob_desc_notes":"NoteFor the first sample, prices for ATK and DEF are extremely high. Master Yang can buy 99 HP, then he can beat the monster with 1 HP left.For the second sample, Master Yang is strong enough to beat the monster, so he doesn't need to buy anything.","exec_outcome":"","difficulty":1800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains three integers HPY,\u2009ATKY,\u2009DEFY, separated by a space, denoting the initial HP, ATK and DEF of Master Yang. The second line contains three integers HPM,\u2009ATKM,\u2009DEFM, separated by a space, denoting the HP, ATK and DEF of the monster. The third line contains three integers h,\u2009a,\u2009d, separated by a space, denoting the price of 1\u00a0HP, 1\u00a0ATK and 1\u00a0DEF. All numbers in input are integer and lie between 1 and 100 inclusively.","prob_desc_sample_outputs":"[\"99\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1 2 1\\r\\n1 100 1\\r\\n1 100 100\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"100 100 100\\r\\n1 1 1\\r\\n1 1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"50 80 92\\r\\n41 51 56\\r\\n75 93 12\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"76 63 14\\r\\n89 87 35\\r\\n20 15 56\\r\\n\", \"output\": [\"915\"]}, {\"input\": \"12 59 66\\r\\n43 15 16\\r\\n12 18 66\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"51 89 97\\r\\n18 25 63\\r\\n22 91 74\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"72 16 49\\r\\n5 21 84\\r\\n48 51 88\\r\\n\", \"output\": [\"3519\"]}, {\"input\": \"74 89 5\\r\\n32 76 99\\r\\n62 95 36\\r\\n\", \"output\": [\"3529\"]}, {\"input\": \"39 49 78\\r\\n14 70 41\\r\\n3 33 23\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"11 82 51\\r\\n90 84 72\\r\\n98 98 43\\r\\n\", \"output\": [\"1376\"]}, {\"input\": \"65 6 5\\r\\n70 78 51\\r\\n88 55 78\\r\\n\", \"output\": [\"7027\"]}, {\"input\": \"14 61 87\\r\\n11 78 14\\r\\n5 84 92\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 28 47\\r\\n31 60 38\\r\\n14 51 77\\r\\n\", \"output\": [\"1562\"]}, {\"input\": \"99 32 20\\r\\n89 72 74\\r\\n1 100 39\\r\\n\", \"output\": [\"5478\"]}, {\"input\": \"1 10 29\\r\\n1 1 43\\r\\n1 1 100\\r\\n\", \"output\": [\"34\"]}, {\"input\": \"1 1 100\\r\\n1 1 1\\r\\n100 1 100\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"79 1 1\\r\\n1 1 10\\r\\n1 1 100\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"10 10 100\\r\\n1 100 100\\r\\n10 100 90\\r\\n\", \"output\": [\"9100\"]}, {\"input\": \"10 10 100\\r\\n1 10 1\\r\\n1 1 100\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 100 1\\r\\n1 1 1\\r\\n1 1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"11 1 1\\r\\n100 1 1\\r\\n100 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 100 100\\r\\n1 1 1\\r\\n87 100 43\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"10 100 1\\r\\n1 100 100\\r\\n100 1 9\\r\\n\", \"output\": [\"811\"]}, {\"input\": \"10 100 55\\r\\n100 100 1\\r\\n1 1 1\\r\\n\", \"output\": [\"37\"]}, {\"input\": \"11 1 1\\r\\n10 1 10\\r\\n100 50 1\\r\\n\", \"output\": [\"500\"]}, {\"input\": \"10 100 1\\r\\n100 1 1\\r\\n1 100 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 10 10\\r\\n1 10 100\\r\\n1 1 61\\r\\n\", \"output\": [\"91\"]}, {\"input\": \"1 1 1\\r\\n1 1 1\\r\\n1 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1 1\\r\\n1 1 1\\r\\n100 100 100\\r\\n\", \"output\": [\"100\"]}, {\"input\": \"1 1 1\\r\\n100 100 100\\r\\n100 100 100\\r\\n\", \"output\": [\"19900\"]}, {\"input\": \"100 100 100\\r\\n100 100 100\\r\\n100 100 100\\r\\n\", \"output\": [\"100\"]}, {\"input\": \"1 1 1\\r\\n1 1 100\\r\\n100 100 1\\r\\n\", \"output\": [\"10000\"]}, {\"input\": \"50 100 51\\r\\n100 100 100\\r\\n1 100 100\\r\\n\", \"output\": [\"1384\"]}, {\"input\": \"1 1 1\\r\\n100 100 100\\r\\n1 2 3\\r\\n\", \"output\": [\"496\"]}, {\"input\": \"100 1 1\\r\\n100 100 100\\r\\n100 1 100\\r\\n\", \"output\": [\"199\"]}, {\"input\": \"1 100 1\\r\\n100 100 100\\r\\n1 100 100\\r\\n\", \"output\": [\"1990\"]}, {\"input\": \"100 100 1\\r\\n100 100 100\\r\\n1 100 100\\r\\n\", \"output\": [\"1891\"]}, {\"input\": \"1 1 1\\r\\n100 100 100\\r\\n1 100 100\\r\\n\", \"output\": [\"11890\"]}, {\"input\": \"20 1 1\\r\\n100 100 100\\r\\n1 100 100\\r\\n\", \"output\": [\"11871\"]}, {\"input\": \"25 38 49\\r\\n84 96 42\\r\\n3 51 92\\r\\n\", \"output\": [\"1692\"]}, {\"input\": \"2 1 1\\r\\n100 2 100\\r\\n100 1 100\\r\\n\", \"output\": [\"199\"]}, {\"input\": \"1 97 1\\r\\n100 99 98\\r\\n1 51 52\\r\\n\", \"output\": [\"1498\"]}, {\"input\": \"1 1 1\\r\\n100 100 100\\r\\n1 1 100\\r\\n\", \"output\": [\"298\"]}, {\"input\": \"1 100 1\\r\\n100 100 99\\r\\n1 100 100\\r\\n\", \"output\": [\"1890\"]}, {\"input\": \"100 1 1\\r\\n100 100 100\\r\\n1 100 100\\r\\n\", \"output\": [\"11791\"]}]"}
{"prob_desc_description":"Vasya decided to learn to play chess. Classic chess doesn't seem interesting to him, so he plays his own sort of chess.The queen is the piece that captures all squares on its vertical, horizontal and diagonal lines. If the cell is located on the same vertical, horizontal or diagonal line with queen, and the cell contains a piece of the enemy color, the queen is able to move to this square. After that the enemy's piece is removed from the board. The queen cannot move to a cell containing an enemy piece if there is some other piece between it and the queen. There is an n\u2009\u00d7\u2009n chessboard. We'll denote a cell on the intersection of the r-th row and c-th column as (r,\u2009c). The square (1,\u20091) contains the white queen and the square (1,\u2009n) contains the black queen. All other squares contain green pawns that don't belong to anyone.The players move in turns. The player that moves first plays for the white queen, his opponent plays for the black queen.On each move the player has to capture some piece with his queen (that is, move to a square that contains either a green pawn or the enemy queen). The player loses if either he cannot capture any piece during his move or the opponent took his queen during the previous move. Help Vasya determine who wins if both players play with an optimal strategy on the board n\u2009\u00d7\u2009n.","prob_desc_output_spec":"On the first line print the answer to problem \u2014 string \"white\" or string \"black\", depending on who wins if the both players play optimally.  If the answer is \"white\", then you should also print two integers r and c representing the cell (r,\u2009c), where the first player should make his first move to win. If there are multiple such cells, print the one with the minimum r. If there are still multiple squares, print the one with the minimum c.","lang_cluster":"","src_uid":"52e07d176aa1d370788f94ee2e61df93","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["games","math","constructive algorithms"],"prob_desc_created_at":"1417618800","prob_desc_sample_inputs":"[\"2\", \"3\"]","prob_desc_notes":"NoteIn the first sample test the white queen can capture the black queen at the first move, so the white player wins.In the second test from the statement if the white queen captures the green pawn located on the central vertical line, then it will be captured by the black queen during the next move. So the only move for the white player is to capture the green pawn located at (2,\u20091). Similarly, the black queen doesn't have any other options but to capture the green pawn located at (2,\u20093), otherwise if it goes to the middle vertical line, it will be captured by the white queen.During the next move the same thing happens \u2014 neither the white, nor the black queen has other options rather than to capture green pawns situated above them. Thus, the white queen ends up on square (3,\u20091), and the black queen ends up on square (3,\u20093). In this situation the white queen has to capture any of the green pawns located on the middle vertical line, after that it will be captured by the black queen. Thus, the player who plays for the black queen wins.","exec_outcome":"","difficulty":1700.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The input contains a single number n (2\u2009\u2264\u2009n\u2009\u2264\u2009109) \u2014 the size of the board.","prob_desc_sample_outputs":"[\"white\\n1 2\", \"black\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}, {\"input\": \"16\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}, {\"input\": \"100\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}, {\"input\": \"10006\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}, {\"input\": \"99966246\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}, {\"input\": \"1000000000\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}, {\"input\": \"999999999\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"999999997\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"900001\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"775681\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"666666\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}, {\"input\": \"12345\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"111111\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"346367\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"13\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"11\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"19\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"939698497\\r\\n\", \"output\": [\"black\"]}, {\"input\": \"999999996\\r\\n\", \"output\": [\"white\\n1 2\", \"white\\r\\n1 2\"]}]"}
{"prob_desc_description":"It's tough to be a superhero. And it's twice as tough to resist the supervillain who is cool at math. Suppose that you're an ordinary Batman in an ordinary city of Gotham. Your enemy Joker mined the building of the city administration and you only have several minutes to neutralize the charge. To do that you should enter the cancel code on the bomb control panel.However, that mad man decided to give you a hint. This morning the mayor found a playing card under his pillow. There was a line written on the card:The bomb has a note saying \"J(x)\u2009=\u2009A\", where A is some positive integer. You suspect that the cancel code is some integer x that meets the equation J(x)\u2009=\u2009A. Now in order to decide whether you should neutralize the bomb or run for your life, you've got to count how many distinct positive integers x meet this equation.","prob_desc_output_spec":"Print the number of solutions of the equation J(x)\u2009=\u2009A.","lang_cluster":"","src_uid":"1f68bd6f8b40e45a5bd360b03a264ef4","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","number theory","hashing","dp","dfs and similar"],"prob_desc_created_at":"1430668800","prob_desc_sample_inputs":"[\"3\", \"24\"]","prob_desc_notes":"NoteRecord x|n means that number n divides number x. is defined as the largest positive integer that divides both a and b.In the first sample test the only suitable value of x is 2. Then J(2)\u2009=\u20091\u2009+\u20092.In the second sample test the following values of x match:  x\u2009=\u200914, J(14)\u2009=\u20091\u2009+\u20092\u2009+\u20097\u2009+\u200914\u2009=\u200924  x\u2009=\u200915, J(15)\u2009=\u20091\u2009+\u20093\u2009+\u20095\u2009+\u200915\u2009=\u200924  x\u2009=\u200923, J(23)\u2009=\u20091\u2009+\u200923\u2009=\u200924 ","exec_outcome":"","difficulty":2600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The single line of the input contains a single integer A (1\u2009\u2264\u2009A\u2009\u2264\u20091012).","prob_desc_sample_outputs":"[\"1\", \"3\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"24\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"11\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"12\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"13\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"14\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"15\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"16\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"17\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"18\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"19\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"20\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"100\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10000\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1000000\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"1000000000000\\r\\n\", \"output\": [\"227\"]}, {\"input\": \"123456789876\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"963761198400\\r\\n\", \"output\": [\"100049\"]}, {\"input\": \"642507465600\\r\\n\", \"output\": [\"102634\"]}, {\"input\": \"481880599200\\r\\n\", \"output\": [\"38983\"]}, {\"input\": \"321253732800\\r\\n\", \"output\": [\"48603\"]}, {\"input\": \"293318625600\\r\\n\", \"output\": [\"99409\"]}, {\"input\": \"200560490130\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"988440062610\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"999999999989\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999999999988\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999999999990\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"999960000396\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"999961000378\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999962000360\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999961000374\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999962000357\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999963000340\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999962000352\\r\\n\", \"output\": [\"90\"]}, {\"input\": \"999963000336\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"999964000320\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"549755813888\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"549755813887\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"549755813889\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"743008370688\\r\\n\", \"output\": [\"7606\"]}, {\"input\": \"743012742140\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"802632499200\\r\\n\", \"output\": [\"248276\"]}, {\"input\": \"330225942528\\r\\n\", \"output\": [\"5397\"]}, {\"input\": \"349479567360\\r\\n\", \"output\": [\"311891\"]}, {\"input\": \"698959134720\\r\\n\", \"output\": [\"399998\"]}, {\"input\": \"390949000000\\r\\n\", \"output\": [\"403\"]}, {\"input\": \"781898000000\\r\\n\", \"output\": [\"673\"]}, {\"input\": \"655274188800\\r\\n\", \"output\": [\"702440\"]}, {\"input\": \"873698918400\\r\\n\", \"output\": [\"804116\"]}, {\"input\": \"86204582016\\r\\n\", \"output\": [\"414\"]}, {\"input\": \"924458\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7882\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"91306\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"207434\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"290858\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"374282\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"457706\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"573834\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"624554\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"569088\\r\\n\", \"output\": [\"79\"]}, {\"input\": \"685216\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"768640\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"852064\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"935488\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"51616\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"102336\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"218464\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"301888\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"418016\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"944011\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"965667225600\\r\\n\", \"output\": [\"906098\"]}, {\"input\": \"804722688000\\r\\n\", \"output\": [\"941359\"]}, {\"input\": \"747242496000\\r\\n\", \"output\": [\"942082\"]}, {\"input\": \"871782912000\\r\\n\", \"output\": [\"996234\"]}, {\"input\": \"75246796800\\r\\n\", \"output\": [\"133237\"]}]"}
{"prob_desc_description":"Limak is a little polar bear. He has n balls, the i-th ball has size ti.Limak wants to give one ball to each of his three friends. Giving gifts isn't easy\u00a0\u2014 there are two rules Limak must obey to make friends happy:  No two friends can get balls of the same size.  No two friends can get balls of sizes that differ by more than 2. For example, Limak can choose balls with sizes 4, 5 and 3, or balls with sizes 90, 91 and 92. But he can't choose balls with sizes 5, 5 and 6 (two friends would get balls of the same size), and he can't choose balls with sizes 30, 31 and 33 (because sizes 30 and 33 differ by more than 2).Your task is to check whether Limak can choose three balls that satisfy conditions above.","prob_desc_output_spec":"Print \"YES\" (without quotes) if Limak can choose three balls of distinct sizes, such that any two of them differ by no more than 2. Otherwise, print \"NO\" (without quotes).","lang_cluster":"","src_uid":"d6c876a84c7b92141710be5d76536eab","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","implementation","sortings"],"prob_desc_created_at":"1458376500","prob_desc_sample_inputs":"[\"4\\n18 55 16 17\", \"6\\n40 41 43 44 44 44\", \"8\\n5 972 3 4 1 4 970 971\"]","prob_desc_notes":"NoteIn the first sample, there are 4 balls and Limak is able to choose three of them to satisfy the rules. He must must choose balls with sizes 18, 16 and 17.In the second sample, there is no way to give gifts to three friends without breaking the rules.In the third sample, there is even more than one way to choose balls:  Choose balls with sizes 3, 4 and 5.  Choose balls with sizes 972, 970, 971. ","exec_outcome":"","difficulty":900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line of the input contains one integer n (3\u2009\u2264\u2009n\u2009\u2264\u200950)\u00a0\u2014 the number of balls Limak has. The second line contains n integers t1,\u2009t2,\u2009...,\u2009tn (1\u2009\u2264\u2009ti\u2009\u2264\u20091000) where ti denotes the size of the i-th ball.","prob_desc_sample_outputs":"[\"YES\", \"NO\", \"YES\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4\\r\\n18 55 16 17\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"6\\r\\n40 41 43 44 44 44\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"8\\r\\n5 972 3 4 1 4 970 971\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n959 747 656\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n1 2 2 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"50\\r\\n998 30 384 289 505 340 872 223 663 31 929 625 864 699 735 589 676 399 745 635 963 381 75 97 324 612 597 797 103 382 25 894 219 458 337 572 201 355 294 275 278 311 586 573 965 704 936 237 715 543\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"50\\r\\n941 877 987 982 966 979 984 810 811 909 872 980 957 897 845 995 924 905 984 914 824 840 868 910 815 808 872 858 883 952 823 835 860 874 959 972 931 867 866 987 982 837 800 921 887 910 982 980 828 869\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n408 410 409\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n903 902 904\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n399 400 398\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n450 448 449\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n390 389 388\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n438 439 440\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"11\\r\\n488 688 490 94 564 615 641 170 489 517 669\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"24\\r\\n102 672 983 82 720 501 81 721 982 312 207 897 159 964 611 956 118 984 37 271 596 403 772 954\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"36\\r\\n175 551 70 479 875 480 979 32 465 402 640 116 76 687 874 678 359 785 753 401 978 629 162 963 886 641 39 845 132 930 2 372 478 947 407 318\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"6\\r\\n10 79 306 334 304 305\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"34\\r\\n787 62 26 683 486 364 684 891 846 801 969 837 359 800 836 359 471 637 732 91 841 836 7 799 959 405 416 841 737 803 615 483 323 365\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"30\\r\\n860 238 14 543 669 100 428 789 576 484 754 274 849 850 586 377 711 386 510 408 520 693 23 477 266 851 728 711 964 73\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"11\\r\\n325 325 324 324 324 325 325 324 324 324 324\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"7\\r\\n517 517 518 517 518 518 518\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"20\\r\\n710 710 711 711 711 711 710 710 710 710 711 710 710 710 710 710 710 711 711 710\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"48\\r\\n29 30 29 29 29 30 29 30 30 30 30 29 30 30 30 29 29 30 30 29 30 29 29 30 29 30 29 30 30 29 30 29 29 30 30 29 29 30 30 29 29 30 30 30 29 29 30 29\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"7\\r\\n880 880 514 536 881 881 879\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"15\\r\\n377 432 262 376 261 375 377 262 263 263 261 376 262 262 375\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"32\\r\\n305 426 404 961 426 425 614 304 404 425 615 403 303 304 615 303 305 405 427 614 403 303 425 615 404 304 427 403 206 616 405 404\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"41\\r\\n115 686 988 744 762 519 745 519 518 83 85 115 520 44 687 686 685 596 988 687 989 988 114 745 84 519 519 746 988 84 745 744 115 114 85 115 520 746 745 116 987\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"47\\r\\n1 2 483 28 7 109 270 651 464 162 353 521 224 989 721 499 56 69 197 716 313 446 580 645 828 197 100 138 789 499 147 677 384 711 783 937 300 543 540 93 669 604 739 122 632 822 116\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"31\\r\\n1 2 1 373 355 692 750 920 578 666 615 232 141 129 663 929 414 704 422 559 568 731 354 811 532 618 39 879 292 602 995\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"50\\r\\n5 38 41 4 15 40 27 39 20 3 44 47 30 6 36 29 35 12 19 26 10 2 21 50 11 46 48 49 17 16 33 13 32 28 31 18 23 34 7 14 24 45 9 37 1 8 42 25 43 22\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"50\\r\\n967 999 972 990 969 978 963 987 954 955 973 970 959 981 995 983 986 994 979 957 965 982 992 977 953 975 956 961 993 997 998 958 980 962 960 951 996 991 1000 966 971 988 976 968 989 984 974 964 985 952\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"50\\r\\n850 536 761 506 842 898 857 723 583 637 536 943 895 929 890 612 832 633 696 731 553 880 710 812 665 877 915 636 711 540 748 600 554 521 813 796 568 513 543 809 798 820 928 504 999 646 907 639 550 911\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n3 1 2\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n500 999 1000\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"10\\r\\n101 102 104 105 107 109 110 112 113 115\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"50\\r\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"50\\r\\n1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n1000 999 998\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"49\\r\\n343 322 248 477 53 156 245 493 209 141 370 66 229 184 434 137 276 472 216 456 147 180 140 114 493 323 393 262 380 314 222 124 98 441 129 346 48 401 347 460 122 125 114 106 189 260 374 165 456\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"20\\r\\n1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n999 999 1000\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"9\\r\\n2 4 5 13 25 100 200 300 400\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"9\\r\\n1 1 1 2 2 2 3 3 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n1 1 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n998 999 1000\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"12\\r\\n1 1 1 1 1 1 1 1 1 2 2 4\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n4 3 4 5\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"6\\r\\n1 1 1 2 2 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n2 3 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n10 5 6 3 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n1 2 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n1 2 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"4\\r\\n998 999 1000 1000\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"5\\r\\n2 3 9 9 4\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"4\\r\\n1 2 4 4\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n1 1 1\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n2 2 3\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"7\\r\\n1 2 2 2 4 5 6\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"5\\r\\n1 3 10 3 10\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n1 2 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"4\\r\\n1000 1000 999 998\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n5 3 7\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 1 2 2 3 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"9\\r\\n6 6 6 5 5 5 4 4 4\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"7\\r\\n5 6 6 6 7 7 7\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"5\\r\\n2 3 3 3 4\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"5\\r\\n2 1 2 1 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n1 2 7\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n1000 1000 1000\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n1 100 2 100 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"5\\r\\n5 4 6 5 5\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"12\\r\\n1 1 1 1 2 2 2 2 3 3 3 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"5\\r\\n9 9 1 2 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"6\\r\\n1 2 3 1 2 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"7\\r\\n1 1 1 1 2 3 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"3\\r\\n13 13 13\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"3\\r\\n42 42 42\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"8\\r\\n1 1 1 1 2 2 2 2\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 1 1 1 2 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"6\\r\\n1 1 2 2 6 6\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"6\\r\\n1 2 5 5 5 5\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"9\\r\\n1 2 3 1 2 3 1 2 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}, {\"input\": \"4\\r\\n1 2 1 100\\r\\n\", \"output\": [\"No\", \"NO\"]}, {\"input\": \"5\\r\\n1 1 2 2 3\\r\\n\", \"output\": [\"YES\", \"Yes\"]}]"}
{"prob_desc_description":"Buses run between the cities A and B, the first one is at 05:00 AM and the last one departs not later than at 11:59 PM. A bus from the city A departs every a minutes and arrives to the city B in a ta minutes, and a bus from the city B departs every b minutes and arrives to the city A in a tb minutes.The driver Simion wants to make his job diverse, so he counts the buses going towards him. Simion doesn't count the buses he meet at the start and finish.You know the time when Simion departed from the city A to the city B. Calculate the number of buses Simion will meet to be sure in his counting.","prob_desc_output_spec":"Print the only integer z \u2014 the number of buses Simion will meet on the way. Note that you should not count the encounters in cities A and B.","lang_cluster":"","src_uid":"1c4cf1c3cb464a483511a8a61f8685a7","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["implementation"],"prob_desc_created_at":"1461164400","prob_desc_sample_inputs":"[\"10 30\\n10 35\\n05:20\", \"60 120\\n24 100\\n13:00\"]","prob_desc_notes":"NoteIn the first example Simion departs form the city A at 05:20 AM and arrives to the city B at 05:50 AM. He will meet the first 5 buses from the city B that departed in the period [05:00 AM - 05:40 AM]. Also Simion will meet a bus in the city B at 05:50 AM, but he will not count it.Also note that the first encounter will be between 05:26 AM and 05:27 AM (if we suggest that the buses are go with the sustained speed).","exec_outcome":"","difficulty":1600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains two integers a,\u2009ta (1\u2009\u2264\u2009a,\u2009ta\u2009\u2264\u2009120) \u2014 the frequency of the buses from the city A to the city B and the travel time. Both values are given in minutes. The second line contains two integers b,\u2009tb (1\u2009\u2264\u2009b,\u2009tb\u2009\u2264\u2009120) \u2014 the frequency of the buses from the city B to the city A and the travel time. Both values are given in minutes. The last line contains the departure time of Simion from the city A in the format hh:mm. It is guaranteed that there are a bus from the city A at that time. Note that the hours and the minutes are given with exactly two digits.","prob_desc_sample_outputs":"[\"5\", \"9\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"10 30\\r\\n10 35\\r\\n05:20\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"60 120\\r\\n24 100\\r\\n13:00\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"30 60\\r\\n60 60\\r\\n22:30\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"30 60\\r\\n10 60\\r\\n23:30\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"5 45\\r\\n4 60\\r\\n21:00\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"1 1\\r\\n1 1\\r\\n10:28\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"4 1\\r\\n5 4\\r\\n18:40\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"8 8\\r\\n1 1\\r\\n13:24\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"20 4\\r\\n1 20\\r\\n06:20\\r\\n\", \"output\": [\"23\"]}, {\"input\": \"15 24\\r\\n23 6\\r\\n21:15\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"30 19\\r\\n21 4\\r\\n10:30\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"31 15\\r\\n36 25\\r\\n07:04\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"24 3\\r\\n54 9\\r\\n18:12\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"18 69\\r\\n62 54\\r\\n08:00\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"33 58\\r\\n70 78\\r\\n22:36\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"68 34\\r\\n84 78\\r\\n10:40\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"15 14\\r\\n32 65\\r\\n05:45\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"40 74\\r\\n100 42\\r\\n05:40\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"65 49\\r\\n24 90\\r\\n07:10\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"1 1\\r\\n1 1\\r\\n23:59\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"23 118\\r\\n118 20\\r\\n23:24\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 88\\r\\n17 38\\r\\n22:33\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"3 1\\r\\n2 3\\r\\n05:03\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1\\r\\n3 2\\r\\n08:44\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 3\\r\\n1 2\\r\\n21:43\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"2 28\\r\\n2 12\\r\\n05:12\\r\\n\", \"output\": [\"19\"]}, {\"input\": \"60 120\\r\\n17 120\\r\\n23:00\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"1 55\\r\\n1 54\\r\\n23:59\\r\\n\", \"output\": [\"54\"]}, {\"input\": \"66 75\\r\\n1 82\\r\\n06:06\\r\\n\", \"output\": [\"141\"]}, {\"input\": \"1 90\\r\\n1 88\\r\\n23:59\\r\\n\", \"output\": [\"88\"]}, {\"input\": \"1 120\\r\\n1 100\\r\\n23:59\\r\\n\", \"output\": [\"100\"]}]"}
{"prob_desc_description":"There are three friend living on the straight line Ox in Lineland. The first friend lives at the point x1, the second friend lives at the point x2, and the third friend lives at the point x3. They plan to celebrate the New Year together, so they need to meet at one point. What is the minimum total distance they have to travel in order to meet at some point and celebrate the New Year?It's guaranteed that the optimal answer is always integer.","prob_desc_output_spec":"Print one integer\u00a0\u2014 the minimum total distance the friends need to travel in order to meet together.","lang_cluster":"","src_uid":"7bffa6e8d2d21bbb3b7f4aec109b3319","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","implementation","sortings"],"prob_desc_created_at":"1475494500","prob_desc_sample_inputs":"[\"7 1 4\", \"30 20 10\"]","prob_desc_notes":"NoteIn the first sample, friends should meet at the point 4. Thus, the first friend has to travel the distance of 3 (from the point 7 to the point 4), the second friend also has to travel the distance of 3 (from the point 1 to the point 4), while the third friend should not go anywhere because he lives at the point 4.","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line of the input contains three distinct integers x1, x2 and x3 (1\u2009\u2264\u2009x1,\u2009x2,\u2009x3\u2009\u2264\u2009100)\u00a0\u2014 the coordinates of the houses of the first, the second and the third friends respectively. ","prob_desc_sample_outputs":"[\"6\", \"20\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"7 1 4\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"30 20 10\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"1 4 100\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"100 1 91\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"1 45 100\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"1 2 3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"71 85 88\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"30 38 99\\r\\n\", \"output\": [\"69\"]}, {\"input\": \"23 82 95\\r\\n\", \"output\": [\"72\"]}, {\"input\": \"22 41 47\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"9 94 77\\r\\n\", \"output\": [\"85\"]}, {\"input\": \"1 53 51\\r\\n\", \"output\": [\"52\"]}, {\"input\": \"25 97 93\\r\\n\", \"output\": [\"72\"]}, {\"input\": \"42 53 51\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"81 96 94\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"21 5 93\\r\\n\", \"output\": [\"88\"]}, {\"input\": \"50 13 75\\r\\n\", \"output\": [\"62\"]}, {\"input\": \"41 28 98\\r\\n\", \"output\": [\"70\"]}, {\"input\": \"69 46 82\\r\\n\", \"output\": [\"36\"]}, {\"input\": \"87 28 89\\r\\n\", \"output\": [\"61\"]}, {\"input\": \"44 45 40\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"86 97 68\\r\\n\", \"output\": [\"29\"]}, {\"input\": \"43 92 30\\r\\n\", \"output\": [\"62\"]}, {\"input\": \"16 70 1\\r\\n\", \"output\": [\"69\"]}, {\"input\": \"40 46 19\\r\\n\", \"output\": [\"27\"]}, {\"input\": \"71 38 56\\r\\n\", \"output\": [\"33\"]}, {\"input\": \"82 21 80\\r\\n\", \"output\": [\"61\"]}, {\"input\": \"75 8 35\\r\\n\", \"output\": [\"67\"]}, {\"input\": \"75 24 28\\r\\n\", \"output\": [\"51\"]}, {\"input\": \"78 23 56\\r\\n\", \"output\": [\"55\"]}, {\"input\": \"85 31 10\\r\\n\", \"output\": [\"75\"]}, {\"input\": \"76 50 9\\r\\n\", \"output\": [\"67\"]}, {\"input\": \"95 37 34\\r\\n\", \"output\": [\"61\"]}, {\"input\": \"84 61 35\\r\\n\", \"output\": [\"49\"]}, {\"input\": \"87 85 37\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"1 3 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 2 6\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"6 9 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"12 4 8\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"15 10 5\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"1 50 17\\r\\n\", \"output\": [\"49\"]}, {\"input\": \"10 5 15\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"8 1 9\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"3 5 4\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2 1 3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 8 2\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1 100 2\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"1 4 6\\r\\n\", \"output\": [\"5\"]}]"}
{"prob_desc_description":"A new airplane SuperPuperJet has an infinite number of rows, numbered with positive integers starting with 1 from cockpit to tail. There are six seats in each row, denoted with letters from 'a' to 'f'. Seats 'a', 'b' and 'c' are located to the left of an aisle (if one looks in the direction of the cockpit), while seats 'd', 'e' and 'f' are located to the right. Seats 'a' and 'f' are located near the windows, while seats 'c' and 'd' are located near the aisle.   \u00a0It's lunch time and two flight attendants have just started to serve food. They move from the first rows to the tail, always maintaining a distance of two rows from each other because of the food trolley. Thus, at the beginning the first attendant serves row 1 while the second attendant serves row 3. When both rows are done they move one row forward: the first attendant serves row 2 while the second attendant serves row 4. Then they move three rows forward and the first attendant serves row 5 while the second attendant serves row 7. Then they move one row forward again and so on.Flight attendants work with the same speed: it takes exactly 1 second to serve one passenger and 1 second to move one row forward. Each attendant first serves the passengers on the seats to the right of the aisle and then serves passengers on the seats to the left of the aisle (if one looks in the direction of the cockpit). Moreover, they always serve passengers in order from the window to the aisle. Thus, the first passenger to receive food in each row is located in seat 'f', and the last one\u00a0\u2014 in seat 'c'. Assume that all seats are occupied.Vasya has seat s in row n and wants to know how many seconds will pass before he gets his lunch.","prob_desc_output_spec":"Print one integer\u00a0\u2014 the number of seconds Vasya has to wait until he gets his lunch.","lang_cluster":"","src_uid":"069d0cb9b7c798a81007fb5b63fa0f45","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","implementation"],"prob_desc_created_at":"1477148700","prob_desc_sample_inputs":"[\"1f\", \"2d\", \"4a\", \"5e\"]","prob_desc_notes":"NoteIn the first sample, the first flight attendant serves Vasya first, so Vasya gets his lunch after 1 second.In the second sample, the flight attendants will spend 6 seconds to serve everyone in the rows 1 and 3, then they will move one row forward in 1 second. As they first serve seats located to the right of the aisle in order from window to aisle, Vasya has to wait 3 more seconds. The total is 6\u2009+\u20091\u2009+\u20093\u2009=\u200910.","exec_outcome":"","difficulty":1200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The only line of input contains a description of Vasya's seat in the format ns, where n (1\u2009\u2264\u2009n\u2009\u2264\u20091018) is the index of the row and s is the seat in this row, denoted as letter from 'a' to 'f'. The index of the row and the seat are not separated by a space.","prob_desc_sample_outputs":"[\"1\", \"10\", \"11\", \"18\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1f\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2d\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"4a\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"5e\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"2c\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"1b\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"1000000000000000000d\\r\\n\", \"output\": [\"3999999999999999994\"]}, {\"input\": \"999999999999999997a\\r\\n\", \"output\": [\"3999999999999999988\"]}, {\"input\": \"1c\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"1d\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"1e\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1a\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"2a\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"2b\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"2e\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"2f\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"3a\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"3b\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"3c\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"3d\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"3e\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3f\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"4b\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"4c\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"4d\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"4e\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"4f\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"999999997a\\r\\n\", \"output\": [\"3999999988\"]}, {\"input\": \"999999997b\\r\\n\", \"output\": [\"3999999989\"]}, {\"input\": \"999999997c\\r\\n\", \"output\": [\"3999999990\"]}, {\"input\": \"999999997d\\r\\n\", \"output\": [\"3999999987\"]}, {\"input\": \"999999997e\\r\\n\", \"output\": [\"3999999986\"]}, {\"input\": \"999999997f\\r\\n\", \"output\": [\"3999999985\"]}, {\"input\": \"999999998a\\r\\n\", \"output\": [\"3999999995\"]}, {\"input\": \"999999998b\\r\\n\", \"output\": [\"3999999996\"]}, {\"input\": \"999999998c\\r\\n\", \"output\": [\"3999999997\"]}, {\"input\": \"999999998d\\r\\n\", \"output\": [\"3999999994\"]}, {\"input\": \"999999998e\\r\\n\", \"output\": [\"3999999993\"]}, {\"input\": \"999999998f\\r\\n\", \"output\": [\"3999999992\"]}, {\"input\": \"999999999a\\r\\n\", \"output\": [\"3999999988\"]}, {\"input\": \"999999999b\\r\\n\", \"output\": [\"3999999989\"]}, {\"input\": \"999999999c\\r\\n\", \"output\": [\"3999999990\"]}, {\"input\": \"999999999d\\r\\n\", \"output\": [\"3999999987\"]}, {\"input\": \"999999999e\\r\\n\", \"output\": [\"3999999986\"]}, {\"input\": \"999999999f\\r\\n\", \"output\": [\"3999999985\"]}, {\"input\": \"1000000000a\\r\\n\", \"output\": [\"3999999995\"]}, {\"input\": \"1000000000b\\r\\n\", \"output\": [\"3999999996\"]}, {\"input\": \"1000000000c\\r\\n\", \"output\": [\"3999999997\"]}, {\"input\": \"1000000000d\\r\\n\", \"output\": [\"3999999994\"]}, {\"input\": \"1000000000e\\r\\n\", \"output\": [\"3999999993\"]}, {\"input\": \"1000000000f\\r\\n\", \"output\": [\"3999999992\"]}, {\"input\": \"100000b\\r\\n\", \"output\": [\"399996\"]}, {\"input\": \"100000f\\r\\n\", \"output\": [\"399992\"]}, {\"input\": \"100001d\\r\\n\", \"output\": [\"400003\"]}, {\"input\": \"100001e\\r\\n\", \"output\": [\"400002\"]}, {\"input\": \"100001f\\r\\n\", \"output\": [\"400001\"]}, {\"input\": \"100002a\\r\\n\", \"output\": [\"400011\"]}, {\"input\": \"100002b\\r\\n\", \"output\": [\"400012\"]}, {\"input\": \"100002d\\r\\n\", \"output\": [\"400010\"]}, {\"input\": \"1231273a\\r\\n\", \"output\": [\"4925092\"]}, {\"input\": \"82784f\\r\\n\", \"output\": [\"331128\"]}, {\"input\": \"88312c\\r\\n\", \"output\": [\"353245\"]}, {\"input\": \"891237e\\r\\n\", \"output\": [\"3564946\"]}, {\"input\": \"999999999999999997b\\r\\n\", \"output\": [\"3999999999999999989\"]}, {\"input\": \"999999999999999997c\\r\\n\", \"output\": [\"3999999999999999990\"]}, {\"input\": \"999999999999999997d\\r\\n\", \"output\": [\"3999999999999999987\"]}, {\"input\": \"999999999999999997e\\r\\n\", \"output\": [\"3999999999999999986\"]}, {\"input\": \"999999999999999997f\\r\\n\", \"output\": [\"3999999999999999985\"]}, {\"input\": \"999999999999999998a\\r\\n\", \"output\": [\"3999999999999999995\"]}, {\"input\": \"999999999999999998b\\r\\n\", \"output\": [\"3999999999999999996\"]}, {\"input\": \"999999999999999998c\\r\\n\", \"output\": [\"3999999999999999997\"]}, {\"input\": \"999999999999999998d\\r\\n\", \"output\": [\"3999999999999999994\"]}, {\"input\": \"999999999999999998e\\r\\n\", \"output\": [\"3999999999999999993\"]}, {\"input\": \"999999999999999998f\\r\\n\", \"output\": [\"3999999999999999992\"]}, {\"input\": \"999999999999999999a\\r\\n\", \"output\": [\"3999999999999999988\"]}, {\"input\": \"999999999999999999b\\r\\n\", \"output\": [\"3999999999999999989\"]}, {\"input\": \"999999999999999999c\\r\\n\", \"output\": [\"3999999999999999990\"]}, {\"input\": \"999999999999999999d\\r\\n\", \"output\": [\"3999999999999999987\"]}, {\"input\": \"1000000000000000000a\\r\\n\", \"output\": [\"3999999999999999995\"]}, {\"input\": \"1000000000000000000e\\r\\n\", \"output\": [\"3999999999999999993\"]}, {\"input\": \"1000000000000000000f\\r\\n\", \"output\": [\"3999999999999999992\"]}, {\"input\": \"1000000000000000000c\\r\\n\", \"output\": [\"3999999999999999997\"]}, {\"input\": \"97a\\r\\n\", \"output\": [\"388\"]}, {\"input\": \"6f\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"7f\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"7e\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"999999999999999992c\\r\\n\", \"output\": [\"3999999999999999965\"]}, {\"input\": \"7a\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"8f\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"999999999999999992a\\r\\n\", \"output\": [\"3999999999999999963\"]}, {\"input\": \"999999999999999992b\\r\\n\", \"output\": [\"3999999999999999964\"]}, {\"input\": \"999999999999999992c\\r\\n\", \"output\": [\"3999999999999999965\"]}, {\"input\": \"999999999999999992d\\r\\n\", \"output\": [\"3999999999999999962\"]}, {\"input\": \"999999999999999992e\\r\\n\", \"output\": [\"3999999999999999961\"]}, {\"input\": \"999999999999999992f\\r\\n\", \"output\": [\"3999999999999999960\"]}, {\"input\": \"999999999999999993a\\r\\n\", \"output\": [\"3999999999999999972\"]}, {\"input\": \"999999999999999993b\\r\\n\", \"output\": [\"3999999999999999973\"]}, {\"input\": \"999999999999999993c\\r\\n\", \"output\": [\"3999999999999999974\"]}, {\"input\": \"999999999999999993d\\r\\n\", \"output\": [\"3999999999999999971\"]}, {\"input\": \"999999999999999993e\\r\\n\", \"output\": [\"3999999999999999970\"]}, {\"input\": \"999999999999999993f\\r\\n\", \"output\": [\"3999999999999999969\"]}, {\"input\": \"999999999999999994a\\r\\n\", \"output\": [\"3999999999999999979\"]}, {\"input\": \"999999999999999994b\\r\\n\", \"output\": [\"3999999999999999980\"]}, {\"input\": \"999999999999999994c\\r\\n\", \"output\": [\"3999999999999999981\"]}, {\"input\": \"999999999999999994d\\r\\n\", \"output\": [\"3999999999999999978\"]}, {\"input\": \"999999999999999994e\\r\\n\", \"output\": [\"3999999999999999977\"]}, {\"input\": \"999999999999999994f\\r\\n\", \"output\": [\"3999999999999999976\"]}, {\"input\": \"999999999999999995a\\r\\n\", \"output\": [\"3999999999999999972\"]}, {\"input\": \"999999999999999995b\\r\\n\", \"output\": [\"3999999999999999973\"]}, {\"input\": \"999999999999999995c\\r\\n\", \"output\": [\"3999999999999999974\"]}, {\"input\": \"999999999999999995d\\r\\n\", \"output\": [\"3999999999999999971\"]}, {\"input\": \"999999999999999995e\\r\\n\", \"output\": [\"3999999999999999970\"]}, {\"input\": \"999999999999999995f\\r\\n\", \"output\": [\"3999999999999999969\"]}, {\"input\": \"10a\\r\\n\", \"output\": [\"43\"]}, {\"input\": \"11f\\r\\n\", \"output\": [\"33\"]}, {\"input\": \"681572647b\\r\\n\", \"output\": [\"2726290581\"]}, {\"input\": \"23f\\r\\n\", \"output\": [\"81\"]}, {\"input\": \"123a\\r\\n\", \"output\": [\"484\"]}, {\"input\": \"999999888888777777a\\r\\n\", \"output\": [\"3999999555555111108\"]}]"}
{"prob_desc_description":"The year 2015 is almost over.Limak is a little polar bear. He has recently learnt about the binary system. He noticed that the passing year has exactly one zero in its representation in the binary system\u00a0\u2014 201510\u2009=\u2009111110111112. Note that he doesn't care about the number of zeros in the decimal representation.Limak chose some interval of years. He is going to count all years from this interval that have exactly one zero in the binary representation. Can you do it faster?Assume that all positive integers are always written without leading zeros.","prob_desc_output_spec":"Print one integer\u00a0\u2013 the number of years Limak will count in his chosen interval.","lang_cluster":"","src_uid":"581f61b1f50313bf4c75833cefd4d022","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","bitmasks","implementation"],"prob_desc_created_at":"1451487900","prob_desc_sample_inputs":"[\"5 10\", \"2015 2015\", \"100 105\", \"72057594000000000 72057595000000000\"]","prob_desc_notes":"NoteIn the first sample Limak's interval contains numbers 510\u2009=\u20091012, 610\u2009=\u20091102, 710\u2009=\u20091112, 810\u2009=\u200910002, 910\u2009=\u200910012 and 1010\u2009=\u200910102. Two of them (1012 and 1102) have the described property.","exec_outcome":"","difficulty":1300.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The only line of the input contains two integers a and b (1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u20091018)\u00a0\u2014 the first year and the last year in Limak's interval respectively.","prob_desc_sample_outputs":"[\"2\", \"1\", \"0\", \"26\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"5 10\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2015 2015\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"100 105\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"72057594000000000 72057595000000000\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"1 100\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"1000000000000000000 1000000000000000000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1000000000000000000\\r\\n\", \"output\": [\"1712\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 3\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 4\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 5\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 6\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"1 7\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 3\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 4\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 5\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2 6\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"2 7\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"3 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 4\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 5\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 6\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3 7\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 5\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"4 6\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 7\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5 5\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"5 6\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5 7\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"6 6\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"6 7\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7 7\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 8\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"6 8\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7 8\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"8 8\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1022\\r\\n\", \"output\": [\"45\"]}, {\"input\": \"1 1023\\r\\n\", \"output\": [\"45\"]}, {\"input\": \"1 1024\\r\\n\", \"output\": [\"45\"]}, {\"input\": \"1 1025\\r\\n\", \"output\": [\"45\"]}, {\"input\": \"1 1026\\r\\n\", \"output\": [\"45\"]}, {\"input\": \"509 1022\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"510 1022\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"511 1022\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"512 1022\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"513 1022\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"509 1023\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"510 1023\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"511 1023\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"512 1023\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"513 1023\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"509 1024\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"510 1024\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"511 1024\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"512 1024\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"513 1024\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"509 1025\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"510 1025\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"511 1025\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"512 1025\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"513 1025\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"1 1000000000\\r\\n\", \"output\": [\"408\"]}, {\"input\": \"10000000000 70000000000000000\\r\\n\", \"output\": [\"961\"]}, {\"input\": \"1 935829385028502935\\r\\n\", \"output\": [\"1712\"]}, {\"input\": \"500000000000000000 1000000000000000000\\r\\n\", \"output\": [\"58\"]}, {\"input\": \"500000000000000000 576460752303423488\\r\\n\", \"output\": [\"57\"]}, {\"input\": \"576460752303423488 1000000000000000000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"999999999999999999 1000000000000000000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1124800395214847 36011204832919551\\r\\n\", \"output\": [\"257\"]}, {\"input\": \"1124800395214847 36011204832919550\\r\\n\", \"output\": [\"256\"]}, {\"input\": \"1124800395214847 36011204832919552\\r\\n\", \"output\": [\"257\"]}, {\"input\": \"1124800395214846 36011204832919551\\r\\n\", \"output\": [\"257\"]}, {\"input\": \"1124800395214848 36011204832919551\\r\\n\", \"output\": [\"256\"]}, {\"input\": \"1 287104476244869119\\r\\n\", \"output\": [\"1603\"]}, {\"input\": \"1 287104476244869118\\r\\n\", \"output\": [\"1602\"]}, {\"input\": \"1 287104476244869120\\r\\n\", \"output\": [\"1603\"]}, {\"input\": \"492581209243647 1000000000000000000\\r\\n\", \"output\": [\"583\"]}, {\"input\": \"492581209243646 1000000000000000000\\r\\n\", \"output\": [\"583\"]}, {\"input\": \"492581209243648 1000000000000000000\\r\\n\", \"output\": [\"582\"]}, {\"input\": \"1099444518911 1099444518911\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1099444518910 1099444518911\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1099444518911 1099444518912\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1099444518910 1099444518912\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"864691128455135231 864691128455135231\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"864691128455135231 864691128455135232\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"864691128455135230 864691128455135232\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"864691128455135230 864691128455135231\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"864691128455135231 1000000000000000000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"864691128455135232 1000000000000000000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"864691128455135230 1000000000000000000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"576460752303423487 576460752303423487\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 576460752303423487\\r\\n\", \"output\": [\"1711\"]}, {\"input\": \"1 576460752303423486\\r\\n\", \"output\": [\"1711\"]}, {\"input\": \"2 1000000000000000000\\r\\n\", \"output\": [\"1712\"]}, {\"input\": \"3 1000000000000000000\\r\\n\", \"output\": [\"1711\"]}, {\"input\": \"4 1000000000000000000\\r\\n\", \"output\": [\"1711\"]}, {\"input\": \"5 1000000000000000000\\r\\n\", \"output\": [\"1711\"]}, {\"input\": \"6 1000000000000000000\\r\\n\", \"output\": [\"1710\"]}]"}
{"prob_desc_description":"Your friend recently gave you some slimes for your birthday. You have n slimes all initially with value 1.You are going to play a game with these slimes. Initially, you put a single slime by itself in a row. Then, you will add the other n\u2009-\u20091 slimes one by one. When you add a slime, you place it at the right of all already placed slimes. Then, while the last two slimes in the row have the same value v, you combine them together to create a slime with value v\u2009+\u20091.You would like to see what the final state of the row is after you've added all n slimes. Please print the values of the slimes in the row from left to right.","prob_desc_output_spec":"Output a single line with k integers, where k is the number of slimes in the row after you've finished the procedure described in the problem statement. The i-th of these numbers should be the value of the i-th slime from the left.","lang_cluster":"","src_uid":"757cd804aba01dc4bc108cb0722f68dc","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["implementation"],"prob_desc_created_at":"1454087400","prob_desc_sample_inputs":"[\"1\", \"2\", \"3\", \"8\"]","prob_desc_notes":"NoteIn the first sample, we only have a single slime with value 1. The final state of the board is just a single slime with value 1.In the second sample, we perform the following steps:Initially we place a single slime in a row by itself. Thus, row is initially 1.Then, we will add another slime. The row is now 1 1. Since two rightmost slimes have the same values, we should replace these slimes with one with value 2. Thus, the final state of the board is 2.In the third sample, after adding the first two slimes, our row is 2. After adding one more slime, the row becomes 2 1.In the last sample, the steps look as follows:   1  2  2 1  3  3 1  3 2  3 2 1  4 ","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line of the input will contain a single integer, n (1\u2009\u2264\u2009n\u2009\u2264\u2009100\u2009000).","prob_desc_sample_outputs":"[\"1\", \"2\", \"2 1\", \"4\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"2 1\", \"2  1\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"100000\\r\\n\", \"output\": [\"17  16  11  10  8  6\", \"17 16 11 10 8 6\"]}, {\"input\": \"12345\\r\\n\", \"output\": [\"14  13  6  5  4  1\", \"14 13 6 5 4 1\"]}, {\"input\": \"32\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"70958\\r\\n\", \"output\": [\"17  13  11  9  6  4  3  2\", \"17 13 11 9 6 4 3 2\"]}, {\"input\": \"97593\\r\\n\", \"output\": [\"17 15 14 13 12 11 9 6 5 4 1\", \"17  15  14  13  12  11  9  6  5  4  1\"]}, {\"input\": \"91706\\r\\n\", \"output\": [\"17  15  14  11  10  6  5  4  2\", \"17 15 14 11 10 6 5 4 2\"]}, {\"input\": \"85371\\r\\n\", \"output\": [\"17 15 12 11 9 7 6 5 4 2 1\", \"17  15  12  11  9  7  6  5  4  2  1\"]}, {\"input\": \"97205\\r\\n\", \"output\": [\"17  15  14  13  12  10  9  8  6  5  3  1\", \"17 15 14 13 12 10 9 8 6 5 3 1\"]}, {\"input\": \"34768\\r\\n\", \"output\": [\"16  11  10  9  8  7  5\", \"16 11 10 9 8 7 5\"]}, {\"input\": \"12705\\r\\n\", \"output\": [\"14 13 9 8 6 1\", \"14  13  9  8  6  1\"]}, {\"input\": \"30151\\r\\n\", \"output\": [\"15 14 13 11 9 8 7 3 2 1\", \"15  14  13  11  9  8  7  3  2  1\"]}, {\"input\": \"4974\\r\\n\", \"output\": [\"13  10  9  7  6  4  3  2\", \"13 10 9 7 6 4 3 2\"]}, {\"input\": \"32728\\r\\n\", \"output\": [\"15  14  13  12  11  10  9  8  7  5  4\", \"15 14 13 12 11 10 9 8 7 5 4\"]}, {\"input\": \"8192\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"65536\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"32\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"256\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"4096\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"33301\\r\\n\", \"output\": [\"16  10  5  3  1\", \"16 10 5 3 1\"]}, {\"input\": \"16725\\r\\n\", \"output\": [\"15 9 7 5 3 1\", \"15  9  7  5  3  1\"]}, {\"input\": \"149\\r\\n\", \"output\": [\"8 5 3 1\", \"8  5  3  1\"]}, {\"input\": \"16277\\r\\n\", \"output\": [\"14 13 12 11 10 9 8 5 3 1\", \"14  13  12  11  10  9  8  5  3  1\"]}, {\"input\": \"99701\\r\\n\", \"output\": [\"17 16 11 9 7 6 5 3 1\", \"17  16  11  9  7  6  5  3  1\"]}]"}
{"prob_desc_description":"You are given an alphabet consisting of n letters, your task is to make a string of the maximum possible length so that the following conditions are satisfied:   the i-th letter occurs in the string no more than ai times;  the number of occurrences of each letter in the string must be distinct for all the letters that occurred in the string at least once. ","prob_desc_output_spec":"Print a single integer \u2014 the maximum length of the string that meets all the requirements.","lang_cluster":"","src_uid":"3c4b2d1c9440515bc3002eddd2b89f6f","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["greedy","sortings"],"prob_desc_created_at":"1454605500","prob_desc_sample_inputs":"[\"3\\n2 5 5\", \"3\\n1 1 2\"]","prob_desc_notes":"NoteFor convenience let's consider an alphabet consisting of three letters: \"a\", \"b\", \"c\". In the first sample, some of the optimal strings are: \"cccaabbccbb\", \"aabcbcbcbcb\". In the second sample some of the optimal strings are: \"acc\", \"cbc\".","exec_outcome":"","difficulty":1100.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line of the input contains a single integer n (2\u2009\u2009\u2264\u2009\u2009n\u2009\u2009\u2264\u2009\u200926)\u00a0\u2014 the number of letters in the alphabet. The next line contains n integers ai (1\u2009\u2264\u2009ai\u2009\u2264\u2009109)\u00a0\u2014 i-th of these integers gives the limitation on the number of occurrences of the i-th character in the string.","prob_desc_sample_outputs":"[\"11\", \"3\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3\\r\\n2 5 5\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"3\\r\\n1 1 2\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"2\\r\\n1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3\\r\\n1 1000000000 2\\r\\n\", \"output\": [\"1000000003\"]}, {\"input\": \"26\\r\\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\\r\\n\", \"output\": [\"25999999675\"]}, {\"input\": \"2\\r\\n559476582 796461544\\r\\n\", \"output\": [\"1355938126\"]}, {\"input\": \"2\\r\\n257775227 621811272\\r\\n\", \"output\": [\"879586499\"]}, {\"input\": \"10\\r\\n876938317 219479349 703839299 977218449 116819315 752405530 393874852 286326991 592978634 155758306\\r\\n\", \"output\": [\"5075639042\"]}, {\"input\": \"26\\r\\n72 49 87 47 94 96 36 91 43 11 19 83 36 38 10 93 95 81 4 96 60 38 97 37 36 41\\r\\n\", \"output\": [\"1478\"]}, {\"input\": \"26\\r\\n243 364 768 766 633 535 502 424 502 283 592 877 137 891 837 990 681 898 831 487 595 604 747 856 805 688\\r\\n\", \"output\": [\"16535\"]}, {\"input\": \"26\\r\\n775 517 406 364 548 951 680 984 466 141 960 513 660 849 152 250 176 601 199 370 971 554 141 224 724 543\\r\\n\", \"output\": [\"13718\"]}, {\"input\": \"26\\r\\n475 344 706 807 925 813 974 166 578 226 624 591 419 894 574 909 544 597 170 990 893 785 399 172 792 748\\r\\n\", \"output\": [\"16115\"]}, {\"input\": \"26\\r\\n130 396 985 226 487 671 188 706 106 649 38 525 210 133 298 418 953 431 577 69 12 982 264 373 283 266\\r\\n\", \"output\": [\"10376\"]}, {\"input\": \"26\\r\\n605 641 814 935 936 547 524 702 133 674 173 102 318 620 248 523 77 718 318 635 322 362 306 86 8 442\\r\\n\", \"output\": [\"11768\"]}, {\"input\": \"26\\r\\n220 675 725 888 725 654 546 806 379 182 604 667 734 394 889 731 572 193 850 651 844 734 163 671 820 887\\r\\n\", \"output\": [\"16202\"]}, {\"input\": \"26\\r\\n1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000\\r\\n\", \"output\": [\"25675\"]}, {\"input\": \"26\\r\\n1001 1001 1000 1000 1001 1000 1001 1001 1001 1000 1000 1001 1001 1000 1000 1000 1000 1001 1000 1001 1001 1000 1001 1001 1001 1000\\r\\n\", \"output\": [\"25701\"]}, {\"input\": \"26\\r\\n1000 1001 1000 1001 1000 1001 1001 1000 1001 1002 1002 1000 1001 1000 1000 1000 1001 1002 1001 1000 1000 1001 1000 1002 1001 1002\\r\\n\", \"output\": [\"25727\"]}, {\"input\": \"26\\r\\n1003 1002 1002 1003 1000 1000 1000 1003 1000 1001 1003 1003 1000 1002 1002 1002 1001 1003 1000 1001 1000 1001 1001 1000 1003 1003\\r\\n\", \"output\": [\"25753\"]}, {\"input\": \"26\\r\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"26\\r\\n8717 9417 1409 7205 3625 6247 8626 9486 464 4271 1698 8449 4551 1528 7456 9198 4886 2889 7534 506 7867 9410 1635 4955 2580 2580\\r\\n\", \"output\": [\"137188\"]}, {\"input\": \"26\\r\\n197464663 125058028 622449215 11119637 587496049 703992162 219591040 965159268 229879004 278894000 841629744 616893922 218779915 362575332 844188865 342411376 369680019 43823059 921419789 999588082 943769007 35365522 301907919 758302419 427454397 807507709\\r\\n\", \"output\": [\"12776400142\"]}, {\"input\": \"26\\r\\n907247856 970380443 957324066 929910532 947150618 944189007 998282297 988343406 981298600 943026596 953932265 972691398 950024048 923033790 996423650 972134755 946404759 918183059 902987271 965507679 906967700 982106487 933997242 972594441 977736332 928874832\\r\\n\", \"output\": [\"24770753129\"]}, {\"input\": \"26\\r\\n999999061 999999688 999999587 999999429 999999110 999999563 999999120 999999111 999999794 999999890 999999004 999999448 999999770 999999543 999999460 999999034 999999361 999999305 999999201 999999778 999999432 999999844 999999133 999999342 999999600 999999319\\r\\n\", \"output\": [\"25999984927\"]}, {\"input\": \"3\\r\\n587951561 282383259 612352726\\r\\n\", \"output\": [\"1482687546\"]}, {\"input\": \"4\\r\\n111637338 992238139 787658714 974622806\\r\\n\", \"output\": [\"2866156997\"]}, {\"input\": \"5\\r\\n694257603 528073418 726928894 596328666 652863391\\r\\n\", \"output\": [\"3198451972\"]}, {\"input\": \"6\\r\\n217943380 532900593 902234882 513005821 369342573 495810412\\r\\n\", \"output\": [\"3031237661\"]}, {\"input\": \"7\\r\\n446656860 478792281 77541870 429682977 85821755 826122363 563802405\\r\\n\", \"output\": [\"2908420511\"]}, {\"input\": \"8\\r\\n29278125 778590752 252847858 51388836 802299938 215370803 901540149 242074772\\r\\n\", \"output\": [\"3273391233\"]}, {\"input\": \"9\\r\\n552962902 724482439 133182550 673093696 518779120 604618242 534250189 847695567 403066553\\r\\n\", \"output\": [\"4992131258\"]}, {\"input\": \"10\\r\\n600386086 862479376 284190454 781950823 672077209 5753052 145701234 680334621 497013634 35429365\\r\\n\", \"output\": [\"4565315854\"]}, {\"input\": \"11\\r\\n183007351 103343359 164525146 698627979 388556391 926007595 483438978 580927711 659384363 201890880 920750904\\r\\n\", \"output\": [\"5310460657\"]}, {\"input\": \"12\\r\\n706692128 108170535 339831134 320333838 810063277 20284739 821176722 481520801 467848308 604388203 881959821 874133307\\r\\n\", \"output\": [\"6436402813\"]}, {\"input\": \"13\\r\\n525349200 54062222 810108418 237010994 821513756 409532178 158915465 87142595 630219037 770849718 843168738 617993222 504443485\\r\\n\", \"output\": [\"6470309028\"]}, {\"input\": \"14\\r\\n812998169 353860693 690443110 153688149 537992938 798779618 791624505 282706982 733654279 468319337 568341847 597888944 649703235 667623671\\r\\n\", \"output\": [\"8107625477\"]}, {\"input\": \"15\\r\\n336683946 299752380 865749098 775393009 959499824 893055762 365399057 419335880 896025008 575845364 529550764 341748859 30999793 464432689 19445239\\r\\n\", \"output\": [\"7772916672\"]}, {\"input\": \"16\\r\\n860368723 540615364 41056086 692070164 970950302 282304201 998108096 24957674 999460249 37279175 490759681 26673285 412295352 671298115 627182888 90740349\\r\\n\", \"output\": [\"7766119704\"]}, {\"input\": \"17\\r\\n148018692 545442539 980325266 313776023 687429485 376580345 40875544 925549764 161831978 144805202 451968598 475560904 262583806 468107133 60900936 281546097 912565045\\r\\n\", \"output\": [\"7237867357\"]}, {\"input\": \"18\\r\\n966674765 786305522 860659958 935480883 108937371 60800080 673584584 826142855 560238516 606238013 413177515 455456626 643879364 969943855 963609881 177380550 544192822 864797474\\r\\n\", \"output\": [\"11417500634\"]}, {\"input\": \"19\\r\\n490360541 496161402 330938242 852158038 120387849 686083328 247359135 431764649 427637949 8736336 843378328 435352349 494167818 766752874 161292122 368186298 470791896 813444279 170758124\\r\\n\", \"output\": [\"8615711557\"]}, {\"input\": \"20\\r\\n654616375 542649443 729213190 188364665 238384327 726353863 974350390 526804424 601329631 886592063 734805196 275562411 861801362 374466292 119830901 403120565 670982545 63210795 130397643 601611646\\r\\n\", \"output\": [\"10304447727\"]}, {\"input\": \"21\\r\\n942265343 252505322 904519178 810069524 954862509 115602302 548124942 132426218 999736168 584061682 696014113 960485837 712089816 581331718 317512142 593926314 302610323 716885305 477125514 813997503 535631456\\r\\n\", \"output\": [\"12951783229\"]}, {\"input\": \"22\\r\\n465951120 788339601 784853870 726746679 376370396 504849742 180834982 33019308 867135601 455551901 657223030 940381560 93386374 378140736 161286599 548696254 934237100 75589518 764917898 731412064 205669368 630662937\\r\\n\", \"output\": [\"11305256638\"]}, {\"input\": \"23\\r\\n989635897 498195481 255132154 643423835 387820874 894097181 223601429 228583694 265543138 153021520 618431947 684241474 943673829 174949754 358967839 444530707 801900686 965299835 347682577 648826625 406714384 129525158 958578251\\r\\n\", \"output\": [\"12022378269\"]}, {\"input\": \"24\\r\\n277285866 739058464 135466846 265129694 104300056 519381429 856310469 834204489 132942572 260547547 343605057 664137197 619941683 676786476 497713592 635336455 138557168 618975345 635474960 861212482 76752297 923357675 517046816 274123722\\r\\n\", \"output\": [\"11607648357\"]}, {\"input\": \"25\\r\\n95942939 979921447 310772834 181806850 525806942 613657573 194049213 734797579 531349109 721980358 304813974 113025815 470230137 473595494 695394833 590106396 770183946 567622150 218239639 778627043 41761505 127248600 134450869 860350034 901937574\\r\\n\", \"output\": [\"11937672853\"]}, {\"input\": \"26\\r\\n619627716 984748623 486078822 98484005 537257421 2906012 62795060 635390669 103777246 829506385 971050595 92921538 851525695 680460920 893076074 780912144 401811723 221297659 269996214 991012900 242806521 626109821 987889730 682613155 209557740 806895799\\r\\n\", \"output\": [\"14070510187\"]}, {\"input\": \"26\\r\\n10 1 20 2 23 3 14 6 7 13 26 21 11 8 16 25 12 15 19 9 17 22 24 18 5 4\\r\\n\", \"output\": [\"351\"]}, {\"input\": \"3\\r\\n1 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"5\\r\\n5 3 3 3 1\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"5\\r\\n2 2 2 2 2\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"10\\r\\n10 10 10 10 10 10 10 10 1 1\\r\\n\", \"output\": [\"53\"]}, {\"input\": \"10\\r\\n100 100 10 10 10 10 10 1 1 1\\r\\n\", \"output\": [\"240\"]}, {\"input\": \"6\\r\\n5 3 3 3 3 1\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"4\\r\\n4 3 2 1\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"5\\r\\n1 1 1 1 1\\r\\n\", \"output\": [\"1\"]}]"}
{"prob_desc_description":"Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.","prob_desc_output_spec":"Print the maximum number of games in which the winner of the tournament can take part.","lang_cluster":"","src_uid":"3d3432b4f7c6a3b901161fa24b415b14","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["greedy","combinatorics","constructive algorithms","dp","math","dfs and similar"],"prob_desc_created_at":"1480264500","prob_desc_sample_inputs":"[\"2\", \"3\", \"4\", \"10\"]","prob_desc_notes":"NoteIn all samples we consider that player number 1 is the winner.In the first sample, there would be only one game so the answer is 1.In the second sample, player 1 can consequently beat players 2 and 3. In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1,\u20092) and (3,\u20094) and then clash the winners.","exec_outcome":"","difficulty":1600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The only line of the input contains a single integer n (2\u2009\u2264\u2009n\u2009\u2264\u20091018)\u00a0\u2014 the number of players to participate in the tournament.","prob_desc_sample_outputs":"[\"1\", \"2\", \"2\", \"4\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"1000\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"2500\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"690000\\r\\n\", \"output\": [\"27\"]}, {\"input\": \"3000000000\\r\\n\", \"output\": [\"45\"]}, {\"input\": \"123456789123456789\\r\\n\", \"output\": [\"81\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"143\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"144\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"145\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"232\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"233\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"234\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"679891637638612257\\r\\n\", \"output\": [\"84\"]}, {\"input\": \"679891637638612258\\r\\n\", \"output\": [\"85\"]}, {\"input\": \"679891637638612259\\r\\n\", \"output\": [\"85\"]}, {\"input\": \"1000000000000000000\\r\\n\", \"output\": [\"85\"]}, {\"input\": \"10235439547\\r\\n\", \"output\": [\"47\"]}, {\"input\": \"1240723548\\r\\n\", \"output\": [\"43\"]}, {\"input\": \"92353046212453\\r\\n\", \"output\": [\"66\"]}, {\"input\": \"192403205846532\\r\\n\", \"output\": [\"68\"]}, {\"input\": \"13925230525389\\r\\n\", \"output\": [\"62\"]}, {\"input\": \"12048230592523\\r\\n\", \"output\": [\"62\"]}, {\"input\": \"19204385325853\\r\\n\", \"output\": [\"63\"]}, {\"input\": \"902353283921\\r\\n\", \"output\": [\"56\"]}, {\"input\": \"793056859214355\\r\\n\", \"output\": [\"70\"]}, {\"input\": \"982045466234565\\r\\n\", \"output\": [\"71\"]}, {\"input\": \"126743950353465\\r\\n\", \"output\": [\"67\"]}, {\"input\": \"12405430465\\r\\n\", \"output\": [\"47\"]}, {\"input\": \"10238439257768\\r\\n\", \"output\": [\"61\"]}, {\"input\": \"1728493055346\\r\\n\", \"output\": [\"58\"]}, {\"input\": \"927553829046\\r\\n\", \"output\": [\"56\"]}, {\"input\": \"62735129403\\r\\n\", \"output\": [\"51\"]}, {\"input\": \"71624823950223\\r\\n\", \"output\": [\"65\"]}, {\"input\": \"8902353464851212\\r\\n\", \"output\": [\"75\"]}, {\"input\": \"61824012598535\\r\\n\", \"output\": [\"65\"]}, {\"input\": \"1294902504603347\\r\\n\", \"output\": [\"71\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"11\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"12\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"13\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"14\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"15\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"16\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"17\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"18\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"19\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"20\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"21\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"22\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"23\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"355687428096000\\r\\n\", \"output\": [\"69\"]}, {\"input\": \"576460752303423488\\r\\n\", \"output\": [\"84\"]}, {\"input\": \"32212254719\\r\\n\", \"output\": [\"49\"]}, {\"input\": \"26388279066623\\r\\n\", \"output\": [\"63\"]}, {\"input\": \"618473717761\\r\\n\", \"output\": [\"56\"]}, {\"input\": \"262406072477\\r\\n\", \"output\": [\"54\"]}]"}
{"prob_desc_description":"Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L'\u00a0\u2014 instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.","prob_desc_output_spec":"Print a single integer\u00a0\u2014 the number of contiguous substrings that Calvin can execute and return to his starting square.","lang_cluster":"","src_uid":"7bd5521531950e2de9a7b0904353184d","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","implementation"],"prob_desc_created_at":"1455384900","prob_desc_sample_inputs":"[\"6\\nURLLDR\", \"4\\nDLUU\", \"7\\nRLRLRLR\"]","prob_desc_notes":"NoteIn the first case, the entire source code works, as well as the \"RL\" substring in the second and third characters.Note that, in the third case, the substring \"LR\" appears three times, and is therefore counted three times to the total result.","exec_outcome":"","difficulty":1000.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line of the input contains a single positive integer, n (1\u2009\u2264\u2009n\u2009\u2264\u2009200)\u00a0\u2014 the number of commands. The next line contains n characters, each either 'U', 'R', 'D', or 'L'\u00a0\u2014 Calvin's source code.","prob_desc_sample_outputs":"[\"2\", \"0\", \"12\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"6\\r\\nURLLDR\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4\\r\\nDLUU\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7\\r\\nRLRLRLR\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"1\\r\\nR\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100\\r\\nURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDLURDL\\r\\n\", \"output\": [\"1225\"]}, {\"input\": \"200\\r\\nLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\\r\\n\", \"output\": [\"100\"]}, {\"input\": \"20\\r\\nLDURLDURRLRUDLRRUDLU\\r\\n\", \"output\": [\"29\"]}, {\"input\": \"140\\r\\nDLDLULULDRDDDLLUDRRDLLUULLDDLDLUURLDLDRDUDDLRRDURUUUUURLDUDDLLRRLLDRRRDDDDDUDUULLURRDLDULUDLLUUDRRLUDULUDUDULULUURURRDUURRDLULLURUDDDDRDRDRD\\r\\n\", \"output\": [\"125\"]}, {\"input\": \"194\\r\\nULLLDLLDRUUDURRULLRLUUURDRLLURDUDDUDLULRLDRUDURLDLRDLLLLUDDRRRULULULUDDULRURURLLDLDLDRUDUUDULRULDDRRLRDRULLDRULLLLRRDDLLLLULDRLUULRUUULDUUDLDLDUUUDDLDDRULDRRLUURRULLDULRRDLLRDURDLUUDUDLLUDDULDDD\\r\\n\", \"output\": [\"282\"]}, {\"input\": \"200\\r\\nDDDURLLUUULUDDURRDLLDDLLRLUULUULDDDLRRDLRRDUDURDUDRRLLDRDUDDLDDRDLURRRLLRDRRLLLRDDDRDRRLLRRLULRUULRLDLUDRRRDDUUURLLUDRLDUDRLLRLRRLUDLRULDUDDRRLLRLURDLRUDDDURLRDUDUUURLLULULRDRLDLDRURDDDLLRUDDRDUDDDLRU\\r\\n\", \"output\": [\"408\"]}, {\"input\": \"197\\r\\nDUUDUDUDUDUUDUUDUUUDDDDUUUDUUUDUUUUUDUUUDDUDDDUUDUDDDUUDDUUUUUUUDUDDDDDUUUUUDDDDDDUUUUDDUDDUDDDUDUUUDUUDUDUDUUUDUDDDDUUDDUDDDDUDDDUDUUUDUUDUUUDDDDUUUDUUDDUUUUUDDDDUUDUUDDDDUDDUUDUUUDDDDUDUUUDDDUUDU\\r\\n\", \"output\": [\"1995\"]}, {\"input\": \"200\\r\\nLLLLRLLRLLRRRRLLRRLRRLRRRLLLRRLRRRRLLRRLLRRRLRLRLRRLLRLLRRLLLRRRRLRLLRLLLRLLLRRLLLRLRLRRRRRRRLRRRLRLRLLLLRLRRRRRLRRLRLLLLRLLLRRLRRLLRLRLLLRRLLRRLRRRRRLRLRRLRLLRLLLLRLRRRLRRLRLLRLRRLRRRRRLRRLLLRRRRRLLR\\r\\n\", \"output\": [\"1368\"]}, {\"input\": \"184\\r\\nUUUDDUDDDDDUDDDDUDDUUUUUDDDUUDDUDUUDUUUDDUDDDDDDDDDDUDUDDUUDDDUUDDUDUDDDUUDUDUUUUDDUDUUUDDUDUUUUDUUDDUUDUUUDUDUDDUDUDDDUUDDDDUUUUUDDDUDUDUDUDUDUUUDUDDUUDDUDUUDUDUUUDUUDDDDUDDDDUDUUDUUD\\r\\n\", \"output\": [\"1243\"]}, {\"input\": \"187\\r\\nRLLRLRRLLRRLRRRRLLRLLRLLLLRRRLLLRLLLLRRLRLRRRRRRLLRRLRLLRRRLLRRLLLRRLRRLRLLLLRRRRLRRLLRRLRRRRLLLLRRLRLRLRRRRRLLRLRLRLRLRLRLLLRLLLLLRRRLLRLRRRLLLRRLLLLLRLLRLLLRRRLLLRRLRRRLLLRRLRLLRRLRLRLR\\r\\n\", \"output\": [\"1501\"]}, {\"input\": \"190\\r\\nUULLLUUULLLULLUULUUUUULUUULLULLULUULLUULLUUULULUULLUULLUUULULLLLLLULLLLLULUULLULLULLLUULUULLLUUUULLLLUUULLUUULLLULULUULULLUULULULUUULLUUUULLUUULULUULLLLULLLLLUULLUULULLULUUUUUULULLLULLUULUUU\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"46\\r\\nULUURRRRLDRDRDDDURRRLLLDDULLRRRRRLUDDLRDRULLLL\\r\\n\", \"output\": [\"23\"]}, {\"input\": \"70\\r\\nUUDRLDRDRUDLLURURULRDULRRDULDUDDRUULLDDDDDRLLRDURRDULRDLRUUUDDLRUURRLD\\r\\n\", \"output\": [\"86\"]}, {\"input\": \"198\\r\\nURLLUDRDUUDRDLLRURULLRRLRRUULRLULUUDRRURLRUURRDRUUDRLRURLLULRDDDDDRDDRRRLRUDULLDDLLLUDRLDRUDRDLDUULLUUUULULLRLDDRDURDRURLULDRURLLDDULURULDLUUUUULDLURRLLDLULLDULRUURRLDLLUUURDLDDUDUULRLUDULLULDRDRLRL\\r\\n\", \"output\": [\"160\"]}, {\"input\": \"22\\r\\nDUDDDURURUDURRUDRDULUL\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"200\\r\\nUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUD\\r\\n\", \"output\": [\"10000\"]}, {\"input\": \"4\\r\\nRRDR\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"6\\r\\nUULLLL\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2\\r\\nDU\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"6\\r\\nUURRRR\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"101\\r\\nRDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD\\r\\n\", \"output\": [\"0\"]}]"}
{"prob_desc_description":"Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a,\u2009b)?","prob_desc_output_spec":"Print a single integer, the number of solutions to the given conditions. If no solutions exist, print 0.","lang_cluster":"","src_uid":"18410980789b14c128dd6adfa501aea5","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","constructive algorithms","dp","implementation"],"prob_desc_created_at":"1456683000","prob_desc_sample_inputs":"[\"9 5\", \"3 3\", \"5 2\"]","prob_desc_notes":"NoteIn the first sample, we have the following solutions: (2,\u20097), (3,\u20096), (6,\u20093), (7,\u20092).In the second sample, the only solutions are (1,\u20092) and (2,\u20091).","exec_outcome":"","difficulty":1700.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line of the input contains two integers s and x (2\u2009\u2264\u2009s\u2009\u2264\u20091012, 0\u2009\u2264\u2009x\u2009\u2264\u20091012), the sum and bitwise xor of the pair of positive integers, respectively.","prob_desc_sample_outputs":"[\"4\", \"2\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"9 5\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"3 3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"6 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"549755813887 549755813887\\r\\n\", \"output\": [\"549755813886\"]}, {\"input\": \"2 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"433864631347 597596794426\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"80 12\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"549755813888 549755813886\\r\\n\", \"output\": [\"274877906944\"]}, {\"input\": \"643057379466 24429729346\\r\\n\", \"output\": [\"2048\"]}, {\"input\": \"735465350041 356516240229\\r\\n\", \"output\": [\"32768\"]}, {\"input\": \"608032203317 318063018433\\r\\n\", \"output\": [\"4096\"]}, {\"input\": \"185407964720 148793115916\\r\\n\", \"output\": [\"16384\"]}, {\"input\": \"322414792152 285840263184\\r\\n\", \"output\": [\"4096\"]}, {\"input\": \"547616456703 547599679487\\r\\n\", \"output\": [\"68719476736\"]}, {\"input\": \"274861129991 274861129463\\r\\n\", \"output\": [\"34359738368\"]}, {\"input\": \"549688705887 549688703839\\r\\n\", \"output\": [\"34359738368\"]}, {\"input\": \"412182675455 412182609919\\r\\n\", \"output\": [\"68719476736\"]}, {\"input\": \"552972910589 546530328573\\r\\n\", \"output\": [\"17179869184\"]}, {\"input\": \"274869346299 274869346299\\r\\n\", \"output\": [\"8589934590\"]}, {\"input\": \"341374319077 341374319077\\r\\n\", \"output\": [\"134217726\"]}, {\"input\": \"232040172650 232040172650\\r\\n\", \"output\": [\"65534\"]}, {\"input\": \"322373798090 322373798090\\r\\n\", \"output\": [\"1048574\"]}, {\"input\": \"18436 18436\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"137707749376 137707749376\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"9126813696 9126813696\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"419432708 419432708\\r\\n\", \"output\": [\"62\"]}, {\"input\": \"1839714 248080\\r\\n\", \"output\": [\"128\"]}, {\"input\": \"497110 38\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"1420572 139928\\r\\n\", \"output\": [\"64\"]}, {\"input\": \"583545 583545\\r\\n\", \"output\": [\"4094\"]}, {\"input\": \"33411 33411\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"66068 66068\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"320 320\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1530587 566563\\r\\n\", \"output\": [\"256\"]}, {\"input\": \"1988518 108632\\r\\n\", \"output\": [\"128\"]}, {\"input\": \"915425594051 155160267299\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"176901202458 21535662096\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"865893190664 224852444148\\r\\n\", \"output\": [\"32768\"]}, {\"input\": \"297044970199 121204864\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"241173201018 236676464482\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1582116 139808\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1707011 656387\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"169616 132704\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"2160101 553812\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1322568 271816\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"228503520839 471917524248\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"32576550340 504864993495\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"910648542843 537125462055\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"751720572344 569387893618\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"629791564846 602334362179\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1000000000000 1000000000000\\r\\n\", \"output\": [\"8190\"]}, {\"input\": \"1000000000000 999999999999\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1000000000000 4\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1000000000000 4096\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2097152 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"40 390\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"22212 39957\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"128 36\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"14 4\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"6 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"43 18467\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7 5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"251059 79687\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"17 7\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 6\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 4\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 7\\r\\n\", \"output\": [\"0\"]}]"}
{"prob_desc_description":"For his computer science class, Jacob builds a model tree with sticks and balls containing n nodes in the shape of a tree. Jacob has spent ai minutes building the i-th ball in the tree.Jacob's teacher will evaluate his model and grade Jacob based on the effort he has put in. However, she does not have enough time to search his whole tree to determine this; Jacob knows that she will examine the first k nodes in a DFS-order traversal of the tree. She will then assign Jacob a grade equal to the minimum ai she finds among those k nodes.Though Jacob does not have enough time to rebuild his model, he can choose the root node that his teacher starts from. Furthermore, he can rearrange the list of neighbors of each node in any order he likes. Help Jacob find the best grade he can get on this assignment.A DFS-order traversal is an ordering of the nodes of a rooted tree, built by a recursive DFS-procedure initially called on the root of the tree. When called on a given node v, the procedure does the following:   Print v.  Traverse the list of neighbors of the node v in order and iteratively call DFS-procedure on each one. Do not call DFS-procedure on node u if you came to node v directly from u. ","prob_desc_output_spec":"Print a single integer\u00a0\u2014 the maximum grade Jacob can get by picking the right root of the tree and rearranging the list of neighbors.","lang_cluster":"","src_uid":"4fb83b890e472f86045981e1743ddaac","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["dfs and similar","graphs","greedy","binary search"],"prob_desc_created_at":"1456683000","prob_desc_sample_inputs":"[\"5 3\\n3 6 1 4 2\\n1 2\\n2 4\\n2 5\\n1 3\", \"4 2\\n1 5 5 5\\n1 2\\n1 3\\n1 4\"]","prob_desc_notes":"NoteIn the first sample, Jacob can root the tree at node 2 and order 2's neighbors in the order 4, 1, 5 (all other nodes have at most two neighbors). The resulting preorder traversal is 2, 4, 1, 3, 5, and the minimum ai of the first 3 nodes is 3.In the second sample, it is clear that any preorder traversal will contain node 1 as either its first or second node, so Jacob cannot do better than a grade of 1.","exec_outcome":"","difficulty":2600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"7 seconds","prob_desc_input_spec":"The first line of the input contains two positive integers, n and k (2\u2009\u2264\u2009n\u2009\u2264\u2009200\u2009000, 1\u2009\u2264\u2009k\u2009\u2264\u2009n)\u00a0\u2014 the number of balls in Jacob's tree and the number of balls the teacher will inspect. The second line contains n integers, ai (1\u2009\u2264\u2009ai\u2009\u2264\u20091\u2009000\u2009000), the time Jacob used to build the i-th ball. Each of the next n\u2009-\u20091 lines contains two integers ui, vi (1\u2009\u2264\u2009ui,\u2009vi\u2009\u2264\u2009n, ui\u2009\u2260\u2009vi) representing a connection in Jacob's tree between balls ui and vi.","prob_desc_sample_outputs":"[\"3\", \"1\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"5 3\\r\\n3 6 1 4 2\\r\\n1 2\\r\\n2 4\\r\\n2 5\\r\\n1 3\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"4 2\\r\\n1 5 5 5\\r\\n1 2\\r\\n1 3\\r\\n1 4\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 1\\r\\n1 100000\\r\\n2 1\\r\\n\", \"output\": [\"100000\"]}, {\"input\": \"2 2\\r\\n1 1000000\\r\\n1 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10 4\\r\\n104325 153357 265088 777795 337716 557321 702646 734430 464449 744072\\r\\n9 4\\r\\n8 1\\r\\n10 7\\r\\n8 6\\r\\n7 9\\r\\n8 2\\r\\n3 5\\r\\n8 3\\r\\n10 8\\r\\n\", \"output\": [\"557321\"]}, {\"input\": \"10 3\\r\\n703660 186846 317819 628672 74457 58472 247014 480113 252764 860936\\r\\n10 6\\r\\n7 4\\r\\n10 9\\r\\n9 5\\r\\n6 3\\r\\n6 2\\r\\n7 1\\r\\n10 7\\r\\n10 8\\r\\n\", \"output\": [\"252764\"]}, {\"input\": \"10 10\\r\\n794273 814140 758469 932911 607860 683826 987442 652494 952171 698608\\r\\n1 3\\r\\n3 8\\r\\n2 7\\r\\n2 1\\r\\n2 9\\r\\n3 10\\r\\n6 4\\r\\n9 6\\r\\n3 5\\r\\n\", \"output\": [\"607860\"]}, {\"input\": \"200000 100000\\r\\n187144 606401 449471 587589 112357 126153 841833 925667 678740 17633 467422 267674 904062 847788 541842 629 275042 289091 218561 379227 149799 611714 52366 74773 960225 265175 358488 322244 877381 375698 708220 166529 452200 796447 842640 278151 574788 450410 566912 803359 705782 665118 302531 273623 937531 611932 676010 421130 448997 258600 597525 737369 848737 756671 690505 585516 903849 704562 969441 785714 936999 987842 471078 982790 782238 377387 340479 472409 777743 232071 357193 76419...\", \"output\": [\"81235\"]}, {\"input\": \"200000 3598\\r\\n897421 716664 387168 767272 417874 425082 217919 987791 74676 663310 19237 407095 339428 725175 355792 263613 283851 786636 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945021 862390 91184 845225 620474 752092 781869 942420 688465 774423 876258 913218 784678 760040 614035 731479 298105 168595 479598 718104 923247 656638 909056 862621 609836 908290 697157 490267 708023 891034 336039 970075 845719 682945 748628 966138 71558 861337 946322 987955 985126 752867 774231 427279 994348 686493 456743 896930 710846 706658 844363 609641 108829 877460 452578 762681 938897 727953 834353 522106 181657 703674 270174 920847 653487 971882 396748 7...\", \"output\": [\"600001\"]}, {\"input\": \"200000 9608\\r\\n226617 481349 287276 88643 969650 135579 183843 493484 336647 218436 527505 131731 514347 2319 801910 247870 538384 415683 362466 49383 98254 524660 251024 30080 354313 510342 518441 978486 748268 174220 292540 493958 521640 696621 442222 206388 137834 322290 299305 552408 175556 13490 13655 38963 481433 282768 581768 353475 57247 117346 542698 73721 178095 166060 177934 572450 368960 387643 106281 212001 131345 57125 378214 569470 65980 385231 145529 892089 819852 63890 461491 33661 130607 55...\", \"output\": [\"526905\"]}, {\"input\": \"200000 127930\\r\\n895944 934205 238521 810240 875129 967169 730163 107386 484627 826132 712351 772236 939252 596 798789 256645 814754 603177 606129 75262 910740 31820 813006 927211 828106 970960 932055 543364 266677 650043 605828 679797 106432 643620 875831 947417 642675 832196 601108 717193 128604 842942 637835 721503 572335 805270 98446 600232 919853 502071 696563 835408 424533 717674 301921 7293 716702 943338 878050 992931 476287 729074 765471 625163 888861 758567 515497 743417 320941 691751 446357 487537 ...\", \"output\": [\"493790\"]}, {\"input\": \"200000 50570\\r\\n826971 49175 933482 482321 705136 485487 358996 28501 302483 398502 98261 105054 825661 70829 295514 936527 244456 793265 306420 93500 965893 315718 439883 291008 73358 219343 95891 116393 479032 565281 439380 968574 671526 387184 537510 799022 443038 853752 15659 592212 614835 148875 909645 189428 519973 283686 84431 196990 232832 20073 70101 49298 380378 593437 966114 35435 73444 454865 686120 761808 357207 118347 152984 298322 90388 513833 549443 360669 585765 193147 168743 397309 586227 5...\", \"output\": [\"355198\"]}]"}
{"prob_desc_description":"The numbers of all offices in the new building of the Tax Office of IT City will have lucky numbers.Lucky number is a number that consists of digits 7 and 8 only. Find the maximum number of offices in the new building of the Tax Office given that a door-plate can hold a number not longer than n digits.","prob_desc_output_spec":"Output one integer \u2014 the maximum number of offices, than can have unique lucky numbers not longer than n digits.","lang_cluster":"","src_uid":"f1b43baa14d4c262ba616d892525dfde","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"64 megabytes","file_name":"prog_syn_val.jsonl","tags":["combinatorics","math"],"prob_desc_created_at":"1455807600","prob_desc_sample_inputs":"[\"2\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1100.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"0.5 seconds","prob_desc_input_spec":"The only line of input contains one integer n (1\u2009\u2264\u2009n\u2009\u2264\u200955) \u2014 the maximum length of a number that a door-plate can hold.","prob_desc_sample_outputs":"[\"6\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"62\"]}, {\"input\": \"12\\r\\n\", \"output\": [\"8190\"]}, {\"input\": \"34\\r\\n\", \"output\": [\"34359738366\"]}, {\"input\": \"43\\r\\n\", \"output\": [\"17592186044414\"]}, {\"input\": \"49\\r\\n\", \"output\": [\"1125899906842622\"]}, {\"input\": \"54\\r\\n\", \"output\": [\"36028797018963966\"]}, {\"input\": \"55\\r\\n\", \"output\": [\"72057594037927934\"]}]"}
{"prob_desc_description":"Vasya started working in a machine vision company of IT City. Vasya's team creates software and hardware for identification of people by their face.One of the project's know-how is a camera rotating around its optical axis on shooting. People see an eye-catching gadget \u2014 a rotating camera \u2014 come up to it to see it better, look into it. And the camera takes their photo at that time. What could be better for high quality identification?But not everything is so simple. The pictures from camera appear rotated too (on clockwise camera rotation frame the content becomes rotated counter-clockwise). But the identification algorithm can work only with faces that are just slightly deviated from vertical.Vasya was entrusted to correct the situation \u2014 to rotate a captured image so that image would be minimally deviated from vertical. Requirements were severe. Firstly, the picture should be rotated only on angle divisible by 90 degrees to not lose a bit of information about the image. Secondly, the frames from the camera are so huge and FPS is so big that adequate rotation speed is provided by hardware FPGA solution only. And this solution can rotate only by 90 degrees clockwise. Of course, one can apply 90 degrees turn several times but for the sake of performance the number of turns should be minimized.Help Vasya implement the program that by the given rotation angle of the camera can determine the minimum number of 90 degrees clockwise turns necessary to get a picture in which up direction deviation from vertical is minimum.The next figure contains frames taken from an unrotated camera, then from rotated 90 degrees clockwise, then from rotated 90 degrees counter-clockwise. Arrows show direction to \"true up\".  The next figure shows 90 degrees clockwise turn by FPGA hardware.  ","prob_desc_output_spec":"Output one integer \u2014 the minimum required number of 90 degrees clockwise turns.","lang_cluster":"","src_uid":"509db9cb6156b692557ba874a09f150e","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"64 megabytes","file_name":"prog_syn_val.jsonl","tags":["geometry","math"],"prob_desc_created_at":"1455807600","prob_desc_sample_inputs":"[\"60\", \"-60\"]","prob_desc_notes":"NoteWhen the camera is rotated 60 degrees counter-clockwise (the second example), an image from it is rotated 60 degrees clockwise. One 90 degrees clockwise turn of the image result in 150 degrees clockwise total rotation and deviation from \"true up\" for one turn is 150 degrees. Two 90 degrees clockwise turns of the image result in 240 degrees clockwise total rotation and deviation from \"true up\" for two turns is 120 degrees because 240 degrees clockwise equal to 120 degrees counter-clockwise. Three 90 degrees clockwise turns of the image result in 330 degrees clockwise total rotation and deviation from \"true up\" for three turns is 30 degrees because 330 degrees clockwise equal to 30 degrees counter-clockwise.From 60, 150, 120 and 30 degrees deviations the smallest is 30, and it it achieved in three 90 degrees clockwise turns.","exec_outcome":"","difficulty":1800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"0.5 seconds","prob_desc_input_spec":"The only line of the input contains one integer x (\u2009-\u20091018\u2009\u2264\u2009x\u2009\u2264\u20091018) \u2014 camera angle in degrees. Positive value denotes clockwise camera rotation, negative \u2014 counter-clockwise.","prob_desc_sample_outputs":"[\"1\", \"3\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"60\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-60\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"44\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"45\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"46\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"134\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"135\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"136\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"224\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"225\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"226\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"227\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"313\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"314\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"315\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"316\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"358\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"359\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"360\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"361\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999999999999999340\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999999999999999325\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999999999999999326\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"999999999999999415\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"999999999999999416\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"999999999999999504\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"999999999999999505\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"999999999999999506\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"999999999999999594\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"999999999999999595\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"999999999999999596\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"999999999999999639\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"999999999999999640\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"6678504591813508\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"201035370138545377\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"441505850043460771\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"252890591709237675\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"272028913373922389\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"141460527912396122\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"479865961765156498\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"-44\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-45\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-46\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"-134\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"-135\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"-136\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"-224\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"-225\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-226\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-227\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-313\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-314\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-315\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-316\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-358\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-359\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-360\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-361\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-999999999999999340\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-999999999999999325\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-999999999999999326\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-999999999999999415\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"-999999999999999416\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"-999999999999999504\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"-999999999999999505\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"-999999999999999506\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"-999999999999999594\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-999999999999999595\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-999999999999999596\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-999999999999999639\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-999999999999999640\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-6678504591813508\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"-201035370138545377\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"-441505850043460771\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"-252890591709237675\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"-272028913373922389\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"-141460527912396122\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"-479865961765156498\\r\\n\", \"output\": [\"2\"]}]"}
{"prob_desc_description":"There are n people, sitting in a line at the table. For each person we know that he always tells either the truth or lies.Little Serge asked them: how many of you always tell the truth? Each of the people at the table knows everything (who is an honest person and who is a liar) about all the people at the table. The honest people are going to say the correct answer, the liars are going to say any integer from 1 to n, which is not the correct answer. Every liar chooses his answer, regardless of the other liars, so two distinct liars may give distinct answer.Serge does not know any information about the people besides their answers to his question. He took a piece of paper and wrote n integers a1,\u2009a2,\u2009...,\u2009an, where ai is the answer of the i-th person in the row. Given this sequence, Serge determined that exactly k people sitting at the table apparently lie.Serge wonders, how many variants of people's answers (sequences of answers a of length n) there are where one can say that exactly k people sitting at the table apparently lie. As there can be rather many described variants of answers, count the remainder of dividing the number of the variants by 777777777.","prob_desc_output_spec":"Print a single integer \u2014 the answer to the problem modulo 777777777.","lang_cluster":"","src_uid":"cfe19131644e5925e32084a581e23286","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp"],"prob_desc_created_at":"1355671800","prob_desc_sample_inputs":"[\"1 1\", \"2 1\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":2700.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains two integers n, k, (1\u2009\u2264\u2009k\u2009\u2264\u2009n\u2009\u2264\u200928). It is guaranteed that n \u2014 is the power of number 2.","prob_desc_sample_outputs":"[\"0\", \"2\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"4 1\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"4 2\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"80\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"109\"]}, {\"input\": \"256 1\\r\\n\", \"output\": [\"412133651\"]}, {\"input\": \"128 39\\r\\n\", \"output\": [\"93337440\"]}, {\"input\": \"8 5\\r\\n\", \"output\": [\"1757896\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"32 26\\r\\n\", \"output\": [\"44684703\"]}, {\"input\": \"16 15\\r\\n\", \"output\": [\"569389279\"]}, {\"input\": \"64 29\\r\\n\", \"output\": [\"582889860\"]}, {\"input\": \"256 184\\r\\n\", \"output\": [\"337388940\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"80\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"80\"]}, {\"input\": \"64 9\\r\\n\", \"output\": [\"459185405\"]}, {\"input\": \"256 188\\r\\n\", \"output\": [\"106017282\"]}, {\"input\": \"128 39\\r\\n\", \"output\": [\"93337440\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"109\"]}, {\"input\": \"4 2\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"64 57\\r\\n\", \"output\": [\"67309914\"]}, {\"input\": \"8 8\\r\\n\", \"output\": [\"7593125\"]}, {\"input\": \"4 1\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"32 29\\r\\n\", \"output\": [\"612549793\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"8 4\\r\\n\", \"output\": [\"415870\"]}, {\"input\": \"4 2\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"128 11\\r\\n\", \"output\": [\"175889805\"]}, {\"input\": \"16 12\\r\\n\", \"output\": [\"515619293\"]}, {\"input\": \"32 19\\r\\n\", \"output\": [\"628771752\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"16 15\\r\\n\", \"output\": [\"569389279\"]}, {\"input\": \"16 9\\r\\n\", \"output\": [\"472062098\"]}, {\"input\": \"32 30\\r\\n\", \"output\": [\"519860281\"]}, {\"input\": \"32 10\\r\\n\", \"output\": [\"360252438\"]}, {\"input\": \"128 119\\r\\n\", \"output\": [\"530767740\"]}, {\"input\": \"8 6\\r\\n\", \"output\": [\"1897056\"]}, {\"input\": \"8 5\\r\\n\", \"output\": [\"1757896\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"128 81\\r\\n\", \"output\": [\"710035809\"]}, {\"input\": \"256 197\\r\\n\", \"output\": [\"494437752\"]}, {\"input\": \"64 56\\r\\n\", \"output\": [\"291740751\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"109\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"80\"]}, {\"input\": \"256 35\\r\\n\", \"output\": [\"191720088\"]}, {\"input\": \"64 30\\r\\n\", \"output\": [\"129676638\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"16 11\\r\\n\", \"output\": [\"117354594\"]}, {\"input\": \"64 11\\r\\n\", \"output\": [\"554790222\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"80\"]}, {\"input\": \"256 74\\r\\n\", \"output\": [\"747135963\"]}, {\"input\": \"32 1\\r\\n\", \"output\": [\"261086313\"]}, {\"input\": \"64 6\\r\\n\", \"output\": [\"509425833\"]}, {\"input\": \"4 2\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"8 1\\r\\n\", \"output\": [\"6824\"]}, {\"input\": \"2 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"256 205\\r\\n\", \"output\": [\"353120823\"]}, {\"input\": \"256 192\\r\\n\", \"output\": [\"612152037\"]}, {\"input\": \"8 7\\r\\n\", \"output\": [\"4898872\"]}, {\"input\": \"256 21\\r\\n\", \"output\": [\"706116537\"]}, {\"input\": \"256 127\\r\\n\", \"output\": [\"708023862\"]}, {\"input\": \"8 5\\r\\n\", \"output\": [\"1757896\"]}, {\"input\": \"128 103\\r\\n\", \"output\": [\"254706039\"]}, {\"input\": \"8 8\\r\\n\", \"output\": [\"7593125\"]}, {\"input\": \"128 74\\r\\n\", \"output\": [\"27702486\"]}, {\"input\": \"16 16\\r\\n\", \"output\": [\"391464593\"]}, {\"input\": \"64 16\\r\\n\", \"output\": [\"383350905\"]}, {\"input\": \"32 14\\r\\n\", \"output\": [\"342079395\"]}, {\"input\": \"128 31\\r\\n\", \"output\": [\"739707108\"]}, {\"input\": \"4 1\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"32 19\\r\\n\", \"output\": [\"628771752\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"80\"]}, {\"input\": \"64 49\\r\\n\", \"output\": [\"156006018\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"64 56\\r\\n\", \"output\": [\"291740751\"]}, {\"input\": \"16 8\\r\\n\", \"output\": [\"428982705\"]}, {\"input\": \"8 2\\r\\n\", \"output\": [\"59808\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"109\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"80\"]}, {\"input\": \"16 5\\r\\n\", \"output\": [\"33900006\"]}, {\"input\": \"32 13\\r\\n\", \"output\": [\"647490480\"]}, {\"input\": \"64 22\\r\\n\", \"output\": [\"374020479\"]}, {\"input\": \"64 32\\r\\n\", \"output\": [\"135769095\"]}, {\"input\": \"8 5\\r\\n\", \"output\": [\"1757896\"]}, {\"input\": \"2 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"256 208\\r\\n\", \"output\": [\"580966092\"]}, {\"input\": \"8 3\\r\\n\", \"output\": [\"147224\"]}, {\"input\": \"64 13\\r\\n\", \"output\": [\"703150560\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"4 2\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"64 20\\r\\n\", \"output\": [\"104256117\"]}, {\"input\": \"32 22\\r\\n\", \"output\": [\"20119449\"]}, {\"input\": \"256 128\\r\\n\", \"output\": [\"569195676\"]}, {\"input\": \"256 256\\r\\n\", \"output\": [\"51933421\"]}]"}
{"prob_desc_description":"There have recently been elections in the zoo. Overall there were 7 main political parties: one of them is the Little Elephant Political Party, 6 other parties have less catchy names.Political parties find their number in the ballot highly important. Overall there are m possible numbers: 1,\u20092,\u2009...,\u2009m. Each of these 7 parties is going to be assigned in some way to exactly one number, at that, two distinct parties cannot receive the same number.The Little Elephant Political Party members believe in the lucky digits 4 and 7. They want to evaluate their chances in the elections. For that, they need to find out, how many correct assignments are there, such that the number of lucky digits in the Little Elephant Political Party ballot number is strictly larger than the total number of lucky digits in the ballot numbers of 6 other parties. Help the Little Elephant Political Party, calculate this number. As the answer can be rather large, print the remainder from dividing it by 1000000007 (109\u2009+\u20097).","prob_desc_output_spec":"In a single line print a single integer \u2014 the answer to the problem modulo 1000000007 (109\u2009+\u20097).","lang_cluster":"","src_uid":"656ed7b1b80de84d65a253e5d14d62a9","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","math","combinatorics","dp"],"prob_desc_created_at":"1356190200","prob_desc_sample_inputs":"[\"7\", \"8\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"A single line contains a single positive integer m (7\u2009\u2264\u2009m\u2009\u2264\u2009109) \u2014 the number of possible numbers in the ballot.","prob_desc_sample_outputs":"[\"0\", \"1440\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"7\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"1440\"]}, {\"input\": \"47\\r\\n\", \"output\": [\"907362803\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"40320\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"10080\"]}, {\"input\": \"11\\r\\n\", \"output\": [\"120960\"]}, {\"input\": \"25\\r\\n\", \"output\": [\"139536000\"]}, {\"input\": \"74\\r\\n\", \"output\": [\"257814864\"]}, {\"input\": \"128\\r\\n\", \"output\": [\"879893164\"]}, {\"input\": \"1000000000\\r\\n\", \"output\": [\"14594961\"]}, {\"input\": \"458754\\r\\n\", \"output\": [\"667496909\"]}, {\"input\": \"987549745\\r\\n\", \"output\": [\"206294274\"]}, {\"input\": \"15478459\\r\\n\", \"output\": [\"638813679\"]}, {\"input\": \"674810014\\r\\n\", \"output\": [\"550536983\"]}, {\"input\": \"245\\r\\n\", \"output\": [\"528398086\"]}, {\"input\": \"1000\\r\\n\", \"output\": [\"193577116\"]}, {\"input\": \"10000\\r\\n\", \"output\": [\"726889821\"]}, {\"input\": \"100000\\r\\n\", \"output\": [\"459307763\"]}, {\"input\": \"1000000\\r\\n\", \"output\": [\"638519268\"]}, {\"input\": \"100000000\\r\\n\", \"output\": [\"133127802\"]}, {\"input\": \"10000000\\r\\n\", \"output\": [\"994715261\"]}, {\"input\": \"54785\\r\\n\", \"output\": [\"118850209\"]}, {\"input\": \"68745844\\r\\n\", \"output\": [\"739902866\"]}, {\"input\": \"545794012\\r\\n\", \"output\": [\"829479797\"]}, {\"input\": \"301542785\\r\\n\", \"output\": [\"763583849\"]}, {\"input\": \"794512405\\r\\n\", \"output\": [\"90508418\"]}, {\"input\": \"30\\r\\n\", \"output\": [\"581454720\"]}, {\"input\": \"40\\r\\n\", \"output\": [\"771100852\"]}, {\"input\": \"44\\r\\n\", \"output\": [\"359621144\"]}, {\"input\": \"42\\r\\n\", \"output\": [\"831345485\"]}]"}
{"prob_desc_description":"Dima and Anya love playing different games. Now Dima has imagined a new game that he wants to play with Anya.Dima writes n pairs of integers on a piece of paper (li,\u2009ri) (1\u2009\u2264\u2009li\u2009<\u2009ri\u2009\u2264\u2009p). Then players take turns. On his turn the player can do the following actions:  choose the number of the pair i (1\u2009\u2264\u2009i\u2009\u2264\u2009n), such that ri\u2009-\u2009li\u2009>\u20092;  replace pair number i by pair  or by pair . Notation \u230ax\u230b means rounding down to the closest integer. The player who can't make a move loses.Of course, Dima wants Anya, who will move first, to win. That's why Dima should write out such n pairs of integers (li,\u2009ri) (1\u2009\u2264\u2009li\u2009<\u2009ri\u2009\u2264\u2009p), that if both players play optimally well, the first one wins. Count the number of ways in which Dima can do it. Print the remainder after dividing the answer by number 1000000007\u00a0(109\u2009+\u20097).Two ways are considered distinct, if the ordered sequences of the written pairs are distinct.","prob_desc_output_spec":"In a single line print the remainder after dividing the answer to the problem by number 1000000007\u00a0(109\u2009+\u20097).","lang_cluster":"","src_uid":"c03b6379e9d186874ac3d97c6968fbd0","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["games","dp"],"prob_desc_created_at":"1360769400","prob_desc_sample_inputs":"[\"2 2\", \"4 4\", \"100 1000\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":2600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains two integers n, p (1\u2009\u2264\u2009n\u2009\u2264\u20091000,\u20091\u2009\u2264\u2009p\u2009\u2264\u2009109). The numbers are separated by a single space.","prob_desc_sample_outputs":"[\"0\", \"520\", \"269568947\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"520\"]}, {\"input\": \"100 1000\\r\\n\", \"output\": [\"269568947\"]}, {\"input\": \"2 8\\r\\n\", \"output\": [\"490\"]}, {\"input\": \"5 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"10 5\\r\\n\", \"output\": [\"216185807\"]}, {\"input\": \"9 9\\r\\n\", \"output\": [\"719488449\"]}, {\"input\": \"3 5\\r\\n\", \"output\": [\"552\"]}, {\"input\": \"6 6\\r\\n\", \"output\": [\"8070484\"]}, {\"input\": \"2 8\\r\\n\", \"output\": [\"490\"]}, {\"input\": \"962 1470546\\r\\n\", \"output\": [\"328714137\"]}, {\"input\": \"943 26239573\\r\\n\", \"output\": [\"974583365\"]}, {\"input\": \"392 56984809\\r\\n\", \"output\": [\"712359417\"]}, {\"input\": \"154 3615545\\r\\n\", \"output\": [\"367576652\"]}, {\"input\": \"422 69042089\\r\\n\", \"output\": [\"667402747\"]}, {\"input\": \"896 18341523\\r\\n\", \"output\": [\"678908486\"]}, {\"input\": \"772 21564523\\r\\n\", \"output\": [\"306664512\"]}, {\"input\": \"913 75016434\\r\\n\", \"output\": [\"921346799\"]}, {\"input\": \"36 83987483\\r\\n\", \"output\": [\"926044206\"]}, {\"input\": \"812 50090227\\r\\n\", \"output\": [\"608714476\"]}, {\"input\": \"674 70617625\\r\\n\", \"output\": [\"460280412\"]}, {\"input\": \"712 94041605\\r\\n\", \"output\": [\"213840765\"]}, {\"input\": \"548 2908329\\r\\n\", \"output\": [\"19475477\"]}, {\"input\": \"758 57655784\\r\\n\", \"output\": [\"280962474\"]}, {\"input\": \"724 68159990\\r\\n\", \"output\": [\"103564821\"]}, {\"input\": \"779 37379061\\r\\n\", \"output\": [\"703004414\"]}, {\"input\": \"191 530497\\r\\n\", \"output\": [\"271739403\"]}, {\"input\": \"107 80835681\\r\\n\", \"output\": [\"410989771\"]}, {\"input\": \"265 21597009\\r\\n\", \"output\": [\"298439147\"]}, {\"input\": \"806 6923811\\r\\n\", \"output\": [\"497709154\"]}, {\"input\": \"371 30342101\\r\\n\", \"output\": [\"967521198\"]}, {\"input\": \"102 86546365\\r\\n\", \"output\": [\"329533568\"]}, {\"input\": \"630 4012333\\r\\n\", \"output\": [\"792227055\"]}, {\"input\": \"955 22071041\\r\\n\", \"output\": [\"939711836\"]}, {\"input\": \"967 2755057\\r\\n\", \"output\": [\"286009469\"]}, {\"input\": \"309 49646417\\r\\n\", \"output\": [\"862961049\"]}, {\"input\": \"627 62695452\\r\\n\", \"output\": [\"936496657\"]}, {\"input\": \"539 33557677\\r\\n\", \"output\": [\"932232256\"]}, {\"input\": \"930 79942654\\r\\n\", \"output\": [\"863722490\"]}, {\"input\": \"1000 100000000\\r\\n\", \"output\": [\"92326252\"]}, {\"input\": \"1000 200000000\\r\\n\", \"output\": [\"503494344\"]}, {\"input\": \"1000 199999999\\r\\n\", \"output\": [\"690144838\"]}, {\"input\": \"997 150000000\\r\\n\", \"output\": [\"200022425\"]}, {\"input\": \"750 199999900\\r\\n\", \"output\": [\"888244974\"]}, {\"input\": \"1000 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1000 1000000000\\r\\n\", \"output\": [\"317623986\"]}, {\"input\": \"750 1000000000\\r\\n\", \"output\": [\"324554228\"]}, {\"input\": \"4 1000000000\\r\\n\", \"output\": [\"433920973\"]}, {\"input\": \"1 1000000000\\r\\n\", \"output\": [\"327451602\"]}, {\"input\": \"1000 999999000\\r\\n\", \"output\": [\"474176509\"]}]"}
{"prob_desc_description":"Vova, the Ultimate Thule new shaman, wants to build a pipeline. As there are exactly n houses in Ultimate Thule, Vova wants the city to have exactly n pipes, each such pipe should be connected to the water supply. A pipe can be connected to the water supply if there's water flowing out of it. Initially Vova has only one pipe with flowing water. Besides, Vova has several splitters.A splitter is a construction that consists of one input (it can be connected to a water pipe) and x output pipes. When a splitter is connected to a water pipe, water flows from each output pipe. You can assume that the output pipes are ordinary pipes. For example, you can connect water supply to such pipe if there's water flowing out from it. At most one splitter can be connected to any water pipe.  The figure shows a 4-output splitter Vova has one splitter of each kind: with 2, 3, 4, ..., k outputs. Help Vova use the minimum number of splitters to build the required pipeline or otherwise state that it's impossible.Vova needs the pipeline to have exactly n pipes with flowing out water. Note that some of those pipes can be the output pipes of the splitters.","prob_desc_output_spec":"Print a single integer \u2014 the minimum number of splitters needed to build the pipeline. If it is impossible to build a pipeline with the given splitters, print -1.","lang_cluster":"","src_uid":"83bcfe32db302fbae18e8a95d89cf411","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","binary search"],"prob_desc_created_at":"1364025600","prob_desc_sample_inputs":"[\"4 3\", \"5 5\", \"8 4\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1700.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"0.4 seconds","prob_desc_input_spec":"The first line contains two space-separated integers n and k (1\u2009\u2264\u2009n\u2009\u2264\u20091018, 2\u2009\u2264\u2009k\u2009\u2264\u2009109). Please, do not use the %lld specifier to read or write 64-bit integers in \u0421++. It is preferred to use the cin, cout streams or the %I64d specifier.","prob_desc_sample_outputs":"[\"2\", \"1\", \"-1\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4 3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5 5\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"8 4\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"1000000000000000000 1000000000\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"499999998500000001 1000000000\\r\\n\", \"output\": [\"999955279\"]}, {\"input\": \"499999998500000000 1000000000\\r\\n\", \"output\": [\"999955279\"]}, {\"input\": \"499999999500000000 1000000000\\r\\n\", \"output\": [\"999999998\"]}, {\"input\": \"499999999500000001 1000000000\\r\\n\", \"output\": [\"999999999\"]}, {\"input\": \"525 34\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"223265034477 726990\\r\\n\", \"output\": [\"440662\"]}, {\"input\": \"15597035789572051 185473109\\r\\n\", \"output\": [\"128849771\"]}, {\"input\": \"499999999500000002 1000000000\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"1 1000000000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1000000000 2\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"462498979 204468265\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"2107921 542531\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"131 49\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"20171878992939541 200857557\\r\\n\", \"output\": [\"200853401\"]}, {\"input\": \"399812655947 894219\\r\\n\", \"output\": [\"893030\"]}, {\"input\": \"93 17\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"1000000000 999999999\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"100000000000000000 1000000000\\r\\n\", \"output\": [\"105572810\"]}]"}
{"prob_desc_description":"Special Agent Smart Beaver works in a secret research department of ABBYY. He's been working there for a long time and is satisfied with his job, as it allows him to eat out in the best restaurants and order the most expensive and exotic wood types there. The content special agent has got an important task: to get the latest research by British scientists on the English Language. These developments are encoded and stored in a large safe. The Beaver's teeth are strong enough, so the authorities assured that upon arriving at the place the beaver won't have any problems with opening the safe.And he finishes his aspen sprig and leaves for this important task. Of course, the Beaver arrived at the location without any problems, but alas. He can't open the safe with his strong and big teeth. At this point, the Smart Beaver get a call from the headquarters and learns that opening the safe with the teeth is not necessary, as a reliable source has sent the following information: the safe code consists of digits and has no leading zeroes. There also is a special hint, which can be used to open the safe. The hint is string s with the following structure:  if si = \"?\", then the digit that goes i-th in the safe code can be anything (between 0 to 9, inclusively);  if si is a digit (between 0 to 9, inclusively), then it means that there is digit si on position i in code;  if the string contains letters from \"A\" to \"J\", then all positions with the same letters must contain the same digits and the positions with distinct letters must contain distinct digits.  The length of the safe code coincides with the length of the hint. For example, hint \"?JGJ9\" has such matching safe code variants: \"51919\", \"55959\", \"12329\", \"93539\" and so on, and has wrong variants such as: \"56669\", \"00111\", \"03539\" and \"13666\".After receiving such information, the authorities change the plan and ask the special agents to work quietly and gently and not to try to open the safe by mechanical means, and try to find the password using the given hint.At a special agent school the Smart Beaver was the fastest in his platoon finding codes for such safes, but now he is not in that shape: the years take their toll ... Help him to determine the number of possible variants of the code to the safe, matching the given hint. After receiving this information, and knowing his own speed of entering codes, the Smart Beaver will be able to determine whether he will have time for tonight's show \"Beavers are on the trail\" on his favorite TV channel, or he should work for a sleepless night...","prob_desc_output_spec":"Print the number of codes that match the given hint.","lang_cluster":"","src_uid":"d3c10d1b1a17ad018359e2dab80d2b82","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["greedy"],"prob_desc_created_at":"1371042000","prob_desc_sample_inputs":"[\"AJ\", \"1?AA\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1100.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains string s \u2014 the hint to the safe code. String s consists of the following characters: ?, 0-9, A-J. It is guaranteed that the first character of string s doesn't equal to character 0. The input limits for scoring 30 points are (subproblem A1):    1\u2009\u2264\u2009|s|\u2009\u2264\u20095.  The input limits for scoring 100 points are (subproblems A1+A2):    1\u2009\u2264\u2009|s|\u2009\u2264\u2009105.  Here |s| means the length of string s.","prob_desc_sample_outputs":"[\"81\", \"100\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"AJ\\r\\n\", \"output\": [\"81\"]}, {\"input\": \"1?AA\\r\\n\", \"output\": [\"100\"]}, {\"input\": \"?\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"A\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"BBB?\\r\\n\", \"output\": [\"90\"]}, {\"input\": \"BC??\\r\\n\", \"output\": [\"8100\"]}, {\"input\": \"CC\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"CB?\\r\\n\", \"output\": [\"810\"]}, {\"input\": \"B??C?\\r\\n\", \"output\": [\"81000\"]}, {\"input\": \"BB?C?\\r\\n\", \"output\": [\"8100\"]}, {\"input\": \"?BCB?\\r\\n\", \"output\": [\"8100\"]}, {\"input\": \"?C\\r\\n\", \"output\": [\"90\"]}, {\"input\": \"??C?C\\r\\n\", \"output\": [\"9000\"]}, {\"input\": \"???2\\r\\n\", \"output\": [\"900\"]}, {\"input\": \"9???\\r\\n\", \"output\": [\"1000\"]}, {\"input\": \"GJH2?\\r\\n\", \"output\": [\"6480\"]}, {\"input\": \"7I9G4\\r\\n\", \"output\": [\"90\"]}, {\"input\": \"JG50?\\r\\n\", \"output\": [\"810\"]}, {\"input\": \"CDEFG\\r\\n\", \"output\": [\"27216\"]}, {\"input\": \"?1????4?1?6?12H1?6?9??F0?H??F3?9F50I???I?5?J832?8J4H57F???44??828??4?F???79H?59?I??2?F4???3?269?????4F?E1??E?9??5??85???H3??6I388?722???8F1H1??2?F?HJ?6?H????5??75??69?H14092218FG6??4?1F?F6??0?I??082?5IJ1EGI427H??J?808?J?99?J??????H130E?HGJE8F???0EF?2?13II...\", \"output\": [\"136080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...\"]}, {\"input\": \"8774???G?G8IIGI11?8??58?4??87?H3?0?I3875??HJ2?68GHH1???70II??JJ24853?I4246HG723???H7JJ2????H55?IIII6I??30?8?28476347?H??H????I38??4?I???76H3?428?2JJ6675??49??440?HH47???61IGJ?0J2??3??3?8??J72H??I?I??J?H38???G7?5??2?I31?HH?J?2??78?67930?JJH807?J7?5I0?6?4G?...\", \"output\": [\"504000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...\"]}, {\"input\": \"?750?9?464J?1C?J08???84?61?G211?364B9?6?H14??????J?C1CH36?8?B4?E??8???402915?4C???9?97??2B??D?89???5?6???3?JE?AB?4??83????0DC?I?BE?F0????026??I3??6B?609??F?G2?ABIH?D2?F??I?9G?7IC?9??GB??24?B57?4?71?74???CGF246?????4??56HD??J1??CH63?CB?5?1D??F?7FH8?590?D?H...\", \"output\": [\"326592000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...\"]}, {\"input\": \"27???A?FAA??????A?????B????????????64?E7?????????????????????F?????C?2??????????D???5???2?A??D?????????????????2???????????9??9?3D???7???????D????D??1?????C?????C?????D?????????4????????????????E8???4C????????C?????????B?????9F?0???????CC??73??8??5???3???...\", \"output\": [\"604800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...\"]}, {\"input\": \"??4?5????C??????6?D??4?2???0???????A??B?????????????F???B?????H37F?????9?????2????????????????4?????????B???F0?0????????FF490?????0???????????2?????G??????7????F????4?????C?????????F???2F?????????????0?C??6?????8????B???7???????G????????0??????D????????1?...\", \"output\": 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{"prob_desc_description":"Smart Beaver is careful about his appearance and pays special attention to shoes so he has a huge number of pairs of shoes from the most famous brands of the forest. He's trying to handle his shoes carefully so that each pair stood side by side. But by the end of the week because of his very active lifestyle in his dressing room becomes a mess.Smart Beaver from ABBYY is not only the brightest beaver in the area, but he also is the most domestically oriented. For example, on Mondays the Smart Beaver cleans everything in his home.It's Monday morning. Smart Beaver does not want to spend the whole day cleaning, besides, there is much in to do and it\u2019s the gym day, so he wants to clean up as soon as possible. Now the floors are washed, the dust is wiped off \u2014 it\u2019s time to clean up in the dressing room. But as soon as the Smart Beaver entered the dressing room, all plans for the day were suddenly destroyed: chaos reigned there and it seemed impossible to handle, even in a week. Give our hero some hope: tell him what is the minimum number of shoes need to change the position to make the dressing room neat.The dressing room is rectangular and is divided into n\u2009\u00d7\u2009m equal squares, each square contains exactly one shoe. Each pair of shoes has a unique number that is integer from 1 to , more formally, a square with coordinates (i,\u2009j) contains an integer number of the pair which is lying on it. The Smart Beaver believes that the dressing room is neat only when each pair of sneakers lies together. We assume that the pair of sneakers in squares (i1,\u2009j1) and (i2,\u2009j2) lies together if |i1\u2009-\u2009i2|\u2009+\u2009|j1\u2009-\u2009j2|\u2009=\u20091.","prob_desc_output_spec":"Print exactly one integer \u2014 the minimum number of the sneakers that need to change their location.","lang_cluster":"","src_uid":"1f0e8bbd5bf4fcdea927fbb505a8949b","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["flows"],"prob_desc_created_at":"1371042000","prob_desc_sample_inputs":"[\"2 3\\n1 1 2\\n2 3 3\", \"3 4\\n1 3 2 6\\n2 1 5 6\\n4 4 5 3\"]","prob_desc_notes":"Note   The second sample.  ","exec_outcome":"","difficulty":2200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"4 seconds","prob_desc_input_spec":"The first line contains two space-separated integers n and m. They correspond to the dressing room size. Next n lines contain m space-separated integers each. Those numbers describe the dressing room. Each number corresponds to a snicker.  It is guaranteed that:    n\u00b7m is even.  All numbers, corresponding to the numbers of pairs of shoes in the dressing room, will lie between 1 and .  Each number from 1 to  will occur exactly twice.  The input limits for scoring 30 points are (subproblem C1):    2\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20098.  The input limits for scoring 100 points are (subproblems C1+C2):    2\u2009\u2264\u2009n,\u2009m\u2009\u2264\u200980. 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{"prob_desc_description":"Iahub got bored, so he invented a game to be played on paper. He writes n integers a1,\u2009a2,\u2009...,\u2009an. Each of those integers can be either 0 or 1. He's allowed to do exactly one move: he chooses two indices i and j (1\u2009\u2264\u2009i\u2009\u2264\u2009j\u2009\u2264\u2009n) and flips all values ak for which their positions are in range [i,\u2009j] (that is i\u2009\u2264\u2009k\u2009\u2264\u2009j). Flip the value of x means to apply operation x\u2009=\u20091 - x.The goal of the game is that after exactly one move to obtain the maximum number of ones. Write a program to solve the little game of Iahub.","prob_desc_output_spec":"Print an integer \u2014 the maximal number of 1s that can be obtained after exactly one move. ","lang_cluster":"","src_uid":"9b543e07e805fe1dd8fa869d5d7c8b99","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","dp","implementation"],"prob_desc_created_at":"1372941000","prob_desc_sample_inputs":"[\"5\\n1 0 0 1 0\", \"4\\n1 0 0 1\"]","prob_desc_notes":"NoteIn the first case, flip the segment from 2 to 5 (i\u2009=\u20092,\u2009j\u2009=\u20095). That flip changes the sequence, it becomes: [1 1 1 0 1]. So, it contains four ones. There is no way to make the whole sequence equal to [1 1 1 1 1].In the second case, flipping only the second and the third element (i\u2009=\u20092,\u2009j\u2009=\u20093) will turn all numbers into 1.","exec_outcome":"","difficulty":1200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line of the input contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100). In the second line of the input there are n integers: a1,\u2009a2,\u2009...,\u2009an. It is guaranteed that each of those n values is either 0 or 1.","prob_desc_sample_outputs":"[\"4\", \"4\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"5\\r\\n1 0 0 1 0\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"4\\r\\n1 0 0 1\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"1\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1\\r\\n0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"8\\r\\n1 0 0 0 1 0 0 0\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"18\\r\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"23\\r\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"100\\r\\n0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1\\r\\n\", \"output\": [\"70\"]}, {\"input\": \"100\\r\\n0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1\\r\\n\", \"output\": [\"60\"]}, {\"input\": \"18\\r\\n0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"25\\r\\n0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"55\\r\\n0 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1\\r\\n\", \"output\": [\"36\"]}, {\"input\": \"75\\r\\n1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0\\r\\n\", \"output\": [\"44\"]}, {\"input\": \"100\\r\\n0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1\\r\\n\", \"output\": [\"61\"]}, {\"input\": \"100\\r\\n0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0\\r\\n\", \"output\": [\"61\"]}, {\"input\": \"100\\r\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\r\\n\", \"output\": [\"100\"]}, {\"input\": \"100\\r\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"100\\r\\n0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 0\\r\\n\", \"output\": [\"61\"]}, {\"input\": \"100\\r\\n0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1\\r\\n\", \"output\": [\"59\"]}, {\"input\": \"99\\r\\n1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1\\r\\n\", \"output\": [\"61\"]}, {\"input\": \"2\\r\\n1 1\\r\\n\", \"output\": [\"1\"]}]"}
{"prob_desc_description":"Gerald is very particular to eight point sets. He thinks that any decent eight point set must consist of all pairwise intersections of three distinct integer vertical straight lines and three distinct integer horizontal straight lines, except for the average of these nine points. In other words, there must be three integers x1,\u2009x2,\u2009x3 and three more integers y1,\u2009y2,\u2009y3, such that x1\u2009<\u2009x2\u2009<\u2009x3, y1\u2009<\u2009y2\u2009<\u2009y3 and the eight point set consists of all points (xi,\u2009yj) (1\u2009\u2264\u2009i,\u2009j\u2009\u2264\u20093), except for point (x2,\u2009y2).You have a set of eight points. Find out if Gerald can use this set?","prob_desc_output_spec":"In a single line print word \"respectable\", if the given set of points corresponds to Gerald's decency rules, and \"ugly\" otherwise.","lang_cluster":"","src_uid":"f3c96123334534056f26b96f90886807","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["sortings"],"prob_desc_created_at":"1374913800","prob_desc_sample_inputs":"[\"0 0\\n0 1\\n0 2\\n1 0\\n1 2\\n2 0\\n2 1\\n2 2\", \"0 0\\n1 0\\n2 0\\n3 0\\n4 0\\n5 0\\n6 0\\n7 0\", \"1 1\\n1 2\\n1 3\\n2 1\\n2 2\\n2 3\\n3 1\\n3 2\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1400.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The input consists of eight lines, the i-th line contains two space-separated integers xi and yi (0\u2009\u2264\u2009xi,\u2009yi\u2009\u2264\u2009106). You do not have any other conditions for these points.","prob_desc_sample_outputs":"[\"respectable\", \"ugly\", \"ugly\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"0 0\\r\\n0 1\\r\\n0 2\\r\\n1 0\\r\\n1 2\\r\\n2 0\\r\\n2 1\\r\\n2 2\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"0 0\\r\\n1 0\\r\\n2 0\\r\\n3 0\\r\\n4 0\\r\\n5 0\\r\\n6 0\\r\\n7 0\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"1 1\\r\\n1 2\\r\\n1 3\\r\\n2 1\\r\\n2 2\\r\\n2 3\\r\\n3 1\\r\\n3 2\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"0 0\\r\\n0 0\\r\\n0 0\\r\\n0 0\\r\\n0 0\\r\\n0 0\\r\\n0 0\\r\\n0 0\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"1000000 1000000\\r\\n1000000 999999\\r\\n1000000 999998\\r\\n999999 1000000\\r\\n999999 999998\\r\\n999998 1000000\\r\\n999998 999999\\r\\n999998 999998\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"0 0\\r\\n1 0\\r\\n0 1\\r\\n1 1\\r\\n0 2\\r\\n1 2\\r\\n0 3\\r\\n1 3\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"0 0\\r\\n2 1\\r\\n1 0\\r\\n0 2\\r\\n2 2\\r\\n1 0\\r\\n2 1\\r\\n0 2\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"791649 383826\\r\\n10864 260573\\r\\n504506 185571\\r\\n899991 511500\\r\\n503197 876976\\r\\n688727 569035\\r\\n343255 961333\\r\\n439355 759581\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"750592 335292\\r\\n226387 434036\\r\\n299976 154633\\r\\n593197 600998\\r\\n62014 689355\\r\\n566268 571630\\r\\n381455 222817\\r\\n50555 288617\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"716334 42808\\r\\n211710 645370\\r\\n515258 96837\\r\\n14392 766713\\r\\n439265 939607\\r\\n430602 918570\\r\\n845044 187545\\r\\n957977 441674\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"337873 813442\\r\\n995185 863182\\r\\n375545 263618\\r\\n310042 130019\\r\\n358572 560779\\r\\n305725 729179\\r\\n377381 267545\\r\\n41376 312626\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"803784 428886\\r\\n995691 328351\\r\\n211844 386054\\r\\n375491 74073\\r\\n692402 660275\\r\\n366073 536431\\r\\n485832 941417\\r\\n96032 356022\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"999231 584954\\r\\n246553 267441\\r\\n697080 920011\\r\\n173593 403511\\r\\n58535 101909\\r\\n131124 924182\\r\\n779830 204560\\r\\n684576 533111\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"666888 741208\\r\\n685852 578759\\r\\n211123 826453\\r\\n244759 601804\\r\\n670436 748132\\r\\n976425 387060\\r\\n587850 804554\\r\\n430242 805528\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"71768 834717\\r\\n13140 834717\\r\\n13140 991083\\r\\n880763 386898\\r\\n71768 386898\\r\\n880763 991083\\r\\n880763 834717\\r\\n13140 386898\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"941532 913025\\r\\n941532 862399\\r\\n686271 913025\\r\\n686271 862399\\r\\n686271 461004\\r\\n941532 461004\\r\\n908398 862399\\r\\n908398 913025\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"251515 680236\\r\\n761697 669947\\r\\n251515 669947\\r\\n761697 680236\\r\\n251515 476629\\r\\n761697 476629\\r\\n453296 669947\\r\\n453296 476629\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"612573 554036\\r\\n195039 655769\\r\\n472305 655769\\r\\n612573 655769\\r\\n195039 160740\\r\\n472305 160740\\r\\n472305 554036\\r\\n612573 160740\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"343395 788566\\r\\n171702 674699\\r\\n171702 788566\\r\\n971214 788566\\r\\n343395 9278\\r\\n971214 9278\\r\\n343395 674699\\r\\n971214 674699\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"38184 589856\\r\\n281207 447136\\r\\n281207 42438\\r\\n38184 42438\\r\\n38184 447136\\r\\n880488 589856\\r\\n281207 589856\\r\\n880488 42438\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"337499 89260\\r\\n337499 565883\\r\\n603778 89260\\r\\n603778 565883\\r\\n234246 89260\\r\\n603778 17841\\r\\n337499 17841\\r\\n234246 17841\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"180952 311537\\r\\n180952 918548\\r\\n126568 918548\\r\\n180952 268810\\r\\n732313 918548\\r\\n126568 311537\\r\\n126568 268810\\r\\n732313 311537\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"323728 724794\\r\\n265581 165113\\r\\n323728 146453\\r\\n265581 146453\\r\\n591097 146453\\r\\n265581 724794\\r\\n323728 165113\\r\\n591097 165113\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"642921 597358\\r\\n922979 597358\\r\\n127181 616833\\r\\n642921 828316\\r\\n922979 828316\\r\\n127181 597358\\r\\n922979 616833\\r\\n127181 828316\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"69586 260253\\r\\n74916 203798\\r\\n985457 203798\\r\\n74916 943932\\r\\n985457 943932\\r\\n69586 943932\\r\\n985457 260253\\r\\n69586 203798\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"57930 637387\\r\\n883991 573\\r\\n57930 573\\r\\n57930 499963\\r\\n399327 573\\r\\n399327 637387\\r\\n883991 637387\\r\\n883991 499963\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"52820 216139\\r\\n52820 999248\\r\\n290345 216139\\r\\n290345 999248\\r\\n308639 216139\\r\\n308639 999248\\r\\n52820 477113\\r\\n308639 477113\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"581646 464672\\r\\n493402 649074\\r\\n581646 649074\\r\\n214619 649074\\r\\n581646 252709\\r\\n214619 252709\\r\\n214619 464672\\r\\n493402 252709\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"787948 77797\\r\\n421941 615742\\r\\n421941 77797\\r\\n400523 77797\\r\\n400523 111679\\r\\n787948 615742\\r\\n400523 615742\\r\\n787948 111679\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"583956 366985\\r\\n759621 567609\\r\\n756846 567609\\r\\n759621 176020\\r\\n583956 567609\\r\\n583956 176020\\r\\n759621 366985\\r\\n756846 176020\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"0 50000\\r\\n0 0\\r\\n0 1000000\\r\\n50000 0\\r\\n50000 1000000\\r\\n1000000 0\\r\\n1000000 50000\\r\\n1000000 1000000\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"0 8\\r\\n0 9\\r\\n0 10\\r\\n1 8\\r\\n3 8\\r\\n3 8\\r\\n3 9\\r\\n3 10\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"0 1\\r\\n0 1\\r\\n0 2\\r\\n1 1\\r\\n1 2\\r\\n2 1\\r\\n2 1\\r\\n2 2\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"1 2\\r\\n1 3\\r\\n1 4\\r\\n2 2\\r\\n2 4\\r\\n4 2\\r\\n4 2\\r\\n4 4\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"0 0\\r\\n0 1\\r\\n0 2\\r\\n0 0\\r\\n1 2\\r\\n2 0\\r\\n2 1\\r\\n2 2\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"0 0\\r\\n0 0\\r\\n0 0\\r\\n1 1\\r\\n1 1\\r\\n2 2\\r\\n2 2\\r\\n2 2\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"0 0\\r\\n0 0\\r\\n0 2\\r\\n1 1\\r\\n1 2\\r\\n2 0\\r\\n2 1\\r\\n2 2\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"0 0\\r\\n0 1\\r\\n0 3\\r\\n1 0\\r\\n1 3\\r\\n2 0\\r\\n2 2\\r\\n2 3\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"0 0\\r\\n0 1\\r\\n0 2\\r\\n1 0\\r\\n1 2\\r\\n3 0\\r\\n3 1\\r\\n3 2\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"1 1\\r\\n1 2\\r\\n1 5\\r\\n2 1\\r\\n2 5\\r\\n5 1\\r\\n5 2\\r\\n5 5\\r\\n\", \"output\": [\"respectable\"]}, {\"input\": \"1 1\\r\\n1 2\\r\\n1 2\\r\\n2 3\\r\\n2 1\\r\\n3 3\\r\\n3 1\\r\\n3 3\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"0 0\\r\\n0 0\\r\\n1 0\\r\\n0 1\\r\\n2 1\\r\\n1 2\\r\\n2 2\\r\\n2 2\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"1 1\\r\\n1 1\\r\\n1 3\\r\\n2 1\\r\\n2 3\\r\\n3 2\\r\\n3 2\\r\\n3 3\\r\\n\", \"output\": [\"ugly\"]}, {\"input\": \"1 0\\r\\n1 0\\r\\n1 0\\r\\n2 3\\r\\n2 3\\r\\n3 4\\r\\n3 4\\r\\n3 4\\r\\n\", \"output\": [\"ugly\"]}]"}
{"prob_desc_description":"Iahub and his friend Floyd have started painting a wall. Iahub is painting the wall red and Floyd is painting it pink. You can consider the wall being made of a very large number of bricks, numbered 1, 2, 3 and so on. Iahub has the following scheme of painting: he skips x\u2009-\u20091 consecutive bricks, then he paints the x-th one. That is, he'll paint bricks x, 2\u00b7x, 3\u00b7x and so on red. Similarly, Floyd skips y\u2009-\u20091 consecutive bricks, then he paints the y-th one. Hence he'll paint bricks y, 2\u00b7y, 3\u00b7y and so on pink.After painting the wall all day, the boys observed that some bricks are painted both red and pink. Iahub has a lucky number a and Floyd has a lucky number b. Boys wonder how many bricks numbered no less than a and no greater than b are painted both red and pink. This is exactly your task: compute and print the answer to the question. ","prob_desc_output_spec":"Output a single integer \u2014 the number of bricks numbered no less than a and no greater than b that are painted both red and pink.","lang_cluster":"","src_uid":"c7aa8a95d5f8832015853cffa1374c48","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math"],"prob_desc_created_at":"1377876600","prob_desc_sample_inputs":"[\"2 3 6 18\"]","prob_desc_notes":"NoteLet's look at the bricks from a to b (a\u2009=\u20096,\u2009b\u2009=\u200918). The bricks colored in red are numbered 6, 8, 10, 12, 14, 16, 18. The bricks colored in pink are numbered 6, 9, 12, 15, 18. The bricks colored in both red and pink are numbered with 6, 12 and 18. ","exec_outcome":"","difficulty":1200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The input will have a single line containing four integers in this order: x, y, a, b. (1\u2009\u2264\u2009x,\u2009y\u2009\u2264\u20091000, 1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u20092\u00b7109, a\u2009\u2264\u2009b).","prob_desc_sample_outputs":"[\"3\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 3 6 18\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"4 6 20 201\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"15 27 100 10000\\r\\n\", \"output\": [\"74\"]}, {\"input\": \"105 60 3456 78910\\r\\n\", \"output\": [\"179\"]}, {\"input\": \"1 1 1000 100000\\r\\n\", \"output\": [\"99001\"]}, {\"input\": \"3 2 5 5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"555 777 1 1000000\\r\\n\", \"output\": [\"257\"]}, {\"input\": \"1000 1000 1 32323\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"45 125 93451125 100000000\\r\\n\", \"output\": [\"5821\"]}, {\"input\": \"101 171 1 1000000000\\r\\n\", \"output\": [\"57900\"]}, {\"input\": \"165 255 69696 1000000000\\r\\n\", \"output\": [\"356482\"]}, {\"input\": \"555 777 666013 1000000000\\r\\n\", \"output\": [\"257229\"]}, {\"input\": \"23 46 123321 900000000\\r\\n\", \"output\": [\"19562537\"]}, {\"input\": \"321 123 15 1000000\\r\\n\", \"output\": [\"75\"]}, {\"input\": \"819 1000 9532 152901000\\r\\n\", \"output\": [\"186\"]}, {\"input\": \"819 1000 10000 1000000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 2 2 1000003\\r\\n\", \"output\": [\"500001\"]}, {\"input\": \"1 1 1 1000000000\\r\\n\", \"output\": [\"1000000000\"]}, {\"input\": \"10 15 69 195610342\\r\\n\", \"output\": [\"6520342\"]}, {\"input\": \"2 1 1 1000000000\\r\\n\", \"output\": [\"500000000\"]}, {\"input\": \"1000 1000 1 20\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 1 1 2000000000\\r\\n\", \"output\": [\"2000000000\"]}, {\"input\": \"1 2 1 2000000000\\r\\n\", \"output\": [\"1000000000\"]}, {\"input\": \"2 1 1 2000000000\\r\\n\", \"output\": [\"1000000000\"]}, {\"input\": \"2 3 1 1000000000\\r\\n\", \"output\": [\"166666666\"]}, {\"input\": \"2 3 1 2000000000\\r\\n\", \"output\": [\"333333333\"]}, {\"input\": \"3 7 1 1000000000\\r\\n\", \"output\": [\"47619047\"]}, {\"input\": \"1 1 1000000000 2000000000\\r\\n\", \"output\": [\"1000000001\"]}, {\"input\": \"2 2 1 2000000000\\r\\n\", \"output\": [\"1000000000\"]}, {\"input\": \"1 1 2 2000000000\\r\\n\", \"output\": [\"1999999999\"]}, {\"input\": \"3 2 1 2000000000\\r\\n\", \"output\": [\"333333333\"]}, {\"input\": \"1 1 2000000000 2000000000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 3 7 7\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 3 3 7\\r\\n\", \"output\": [\"2\"]}]"}
{"prob_desc_description":"Mad scientist Mike is busy carrying out experiments in chemistry. Today he will attempt to join three atoms into one molecule.A molecule consists of atoms, with some pairs of atoms connected by atomic bonds. Each atom has a valence number \u2014 the number of bonds the atom must form with other atoms. An atom can form one or multiple bonds with any other atom, but it cannot form a bond with itself. The number of bonds of an atom in the molecule must be equal to its valence number.  Mike knows valence numbers of the three atoms. Find a molecule that can be built from these atoms according to the stated rules, or determine that it is impossible.","prob_desc_output_spec":"If such a molecule can be built, print three space-separated integers \u2014 the number of bonds between the 1-st and the 2-nd, the 2-nd and the 3-rd, the 3-rd and the 1-st atoms, correspondingly. If there are multiple solutions, output any of them. If there is no solution, print \"Impossible\" (without the quotes).","lang_cluster":"","src_uid":"b3b986fddc3770fed64b878fa42ab1bc","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","math","graphs"],"prob_desc_created_at":"1379172600","prob_desc_sample_inputs":"[\"1 1 2\", \"3 4 5\", \"4 1 1\"]","prob_desc_notes":"NoteThe first sample corresponds to the first figure. There are no bonds between atoms 1 and 2 in this case.The second sample corresponds to the second figure. There is one or more bonds between each pair of atoms.The third sample corresponds to the third figure. There is no solution, because an atom cannot form bonds with itself.The configuration in the fourth figure is impossible as each atom must have at least one atomic bond.","exec_outcome":"","difficulty":1200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The single line of the input contains three space-separated integers a, b and c (1\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u2009106) \u2014 the valence numbers of the given atoms.","prob_desc_sample_outputs":"[\"0 1 1\", \"1 3 2\", \"Impossible\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1 1 2\\r\\n\", \"output\": [\"0 1 1\"]}, {\"input\": \"3 4 5\\r\\n\", \"output\": [\"1 3 2\"]}, {\"input\": \"4 1 1\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"1 1 1\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"1000000 1000000 1000000\\r\\n\", \"output\": [\"500000 500000 500000\"]}, {\"input\": \"3 11 8\\r\\n\", \"output\": [\"3 8 0\"]}, {\"input\": \"8 5 12\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"1000000 500000 1\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"1000000 500000 2\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"2 2 2\\r\\n\", \"output\": [\"1 1 1\"]}, {\"input\": \"3 3 3\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"4 4 4\\r\\n\", \"output\": [\"2 2 2\"]}, {\"input\": \"2 4 2\\r\\n\", \"output\": [\"2 2 0\"]}, {\"input\": \"10 5 14\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"10 5 15\\r\\n\", \"output\": [\"0 5 10\"]}, {\"input\": \"10 4 16\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"3 3 6\\r\\n\", \"output\": [\"0 3 3\"]}, {\"input\": \"9 95 90\\r\\n\", \"output\": [\"7 88 2\"]}, {\"input\": \"3 5 8\\r\\n\", \"output\": [\"0 5 3\"]}, {\"input\": \"5 8 13\\r\\n\", \"output\": [\"0 8 5\"]}, {\"input\": \"6 1 5\\r\\n\", \"output\": [\"1 0 5\"]}, {\"input\": \"59 54 56\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"246 137 940\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"7357 3578 9123\\r\\n\", \"output\": [\"906 2672 6451\"]}, {\"input\": \"93952 49553 83405\\r\\n\", \"output\": [\"30050 19503 63902\"]}, {\"input\": \"688348 726472 442198\\r\\n\", \"output\": [\"486311 240161 202037\"]}, {\"input\": \"602752 645534 784262\\r\\n\", \"output\": [\"232012 413522 370740\"]}, {\"input\": \"741349 48244 642678\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"655754 418251 468390\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"310703 820961 326806\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"1 1 3\\r\\n\", \"output\": [\"Impossible\"]}, {\"input\": \"5 1 4\\r\\n\", \"output\": [\"1 0 4\"]}]"}
{"prob_desc_description":"In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence BDF is a subsequence of ABCDEF. A substring of a string is a continuous subsequence of the string. For example, BCD is a substring of ABCDEF.You are given two strings s1, s2 and another string called virus. Your task is to find the longest common subsequence of s1 and s2, such that it doesn't contain virus as a substring.","prob_desc_output_spec":"Output the longest common subsequence of s1 and s2 without virus as a substring. If there are multiple answers, any of them will be accepted.  If there is no valid common subsequence, output 0.","lang_cluster":"","src_uid":"391c2abbe862139733fcb997ba1629b8","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"512 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp","strings"],"prob_desc_created_at":"1379691000","prob_desc_sample_inputs":"[\"AJKEQSLOBSROFGZ\\nOVGURWZLWVLUXTH\\nOZ\", \"AA\\nA\\nA\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":2000.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"3 seconds","prob_desc_input_spec":"The input contains three strings in three separate lines: s1, s2 and virus (1\u2009\u2264\u2009|s1|,\u2009|s2|,\u2009|virus|\u2009\u2264\u2009100). Each string consists only of uppercase English letters.","prob_desc_sample_outputs":"[\"ORZ\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"AJKEQSLOBSROFGZ\\r\\nOVGURWZLWVLUXTH\\r\\nOZ\\r\\n\", \"output\": [\"OGZ\", \"ORZ\"]}, {\"input\": \"AA\\r\\nA\\r\\nA\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"PWBJTZPQHA\\r\\nZJMKLWSROQ\\r\\nUQ\\r\\n\", \"output\": [\"WQ\", \"ZQ\"]}, {\"input\": \"QNHRPFYMAAPJDUHBAEXNEEZSTMYHVGQPYKNMVKMBVSVLIYGUVMJHEFLJEPIWFHSLISTGOKRXNMSCXYKMAXBPKCOCNTIRPCUEPHXM\\r\\nRRFCZUGFDRKKMQTOETNELXMEWGOCDHFKIXOPVHHEWTCDNXVFKFKTKNWKEIKTCMHMHDNCLLVQSGKHBCDDYVVVQIRPZEOPUGQUGRHH\\r\\nR\\r\\n\", \"output\": [\"FUENEMGKIVHEFEIHLSGKBCIPEPH\", \"FDENEMGKIVHEWFTKNMCKBCIPEPH\", \"FMENEEHKIVHEFEIHLSGKCYPOPUH\", \"QNHFPHEXNETMHMHLLSGKCYPOPUH\", \"QNHFPHETVKNKMMHLLSGKBCIPEPH\", \"FDENEMGKIVHEFEIHLSGKCYPOPUH\"]}, {\"input\": \"CGPWTAPEVBTGANLCLVSHQIIKHDPVUHRSQPXHSNYAHPGBECICFQYDFRTRELLLEDZYWJSLOBSKDGRRDHNRRGIXAMEBGFJJTEIGUGRU\\r\\nHAWYVKRRBEIWNOGYMIYQXDCFXMMCSAYSOXQFHHIFRRCJRAWHLDDHHHAKHXVKCVPBFGGEXUKWTFWMOUUGMXTSBUTHXCJCWHCQQTYQ\\r\\nANKFDWLYSX\\r\\n\", \"output\": [\"WVBGIQXSYHIFRRWLDDHXBGEUGU\", \"WVBNIQXSYHIFRRJLDDHXBFGUGU\", \"AVBIIQXSAHIFRRWLDDHXBFGUGU\", \"WVBGCSSQHHIFRRWLDDHXBGFUGU\", \"AVBNIQXSAHIFRRJLDDHABFGUGU\", \"WVBNIDXSYHIFRRWLDDHXBGFUGU\"]}, {\"input\": \"AUNBEKNURNUPHXQYKUTAHCOLMPRQZZTVDUYCTNIRACQQTQAIDTAWJXBUTIZUASDIJZWLHAQVGCAHKTZMXSDVVWAIGQEALRFKFYTT\\r\\nQBVRFKPKLYZLYNRFTRJZZQEYAEKPFXVICUVFVQSDENBJYYNCFTOZHULSWJQTNELYLKCZTGHOARDCFXBXQGGSQIVUCJVNGFZEEZQE\\r\\nN\\r\\n\", \"output\": [\"BKPYTRZZVICQDJTZUSJZHAQGSVVGQE\", \"BRPKLZYTRQAXIUSDJZWLHACXSVVGQE\", \"BRPKLRZZYACQDBTZUSWLHACXSVVGQE\", \"BRPKLRZZYICQDJTZUSJZHAQGSVVGQE\", \"BKPKLRZZVICQDJTZUSJZHAQGSVVGQE\"]}, {\"input\": \"BGIIURZTEUJJULBWKHDQBRFGEUOMQSREOTILICRSBUHBGTSRDHKVDDEBVHGMHXUVFJURSMFDJOOOWCYPJDVRVKLDHICPNKTBFXDJ\\r\\nXOADNTKNILGNHHBNFYNDWUNXBGDFUKUVHLPDOGOYRMOTAQELLRMHFAQEOXFWGAQUROVUSWOAWFRVIRJQVXPCXLSCQLCUWKBZUFQP\\r\\nYVF\\r\\n\", \"output\": [\"TLBWKHDGOROTLRHEGUVUSOWVRVLCKBF\", \"ILBWKHDGOMQELRHEGUVUSOWVRVLCKBF\", \"TLBWKHDGOROTLRMHXFUROOWVRVLCKBF\", \"TLBWKHDGOROTLRMHXFURSOWVRVLCKBF\"]}, {\"input\": \"AXBPBDEYIYKKCZBTLKBUNEQLCXXLKIUTOOATYDXYYQCLFAXAEIGTFMNTTQKCQRMEEFRYVYXAOLMUQNPJBMFBUGVXFZAJSBXWALSI\\r\\nVWFONLLKSHGHHQSFBBFWTXAITPUKNDANOCLMNFTAAMJVDLXYPILPCJCFWTNBQWEOMMXHRYHEGBJIVSXBBGQKXRIYNZFIWSZPPUUM\\r\\nPPKKLHXWWT\\r\\n\", \"output\": [\"BBITKNCLTADXYCFTNQMRYVXBBGXFWS\", \"BBITUNCLTADXYLFTNQERYVXBBGXZWS\", \"BBITKNCLTADXYCFTNQMRYVXBBGXZWS\"]}, {\"input\": \"XKTAOCPCVMIOGCQKPENDKIZRZBZVRTBTGCDRQUIMVHABDIHSCGWPUTQKLPBOXAYICPWJBFLFSEPERGJZHRINEHQMYTOTKLCQCSMZ\\r\\nAITFIOUTUVZLSSIYWXSYTQMFLICCXOFSACHTKGPXRHRCGXFZXPYWKWPUOIDNEEZOKMOUYGVUJRQTIRQFCSBCWXVFCIAOLZDGENNI\\r\\nDBHOIORVCPNXCDOJKSYYIENQRJGZFHOWBYQIITMTVWXRMAMYILTHBBAJRJELWMIZOZBGPDGSTIRTQIILJRYICMUQTUAFKDYGECPY\\r\\n\", \"output\": [\"AITTUVSWTQLICFSPRGZINEMOTQCSZ\", \"TOVMIOCKGRHCGWPUOIEEGJRQTQCSZ\", \"TOVMIOCKPRRCGWPUOIEEGJRQTQCSZ\", \"AIITUVSWTQLICFSPRGZINEMYTQCSZ\", \"AIITUVSWTQLICFSPRHRINEMYTQCSZ\"]}, {\"input\": \"UNGXODEEINVYVPHYVGSWPIPFMFLZJYRJIPCUSWVUDLLSLRPJJFWCUOYDUGXBRKWPARGLXFJCNNFUIGEZUCTPFYUIMQMJLQHTIVPO\\r\\nBWDEGORKXYCXIDWZKGFCUYIDYLTWLCDBUVHPAPFLIZPEUINQSTNRAOVYKZCKFWIJQVLSVCGLTCOEMAYRCDVVQWQENTWZALWUKKKA\\r\\nXDGPZXADAFCHKILONSXFGRHIQVMIYWUTJUPCCEKYQVYAENRHVWERJSNPVEMRYSZGYBNTQLIFKFISKZJQIQQGSKVGCNMPNIJDRTXI\\r\\n\", \"output\": [\"GODIYVHPPFLZPUSWVLSLCOYDWALU\", \"GODIYVHPPFLIPUSROYKFJCGTMQQT\", \"GXDIYVHPPFLIPUSROYKCFICTMQQT\", \"GODIYVHPPFLIPUSROYKCFICTMQQT\", \"GXDIYVHPPFLZPUSWVLSLCOYDWALU\", \"GXDIYVHPPFLZPUSROYKWGLCECQQT\"]}, {\"input\": \"KOROXDDWEUVYWJIXSFPEJFYZJDDUXISOFJTIFJSBTWIJQHMTQWLAGGMXTFALRXYCMGZNKYQRCDVTPRQDBAALTWAXTNLDPYWNSFKE\\r\\nNHZGRZFMFQGSAYOJTFKMMUPOOQXWCPPAIVRJHINJPHXTTBWRIYNOHMJKBBGXVXYZDBVBBTQRXTOFLBBCXGNICBKAAGOKAYCCJYCW\\r\\nXCXLBESCRBNKWYGFDZFKWYNLFAKEWWGRUIAQGNCFDQXCHDBEQDSWSNGVKUFOGGSPFFZWTXGZQMMFJXDWOPUEZCMZEFDHXTRJTNLW\\r\\n\", \"output\": [\"RFFYJUXIJIJTWIHMTQXTFLCGNCBAAAYW\", \"KOOXWVJIJXTBWIHMTQXTFLCGNCBAAAYW\", \"KOOXWVJIPXTBWIHMTQXTFLXGNCBAAAYW\", \"RFFYJUXIJIJTWIHMTQXTFLXGNCBAAAYW\", \"KOOXWVJIPXTBWIHMTQXTFLCGNCBAAAYW\"]}, {\"input\": \"ESQZPIRAWBTUZSOWLYKIYCHZJPYERRXPJANKPZVPEDCXCJIDTLCARMAOTZMHJVDJXRDNQRIIOFIUTALVSCKDUSAKANKKOFKWINLQ\\r\\nGKSTYEAXFJQQUTKPZDAKHZKXCJDONKBZOTYGLYQJOGKOYMYNNNQRRVAGARKBQYJRVYYPFXTIBJJYQUWJUGAUQZUVMUHXLIQWGRMP\\r\\nUFPHNRDXLNYRIIYVOFRKRUQCWAICQUUBPHHEGBCILXHHGLOBKADQVPSQCMXJRLIZQPSRLZJNZVQPIURDQUKNHVVYNVBYGXXXXJDI\\r\\n\", \"output\": [\"STYEXJKPZDXCJDTLOMVRQRFIUAVULQ\", \"STYEXJKPZDXCJDTLOMVRQRFIUAVUIQ\"]}, {\"input\": \"UAYQUMTSNGMYBORUYXJJQZVAGBRVDWUTGUYYYOTWAHVKGGOHADXULFUFQULSAGDWFJCSDKPWBROYZIFRGGRVZQMEHKHCKNHTQSMK\\r\\nSVKVTPUZOBRKGLEAAXMIUSRISOTDIFFUCODYGNYIPSWEEBHGNWRZETXSVVMQTRBVFZMYHOHUCMLBUXBMPMSNCSHFZTAFUVTMQFGL\\r\\nTNICVANBEBOQASUEJJAOJXWNMDGAAVYNHRPSMKGMXZDJHCZHFHRRMIDWUOQCZSBKDPLSGHNHFKFYDRGVKXOLPOOWBPOWSDFLEJVX\\r\\n\", \"output\": [\"SVVTUOKGAXUFFUCDPWBRZRVZMHHCNHTQ\", \"SVVTUOKGAXUSDFCDPWBRZRVZMHHCNHTQ\", \"SVVTUOKGAXUSDFCDPWBRZRVZMHHCNHTM\"]}, {\"input\": \"KEJHTOKHMKWTYSJEAJAXGADRHUKBCRHACSRDNSZIHTPQNLOSRKYBGYIIJDINTXRPMWSVMMBODAYPVVDDTIXGDIOMWUAKZVFKDAUM\\r\\nWTEVPIFAAJYIDTZSZKPPQKIOMHDZTKDMFVKSJRUFMNHZJPVSQYELWYAFACGGNRORSLGYVXAEYVLZBLDEHYDGOFDSWUYCXLXDKFSU\\r\\nTUZEQBWVBVTKETQ\\r\\n\", \"output\": [\"EJTKHMKSJRUNHPQLYGNRSVAYVDDGOWUKFU\", \"EJTOKMKSJRUHZPQLYGNRSVAYVDDGDWUKFU\", \"EJTOKMKSJRUNZPQLYGNRSVAYVDDGDWUKFU\", \"EJHTKMKSJRUHZPQLYGNRSVAYVDDGDWUKFU\"]}, {\"input\": \"EGQYYSKTFTURZNRDVIWBYXMRDGFWMYKFXGIFOGYJSXKDCJUAGZPVTYCHIXVFTVTCXMKHZFTXSMMQVFXZGKHCIYODDRZEYECDLKNG\\r\\nPEXXCTRFJAAKPOTBAEFRLDRZKORNMXHHXTLKMKCGPVPUOBELPLFQFXOBZWIVIQCHEJQPXKGSCQAWIMETCJVTAGXJIINTADDXJTKQ\\r\\nQURSEKPMSSEVQZI\\r\\n\", \"output\": [\"ETFTBRDKOXKCGPVFVCHQXKCIECDK\", \"EKTFRZRXMGFFXOZVCHXCMTVGIDDK\", \"ETFTBRDKOXKCGPVXVCHQXKCIECDK\", \"EKTFRZNXMGFFXIJXKCATCVTXTDDK\", \"EKTFRZNXMGFFXIJXKCATCVTXIDDK\"]}, {\"input\": \"ZFFBNYVXOZCJPSRAEACVPAUKVTCVZYQPHVENTKOCMHNIYYMIKKLNKHLWHHWAQMWFTSYEOQQFEYAAYGMPNZCRYBVNAQTDSLXZGBCG\\r\\nPIQHLNEWAMFAKGHBGZAWRWAXCSKUDZBDOCTXAHSVFZACXGFMDSYBYYDDNQNBEZCYCULSMMPBTQOJQNRPZTRCSDLIYPLVUGJPKDTG\\r\\nZBFJPLNAKWQBTUVJKMHVBATAM\\r\\n\", \"output\": [\"FBZRACKZOCHAFSYYYNZCYBQTSLGG\", \"FBZAACKZOCHAFSYYYNZCYBQTSLGG\", \"FBZRACKZOCHAMSYYYNZCYBNTDLGG\", \"FBZRACUZOCHAMSYYYNZCYBNTDLGG\"]}, {\"input\": \"BTWZLIKDACZVLCKMVTIQHLFBNRCBDSWPFFKGPCQFPTOIJLPFCDMFGQKFHTDFFCCULUAYPXXIIIWBZIDMOPNHPZBEXLVARJFTBFOE\\r\\nMDXYKKWZVASJPPWRCYNMRAOBBLUNBSMQAPCPSFAGLXWJRBQTBRWXYNQGWECYNFIAJXDMUHIIMDFMSHLPIMYQXNRRUSSNXALGNWIK\\r\\nKNFVBVAOWXMZVUHAVUDKDBUVAKNHACZBGBHMUOPHWGQSDFXLHB\\r\\n\", \"output\": [\"WZACMLNBSPFGCFIJDMHDFLPIMNXL\", \"WZACLMQLBRWGCFIJDMHDFLPIMNXL\", \"WZACMBNBSPFGQTIJDMHDFLPIMNXA\", \"WZVCMLNBSPFGCFIJDMHDFLPIMNXL\", \"WZACMLNBSPFGQTIJDMHDFLPIMNXL\", \"DZVCMBNBSPFGCFIJDMHDFLPIMNXA\"]}, {\"input\": \"GOZVMIRQIGYGVAGOREQTXFXPEZYOJOXPNDGAESICXHMKQDXQPRLMRVWHXFEJVCWZDLYMQLDURUXZPTLEHPTSKXGSNEQDKLVFFLDX\\r\\nIMEVFCZXACKRRJVXDRKFWTLTRTLQQDHEBZLCOCNVPABQMIWJHRLKFUKWOVVWGGNWCJNRYOYOAJFQWCLHQIQRBZTVWKBFOXKEHHQP\\r\\nSZ\\r\\n\", \"output\": [\"IEFZXACKRRVXFWLRTLHPKGNQLVFX\", \"IVARXFEZONAIHRLVWJWLQRZTKXEQ\", \"MVARXFEZOPAIHRLVWFCLQRZTKXEQ\"]}, {\"input\": \"BBYUVCIYLNUJPSEYCAAPQSDNSDDTNEHQZDPBEKQAWNAKEYFBNEEBGPDPRLCSVOWYDEDRPPEDOROCHRCNQUSPNVXGRXHNLKDETWQC\\r\\nBQCQXCAHADGJHBYIKEUWNXFUOOTVCCKJPJJCMWLAWWKSDGHFNZTCPSQNRTPCBLXDTSJLRHSCCZXQXCVLVGTROOUCUQASIQHZGNEI\\r\\nRYE\\r\\n\", \"output\": [\"BBYUVCJPCASDNZPQNBDRLVROOCQSGNE\", \"BBYINUJPCASDHZPQNPDRSVROOCUSHNE\", \"BBYINUJPCASDHZPQNPDLSVROOCUSHNE\", \"BBYUVCJPCASDNTPQNBDRLVROOCQSGNE\", \"BBYUVCJPCASDNTPQNBDLCVROOCQSGNE\"]}, {\"input\": \"WZRKLETJRBBRZKGHEFBVEFVLIERBPSEGJVSNUZUICONWWBOOTHCOJLLZFNOCNOFJQZTZWBLKHGIWWWPBUYWBAHYJGEBJZJDTNBGN\\r\\nZINFGDCNKHYFZYYWHTIHZTKWXXXMSWOVOPQDTRWSQKBWWCPEMYFVGARELELBLGEVJCMOCFTTUVCYUQUSFONAMWKVDWMGXVNZJBWH\\r\\nAFPA\\r\\n\", \"output\": [\"WZKTRKBEFVLEBGVCOTCFONWKWGZJB\", \"WZKTRBEFVELEBEJCOTCFONWKWGZJB\", \"WZKTRBEFVELEBGVCOTCFONWKWGZJB\", \"WZKTRKEFVELEBEJCOTCFONWKWGZJB\"]}, {\"input\": \"ABABABB\\r\\nABABABB\\r\\nABABB\\r\\n\", \"output\": [\"ABABAB\", \"ABBABB\"]}, {\"input\": \"ABBB\\r\\nABBB\\r\\nABB\\r\\n\", \"output\": [\"BBB\"]}, {\"input\": \"A\\r\\nBABAABAAABABABABABABAABABABABBABABABABAABBABBABAABABAABAABBAAAAAABBABABABABAABABAABABABABAABAABABABA\\r\\nB\\r\\n\", \"output\": [\"A\"]}, {\"input\": \"ABBAABAAABABAABAABABABABAABBBABABABAAABBABAAABABABABBABBABABAABABABABABABBABAABABAABABABAAABBABABABA\\r\\nA\\r\\nB\\r\\n\", \"output\": [\"A\"]}, {\"input\": \"ABBBABABABABABBABAABAAABABAABABABABBABAAAABABABBABAABABAAABAABBAAABAABABBABBABABBABAABABABAAAAABABAB\\r\\nB\\r\\nBABBABAABABABABABABABABABBAABABBABABBAAABAAABABBAABAABBABABBABABAABBABAABABBAABAABAABABABABABBABABAB\\r\\n\", \"output\": [\"B\"]}, {\"input\": \"AABABAABAAABABAAABAAAABBAAABABAAABABAABAABAAAABAABAAAABAAAABAAAABBAABAAAAABAAAAABABAAAAAABABAABAAAAA\\r\\nABAABABABAAABABAABABBAABAABAABABAABABAAABBAABAAAABABABAAAAABAAAAABABABABAABAABAABAABABAABABAABAABAAB\\r\\nBABAAABABBAABABAABAA\\r\\n\", \"output\": [\"AABABABAAABABAAABAAAABAABABAABABAABAABAAAABAABAAAABAAAABAAABAABAAAABAABABAABABAABAAAA\", \"ABAABABABAAABAAAABBAABAAAABABAABABAAABAABAAAABAAAAAAABAAAAAAABAAAAABAAAAAAABABAABAAAA\", \"AABABABAAABABAAABAAAABAABABAAABAAABAABAAAABAABAAAABAAAABAAABAABAAAABAABABAABABAABAAAA\", \"ABAABABABAAABAAAABBAAAABAABABAABABAAABAABAAAABAABAAAAABAAAAABAAAAABABAAAAAABABAABAAAA\", \"AABABABAAABABAABABBAABABAABABAABABAAABAABAAAABABAAAAAABAAAAABAAAAABABAAAAAABABAABAAAA\", \"ABAABABABAAABAAAABBAAAABAABABAABABAAABAABAAAABAAAAAAABAAAAAAABAAAAABABAAAAABABAABAAAA\", \"ABAABABABAAABAAAABBAABABAABABAABABAAABAABAAAABABAAAAAABAAAAABAAAAABABAAAAAABABAABAAAA\", \"ABAABABABAAABAAAABBAABAAAABABAABABAAABAABAAAABAABAAAABAAAAAAABAAAAABAAAAAAABABAABAAAA\"]}, {\"input\": \"AABABABABAAAABBAAAABABABABAAAAABABAAAA\\r\\nAABABAAABABABAAABAAAAABAAABAAABABABBBABBAAABAABAAAAABABBABAAABAABAABABAAAABABAAABAAABAABABBBABBABABA\\r\\nAAAAA\\r\\n\", \"output\": [\"AABABABABAAAABBAAAABABABABAAAABABAAAA\"]}, {\"input\": \"ZZXXAAZZAXAAZZAZZXXAAZZAXAXZZXXAAZZZZXXAZZXXAAAZZXXAAAZZXXZZXXXAAAZZXZZXXAZZXXZXXAAXAAZZZXXAXAXAZZXZ\\r\\nAZZXXAAZZXXAAXZXXAZZXAZZXZZXXAAZZXXAAZAAZZAAZZXXAA\\r\\nAAZZXAAXXAAAZZXXAZZXXAAZZXXAAAZZXXZ\\r\\n\", \"output\": [\"ZZXXAAZZXXAAXZXXAZZXAZZXZZXXAAZZXXAAZAZZAAZZXXAA\", \"ZZXXAAZZXXAAXZXXAZZXAZZXZZXXAAZZXXAAAAZZAAZZXXAA\", \"AZZXAAZZXXAAXZXXAZZXAZZXZZXXAAZZXXAAZAZZAAZZXXAA\"]}, {\"input\": \"SDASSDADASDASDASDSDADASASDAAASDASDDASDDASDADASDASDSSDASDD\\r\\nSDASDASDDASDASDASDSDSDASDASDASDASDASDASDASDADASDASDASDSDASDASDDDASSD\\r\\nSDASDSDDAA\\r\\n\", \"output\": [\"SDASSDADASDASDSDSDADASASDAAASDASDDASDDASDDASDASDDASD\", \"SDASSDDASDASDASDSDDASASDAASDASDDASDDASDADASDSDSSDASD\", \"SDASDADASDASDASDSDADASASDASDASDASDASDADASDASDSSDASDD\", \"SDASSDDASDASDASDSDDASASDAASDASDDASDDASDADASDSDSDASDD\", \"SDASDADASDASDASDSDADASASDAASDASDASDDASDADASDASDSDASD\", \"SDASDADASDASDASDSDDASASDAASDASDDASDDASDADASDSDSSDASD\", \"SDASDADASDASDASDSDDASASDASDASDASDDASDADASDASDSSDASDD\"]}, {\"input\": \"DASSDASDASDDAASDASDADASDASASDAS\\r\\nSDADASDASSDAASDASDASDADASSDDA\\r\\nSD\\r\\n\", \"output\": [\"DADADADAADADADADASSA\", \"DADASASAASASADADASSA\"]}, {\"input\": \"ASDASSDASDS\\r\\nDASDASDDDASDADASDASDASDASSDADASDDAASDA\\r\\nDSD\\r\\n\", \"output\": [\"ASDASSDASDS\"]}, {\"input\": \"ASDASASDASDASDAASDASDASDASASDDAASDASSASDSDAD\\r\\nDASDASSSDASDASDASASDASSDAASDASSDDSASDASDAASDDAASDASDAASDASDDASDASDASDASDASS\\r\\nDASD\\r\\n\", \"output\": [\"ASDASASDASASDAASDASASDASASDDAASDASSASDSDAD\"]}, {\"input\": \"DASDSDASDADASDDDSDASSDDAASDA\\r\\nDASDDASDSDADSDASDADSDSDADDASDASDDASDASDASDSDASD\\r\\nDAASD\\r\\n\", \"output\": [\"DASDSDASDADASDDDSDASSDDASDA\"]}, {\"input\": \"ABAAAABABADABAABAABCCABADABACABACABCABADABADABACABBACAADABACABABACABADABACABABA\\r\\nBACAACABABABACABCABADABAACABADABACABAA\\r\\nABBAB\\r\\n\", \"output\": [\"BACAACABABABACABCAADABAACABADABACABAA\", \"BACAACABABABACABCABAABAACABADABACABAA\", \"BAAACABABABACABCABADABAACABADABACABAA\"]}, {\"input\": \"ABAABACABADAACADABACAAB\\r\\nBAACABADABACABAAAADADAABACABACABADABABADABACABAADABBADABACAAACAABACABADABBBAA\\r\\nDABACA\\r\\n\", \"output\": [\"ABAABACABADAACAABACAAB\", \"ABAABACABADAACADABAAAB\"]}, {\"input\": \"BACABACABAACABADABABACAABACABBACAACAACABCABADAACABAABAABBADABACABADABCABAD\\r\\nBACAABADABABADABACABABACABADABACABCBADABACADABCABABADAABA\\r\\nBADABAA\\r\\n\", \"output\": [\"BACABAABABADABACAABACABAAACABCBADAACAABABABADAABA\", \"BACAABADABABAABACABBACAAAACABCBADAACADABAABADAABA\", \"BACAABAAABADABACAABACABAAACABCBADAACADABCABADAABA\", \"BACAABADABABAABACABBACAAAACABCBADAACADABCABADAABA\", \"BACAABAAABADABACAABACABAAACABCBADAACAABABABADAABA\", \"BACABAABABADABACAABACABAAACABCBADAACADABCABADAABA\"]}, {\"input\": \"ACABADABACABCABAAB\\r\\nBADAB\\r\\nACAACABA\\r\\n\", \"output\": [\"BADAB\"]}, {\"input\": \"ABABAC\\r\\nABABAC\\r\\nABAC\\r\\n\", \"output\": [\"ABBAC\", \"ABABA\"]}, {\"input\": \"BCBCBC\\r\\nBCBCBC\\r\\nBC\\r\\n\", \"output\": [\"CCC\", \"BBB\", \"CCB\"]}, {\"input\": \"AAACAAACAAADAAAAAAA\\r\\nAADAAAAAAAACDAAAAAAAAAAACAAAAABCACAAACAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADA\\r\\nAAACAADAAAAADD\\r\\n\", \"output\": [\"AAACAAACAAAAAAAAAA\"]}, {\"input\": \"ABABBB\\r\\nABABBB\\r\\nABB\\r\\n\", \"output\": [\"BBBB\", \"ABAB\"]}, {\"input\": \"ABABABAC\\r\\nABABABAC\\r\\nABABAC\\r\\n\", \"output\": [\"ABABBAC\", \"ABBABAC\", \"ABABABA\"]}, {\"input\": \"BBAABAAAAABBBBBBBABABAABAABAABBABABABBBABBABBABBBABAABBBBBBAABAAAAAAAAABABAAABBABBAAAAAABAABABBAAABB\\r\\nBBAABAAAAABBBBBBBABABAABAABAABBABABABBBABBABBABBBABAABBBBBBAABAAAAAAAAABABAAABBABBAAAAAABAABABBAAABB\\r\\nBBBAA\\r\\n\", \"output\": [\"BBAABAAAAABBBBBBBABABAABAABAABBABABABBBABBABBABBBABAABBBBBBABAAAAAAAAABABAAABBABBAAAAAABAABABBAAABB\"]}, {\"input\": \"ABABC\\r\\nABABC\\r\\nABC\\r\\n\", \"output\": [\"ABBC\", \"ABAB\"]}, {\"input\": \"BABBB\\r\\nBABBB\\r\\nABB\\r\\n\", \"output\": [\"BBBB\"]}, {\"input\": \"ABCCCCCCCC\\r\\nABCCCCCCCC\\r\\nABC\\r\\n\", \"output\": [\"BCCCCCCCC\", \"ACCCCCCCC\"]}]"}
{"prob_desc_description":"Jeff loves regular bracket sequences.Today Jeff is going to take a piece of paper and write out the regular bracket sequence, consisting of nm brackets. Let's number all brackets of this sequence from 0 to nm - 1 from left to right. Jeff knows that he is going to spend ai mod n liters of ink on the i-th bracket of the sequence if he paints it opened and bi mod n liters if he paints it closed.You've got sequences a, b and numbers n, m. What minimum amount of ink will Jeff need to paint a regular bracket sequence of length nm?Operation x mod y means taking the remainder after dividing number x by number y.","prob_desc_output_spec":"In a single line print the answer to the problem \u2014 the minimum required amount of ink in liters.","lang_cluster":"","src_uid":"f40900973f4ebeb6fdafd75ebe4e9601","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp","matrices"],"prob_desc_created_at":"1380900600","prob_desc_sample_inputs":"[\"2 6\\n1 2\\n2 1\", \"1 10000000\\n2\\n3\"]","prob_desc_notes":"NoteIn the first test the optimal sequence is: ()()()()()(), the required number of ink liters is 12.","exec_outcome":"","difficulty":2500.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains two integers n and m (1\u2009\u2264\u2009n\u2009\u2264\u200920;\u00a01\u2009\u2264\u2009m\u2009\u2264\u2009107; m is even). The next line contains n integers: a0, a1, ..., an\u2009-\u20091 (1\u2009\u2264\u2009ai\u2009\u2264\u200910). The next line contains n integers: b0, b1, ..., bn\u2009-\u20091 (1\u2009\u2264\u2009bi\u2009\u2264\u200910). The numbers are separated by spaces.","prob_desc_sample_outputs":"[\"12\", \"25000000\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 6\\r\\n1 2\\r\\n2 1\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"1 10000000\\r\\n2\\r\\n3\\r\\n\", \"output\": [\"25000000\"]}, {\"input\": \"3 184\\r\\n3 2 8\\r\\n3 9 2\\r\\n\", \"output\": [\"1288\"]}, {\"input\": \"4 26\\r\\n10 2 5 9\\r\\n5 4 2 5\\r\\n\", \"output\": [\"444\"]}, {\"input\": \"3 76\\r\\n4 7 9\\r\\n10 1 1\\r\\n\", \"output\": [\"684\"]}, {\"input\": \"3 98\\r\\n6 1 9\\r\\n10 2 4\\r\\n\", \"output\": [\"1127\"]}, {\"input\": \"5 114\\r\\n7 5 8 10 10\\r\\n2 7 9 4 5\\r\\n\", \"output\": [\"3021\"]}, {\"input\": \"1 14\\r\\n7\\r\\n6\\r\\n\", \"output\": [\"91\"]}, {\"input\": \"5 142\\r\\n8 7 6 2 2\\r\\n8 2 6 1 7\\r\\n\", \"output\": [\"2703\"]}, {\"input\": \"1 184\\r\\n8\\r\\n8\\r\\n\", \"output\": [\"1472\"]}, {\"input\": \"2 1900670\\r\\n10 3\\r\\n9 6\\r\\n\", \"output\": [\"22808044\"]}, {\"input\": \"6 17656\\r\\n2 7 4 7 7 3\\r\\n3 5 3 6 9 10\\r\\n\", \"output\": [\"459064\"]}, {\"input\": \"16 3273408\\r\\n3 2 8 8 10 1 1 7 1 4 5 7 5 8 10 10\\r\\n4 4 3 4 7 9 5 1 7 10 7 2 7 9 4 5\\r\\n\", \"output\": [\"186584261\"]}, {\"input\": \"11 4532614\\r\\n7 3 4 1 8 3 5 2 8 10 9\\r\\n6 10 3 7 5 1 1 8 4 9 7\\r\\n\", \"output\": [\"201701323\"]}, {\"input\": \"7 3952828\\r\\n1 1 9 3 5 9 2\\r\\n3 5 6 2 7 9 4\\r\\n\", \"output\": [\"106726356\"]}, {\"input\": \"20 807878\\r\\n9 4 2 5 2 7 9 3 4 4 9 2 8 3 8 9 5 7 4 7\\r\\n8 4 8 7 10 4 10 6 8 1 7 9 3 10 2 2 6 7 3 9\\r\\n\", \"output\": [\"67053877\"]}, {\"input\": \"3 3684044\\r\\n8 6 4\\r\\n3 1 2\\r\\n\", \"output\": [\"38682465\"]}, {\"input\": \"9 7683580\\r\\n4 6 8 5 10 6 3 4 7\\r\\n6 7 3 10 3 10 1 4 10\\r\\n\", \"output\": [\"303501412\"]}, {\"input\": \"10 6007734\\r\\n4 7 6 7 4 3 4 7 7 6\\r\\n8 9 5 7 6 3 2 2 10 4\\r\\n\", \"output\": [\"270348030\"]}, {\"input\": \"7 859320\\r\\n10 1 4 9 2 5 5\\r\\n5 10 3 6 6 5 10\\r\\n\", \"output\": [\"23201650\"]}, {\"input\": \"20 10000000\\r\\n10 3 2 6 2 3 9 2 8 4 4 4 3 4 7 9 5 1 7 10\\r\\n9 6 2 8 3 2 8 10 6 3 2 8 8 10 1 1 7 1 4 5\\r\\n\", \"output\": [\"730000001\"]}, {\"input\": \"20 10000000\\r\\n7 10 9 2 9 7 6 10 3 7 5 1 1 8 4 9 7 9 6 8\\r\\n9 4 3 6 1 7 3 4 1 8 3 5 2 8 10 9 1 2 10 4\\r\\n\", \"output\": [\"780000008\"]}, {\"input\": \"20 10000000\\r\\n2 7 9 4 1 9 8 4 6 10 5 10 4 5 9 9 10 9 1 6\\r\\n5 9 2 9 8 9 1 10 1 9 5 6 4 9 1 10 3 9 9 7\\r\\n\", \"output\": [\"890000001\"]}, {\"input\": \"20 10000000\\r\\n6 7 3 9 10 10 1 9 4 6 8 5 10 6 3 4 7 8 6 6\\r\\n7 4 7 2 7 3 10 10 6 7 3 10 3 10 1 4 10 10 7 3\\r\\n\", \"output\": [\"920000004\"]}, {\"input\": \"20 10000000\\r\\n7 4 3 4 7 7 6 5 4 6 5 8 3 5 3 8 4 3 4 8\\r\\n7 6 3 2 2 10 4 3 5 7 9 9 8 5 4 9 4 3 3 4\\r\\n\", \"output\": [\"880000001\"]}, {\"input\": \"1 2\\r\\n1\\r\\n1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"20 10000000\\r\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\r\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\r\\n\", \"output\": [\"200000000\"]}, {\"input\": \"20 10000000\\r\\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\\r\\n10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\\r\\n\", \"output\": [\"2000000000\"]}]"}
{"prob_desc_description":"Little Petya is learning to play chess. He has already learned how to move a king, a rook and a bishop. Let us remind you the rules of moving chess pieces. A chessboard is 64 square fields organized into an 8\u2009\u00d7\u20098 table. A field is represented by a pair of integers (r,\u2009c) \u2014 the number of the row and the number of the column (in a classical game the columns are traditionally indexed by letters). Each chess piece takes up exactly one field. To make a move is to move a chess piece, the pieces move by the following rules:  A rook moves any number of fields horizontally or vertically.  A bishop moves any number of fields diagonally.  A king moves one field in any direction \u2014 horizontally, vertically or diagonally.     The pieces move like that Petya is thinking about the following problem: what minimum number of moves is needed for each of these pieces to move from field (r1,\u2009c1) to field (r2,\u2009c2)? At that, we assume that there are no more pieces besides this one on the board. Help him solve this problem.","prob_desc_output_spec":"Print three space-separated integers: the minimum number of moves the rook, the bishop and the king (in this order) is needed to move from field (r1,\u2009c1) to field (r2,\u2009c2). If a piece cannot make such a move, print a 0 instead of the corresponding number.","lang_cluster":"","src_uid":"7dbf58806db185f0fe70c00b60973f4b","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","shortest paths","graphs"],"prob_desc_created_at":"1386399600","prob_desc_sample_inputs":"[\"4 3 1 6\", \"5 5 5 6\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1100.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The input contains four integers r1,\u2009c1,\u2009r2,\u2009c2 (1\u2009\u2264\u2009r1,\u2009c1,\u2009r2,\u2009c2\u2009\u2264\u20098) \u2014 the coordinates of the starting and the final field. The starting field doesn't coincide with the final one. You can assume that the chessboard rows are numbered from top to bottom 1 through 8, and the columns are numbered from left to right 1 through 8.","prob_desc_sample_outputs":"[\"2 1 3\", \"1 0 1\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4 3 1 6\\r\\n\", \"output\": [\"2 1 3\", \"2\\r\\n1\\r\\n3\"]}, {\"input\": \"5 5 5 6\\r\\n\", \"output\": [\"1\\r\\n0\\r\\n1\", \"1 0 1\"]}, {\"input\": \"1 1 8 8\\r\\n\", \"output\": [\"2 1 7\", \"2\\r\\n1\\r\\n7\"]}, {\"input\": \"1 1 8 1\\r\\n\", \"output\": [\"1 0 7\", \"1\\r\\n0\\r\\n7\"]}, {\"input\": \"1 1 1 8\\r\\n\", \"output\": [\"1 0 7\", \"1\\r\\n0\\r\\n7\"]}, {\"input\": \"8 1 1 1\\r\\n\", \"output\": [\"1 0 7\", \"1\\r\\n0\\r\\n7\"]}, {\"input\": \"8 1 1 8\\r\\n\", \"output\": [\"2 1 7\", \"2\\r\\n1\\r\\n7\"]}, {\"input\": \"7 7 6 6\\r\\n\", \"output\": [\"2 1 1\", \"2\\r\\n1\\r\\n1\"]}, {\"input\": \"8 1 8 8\\r\\n\", \"output\": [\"1 0 7\", \"1\\r\\n0\\r\\n7\"]}, {\"input\": \"1 8 1 1\\r\\n\", \"output\": [\"1 0 7\", \"1\\r\\n0\\r\\n7\"]}, {\"input\": \"1 8 8 1\\r\\n\", \"output\": [\"2 1 7\", \"2\\r\\n1\\r\\n7\"]}, {\"input\": \"1 8 8 8\\r\\n\", \"output\": [\"1 0 7\", \"1\\r\\n0\\r\\n7\"]}, {\"input\": \"8 8 1 1\\r\\n\", \"output\": [\"2 1 7\", \"2\\r\\n1\\r\\n7\"]}, {\"input\": \"8 8 1 8\\r\\n\", \"output\": [\"1 0 7\", \"1\\r\\n0\\r\\n7\"]}, {\"input\": \"8 8 8 1\\r\\n\", \"output\": [\"1 0 7\", \"1\\r\\n0\\r\\n7\"]}, {\"input\": \"1 3 1 6\\r\\n\", \"output\": [\"1\\r\\n0\\r\\n3\", \"1 0 3\"]}, {\"input\": \"1 3 1 4\\r\\n\", \"output\": [\"1\\r\\n0\\r\\n1\", \"1 0 1\"]}, {\"input\": \"1 3 1 5\\r\\n\", \"output\": [\"1 2 2\", \"1\\r\\n2\\r\\n2\"]}, {\"input\": \"3 3 2 4\\r\\n\", \"output\": [\"2 1 1\", \"2\\r\\n1\\r\\n1\"]}, {\"input\": \"3 3 1 5\\r\\n\", \"output\": [\"2\\r\\n1\\r\\n2\", \"2 1 2\"]}, {\"input\": \"1 6 2 1\\r\\n\", \"output\": [\"2\\r\\n2\\r\\n5\", \"2 2 5\"]}, {\"input\": \"1 5 6 4\\r\\n\", \"output\": [\"2\\r\\n2\\r\\n5\", \"2 2 5\"]}, {\"input\": \"1 3 3 7\\r\\n\", \"output\": [\"2 2 4\", \"2\\r\\n2\\r\\n4\"]}, {\"input\": \"1 1 8 1\\r\\n\", \"output\": [\"1 0 7\", \"1\\r\\n0\\r\\n7\"]}, {\"input\": \"1 7 5 4\\r\\n\", \"output\": [\"2\\r\\n0\\r\\n4\", \"2 0 4\"]}, {\"input\": \"1 5 2 7\\r\\n\", \"output\": [\"2 0 2\", \"2\\r\\n0\\r\\n2\"]}, {\"input\": \"1 4 6 2\\r\\n\", \"output\": [\"2\\r\\n0\\r\\n5\", \"2 0 5\"]}, {\"input\": \"1 2 3 5\\r\\n\", \"output\": [\"2\\r\\n0\\r\\n3\", \"2 0 3\"]}, {\"input\": \"1 8 8 7\\r\\n\", \"output\": [\"2 2 7\", \"2\\r\\n2\\r\\n7\"]}, {\"input\": \"6 5 6 2\\r\\n\", \"output\": [\"1\\r\\n0\\r\\n3\", \"1 0 3\"]}, {\"input\": \"6 3 3 5\\r\\n\", \"output\": [\"2\\r\\n0\\r\\n3\", \"2 0 3\"]}, {\"input\": \"6 1 7 8\\r\\n\", \"output\": [\"2 2 7\", \"2\\r\\n2\\r\\n7\"]}, {\"input\": \"1 2 3 2\\r\\n\", \"output\": [\"1 2 2\", \"1\\r\\n2\\r\\n2\"]}, {\"input\": \"3 8 7 2\\r\\n\", \"output\": [\"2 2 6\", \"2\\r\\n2\\r\\n6\"]}, {\"input\": \"4 2 6 4\\r\\n\", \"output\": [\"2\\r\\n1\\r\\n2\", \"2 1 2\"]}, {\"input\": \"1 1 1 3\\r\\n\", \"output\": [\"1 2 2\", \"1\\r\\n2\\r\\n2\"]}, {\"input\": \"6 8 8 6\\r\\n\", \"output\": [\"2\\r\\n1\\r\\n2\", \"2 1 2\"]}, {\"input\": \"6 7 4 1\\r\\n\", \"output\": [\"2 2 6\", \"2\\r\\n2\\r\\n6\"]}, {\"input\": \"6 5 1 4\\r\\n\", \"output\": [\"2\\r\\n2\\r\\n5\", \"2 2 5\"]}, {\"input\": \"3 2 7 6\\r\\n\", \"output\": [\"2 1 4\", \"2\\r\\n1\\r\\n4\"]}, {\"input\": \"3 8 4 1\\r\\n\", \"output\": [\"2 2 7\", \"2\\r\\n2\\r\\n7\"]}, {\"input\": \"3 6 1 4\\r\\n\", \"output\": [\"2\\r\\n1\\r\\n2\", \"2 1 2\"]}]"}
{"prob_desc_description":"Cucumber boy is fan of Kyubeat, a famous music game.Kyubeat has 16 panels for playing arranged in 4\u2009\u00d7\u20094 table. When a panel lights up, he has to press that panel.Each panel has a timing to press (the preffered time when a player should press it), and Cucumber boy is able to press at most k panels in a time with his one hand. Cucumber boy is trying to press all panels in perfect timing, that is he wants to press each panel exactly in its preffered time. If he cannot press the panels with his two hands in perfect timing, his challenge to press all the panels in perfect timing will fail.You are given one scene of Kyubeat's panel from the music Cucumber boy is trying. Tell him is he able to press all the panels in perfect timing.","prob_desc_output_spec":"Output \"YES\" (without quotes), if he is able to press all the panels in perfect timing. If not, output \"NO\" (without quotes).","lang_cluster":"","src_uid":"5fdaf8ee7763cb5815f49c0c38398f16","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["implementation"],"prob_desc_created_at":"1386943200","prob_desc_sample_inputs":"[\"1\\n.135\\n1247\\n3468\\n5789\", \"5\\n..1.\\n1111\\n..1.\\n..1.\", \"1\\n....\\n12.1\\n.2..\\n.2..\"]","prob_desc_notes":"NoteIn the third sample boy cannot press all panels in perfect timing. He can press all the panels in timing in time 1, but he cannot press the panels in time 2 in timing with his two hands.","exec_outcome":"","difficulty":900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains a single integer k (1\u2009\u2264\u2009k\u2009\u2264\u20095) \u2014 the number of panels Cucumber boy can press with his one hand. Next 4 lines contain 4 characters each (digits from 1 to 9, or period) \u2014 table of panels. If a digit i was written on the panel, it means the boy has to press that panel in time i. If period was written on the panel, he doesn't have to press that panel.","prob_desc_sample_outputs":"[\"YES\", \"YES\", \"NO\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1\\r\\n.135\\r\\n1247\\r\\n3468\\r\\n5789\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"5\\r\\n..1.\\r\\n1111\\r\\n..1.\\r\\n..1.\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1\\r\\n....\\r\\n12.1\\r\\n.2..\\r\\n.2..\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"1\\r\\n....\\r\\n....\\r\\n....\\r\\n....\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1\\r\\n6981\\r\\n.527\\r\\n4163\\r\\n2345\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"5\\r\\n9999\\r\\n9999\\r\\n9999\\r\\n9999\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2\\r\\n4444\\r\\n3333\\r\\n2222\\r\\n1111\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"3\\r\\n2123\\r\\n1232\\r\\n2321\\r\\n3213\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2\\r\\n1...\\r\\n.1..\\r\\n..1.\\r\\n...1\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"2\\r\\n1.1.\\r\\n.1.1\\r\\n2.2.\\r\\n.222\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"1\\r\\n1..2\\r\\n.3.4\\r\\n567.\\r\\n.89.\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1\\r\\n1122\\r\\n3344\\r\\n5588\\r\\n6699\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"4\\r\\n1111\\r\\n1221\\r\\n1221\\r\\n1111\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"5\\r\\n3141\\r\\n5926\\r\\n5358\\r\\n9793\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"5\\r\\n5454\\r\\n4343\\r\\n3232\\r\\n2121\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"5\\r\\n1222\\r\\n2221\\r\\n2221\\r\\n1122\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4\\r\\n...1\\r\\n..2.\\r\\n.3..\\r\\n4...\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1\\r\\n....\\r\\n5..5\\r\\n6..6\\r\\n7..7\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1\\r\\n9875\\r\\n8643\\r\\n7421\\r\\n531.\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"1\\r\\n..1.\\r\\n..1.\\r\\n..1.\\r\\n..1.\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"3\\r\\n7777\\r\\n..7.\\r\\n.7..\\r\\n7...\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"4\\r\\n7777\\r\\n..7.\\r\\n.7..\\r\\n7...\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"4\\r\\n4.4.\\r\\n4.4.\\r\\n4444\\r\\n..4.\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"5\\r\\n4.4.\\r\\n4.4.\\r\\n4444\\r\\n..4.\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"3\\r\\n1.1.\\r\\n.1.1\\r\\n1.1.\\r\\n.1.1\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"2\\r\\n1131\\r\\n4412\\r\\n2569\\r\\n3478\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"2\\r\\n8888\\r\\n8888\\r\\n8888\\r\\n8888\\r\\n\", \"output\": [\"NO\"]}]"}
{"prob_desc_description":"Our bear's forest has a checkered field. The checkered field is an n\u2009\u00d7\u2009n table, the rows are numbered from 1 to n from top to bottom, the columns are numbered from 1 to n from left to right. Let's denote a cell of the field on the intersection of row x and column y by record (x,\u2009y). Each cell of the field contains growing raspberry, at that, the cell (x,\u2009y) of the field contains x\u2009+\u2009y raspberry bushes.The bear came out to walk across the field. At the beginning of the walk his speed is (dx,\u2009dy). Then the bear spends exactly t seconds on the field. Each second the following takes place:  Let's suppose that at the current moment the bear is in cell (x,\u2009y).  First the bear eats the raspberry from all the bushes he has in the current cell. After the bear eats the raspberry from k bushes, he increases each component of his speed by k. In other words, if before eating the k bushes of raspberry his speed was (dx,\u2009dy), then after eating the berry his speed equals (dx\u2009+\u2009k,\u2009dy\u2009+\u2009k).  Let's denote the current speed of the bear (dx,\u2009dy) (it was increased after the previous step). Then the bear moves from cell (x,\u2009y) to cell (((x\u2009+\u2009dx\u2009-\u20091)\u00a0mod\u00a0n)\u2009+\u20091,\u2009((y\u2009+\u2009dy\u2009-\u20091)\u00a0mod\u00a0n)\u2009+\u20091).  Then one additional raspberry bush grows in each cell of the field. You task is to predict the bear's actions. Find the cell he ends up in if he starts from cell (sx,\u2009sy). Assume that each bush has infinitely much raspberry and the bear will never eat all of it.","prob_desc_output_spec":"Print two integers \u2014 the coordinates of the cell the bear will end up in after t seconds.","lang_cluster":"","src_uid":"ee9fa8be2ae05a4e831a4f608c0cc785","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","matrices"],"prob_desc_created_at":"1390577700","prob_desc_sample_inputs":"[\"5 1 2 0 1 2\", \"1 1 1 -1 -1 2\"]","prob_desc_notes":"NoteOperation a\u00a0mod\u00a0b means taking the remainder after dividing a by b. Note that the result of the operation is always non-negative. For example, (\u2009-\u20091)\u00a0mod\u00a03\u2009=\u20092.In the first sample before the first move the speed vector will equal (3,4) and the bear will get to cell (4,1). Before the second move the speed vector will equal (9,10) and he bear will get to cell (3,1). Don't forget that at the second move, the number of berry bushes increased by 1.In the second sample before the first move the speed vector will equal (1,1) and the bear will get to cell (1,1). Before the second move, the speed vector will equal (4,4) and the bear will get to cell (1,1). Don't forget that at the second move, the number of berry bushes increased by 1.","exec_outcome":"","difficulty":2300.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line of the input contains six space-separated integers: n, sx, sy, dx, dy, t (1\u2009\u2264\u2009n\u2009\u2264\u2009109;\u00a01\u2009\u2264\u2009sx,\u2009sy\u2009\u2264\u2009n;\u00a0\u2009-\u2009100\u2009\u2264\u2009dx,\u2009dy\u2009\u2264\u2009100;\u00a00\u2009\u2264\u2009t\u2009\u2264\u20091018).","prob_desc_sample_outputs":"[\"3 1\", \"1 1\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"5 1 2 0 1 2\\r\\n\", \"output\": [\"3 1\"]}, {\"input\": \"1 1 1 -1 -1 2\\r\\n\", \"output\": [\"1 1\"]}, {\"input\": \"1 1 1 1 1 0\\r\\n\", \"output\": [\"1 1\"]}, {\"input\": \"2 2 1 -2 -2 5\\r\\n\", \"output\": [\"1 2\"]}, {\"input\": \"1000000000 1 1 1 1 1000000000000000000\\r\\n\", \"output\": [\"168318977 168318977\"]}, {\"input\": \"1000000000 1 2 -100 -100 1\\r\\n\", \"output\": [\"999999904 999999905\"]}, {\"input\": \"3 2 2 -100 -100 2\\r\\n\", \"output\": [\"1 1\"]}, {\"input\": \"1000000000 1000000000 1000000000 100 -100 1000000000000000000\\r\\n\", \"output\": [\"969796608 969796608\"]}, {\"input\": \"907122235 107269653 309181328 26 -64 242045007473044676\\r\\n\", \"output\": [\"23731316 525833901\"]}, {\"input\": \"804 658 177 -95 37 9\\r\\n\", \"output\": [\"270 173\"]}, {\"input\": \"2 1 1 31 -74 2712360435504330\\r\\n\", \"output\": [\"1 1\"]}, {\"input\": \"230182675 73108597 42152975 -72 -8 93667970058209518\\r\\n\", \"output\": [\"34918692 197804272\"]}, {\"input\": \"487599125 469431740 316230350 -77 57 18\\r\\n\", \"output\": [\"320939970 167740992\"]}, {\"input\": \"1710 654 941 -81 -37 1281183940\\r\\n\", \"output\": [\"1568 945\"]}, {\"input\": \"568980902 147246752 87068387 -17 58 677739653\\r\\n\", \"output\": [\"150920864 281916196\"]}, {\"input\": \"38 10 36 19 30 4054886\\r\\n\", \"output\": [\"18 36\"]}, {\"input\": \"546978166 115293871 313560296 -33 54 215761558342792301\\r\\n\", \"output\": [\"353006839 497349709\"]}, {\"input\": \"323544442 39059198 2970015 92 17 98\\r\\n\", \"output\": [\"105890973 69794440\"]}, {\"input\": \"321575625 2929581 31407414 -40 -44 920902537044\\r\\n\", \"output\": [\"320222592 65760999\"]}, {\"input\": \"5928 1508 4358 75 -4 794927060433551549\\r\\n\", \"output\": [\"4973 5148\"]}, {\"input\": \"7310962 7564 6333485 -45 41 81980903005818\\r\\n\", \"output\": [\"5246110 6302893\"]}, {\"input\": \"224 81 30 57 -13 8363\\r\\n\", \"output\": [\"130 205\"]}, {\"input\": \"75081054 91 47131957 -94 -54 5588994022550344\\r\\n\", \"output\": [\"6742019 52104963\"]}, {\"input\": \"185144 100489 52 32 -21 5752324832726786\\r\\n\", \"output\": [\"56326 173503\"]}, {\"input\": \"61728 24280 17963 -19 81 652432745607745078\\r\\n\", \"output\": [\"3174 1169\"]}, {\"input\": \"25699863 23288611 24796719 -45 46 437606836\\r\\n\", \"output\": [\"24072870 13015404\"]}, {\"input\": \"475875319 333393831 284835031 22 7 90332975949346\\r\\n\", \"output\": [\"441571464 288459461\"]}, {\"input\": \"372903 106681 40781 54 -40 6188704\\r\\n\", \"output\": [\"161485 86089\"]}, {\"input\": \"923 452 871 -95 -55 273135237285890\\r\\n\", \"output\": [\"563 142\"]}, {\"input\": \"672939 589365 391409 -54 -70 205083640\\r\\n\", \"output\": [\"503747 218115\"]}, {\"input\": \"560010572 4172512 514044248 -78 13 97386\\r\\n\", \"output\": [\"11882888 530616750\"]}, {\"input\": \"717485513 5935 3 -5 -67 28\\r\\n\", \"output\": [\"71683921 71676253\"]}, {\"input\": \"138971202 137695723 48931985 -28 -3 68901440898766\\r\\n\", \"output\": [\"110585553 85995539\"]}, {\"input\": \"910958510 60 98575 38 -99 97880\\r\\n\", \"output\": [\"304849180 291538135\"]}, {\"input\": \"67163467 36963416 50381 -49 -12 76558237\\r\\n\", \"output\": [\"23368224 65407811\"]}, {\"input\": \"557911547 9 460221236 -58 -96 74518856\\r\\n\", \"output\": [\"246089810 106240697\"]}, {\"input\": \"85 37 69 30 47 131\\r\\n\", \"output\": [\"74 38\"]}, {\"input\": \"852525230 538352221 97088953 -12 98 9197937568\\r\\n\", \"output\": [\"84737577 321684009\"]}, {\"input\": \"885849694 703278210 46391 33 23 965949118732\\r\\n\", \"output\": [\"16593182 13087113\"]}, {\"input\": \"976890548 675855343 988 -11 46 796041265897304\\r\\n\", \"output\": [\"652954007 789518296\"]}, {\"input\": \"108774060 15274597 430014 -85 -94 6\\r\\n\", \"output\": [\"98184736 83340099\"]}, {\"input\": \"2 2 2 -36 94 9429569334\\r\\n\", \"output\": [\"1 1\"]}, {\"input\": \"713835677 404390162 67429 -91 10 178697004637242062\\r\\n\", \"output\": [\"244834060 560206120\"]}, {\"input\": \"620330674 603592488 3 38 94 34309127789188\\r\\n\", \"output\": [\"200990066 258175045\"]}, {\"input\": \"95 70 7 -36 -100 5\\r\\n\", \"output\": [\"85 82\"]}, {\"input\": \"900854530 82 7 30 -88 6797628981503799\\r\\n\", \"output\": [\"66039616 641057009\"]}, {\"input\": \"147834 6 2565 15 -35 166779\\r\\n\", \"output\": [\"54423 144570\"]}, {\"input\": \"642762664 588605882 1 -47 82 8\\r\\n\", \"output\": [\"355500874 409658689\"]}, {\"input\": \"122740849 8646067 70003215 -100 -80 70\\r\\n\", \"output\": [\"80795619 19413318\"]}, {\"input\": \"73221379 4311914 992324 65 -40 705623357422685593\\r\\n\", \"output\": [\"62692638 21726334\"]}]"}
{"prob_desc_description":"You will receive 3 points for solving this problem.Manao is designing the genetic code for a new type of algae to efficiently produce fuel. Specifically, Manao is focusing on a stretch of DNA that encodes one protein. The stretch of DNA is represented by a string containing only the characters 'A', 'T', 'G' and 'C'.Manao has determined that if the stretch of DNA contains a maximal sequence of consecutive identical nucleotides that is of even length, then the protein will be nonfunctional. For example, consider a protein described by DNA string \"GTTAAAG\". It contains four maximal sequences of consecutive identical nucleotides: \"G\", \"TT\", \"AAA\", and \"G\". The protein is nonfunctional because sequence \"TT\" has even length.Manao is trying to obtain a functional protein from the protein he currently has. Manao can insert additional nucleotides into the DNA stretch. Each additional nucleotide is a character from the set {'A', 'T', 'G', 'C'}. Manao wants to determine the minimum number of insertions necessary to make the DNA encode a functional protein.","prob_desc_output_spec":"The program should print on one line a single integer representing the minimum number of 'A', 'T', 'G', 'C' characters that are required to be inserted into the input string in order to make all runs of identical characters have odd length.","lang_cluster":"","src_uid":"8b26ca1ca2b28166c3d25dceb1f3d49f","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["implementation","two pointers"],"prob_desc_created_at":"1392573600","prob_desc_sample_inputs":"[\"GTTAAAG\", \"AACCAACCAAAAC\"]","prob_desc_notes":"NoteIn the first example, it is sufficient to insert a single nucleotide of any type between the two 'T's in the sequence to restore the functionality of the protein.","exec_outcome":"","difficulty":null,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The input consists of a single line, containing a string s of length n (1\u2009\u2264\u2009n\u2009\u2264\u2009100). Each character of s will be from the set {'A', 'T', 'G', 'C'}. This problem doesn't have subproblems. You will get 3 points for the correct submission.","prob_desc_sample_outputs":"[\"1\", \"5\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"GTTAAAG\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"AACCAACCAAAAC\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"GTGAATTTCC\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"CAGGGGGCCGCCCATGAAAAAAACCCGGCCCCTTGGGAAAACTTGGGTTA\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"CCCTTCACCCGGATCCAAATCCCTTAGAAATAATCCCCGACGGCGTTGTATCACCTCTGCACTTGTTAGTAAGGTCAGGCGTCCATTACGGAAGAACGTA\\r\\n\", \"output\": [\"19\"]}, {\"input\": \"GCATTACATGGGGGGGTCCTACGAGCCCGGCATCCCGGAAACTAGCCGGTTAATTTGGTTTAAACCCTCCCACCCCGGATTGTAACCCCCCTCATTGGTT\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"TTCCCAGAGAAAAAAAGGGGCCCAAATGCCCTAAAAACCCCCTTTGCCCCCCAACCCCTTTTTAAAATAAAAAGGGGCCCATTCCCTTAAAAATTTTTTG\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"AGCCGCCCCCCCAAAAAAGGGGGAAAAAAAAAAAAAAAAAAAAACTTTTGGAAACCCCCCCCTTTTTTTTTTTTTTTTTTTTTTTTTGGGGAAGGGGGGG\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"AAAAAAAAAAAAAAAAAATTTTTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGAAAAATTTT\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"AACCGGTTAACCGGTTAACCGGTTAACCGGTTAACCGGTTAACCGGTTAACCGGTTAACCGGTTAACCGGTTAACCGGTTAACCGGTTAACCGGTTCCGG\\r\\n\", \"output\": [\"50\"]}, {\"input\": \"A\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"TTT\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"G\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"T\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"C\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"AA\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"GGG\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"AAG\\r\\n\", \"output\": [\"1\"]}]"}
{"prob_desc_description":"The employees of the F company have lots of ways to entertain themselves. Today they invited a famous magician who shows a trick with plastic cups and a marble.The point is to trick the spectator's attention. Initially, the spectator stands in front of a line of n plastic cups. Then the magician places a small marble under one cup and shuffles the cups. Then the spectator should guess which cup hides the marble.But the head coder of the F company isn't easy to trick. When he saw the performance, he noticed several important facts:  each cup contains a mark \u2014 a number from 1 to n; all marks on the cups are distinct;  the magician shuffles the cups in m operations, each operation looks like that: take a cup marked xi, sitting at position yi in the row of cups (the positions are numbered from left to right, starting from 1) and shift it to the very beginning of the cup row (on the first position). When the head coder came home after work he wanted to re-do the trick. Unfortunately, he didn't remember the starting or the final position of the cups. He only remembered which operations the magician performed. Help the coder: given the operations in the order they were made find at least one initial permutation of the cups that can go through the described operations in the given order. Otherwise, state that such permutation doesn't exist.","prob_desc_output_spec":"If the described permutation doesn't exist (the programmer remembered wrong operations), print -1. Otherwise, print n distinct integers, each from 1 to n: the i-th number should represent the mark on the cup that initially is in the row in position i. If there are multiple correct answers, you should print the lexicographically minimum one.","lang_cluster":"","src_uid":"a2616b1681f30ce4b2a5fdc81cf52b50","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["data structures"],"prob_desc_created_at":"1398169140","prob_desc_sample_inputs":"[\"2 1\\n2 1\", \"3 2\\n1 2\\n1 1\", \"3 3\\n1 3\\n2 3\\n1 3\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":2200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"3 seconds","prob_desc_input_spec":"The first line contains integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009106). Each of the next m lines contains a couple of integers. The i-th line contains integers xi, yi (1\u2009\u2264\u2009xi,\u2009yi\u2009\u2264\u2009n) \u2014 the description of the i-th operation of the magician. Note that the operations are given in the order in which the magician made them and the coder wants to make them in the same order.","prob_desc_sample_outputs":"[\"2 1\", \"2 1 3\", \"-1\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 1\\r\\n2 1\\r\\n\", \"output\": [\"2 1\"]}, {\"input\": \"3 2\\r\\n1 2\\r\\n1 1\\r\\n\", \"output\": [\"2 1 3\"]}, {\"input\": \"3 3\\r\\n1 3\\r\\n2 3\\r\\n1 3\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"3 2\\r\\n1 1\\r\\n3 2\\r\\n\", \"output\": [\"1 3 2\"]}, {\"input\": \"5 2\\r\\n3 3\\r\\n3 1\\r\\n\", \"output\": [\"1 2 3 4 5\"]}, {\"input\": \"5 3\\r\\n3 1\\r\\n4 3\\r\\n5 4\\r\\n\", \"output\": [\"3 1 4 5 2\"]}, {\"input\": \"7 3\\r\\n4 4\\r\\n5 4\\r\\n2 4\\r\\n\", \"output\": [\"1 2 5 4 3 6 7\"]}, {\"input\": \"10 3\\r\\n7 10\\r\\n8 7\\r\\n5 5\\r\\n\", \"output\": [\"1 2 5 3 4 8 6 9 10 7\"]}, {\"input\": \"100 50\\r\\n11 28\\r\\n11 1\\r\\n98 58\\r\\n38 27\\r\\n24 27\\r\\n67 37\\r\\n90 48\\r\\n91 14\\r\\n43 29\\r\\n3 64\\r\\n24 6\\r\\n53 19\\r\\n97 65\\r\\n13 27\\r\\n75 53\\r\\n37 82\\r\\n69 75\\r\\n94 99\\r\\n1 26\\r\\n95 60\\r\\n45 27\\r\\n100 82\\r\\n71 49\\r\\n86 99\\r\\n74 58\\r\\n88 68\\r\\n39 63\\r\\n38 23\\r\\n22 39\\r\\n29 58\\r\\n62 83\\r\\n62 1\\r\\n61 58\\r\\n2 30\\r\\n41 48\\r\\n83 90\\r\\n1 17\\r\\n73 81\\r\\n23 53\\r\\n71 16\\r\\n43 29\\r\\n27 78\\r\\n54 48\\r\\n6 89\\r\\n75 27\\r\\n16 93\\r\\n81 81\\r\\n97 31\\r\\n53 32\\r\\n15 96\\r\\n\", \"output\": [\"2 4 5 7 8 9 10 91 12 45 53 1 14 17 18 19 20 13 22 54 21 25 43 24 38 26 28 11 41 30 31 23 32 33 34 67 35 36 71 40 42 61 44 29 46 47 90 74 48 75 49 50 39 95 51 52 55 98 56 57 88 58 59 3 97 60 63 64 65 27 81 66 68 69 73 70 72 76 62 100 77 37 78 79 80 6 82 83 84 85 16 87 89 15 92 93 96 86 94 99\"]}, {\"input\": \"1000000 1000000\\r\\n700833 953480\\r\\n302784 979572\\r\\n292527 1307\\r\\n858668 290285\\r\\n951562 855901\\r\\n810645 427870\\r\\n876834 98466\\r\\n273375 237878\\r\\n464842 946463\\r\\n322686 774281\\r\\n968231 501596\\r\\n721715 494597\\r\\n932210 724682\\r\\n161646 44819\\r\\n908489 549667\\r\\n197570 531975\\r\\n636824 610507\\r\\n904192 539002\\r\\n468366 913132\\r\\n388151 793408\\r\\n535586 995449\\r\\n498191 549071\\r\\n480046 212113\\r\\n553820 77387\\r\\n301144 933938\\r\\n593949 637897\\r\\n56113 336121\\r\\n337463 574591\\r\\n863181 491155\\r\\n861957 441846\\r\\n935887 790693\\r\\n936526 136302\\r\\n772527 677843\\r\\n75477...\", \"output\": [\"287979 230793 805881 397585 695359 3 296206 4 257828 7 649020 9 622178 482759 161855 499413 690372 14 541524 906954 116709 15 17736 555558 848745 16 532778 20 28 752084 32 248311 37 697678 323802 224937 41 44 886110 635290 46 451068 50 79451 52 54 299392 214455 319511 55 56 57 532938 349206 621734 730138 59 61 436368 63 783682 66 608715 997853 823656 79353 73 739717 914085 74 726928 353300 174944 367702 722155 75 991004 341644 492185 79 157363 826980 82 121357 325844 825977 85 87 173852 653068 285829 88 8...\", \"287979 230793 805881 397585 695359 3 296206 4 257828 7 649020 9 622178 482759 161855 499413 690372 14 541524 906954 116709 15 17736 555558 848745 16 532778 20 28 752084 32 248311 37 697678 323802 224937 41 44 886110 635290 46 451068 50 79451 52 54 299392 214455 319511 55 56 57 532938 349206 621734 730138 59 61 436368 63 783682 66 608715 997853 823656 79353 73 739717 914085 74 726928 353300 174944 367702 722155 75 991004 341644 492185 79 157363 826980 82 121357 325844 825977 85 87 173852 653068 285829 88 89...\"]}, {\"input\": \"1 1\\r\\n1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 1\\r\\n1 1\\r\\n\", \"output\": [\"1 2\"]}, {\"input\": \"2 1\\r\\n1 2\\r\\n\", \"output\": [\"2 1\"]}, {\"input\": \"2 1\\r\\n2 2\\r\\n\", \"output\": [\"1 2\"]}, {\"input\": \"2 2\\r\\n1 1\\r\\n2 1\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"2 2\\r\\n1 2\\r\\n2 2\\r\\n\", \"output\": [\"2 1\"]}, {\"input\": \"1000000 1\\r\\n458596 373648\\r\\n\", \"output\": [\"1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 15...\", \"1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155...\"]}, {\"input\": \"1000000 1000000\\r\\n731129 48813\\r\\n411546 534931\\r\\n500799 719558\\r\\n39726 355640\\r\\n72122 769210\\r\\n982992 821130\\r\\n607720 707439\\r\\n395072 960368\\r\\n411414 286147\\r\\n508491 72669\\r\\n963634 316245\\r\\n866688 283962\\r\\n310688 372849\\r\\n251056 422517\\r\\n148593 509187\\r\\n816258 455977\\r\\n858080 296300\\r\\n326170 795291\\r\\n159288 884331\\r\\n979105 588144\\r\\n823563 372590\\r\\n611626 544803\\r\\n136506 806211\\r\\n690071 606045\\r\\n242673 270451\\r\\n215281 197109\\r\\n24668 828553\\r\\n632795 108982\\r\\n165283 834509\\r\\n699264 509305\\r\\n213071 263720\\r\\n198166 62575\\r\\n399046 737811\\r\\n87394...\", \"output\": [\"821273 246590 590490 524668 836635 4 9 10 267943 642594 668620 817485 13 94745 131772 15 70102 270675 17 640287 301334 948927 22 194651 23 29 43124 32 186904 343425 82128 33 34 832597 252217 37 648232 578816 799253 196663 41 43 46 251828 400616 47 749074 670231 995189 295270 50 57 905201 190342 60 63 64 350022 3581 65 455405 66 471585 109369 425981 752815 163963 67 68 945210 69 633720 218102 70 103860 7932 71 717197 784072 72 329416 74 696305 765540 75 79 81 82 803752 867534 83 241162 4207 213624 680152 5...\", \"821273 246590 590490 524668 836635 4 9 10 267943 642594 668620 817485 13 94745 131772 15 70102 270675 17 640287 301334 948927 22 194651 23 29 43124 32 186904 343425 82128 33 34 832597 252217 37 648232 578816 799253 196663 41 43 46 251828 400616 47 749074 670231 995189 295270 50 57 905201 190342 60 63 64 350022 3581 65 455405 66 471585 109369 425981 752815 163963 67 68 945210 69 633720 218102 70 103860 7932 71 717197 784072 72 329416 74 696305 765540 75 79 81 82 803752 867534 83 241162 4207 213624 680152 51...\"]}, {\"input\": \"1000000 1000000\\r\\n248060 999999\\r\\n447756 1000000\\r\\n681182 1000000\\r\\n86296 1000000\\r\\n458962 999997\\r\\n729332 1000000\\r\\n698076 1000000\\r\\n25643 1000000\\r\\n522391 1000000\\r\\n767795 999999\\r\\n235938 1000000\\r\\n942695 1000000\\r\\n96224 999992\\r\\n234167 1000000\\r\\n618507 999999\\r\\n556764 1000000\\r\\n122707 1000000\\r\\n418520 1000000\\r\\n536574 1000000\\r\\n153893 999999\\r\\n844291 1000000\\r\\n457188 1000000\\r\\n604145 1000000\\r\\n326690 999998\\r\\n309815 1000000\\r\\n715554 1000000\\r\\n151397 1000000\\r\\n866520 999998\\r\\n39977 1000000\\r\\n416373 1000000\\r\\n952765 1000000\\r\\n314450 100...\", \"output\": [\"257581 365845 438294 925353 46675 223563 16659 845540 342813 843913 267501 198150 19593 674899 548589 783170 642246 56134 363583 215362 449555 304971 375850 649610 405484 701400 754009 197400 319265 879998 9118 1783 769183 822290 174724 848811 845276 108145 311352 562645 301825 936889 296988 524929 936132 319721 127483 981999 956061 572761 191812 99639 490682 620683 68099 54675 275208 423004 329898 746270 45838 953317 738471 775551 951107 179114 286271 839755 224699 45250 409151 24891 327761 587249 834162...\", \"257581 365845 438294 925353 46675 223563 16659 845540 342813 843913 267501 198150 19593 674899 548589 783170 642246 56134 363583 215362 449555 304971 375850 649610 405484 701400 754009 197400 319265 879998 9118 1783 769183 822290 174724 848811 845276 108145 311352 562645 301825 936889 296988 524929 936132 319721 127483 981999 956061 572761 191812 99639 490682 620683 68099 54675 275208 423004 329898 746270 45838 953317 738471 775551 951107 179114 286271 839755 224699 45250 409151 24891 327761 587249 834162 ...\"]}, {\"input\": \"1000000 1000000\\r\\n686437 1\\r\\n686437 1\\r\\n684166 2\\r\\n684166 1\\r\\n684166 1\\r\\n684166 1\\r\\n684166 1\\r\\n684166 1\\r\\n684166 1\\r\\n686437 2\\r\\n305093 4\\r\\n305093 1\\r\\n305093 1\\r\\n305093 1\\r\\n608490 4\\r\\n686437 3\\r\\n686437 1\\r\\n686437 1\\r\\n686437 1\\r\\n686437 1\\r\\n686437 1\\r\\n686437 1\\r\\n686437 1\\r\\n686437 1\\r\\n686437 1\\r\\n686437 1\\r\\n684166 4\\r\\n686437 2\\r\\n686437 1\\r\\n686437 1\\r\\n608490 3\\r\\n686437 2\\r\\n686437 1\\r\\n608490 2\\r\\n608490 1\\r\\n686437 2\\r\\n686437 1\\r\\n608490 2\\r\\n608490 1\\r\\n686437 2\\r\\n684166 3\\r\\n684166 1\\r\\n684166 1\\r\\n686437 2\\r\\n684166 2\\r\\n684166 1\\r\\n686437 2\\r\\n684166 2\\r\\n686437 2\\r\\n6864...\", \"output\": [\"686437 684166 608490 305093 931589 26069 753320 647738 286711 121954 463009 189179 906660 970639 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 1...\", \"686437 684166 608490 305093 931589 26069 753320 647738 286711 121954 463009 189179 906660 970639 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 13...\"]}, {\"input\": \"5 3\\r\\n2 4\\r\\n3 5\\r\\n5 2\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"10 10\\r\\n9 1\\r\\n6 7\\r\\n4 2\\r\\n8 7\\r\\n3 1\\r\\n10 10\\r\\n3 5\\r\\n6 7\\r\\n10 1\\r\\n6 6\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"100 200\\r\\n97 26\\r\\n71 59\\r\\n1 17\\r\\n52 66\\r\\n58 51\\r\\n76 59\\r\\n23 26\\r\\n91 96\\r\\n32 29\\r\\n61 60\\r\\n34 85\\r\\n4 71\\r\\n99 33\\r\\n76 73\\r\\n63 80\\r\\n31 11\\r\\n84 69\\r\\n17 24\\r\\n15 62\\r\\n73 22\\r\\n44 98\\r\\n41 59\\r\\n70 54\\r\\n34 8\\r\\n81 1\\r\\n87 97\\r\\n14 99\\r\\n41 14\\r\\n47 6\\r\\n49 64\\r\\n60 44\\r\\n26 70\\r\\n11 15\\r\\n98 72\\r\\n97 97\\r\\n46 68\\r\\n19 8\\r\\n79 76\\r\\n62 31\\r\\n98 90\\r\\n71 63\\r\\n44 36\\r\\n19 79\\r\\n34 84\\r\\n56 65\\r\\n59 100\\r\\n58 63\\r\\n93 19\\r\\n59 14\\r\\n72 87\\r\\n44 38\\r\\n27 25\\r\\n17 20\\r\\n81 96\\r\\n97 79\\r\\n53 30\\r\\n92 68\\r\\n46 9\\r\\n20 38\\r\\n12 23\\r\\n52 86\\r\\n25 39\\r\\n48 76\\r\\n85 54\\r\\n11 92\\r\\n71 71\\r\\n71 94\\r\\n33 84\\r\\n32 58\\r\\n51 50\\r\\n37 1\\r\\n97 12\\r\\n66 10...\", \"output\": [\"-1\"]}, {\"input\": \"100 1000000\\r\\n5 75\\r\\n69 13\\r\\n34 26\\r\\n98 37\\r\\n49 10\\r\\n39 9\\r\\n49 22\\r\\n27 37\\r\\n28 6\\r\\n95 80\\r\\n54 30\\r\\n40 37\\r\\n51 28\\r\\n66 21\\r\\n9 77\\r\\n43 63\\r\\n7 36\\r\\n54 74\\r\\n99 90\\r\\n36 31\\r\\n49 57\\r\\n26 17\\r\\n42 50\\r\\n41 35\\r\\n82 26\\r\\n77 30\\r\\n10 52\\r\\n27 40\\r\\n51 30\\r\\n43 97\\r\\n100 11\\r\\n42 10\\r\\n33 32\\r\\n77 93\\r\\n2 12\\r\\n77 99\\r\\n16 14\\r\\n53 54\\r\\n29 6\\r\\n83 11\\r\\n99 64\\r\\n99 29\\r\\n57 20\\r\\n97 88\\r\\n18 5\\r\\n23 83\\r\\n7 71\\r\\n34 54\\r\\n93 88\\r\\n40 97\\r\\n97 18\\r\\n85 71\\r\\n67 67\\r\\n31 44\\r\\n68 52\\r\\n99 44\\r\\n59 71\\r\\n71 17\\r\\n3 98\\r\\n7 93\\r\\n88 57\\r\\n63 94\\r\\n62 67\\r\\n48 32\\r\\n25 58\\r\\n11 58\\r\\n67 18\\r\\n4 9\\r\\n40 74\\r\\n52 40\\r\\n66 19\\r\\n67 82\\r\\n98 72\\r...\", \"output\": [\"-1\"]}, {\"input\": \"1 1000000\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n1 1\\r\\n...\", \"output\": [\"1\"]}, {\"input\": \"1000000 1000000\\r\\n145493 709877\\r\\n915888 170549\\r\\n680394 2504\\r\\n24665 758139\\r\\n242644 365499\\r\\n994789 535590\\r\\n518365 297247\\r\\n852392 834337\\r\\n480961 945750\\r\\n485671 126953\\r\\n262033 11673\\r\\n199902 473744\\r\\n91856 743475\\r\\n779195 394619\\r\\n60537 616388\\r\\n570144 756645\\r\\n285494 510464\\r\\n298148 932570\\r\\n110058 627373\\r\\n686867 469501\\r\\n82153 559208\\r\\n231338 90754\\r\\n748347 478689\\r\\n716892 749236\\r\\n849948 326682\\r\\n733583 653616\\r\\n724863 883500\\r\\n683104 347625\\r\\n780294 675841\\r\\n482075 61922\\r\\n263884 391899\\r\\n777411 701879\\r\\n519515 168716\\r\\n398224 9...\", \"output\": [\"-1\"]}, {\"input\": \"1000000 500000\\r\\n158922 612043\\r\\n520750 458508\\r\\n43377 689461\\r\\n499760 598167\\r\\n59809 158478\\r\\n528215 828265\\r\\n776195 306192\\r\\n969661 949090\\r\\n716100 804829\\r\\n226883 642563\\r\\n789973 77177\\r\\n842955 700209\\r\\n677612 596299\\r\\n768381 990264\\r\\n59201 301792\\r\\n415811 70469\\r\\n351314 702568\\r\\n827596 439659\\r\\n319263 51319\\r\\n967564 61471\\r\\n490158 376261\\r\\n582779 636988\\r\\n56264 709743\\r\\n488338 80832\\r\\n419834 664820\\r\\n200209 434893\\r\\n761686 878648\\r\\n767036 854889\\r\\n678383 272516\\r\\n919705 583934\\r\\n36064 785412\\r\\n14963 292187\\r\\n450118 913031\\r\\n116570 9329...\", \"output\": [\"-1\"]}, {\"input\": \"10000 3000\\r\\n7531 5050\\r\\n1786 5222\\r\\n8170 8065\\r\\n2280 9993\\r\\n7701 1972\\r\\n9237 4740\\r\\n7465 6285\\r\\n9264 500\\r\\n3162 6281\\r\\n3438 3815\\r\\n8397 474\\r\\n8294 5168\\r\\n3196 195\\r\\n3541 2583\\r\\n9093 6176\\r\\n2635 8118\\r\\n9243 2507\\r\\n6413 9357\\r\\n9987 9400\\r\\n6705 8270\\r\\n2009 4618\\r\\n9588 2769\\r\\n9833 1307\\r\\n7655 8082\\r\\n2662 5224\\r\\n974 1534\\r\\n9222 1971\\r\\n2912 3402\\r\\n8467 3840\\r\\n938 1276\\r\\n9164 1848\\r\\n1436 384\\r\\n5154 8969\\r\\n9562 7652\\r\\n6107 1235\\r\\n5452 3084\\r\\n1539 6716\\r\\n1134 607\\r\\n9558 3085\\r\\n7041 3447\\r\\n3127 9492\\r\\n5192 9429\\r\\n7229 9168\\r\\n4780 5324\\r\\n6176 5880\\r\\n8009 5841\\r\\n...\", \"output\": [\"-1\"]}, {\"input\": \"50000 77000\\r\\n11640 12953\\r\\n24857 19131\\r\\n10379 33514\\r\\n48482 41888\\r\\n14804 32268\\r\\n13579 10572\\r\\n38169 40\\r\\n45500 15067\\r\\n6563 17385\\r\\n4128 32716\\r\\n26911 1327\\r\\n12822 2815\\r\\n47262 38911\\r\\n41105 45371\\r\\n47717 38816\\r\\n12473 59\\r\\n42590 111\\r\\n1576 18411\\r\\n43653 1788\\r\\n39614 14016\\r\\n40589 13659\\r\\n45806 9726\\r\\n9977 41444\\r\\n2319 20223\\r\\n34898 12420\\r\\n5659 3299\\r\\n49351 794\\r\\n15891 18186\\r\\n46233 37946\\r\\n34393 10940\\r\\n29371 18509\\r\\n26772 28065\\r\\n36648 271\\r\\n34128 47610\\r\\n33980 27568\\r\\n29259 49702\\r\\n15690 47604\\r\\n17545 11997\\r\\n2501 18563\\r\\n17297 31481\\r\\n14...\", \"output\": [\"-1\"]}]"}
{"prob_desc_description":"Let's assume that set S consists of m distinct intervals [l1,\u2009r1], [l2,\u2009r2], ..., [lm,\u2009rm] (1\u2009\u2264\u2009li\u2009\u2264\u2009ri\u2009\u2264\u2009n; li,\u2009ri are integers).Let's assume that f(S) is the maximum number of intervals that you can choose from the set S, such that every two of them do not intersect. We assume that two intervals, [l1,\u2009r1] and [l2,\u2009r2], intersect if there is an integer x, which meets two inequalities: l1\u2009\u2264\u2009x\u2009\u2264\u2009r1 and l2\u2009\u2264\u2009x\u2009\u2264\u2009r2.Sereja wonders, how many sets S are there, such that f(S)\u2009=\u2009k? Count this number modulo 1000000007 (109\u2009+\u20097).","prob_desc_output_spec":"In a single line, print the answer to the problem modulo 1000000007 (109\u2009+\u20097).","lang_cluster":"","src_uid":"111673158df2e37ac6c019bb99225ccb","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp"],"prob_desc_created_at":"1398612600","prob_desc_sample_inputs":"[\"3 1\", \"3 2\", \"2 0\", \"2 2\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":2500.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1.5 seconds","prob_desc_input_spec":"The first line contains integers n, k (1\u2009\u2264\u2009n\u2009\u2264\u2009500;\u00a00\u2009\u2264\u2009k\u2009\u2264\u2009500).","prob_desc_sample_outputs":"[\"23\", \"32\", \"1\", \"2\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3 1\\r\\n\", \"output\": [\"23\"]}, {\"input\": \"3 2\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"2 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"20 10\\r\\n\", \"output\": [\"169364726\"]}, {\"input\": \"50 49\\r\\n\", \"output\": [\"560578792\"]}, {\"input\": \"50 100\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"10 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"50 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10 9\\r\\n\", \"output\": [\"391716853\"]}, {\"input\": \"100 10\\r\\n\", \"output\": [\"209177805\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 100\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"100 100\\r\\n\", \"output\": [\"281603733\"]}, {\"input\": \"100 99\\r\\n\", \"output\": [\"599757793\"]}, {\"input\": \"100 50\\r\\n\", \"output\": [\"820383341\"]}, {\"input\": \"99 60\\r\\n\", \"output\": [\"97903617\"]}, {\"input\": \"95 93\\r\\n\", \"output\": [\"483334618\"]}, {\"input\": \"400 399\\r\\n\", \"output\": [\"760864214\"]}, {\"input\": \"500 499\\r\\n\", \"output\": [\"582854781\"]}, {\"input\": \"500 500\\r\\n\", \"output\": [\"731931766\"]}, {\"input\": \"400 500\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"500 20\\r\\n\", \"output\": [\"211189748\"]}, {\"input\": \"5 3\\r\\n\", \"output\": [\"14720\"]}, {\"input\": \"5 5\\r\\n\", \"output\": [\"1024\"]}, {\"input\": \"4 1\\r\\n\", \"output\": [\"127\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"64\"]}]"}
{"prob_desc_description":"Iahub is training for the IOI. What is a better way to train than playing a Zuma-like game? There are n balls put in a row. Each ball is colored in one of k colors. Initially the row doesn't contain three or more contiguous balls with the same color. Iahub has a single ball of color x. He can insert his ball at any position in the row (probably, between two other balls). If at any moment there are three or more contiguous balls of the same color in the row, they are destroyed immediately. This rule is applied multiple times, until there are no more sets of 3 or more contiguous balls of the same color. For example, if Iahub has the row of balls [black, black, white, white, black, black] and a white ball, he can insert the ball between two white balls. Thus three white balls are destroyed, and then four black balls become contiguous, so all four balls are destroyed. The row will not contain any ball in the end, so Iahub can destroy all 6 balls.Iahub wants to destroy as many balls as possible. You are given the description of the row of balls, and the color of Iahub's ball. Help Iahub train for the IOI by telling him the maximum number of balls from the row he can destroy.","prob_desc_output_spec":"Print a single integer \u2014 the maximum number of balls Iahub can destroy.","lang_cluster":"","src_uid":"d73d9610e3800817a3109314b1e6f88c","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","two pointers"],"prob_desc_created_at":"1399822800","prob_desc_sample_inputs":"[\"6 2 2\\n1 1 2 2 1 1\", \"1 1 1\\n1\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1400.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line of input contains three integers: n (1\u2009\u2264\u2009n\u2009\u2264\u2009100), k (1\u2009\u2264\u2009k\u2009\u2264\u2009100) and x (1\u2009\u2264\u2009x\u2009\u2264\u2009k). The next line contains n space-separated integers c1,\u2009c2,\u2009...,\u2009cn (1\u2009\u2264\u2009ci\u2009\u2264\u2009k). Number ci means that the i-th ball in the row has color ci. It is guaranteed that the initial row of balls will never contain three or more contiguous balls of the same color. ","prob_desc_sample_outputs":"[\"6\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"6 2 2\\r\\n1 1 2 2 1 1\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"1 1 1\\r\\n1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"10 2 1\\r\\n2 1 2 2 1 2 2 1 1 2\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"50 2 1\\r\\n1 1 2 2 1 2 1 1 2 2 1 2 1 2 1 1 2 2 1 2 1 2 2 1 2 1 2 1 2 2 1 1 2 2 1 1 2 2 1 2 1 1 2 1 1 2 2 1 1 2\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"75 5 5\\r\\n1 1 5 5 3 5 2 3 3 2 2 1 1 5 4 4 3 4 5 4 3 3 1 2 2 1 2 1 2 5 5 2 1 3 2 2 3 1 2 1 1 5 5 1 1 2 1 1 2 2 5 2 2 1 1 2 1 2 1 1 3 3 5 4 4 3 3 4 4 5 5 1 1 2 2\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"100 3 2\\r\\n1 1 2 3 1 3 2 1 1 3 3 2 2 1 1 2 2 1 1 3 2 2 3 2 3 2 2 3 3 1 1 2 2 1 2 2 1 3 3 1 3 3 1 2 1 2 2 1 2 3 2 1 1 2 1 1 3 3 1 3 3 1 1 2 2 1 1 2 1 3 2 2 3 2 2 3 3 1 2 1 2 2 1 1 2 3 1 3 3 1 2 3 2 2 1 3 2 2 3 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"100 2 1\\r\\n2 2 1 2 1 2 1 2 2 1 1 2 1 1 2 1 1 2 2 1 1 2 1 1 2 1 2 2 1 2 1 2 1 2 1 1 2 1 1 2 1 1 2 2 1 1 2 1 2 2 1 2 1 2 1 2 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 2 1 2 2 1 2 1 1 2 1 2 1 1 2 1 1 2 1 1 2 2 1 2 2 1 1 2 1\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"100 2 2\\r\\n1 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2 2 1 1 2 1 1 2 2 1 1 2 1 2 2 1 2 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 1 2 1 1 2 2 1 1 2 2 1 2 1 2 1 2 1 2 2 1 2 1 2 2 1 1 2 1 2 2 1 1 2 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 2 1 2 2\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"100 2 2\\r\\n1 2 1 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 2 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 2 1 1 2 1 1 2 1 2 2 1 1 2 2 1 1 2 1 2 2 1 1 2 1 2 1 2 2 1 2 2 1 1 2 1 2 2 1 2 2 1 2 1 1 2 1 2 2 1 2 2 1 2 1 2 1 2 1 1 2 2 1 1 2 2\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"100 2 2\\r\\n2 1 1 2 2 1 1 2 1 2 1 1 2 2 1 2 1 2 1 2 2 1 2 1 1 2 1 2 1 2 1 2 1 1 2 2 1 1 2 1 1 2 1 2 2 1 1 2 1 2 1 1 2 2 1 1 2 1 2 1 2 1 2 2 1 1 2 2 1 1 2 2 1 2 1 2 1 1 2 1 1 2 2 1 2 1 2 2 1 2 2 1 1 2 1 2 2 1 2 2\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"100 2 2\\r\\n1 2 2 1 2 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 2 1 2 1 2 1 2 1 2 1 1 2 1 1 2 1 2 2 1 1 2 2 1 1 2 1 1 2 2 1 2 1 2 1 2 1 2 1 1 2 2 1 1 2 2 1 1 2 2 1 2 2 1 1 2 1 2 2 1 2 2 1 2 2 1 2 2 1 1 2 2 1 2 1 2 1 2 1\\r\\n\", \"output\": [\"28\"]}, {\"input\": \"100 2 2\\r\\n1 1 2 1 2 1 1 2 1 2 1 2 2 1 2 1 2 1 1 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1 2 2 1 2 1 2 1 1 2 1 2 1 1 2 2 1 1 2 1 2 1 2 1 2 1 2 2 1 1 2 1 2 2 1 2 1 1 2 1 1 2 1 2 1 2 1 1 2 1 2 2 1 2 1 2 2 1 1 2 1 2 2 1 1 2 2\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"100 100 50\\r\\n15 44 5 7 75 40 52 82 78 90 48 32 16 53 69 2 21 84 7 21 21 87 29 8 42 54 10 21 38 55 54 88 48 63 3 17 45 82 82 91 7 11 11 24 24 79 1 32 32 38 41 41 4 4 74 17 26 26 96 96 3 3 50 50 96 26 26 17 17 74 74 4 41 38 38 32 1 1 79 79 24 11 11 7 7 91 91 82 45 45 97 9 74 60 32 91 61 64 100 26\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"100 50 22\\r\\n15 2 18 15 48 35 46 33 32 39 39 5 5 27 27 50 50 47 47 10 10 6 3 3 7 8 7 17 17 29 14 10 10 46 13 13 31 32 31 22 22 32 31 31 32 13 13 46 46 10 10 14 14 29 29 17 7 7 8 3 6 6 10 47 50 50 27 5 5 39 39 21 47 4 40 47 21 28 21 21 40 27 34 17 3 36 5 7 21 14 25 49 40 34 32 13 23 29 2 4\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"100 3 3\\r\\n3 1 1 2 1 1 3 1 3 3 1 3 3 1 2 1 1 2 2 3 3 2 3 2 2 3 1 3 3 2 2 1 3 3 2 2 1 2 3 3 1 3 1 3 1 2 2 1 2 1 2 3 1 3 1 3 2 1 3 2 3 3 2 3 2 3 1 3 2 2 1 2 1 2 1 1 3 1 3 1 2 1 2 1 2 3 2 2 3 3 2 2 3 2 2 3 1 1 2 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"100 100 100\\r\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"100 2 2\\r\\n1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2\\r\\n\", \"output\": [\"98\"]}, {\"input\": \"6 20 10\\r\\n10 2 10 10 2 2\\r\\n\", \"output\": [\"5\"]}]"}
{"prob_desc_description":"Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?","prob_desc_output_spec":"Print a single integer \u2014 the minimum sum in rubles that Ann will need to spend.","lang_cluster":"","src_uid":"faa343ad6028c5a069857a38fa19bb24","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["implementation"],"prob_desc_created_at":"1410535800","prob_desc_sample_inputs":"[\"6 2 1 2\", \"5 2 2 3\"]","prob_desc_notes":"NoteIn the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.","exec_outcome":"","difficulty":1200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The single line contains four space-separated integers n, m, a, b (1\u2009\u2264\u2009n,\u2009m,\u2009a,\u2009b\u2009\u2264\u20091000) \u2014 the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket. ","prob_desc_sample_outputs":"[\"6\", \"8\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"6 2 1 2\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"5 2 2 3\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"10 3 5 1\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"1000 1 1000 1000\\r\\n\", \"output\": [\"1000000\"]}, {\"input\": \"1000 3 1000 1000\\r\\n\", \"output\": [\"334000\"]}, {\"input\": \"1 1 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10 2 1 1\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"1 1000 1 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1000 3 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"10 3 1 2\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"995 1 2 1\\r\\n\", \"output\": [\"995\"]}, {\"input\": \"556 2 16 15\\r\\n\", \"output\": [\"4170\"]}, {\"input\": \"477 2 16 14\\r\\n\", \"output\": [\"3346\"]}, {\"input\": \"101 110 1 100\\r\\n\", \"output\": [\"100\"]}, {\"input\": \"9 3 3 10\\r\\n\", \"output\": [\"27\"]}, {\"input\": \"100 8 10 1\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"6 4 1 3\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"8 5 2 8\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"1000 2 1 1000\\r\\n\", \"output\": [\"1000\"]}]"}
{"prob_desc_description":"Pasha has a positive integer a without leading zeroes. Today he decided that the number is too small and he should make it larger. Unfortunately, the only operation Pasha can do is to swap two adjacent decimal digits of the integer.Help Pasha count the maximum number he can get if he has the time to make at most k swaps.","prob_desc_output_spec":"Print the maximum number that Pasha can get if he makes at most k swaps.","lang_cluster":"","src_uid":"e56f6c343167745821f0b18dcf0d0cde","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["greedy"],"prob_desc_created_at":"1401463800","prob_desc_sample_inputs":"[\"1990 1\", \"300 0\", \"1034 2\", \"9090000078001234 6\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1400.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The single line contains two integers a and k (1\u2009\u2264\u2009a\u2009\u2264\u20091018;\u00a00\u2009\u2264\u2009k\u2009\u2264\u2009100).","prob_desc_sample_outputs":"[\"9190\", \"300\", \"3104\", \"9907000008001234\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1990 1\\r\\n\", \"output\": [\"9190\"]}, {\"input\": \"300 0\\r\\n\", \"output\": [\"300\"]}, {\"input\": \"1034 2\\r\\n\", \"output\": [\"3104\"]}, {\"input\": \"9090000078001234 6\\r\\n\", \"output\": [\"9907000008001234\"]}, {\"input\": \"1234 3\\r\\n\", \"output\": [\"4123\"]}, {\"input\": \"5 100\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"1234 5\\r\\n\", \"output\": [\"4312\"]}, {\"input\": \"1234 6\\r\\n\", \"output\": [\"4321\"]}, {\"input\": \"9022 2\\r\\n\", \"output\": [\"9220\"]}, {\"input\": \"66838 4\\r\\n\", \"output\": [\"86863\"]}, {\"input\": \"39940894417248510 10\\r\\n\", \"output\": [\"99984304417248510\"]}, {\"input\": \"5314 4\\r\\n\", \"output\": [\"5431\"]}, {\"input\": \"1026 9\\r\\n\", \"output\": [\"6210\"]}, {\"input\": \"4529 8\\r\\n\", \"output\": [\"9542\"]}, {\"input\": \"83811284 3\\r\\n\", \"output\": [\"88321184\"]}, {\"input\": \"92153348 6\\r\\n\", \"output\": [\"98215334\"]}, {\"input\": \"5846059 3\\r\\n\", \"output\": [\"8654059\"]}, {\"input\": \"521325125110071928 4\\r\\n\", \"output\": [\"552132125110071928\"]}, {\"input\": \"39940894417248510 10\\r\\n\", \"output\": [\"99984304417248510\"]}, {\"input\": \"77172428736634377 29\\r\\n\", \"output\": [\"87777764122363437\"]}, {\"input\": \"337775999910796051 37\\r\\n\", \"output\": [\"999997733751076051\"]}, {\"input\": \"116995340392134308 27\\r\\n\", \"output\": [\"999654331120134308\"]}, {\"input\": \"10120921290110921 20\\r\\n\", \"output\": [\"99221010120110921\"]}, {\"input\": \"929201010190831892 30\\r\\n\", \"output\": [\"999928201010103182\"]}, {\"input\": \"111111111111111119 8\\r\\n\", \"output\": [\"111111111911111111\"]}, {\"input\": \"219810011901120912 100\\r\\n\", \"output\": [\"999822211111110000\"]}, {\"input\": \"191919191919119911 100\\r\\n\", \"output\": [\"999999991111111111\"]}, {\"input\": \"801211288881101019 22\\r\\n\", \"output\": [\"982111028888110101\"]}, {\"input\": \"619911311932347059 3\\r\\n\", \"output\": [\"969111311932347059\"]}, {\"input\": \"620737553540689123 2\\r\\n\", \"output\": [\"672037553540689123\"]}, {\"input\": \"621563797296514835 3\\r\\n\", \"output\": [\"662153797296514835\"]}, {\"input\": \"915277434701161 9\\r\\n\", \"output\": [\"977541234701161\"]}, {\"input\": \"15603712376708 28\\r\\n\", \"output\": [\"87761503123670\"]}, {\"input\": \"784069392990841 0\\r\\n\", \"output\": [\"784069392990841\"]}, {\"input\": \"787464780004 2\\r\\n\", \"output\": [\"877644780004\"]}, {\"input\": \"74604713975 29\\r\\n\", \"output\": [\"97776544310\"]}, {\"input\": \"901000000954321789 5\\r\\n\", \"output\": [\"910009000054321789\"]}, {\"input\": \"901000000954321789 10\\r\\n\", \"output\": [\"991000000504321789\"]}, {\"input\": \"901000000954321789 28\\r\\n\", \"output\": [\"999100050000432178\"]}, {\"input\": \"901000000954321789 40\\r\\n\", \"output\": [\"999810000050043217\"]}, {\"input\": \"901000000954321789 70\\r\\n\", \"output\": [\"999875410000300021\"]}, {\"input\": \"1234567891234567 99\\r\\n\", \"output\": [\"9877665544332211\"]}, {\"input\": \"123456789123456789 100\\r\\n\", \"output\": [\"998877665544213123\"]}, {\"input\": \"12345670123456789 100\\r\\n\", \"output\": [\"98776655443322101\"]}, {\"input\": \"12 100\\r\\n\", \"output\": [\"21\"]}, {\"input\": \"11223344556677889 47\\r\\n\", \"output\": [\"98821213344556677\"]}]"}
{"prob_desc_description":"This winter is so cold in Nvodsk! A group of n friends decided to buy k bottles of a soft drink called \"Take-It-Light\" to warm up a bit. Each bottle has l milliliters of the drink. Also they bought c limes and cut each of them into d slices. After that they found p grams of salt.To make a toast, each friend needs nl milliliters of the drink, a slice of lime and np grams of salt. The friends want to make as many toasts as they can, provided they all drink the same amount. How many toasts can each friend make?","prob_desc_output_spec":"Print a single integer \u2014 the number of toasts each friend can make.","lang_cluster":"","src_uid":"67410b7d36b9d2e6a97ca5c7cff317c1","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","implementation"],"prob_desc_created_at":"1329490800","prob_desc_sample_inputs":"[\"3 4 5 10 8 100 3 1\", \"5 100 10 1 19 90 4 3\", \"10 1000 1000 25 23 1 50 1\"]","prob_desc_notes":"NoteA comment to the first sample: Overall the friends have 4\u2009*\u20095\u2009=\u200920 milliliters of the drink, it is enough to make 20\u2009\/\u20093\u2009=\u20096 toasts. The limes are enough for 10\u2009*\u20098\u2009=\u200980 toasts and the salt is enough for 100\u2009\/\u20091\u2009=\u2009100 toasts. However, there are 3 friends in the group, so the answer is min(6,\u200980,\u2009100)\u2009\/\u20093\u2009=\u20092.","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first and only line contains positive integers n, k, l, c, d, p, nl, np, not exceeding 1000 and no less than 1. The numbers are separated by exactly one space.","prob_desc_sample_outputs":"[\"2\", \"3\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3 4 5 10 8 100 3 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"5 100 10 1 19 90 4 3\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"10 1000 1000 25 23 1 50 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 7 4 5 5 8 3 2\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"2 3 3 5 5 10 1 3\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 6 4 5 6 5 1 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 7 3 5 3 6 2 1\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"2 4 5 4 5 7 3 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 3 6 5 7 8 2 1\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"1 4 5 5 3 10 3 1\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"1 4 6 7 3 5 1 3\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 6 5 5 5 8 3 1\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"1 7 5 3 3 9 2 1\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"3 5 3 7 6 10 3 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 6 3 5 3 6 3 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 7 5 5 5 5 2 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2 5 3 5 6 9 2 1\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"3 4 3 5 3 6 2 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 5 5 4 7 6 3 1\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"2 3 7 6 5 9 3 1\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"2 6 5 3 3 8 1 1\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"2 4 7 3 4 10 2 1\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"1 1000 1000 1000 1000 1000 1 1\\r\\n\", \"output\": [\"1000\"]}, {\"input\": \"17 1000 1000 1000 1000 1000 3 7\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"115 1000 1000 1000 1000 1000 17 15\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 587 981 1 2 1 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 1 2 1 2 2 1 1\\r\\n\", \"output\": [\"2\"]}]"}
{"prob_desc_description":"Lavrenty, a baker, is going to make several buns with stuffings and sell them.Lavrenty has n grams of dough as well as m different stuffing types. The stuffing types are numerated from 1 to m. Lavrenty knows that he has ai grams left of the i-th stuffing. It takes exactly bi grams of stuffing i and ci grams of dough to cook a bun with the i-th stuffing. Such bun can be sold for di tugriks.Also he can make buns without stuffings. Each of such buns requires c0 grams of dough and it can be sold for d0 tugriks. So Lavrenty can cook any number of buns with different stuffings or without it unless he runs out of dough and the stuffings. Lavrenty throws away all excess material left after baking.Find the maximum number of tugriks Lavrenty can earn.","prob_desc_output_spec":"Print the only number \u2014 the maximum number of tugriks Lavrenty can earn.","lang_cluster":"","src_uid":"4e166b8b44427b1227e0f811161d3a6f","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp"],"prob_desc_created_at":"1313766000","prob_desc_sample_inputs":"[\"10 2 2 1\\n7 3 2 100\\n12 3 1 10\", \"100 1 25 50\\n15 5 20 10\"]","prob_desc_notes":"NoteTo get the maximum number of tugriks in the first sample, you need to cook 2 buns with stuffing 1, 4 buns with stuffing 2 and a bun without any stuffing.In the second sample Lavrenty should cook 4 buns without stuffings.","exec_outcome":"","difficulty":1700.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains 4 integers n, m, c0 and d0 (1\u2009\u2264\u2009n\u2009\u2264\u20091000, 1\u2009\u2264\u2009m\u2009\u2264\u200910, 1\u2009\u2264\u2009c0,\u2009d0\u2009\u2264\u2009100). Each of the following m lines contains 4 integers. The i-th line contains numbers ai, bi, ci and di (1\u2009\u2264\u2009ai,\u2009bi,\u2009ci,\u2009di\u2009\u2264\u2009100).","prob_desc_sample_outputs":"[\"241\", \"200\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"10 2 2 1\\r\\n7 3 2 100\\r\\n12 3 1 10\\r\\n\", \"output\": [\"241\"]}, {\"input\": \"100 1 25 50\\r\\n15 5 20 10\\r\\n\", \"output\": [\"200\"]}, {\"input\": \"10 1 5 2\\r\\n100 1 2 3\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"10 1 5 11\\r\\n3 1 3 8\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"10 2 11 5\\r\\n100 1 3 10\\r\\n100 1 2 4\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"5 8 6 5\\r\\n1 2 5 4\\r\\n1 2 6 7\\r\\n1 2 3 5\\r\\n1 2 1 6\\r\\n1 2 8 3\\r\\n1 2 2 4\\r\\n1 2 5 6\\r\\n1 2 7 7\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"300 4 100 2\\r\\n10 1 24 5\\r\\n10 1 25 6\\r\\n10 1 26 7\\r\\n10 1 27 8\\r\\n\", \"output\": [\"87\"]}, {\"input\": \"1 1 1 1\\r\\n1 1 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 1 2 1\\r\\n1 2 1 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10 2 13 100\\r\\n20 1 3 10\\r\\n20 1 2 6\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"100 5 8 80\\r\\n25 8 2 70\\r\\n27 6 7 30\\r\\n26 1 6 5\\r\\n7 1 1 86\\r\\n18 8 4 54\\r\\n\", \"output\": [\"1670\"]}, {\"input\": \"150 8 3 46\\r\\n39 4 10 25\\r\\n31 17 8 70\\r\\n37 2 13 1\\r\\n29 17 17 59\\r\\n54 20 5 39\\r\\n53 14 10 23\\r\\n50 12 16 41\\r\\n8 2 6 61\\r\\n\", \"output\": [\"2300\"]}, {\"input\": \"231 10 9 30\\r\\n98 11 5 17\\r\\n59 13 1 47\\r\\n83 1 7 2\\r\\n42 21 1 6\\r\\n50 16 2 9\\r\\n44 10 5 31\\r\\n12 20 8 9\\r\\n61 23 7 2\\r\\n85 18 2 19\\r\\n82 25 10 20\\r\\n\", \"output\": [\"1065\"]}, {\"input\": \"345 10 5 45\\r\\n1 23 14 55\\r\\n51 26 15 11\\r\\n65 4 16 36\\r\\n81 14 13 25\\r\\n8 9 13 60\\r\\n43 4 7 59\\r\\n85 11 14 35\\r\\n82 13 5 49\\r\\n85 28 15 3\\r\\n51 21 18 53\\r\\n\", \"output\": [\"3129\"]}, {\"input\": \"401 10 2 82\\r\\n17 9 14 48\\r\\n79 4 3 38\\r\\n1 2 6 31\\r\\n45 2 9 60\\r\\n45 2 4 50\\r\\n6 1 3 36\\r\\n3 1 19 37\\r\\n78 3 8 33\\r\\n59 8 19 19\\r\\n65 10 2 61\\r\\n\", \"output\": [\"16400\"]}, {\"input\": \"777 10 23 20\\r\\n50 90 86 69\\r\\n33 90 59 73\\r\\n79 26 35 31\\r\\n57 48 97 4\\r\\n5 10 48 87\\r\\n35 99 33 34\\r\\n7 32 54 35\\r\\n56 25 10 38\\r\\n5 3 89 76\\r\\n13 33 91 66\\r\\n\", \"output\": [\"734\"]}, {\"input\": \"990 10 7 20\\r\\n38 82 14 69\\r\\n5 66 51 5\\r\\n11 26 91 11\\r\\n29 12 73 96\\r\\n93 82 48 59\\r\\n19 15 5 50\\r\\n15 36 6 63\\r\\n16 57 94 90\\r\\n45 3 57 72\\r\\n61 41 47 18\\r\\n\", \"output\": [\"2850\"]}, {\"input\": \"1000 10 51 56\\r\\n2 62 82 65\\r\\n37 90 87 97\\r\\n11 94 47 95\\r\\n49 24 97 24\\r\\n33 38 40 31\\r\\n27 15 17 66\\r\\n91 80 34 71\\r\\n60 93 42 94\\r\\n9 35 73 68\\r\\n93 65 83 58\\r\\n\", \"output\": [\"1145\"]}, {\"input\": \"1000 10 1 53\\r\\n63 1 1 58\\r\\n58 1 2 28\\r\\n100 1 1 25\\r\\n61 1 1 90\\r\\n96 2 2 50\\r\\n19 2 1 90\\r\\n7 2 1 30\\r\\n90 1 2 5\\r\\n34 2 1 12\\r\\n3 2 1 96\\r\\n\", \"output\": [\"55948\"]}, {\"input\": \"1000 10 1 65\\r\\n77 1 1 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100 100\\r\\n100 1 100 100\\r\\n100 1 100 100\\r\\n100 1 100 100\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1000 10 100 75\\r\\n100 97 100 95\\r\\n100 64 100 78\\r\\n100 82 100 35\\r\\n100 51 100 64\\r\\n100 67 100 25\\r\\n100 79 100 33\\r\\n100 65 100 85\\r\\n100 99 100 78\\r\\n100 53 100 74\\r\\n100 87 100 73\\r\\n\", \"output\": [\"786\"]}, {\"input\": \"999 10 5 100\\r\\n100 1 10 100\\r\\n100 1 10 100\\r\\n100 1 10 100\\r\\n100 1 10 100\\r\\n100 1 10 100\\r\\n100 1 10 100\\r\\n100 1 10 100\\r\\n100 1 10 100\\r\\n100 1 10 100\\r\\n100 1 10 100\\r\\n\", \"output\": [\"19900\"]}, {\"input\": \"1000 10 50 100\\r\\n7 1 80 100\\r\\n5 1 37 100\\r\\n9 1 25 100\\r\\n7 1 17 100\\r\\n6 1 10 100\\r\\n5 1 15 100\\r\\n6 1 13 100\\r\\n2 1 14 100\\r\\n4 1 17 100\\r\\n3 1 32 100\\r\\n\", \"output\": [\"4800\"]}, {\"input\": \"1000 10 1 1\\r\\n1 2 1 97\\r\\n1 2 1 95\\r\\n1 2 1 99\\r\\n1 2 1 98\\r\\n1 2 1 93\\r\\n1 2 1 91\\r\\n1 2 1 90\\r\\n1 2 1 94\\r\\n1 2 1 92\\r\\n1 2 1 99\\r\\n\", \"output\": [\"1000\"]}, {\"input\": \"1 10 1 97\\r\\n1 1 1 98\\r\\n1 1 1 99\\r\\n1 1 1 76\\r\\n1 1 1 89\\r\\n1 1 1 64\\r\\n1 1 1 83\\r\\n1 1 1 72\\r\\n1 1 1 66\\r\\n1 1 1 54\\r\\n1 1 1 73\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"3 10 10 98\\r\\n10 5 5 97\\r\\n6 7 1 56\\r\\n23 10 5 78\\r\\n40 36 4 35\\r\\n30 50 1 30\\r\\n60 56 8 35\\r\\n70 90 2 17\\r\\n10 11 3 68\\r\\n1 2 17 70\\r\\n13 4 8 19\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1000 1 23 76\\r\\n74 22 14 5\\r\\n\", \"output\": [\"3268\"]}, {\"input\": \"1000 2 95 56\\r\\n58 54 66 61\\r\\n61 14 67 65\\r\\n\", \"output\": [\"713\"]}, {\"input\": \"1000 3 67 88\\r\\n90 86 66 17\\r\\n97 38 63 17\\r\\n55 78 39 51\\r\\n\", \"output\": [\"1232\"]}, {\"input\": \"1000 4 91 20\\r\\n74 18 18 73\\r\\n33 10 59 21\\r\\n7 42 87 79\\r\\n9 100 77 100\\r\\n\", \"output\": [\"515\"]}, {\"input\": \"1000 5 63 52\\r\\n6 98 18 77\\r\\n17 34 3 73\\r\\n59 6 35 7\\r\\n61 16 85 64\\r\\n73 62 40 11\\r\\n\", \"output\": [\"804\"]}, {\"input\": \"1000 6 87 32\\r\\n90 30 70 33\\r\\n53 6 99 77\\r\\n59 22 83 35\\r\\n65 32 93 28\\r\\n85 50 60 7\\r\\n15 15 5 82\\r\\n\", \"output\": [\"771\"]}, {\"input\": \"1000 7 59 64\\r\\n22 62 70 89\\r\\n37 78 43 29\\r\\n11 86 83 63\\r\\n17 48 1 92\\r\\n97 38 80 55\\r\\n15 3 89 42\\r\\n87 80 62 35\\r\\n\", \"output\": [\"1024\"]}, {\"input\": \"1000 8 31 96\\r\\n6 94 70 93\\r\\n73 2 39 33\\r\\n63 50 31 91\\r\\n21 64 9 56\\r\\n61 26 100 51\\r\\n67 39 21 50\\r\\n79 4 2 71\\r\\n100 9 18 86\\r\\n\", \"output\": [\"4609\"]}, {\"input\": \"1000 9 55 28\\r\\n38 74 22 49\\r\\n9 74 83 85\\r\\n63 66 79 19\\r\\n25 32 17 20\\r\\n73 62 20 47\\r\\n19 27 53 58\\r\\n71 80 94 7\\r\\n56 69 62 98\\r\\n49 7 65 76\\r\\n\", \"output\": [\"831\"]}, {\"input\": \"1000 10 67 55\\r\\n10 21 31 19\\r\\n95 29 53 1\\r\\n55 53 19 18\\r\\n26 88 19 94\\r\\n31 1 45 50\\r\\n70 38 33 93\\r\\n2 12 7 95\\r\\n54 37 81 31\\r\\n65 32 63 16\\r\\n93 66 98 38\\r\\n\", \"output\": [\"1161\"]}, {\"input\": \"1000 10 37 38\\r\\n65 27 78 14\\r\\n16 70 78 66\\r\\n93 86 91 43\\r\\n95 6 72 86\\r\\n72 59 94 36\\r\\n66 58 96 40\\r\\n41 72 64 4\\r\\n26 47 69 13\\r\\n85 2 52 15\\r\\n34 62 16 79\\r\\n\", \"output\": [\"1156\"]}, {\"input\": \"1000 10 58 21\\r\\n73 85 73 10\\r\\n38 60 55 31\\r\\n32 66 62 16\\r\\n63 76 73 78\\r\\n61 17 92 70\\r\\n61 79 11 87\\r\\n27 31 21 62\\r\\n47 9 4 94\\r\\n4 71 42 61\\r\\n76 5 35 72\\r\\n\", \"output\": [\"1823\"]}, {\"input\": \"12 2 100 1\\r\\n100 1 9 10\\r\\n100 1 4 4\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"1 1 1 10\\r\\n100 100 1 100\\r\\n\", \"output\": [\"100\"]}, {\"input\": \"10 3 5 1\\r\\n100 1 3 7\\r\\n100 1 2 5\\r\\n1 1 1 10\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"10 3 5 1\\r\\n100 1 3 7\\r\\n100 1 2 5\\r\\n1 1 1 10\\r\\n\", \"output\": [\"32\"]}, {\"input\": \"1000 10 1 1\\r\\n100 1 1 1\\r\\n100 1 1 1\\r\\n100 1 1 1\\r\\n100 1 1 1\\r\\n100 1 1 1\\r\\n100 1 1 1\\r\\n100 1 1 1\\r\\n100 1 1 1\\r\\n100 1 1 1\\r\\n100 1 1 1\\r\\n\", \"output\": [\"1000\"]}, {\"input\": \"10 2 100 1\\r\\n4 4 5 7\\r\\n6 2 3 4\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"8 2 10 10\\r\\n5 5 5 15\\r\\n50 5 4 8\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"8 2 10 10\\r\\n5 5 5 15\\r\\n50 5 4 8\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"4 1 2 4\\r\\n10 1 3 7\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"4 1 2 4\\r\\n10 1 3 7\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"10 2 5 1\\r\\n100 1 2 5\\r\\n100 1 3 8\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"1000 10 10 10\\r\\n100 1 1 1\\r\\n100 1 1 2\\r\\n100 1 2 1\\r\\n100 1 2 2\\r\\n100 1 1 1\\r\\n100 1 2 3\\r\\n100 1 3 2\\r\\n100 1 3 3\\r\\n100 1 1 3\\r\\n100 1 3 1\\r\\n\", \"output\": [\"1400\"]}, {\"input\": \"10 3 5 1\\r\\n100 1 3 7\\r\\n100 1 2 5\\r\\n1 1 1 10\\r\\n\", \"output\": [\"32\"]}]"}
{"prob_desc_description":"Little Petya loves training spiders. Petya has a board n\u2009\u00d7\u2009m in size. Each cell of the board initially has a spider sitting on it. After one second Petya chooses a certain action for each spider, and all of them humbly perform its commands. There are 5 possible commands: to stay idle or to move from current cell to some of the four side-neighboring cells (that is, one command for each of the four possible directions). Petya gives the commands so that no spider leaves the field. It is allowed for spiders to pass through each other when they crawl towards each other in opposite directions. All spiders crawl simultaneously and several spiders may end up in one cell. Petya wants to know the maximum possible number of spider-free cells after one second.","prob_desc_output_spec":"In the first line print the maximum number of cells without spiders.","lang_cluster":"","src_uid":"097674b4dd696b30e102938f71dd39b9","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["bitmasks","dp","dsu"],"prob_desc_created_at":"1315051200","prob_desc_sample_inputs":"[\"1 1\", \"2 3\"]","prob_desc_notes":"NoteIn the first sample the only possible answer is:sIn the second sample one of the possible solutions is: rdlruls denotes command \"stay idle\", l, r, d, u denote commands \"crawl left\", \"crawl right\", \"crawl down\", \"crawl up\", correspondingly.","exec_outcome":"","difficulty":2100.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains two space-separated integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u200940,\u2009n\u00b7m\u2009\u2264\u200940) \u2014 the board sizes.","prob_desc_sample_outputs":"[\"0\", \"4\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 3\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"4 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"4 2\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"1 40\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"1 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 3\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 4\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1 5\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"1 6\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"1 7\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"1 8\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"1 9\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"1 10\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"1 11\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1 12\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"1 13\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"1 14\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"1 15\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"1 16\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"1 17\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"1 18\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"1 19\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"1 20\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"1 21\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"1 22\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"1 23\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"1 24\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"1 25\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"1 26\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"1 27\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"1 28\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"1 29\\r\\n\", \"output\": [\"19\"]}, {\"input\": \"1 30\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"1 31\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"1 32\\r\\n\", \"output\": [\"21\"]}, {\"input\": \"1 33\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"1 34\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"1 35\\r\\n\", \"output\": [\"23\"]}, {\"input\": \"1 36\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"1 37\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"1 38\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"1 39\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"2 1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"2 4\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"2 5\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"2 6\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"2 7\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"2 8\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"2 9\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"2 10\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"2 11\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"2 12\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"2 13\\r\\n\", \"output\": [\"19\"]}, {\"input\": \"2 14\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"2 15\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"2 16\\r\\n\", \"output\": [\"23\"]}, {\"input\": \"2 17\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"2 18\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"2 19\\r\\n\", \"output\": [\"28\"]}, {\"input\": \"2 20\\r\\n\", \"output\": [\"29\"]}, {\"input\": \"3 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"3 2\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"3 3\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"3 4\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"3 5\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"3 6\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"3 7\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"3 8\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"3 9\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"3 10\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"3 11\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"3 12\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"3 13\\r\\n\", \"output\": [\"29\"]}, {\"input\": \"4 5\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"4 6\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"4 7\\r\\n\", \"output\": [\"21\"]}, {\"input\": \"4 8\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"4 9\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"4 10\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"5 1\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"5 2\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"5 3\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"5 4\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"5 5\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"5 6\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"5 7\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"5 8\\r\\n\", \"output\": [\"29\"]}, {\"input\": \"6 1\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"6 2\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"6 3\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"6 4\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"6 5\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"6 6\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"7 1\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"7 2\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"7 3\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"7 4\\r\\n\", \"output\": [\"21\"]}, {\"input\": \"7 5\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"8 1\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"8 2\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"8 3\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"8 4\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"8 5\\r\\n\", \"output\": [\"29\"]}, {\"input\": \"9 1\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"9 2\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"9 3\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"9 4\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"10 1\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"10 2\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"10 3\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"10 4\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"11 1\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"11 2\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"11 3\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"12 1\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"12 2\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"12 3\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"13 1\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"13 2\\r\\n\", \"output\": [\"19\"]}, {\"input\": \"13 3\\r\\n\", \"output\": [\"29\"]}, {\"input\": \"14 1\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"14 2\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"15 1\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"15 2\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"16 1\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"16 2\\r\\n\", \"output\": [\"23\"]}, {\"input\": \"17 1\\r\\n\", \"output\": [\"11\"]}, {\"input\": \"17 2\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"18 1\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"18 2\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"19 1\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"19 2\\r\\n\", \"output\": [\"28\"]}, {\"input\": \"20 1\\r\\n\", \"output\": [\"13\"]}, {\"input\": \"20 2\\r\\n\", \"output\": [\"29\"]}, {\"input\": \"21 1\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"22 1\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"23 1\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"24 1\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"25 1\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"26 1\\r\\n\", \"output\": [\"17\"]}, {\"input\": \"27 1\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"28 1\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"29 1\\r\\n\", \"output\": [\"19\"]}, {\"input\": \"30 1\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"31 1\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"32 1\\r\\n\", \"output\": [\"21\"]}, {\"input\": \"33 1\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"34 1\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"35 1\\r\\n\", \"output\": [\"23\"]}, {\"input\": \"36 1\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"37 1\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"38 1\\r\\n\", \"output\": [\"25\"]}, {\"input\": \"39 1\\r\\n\", \"output\": [\"26\"]}, {\"input\": \"40 1\\r\\n\", \"output\": [\"26\"]}]"}
{"prob_desc_description":"Petya loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.One day Petya dreamt of a lexicographically k-th permutation of integers from 1 to n. Determine how many lucky numbers in the permutation are located on the positions whose indexes are also lucky numbers.","prob_desc_output_spec":"If the k-th permutation of numbers from 1 to n does not exist, print the single number \"-1\" (without the quotes). Otherwise, print the answer to the problem: the number of such indexes i, that i and ai are both lucky numbers.","lang_cluster":"","src_uid":"cb2aa02772f95fefd1856960b6ceac4c","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","combinatorics","number theory"],"prob_desc_created_at":"1319727600","prob_desc_sample_inputs":"[\"7 4\", \"4 7\"]","prob_desc_notes":"NoteA permutation is an ordered set of n elements, where each integer from 1 to n occurs exactly once. The element of permutation in position with index i is denoted as ai (1\u2009\u2264\u2009i\u2009\u2264\u2009n). Permutation a is lexicographically smaller that permutation b if there is such a i (1\u2009\u2264\u2009i\u2009\u2264\u2009n), that ai\u2009<\u2009bi, and for any j (1\u2009\u2264\u2009j\u2009<\u2009i) aj\u2009=\u2009bj. Let's make a list of all possible permutations of n elements and sort it in the order of lexicographical increasing. Then the lexicographically k-th permutation is the k-th element of this list of permutations.In the first sample the permutation looks like that:1 2 3 4 6 7 5The only suitable position is 4.In the second sample the permutation looks like that:2 1 3 4The only suitable position is 4.","exec_outcome":"","difficulty":1900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains two integers n and k (1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u2009109) \u2014 the number of elements in the permutation and the lexicographical number of the permutation.","prob_desc_sample_outputs":"[\"1\", \"1\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"7 4\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"4 7\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"7 5040\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10 1023\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7 7477\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"10 10000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"3 7\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"27 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"40 8544\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"47 1\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"47 8547744\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"50 1000000000\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"64 87\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"98 854555\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"100 1\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"9985 5888454\\r\\n\", \"output\": [\"30\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 2\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"2 1000000000\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"10 1000000000\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"20 1000000000\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"777777 1\\r\\n\", \"output\": [\"126\"]}, {\"input\": \"777777 2\\r\\n\", \"output\": [\"125\"]}, {\"input\": \"777474 10000\\r\\n\", \"output\": [\"120\"]}, {\"input\": \"1000000000 1\\r\\n\", \"output\": [\"1022\"]}, {\"input\": \"777777777 5\\r\\n\", \"output\": [\"1021\"]}, {\"input\": \"777777777 1\\r\\n\", \"output\": [\"1022\"]}, {\"input\": \"777477774 1\\r\\n\", \"output\": [\"989\"]}, {\"input\": \"444747744 1000000000\\r\\n\", \"output\": [\"554\"]}, {\"input\": \"475 88555458\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"12 855448\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"20 1000000000\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"47 99998544\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"49 1000000000\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"854459 95554455\\r\\n\", \"output\": [\"126\"]}, {\"input\": \"77777779 1000000000\\r\\n\", \"output\": [\"508\"]}, {\"input\": \"77 47\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"6999 85488877\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"7479 58884598\\r\\n\", \"output\": [\"24\"]}, {\"input\": \"1000000000 1000000000\\r\\n\", \"output\": [\"1022\"]}, {\"input\": \"7 1000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7 124\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7 2048\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7 3001\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7 127\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7 980\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"7 5000\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7 4095\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"7 3856\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7 5032\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"7 4999\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 3\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"2 4\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"7 985\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"4 25\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"6 121\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"11 39916801\\r\\n\", \"output\": [\"-1\"]}, {\"input\": \"29 1000000000\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"10 4589\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10 100000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10 98564\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"10 1\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"10 100000009\\r\\n\", \"output\": [\"-1\"]}]"}
{"prob_desc_description":"Little Petya very much likes strings. Recently he has received a voucher to purchase a string as a gift from his mother. The string can be bought in the local shop. One can consider that the shop has all sorts of strings over the alphabet of fixed size. The size of the alphabet is equal to k. However, the voucher has a string type limitation: specifically, the voucher can be used to purchase string s if the length of string's longest substring that is also its weak subsequence (see the definition given below) equals w.String a with the length of n is considered the weak subsequence of the string s with the length of m, if there exists such a set of indexes 1\u2009\u2264\u2009i1\u2009<\u2009i2\u2009<\u2009...\u2009<\u2009in\u2009\u2264\u2009m, that has the following two properties:   ak\u2009=\u2009sik for all k from 1 to n;  there exists at least one such k (1\u2009\u2264\u2009k\u2009<\u2009n), for which ik\u2009+\u20091\u2009\u2013\u2009ik\u2009>\u20091. Petya got interested how many different strings are available for him to purchase in the shop. As the number of strings can be very large, please find it modulo 1000000007 (109\u2009+\u20097). If there are infinitely many such strings, print \"-1\".","prob_desc_output_spec":"Print a single number \u2014 the number of strings Petya can buy using the voucher, modulo 1000000007 (109\u2009+\u20097). If there are infinitely many such strings, print \"-1\" (without the quotes).","lang_cluster":"","src_uid":"b715f0fdc83ec539eb3ae2b0371ee130","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["combinatorics"],"prob_desc_created_at":"1323443100","prob_desc_sample_inputs":"[\"2 2\", \"3 5\", \"2 139\"]","prob_desc_notes":"NoteIn the first sample Petya can buy the following strings: aaa, aab, abab, abb, abba, baa, baab, baba, bba, bbb.","exec_outcome":"","difficulty":3000.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"3 seconds","prob_desc_input_spec":"The first line contains two integers k (1\u2009\u2264\u2009k\u2009\u2264\u2009106) and w (2\u2009\u2264\u2009w\u2009\u2264\u2009109) \u2014 the alphabet size and the required length of the maximum substring that also is the weak subsequence, correspondingly.","prob_desc_sample_outputs":"[\"10\", \"1593\", \"717248223\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 2\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"3 5\\r\\n\", \"output\": [\"1593\"]}, {\"input\": \"2 139\\r\\n\", \"output\": [\"717248223\"]}, {\"input\": \"5 6\\r\\n\", \"output\": [\"983725\"]}, {\"input\": \"1000 1002\\r\\n\", \"output\": [\"9396758\"]}, {\"input\": \"131 132\\r\\n\", \"output\": [\"757914194\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"4912\"]}, {\"input\": \"3 2\\r\\n\", \"output\": [\"57\"]}, {\"input\": \"1 1000000000\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"666 888888888\\r\\n\", \"output\": [\"424798470\"]}, {\"input\": \"1000000 1000000000\\r\\n\", \"output\": [\"600002237\"]}, {\"input\": \"1000000 1000000\\r\\n\", \"output\": [\"438349146\"]}, {\"input\": \"1000000 2\\r\\n\", \"output\": [\"739181318\"]}, {\"input\": \"2 1000000000\\r\\n\", \"output\": [\"851562506\"]}, {\"input\": \"1000000 500000\\r\\n\", \"output\": [\"53435433\"]}, {\"input\": \"12345 543210123\\r\\n\", \"output\": [\"290786804\"]}, {\"input\": \"1 2\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 3\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 4\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 5\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 6\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 7\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1 8\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2 3\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"2 4\\r\\n\", \"output\": [\"40\"]}, {\"input\": \"2 5\\r\\n\", \"output\": [\"80\"]}, {\"input\": \"2 6\\r\\n\", \"output\": [\"160\"]}, {\"input\": \"2 7\\r\\n\", \"output\": [\"320\"]}, {\"input\": \"2 8\\r\\n\", \"output\": [\"640\"]}, {\"input\": \"3 3\\r\\n\", \"output\": [\"177\"]}, {\"input\": \"3 4\\r\\n\", \"output\": [\"531\"]}, {\"input\": \"3 6\\r\\n\", \"output\": [\"4779\"]}, {\"input\": \"3 7\\r\\n\", \"output\": [\"14337\"]}, {\"input\": \"3 8\\r\\n\", \"output\": [\"43011\"]}, {\"input\": \"4 2\\r\\n\", \"output\": [\"292\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"1216\"]}, {\"input\": \"4 5\\r\\n\", \"output\": [\"19648\"]}, {\"input\": \"4 6\\r\\n\", \"output\": [\"78592\"]}, {\"input\": \"4 7\\r\\n\", \"output\": [\"314368\"]}, {\"input\": \"4 8\\r\\n\", \"output\": [\"1257472\"]}, {\"input\": \"5 2\\r\\n\", \"output\": [\"1585\"]}, {\"input\": \"5 3\\r\\n\", \"output\": [\"7745\"]}, {\"input\": \"5 4\\r\\n\", \"output\": [\"39205\"]}, {\"input\": \"5 5\\r\\n\", \"output\": [\"196745\"]}, {\"input\": \"5 7\\r\\n\", \"output\": [\"4918625\"]}, {\"input\": \"5 8\\r\\n\", \"output\": [\"24593125\"]}, {\"input\": \"6 2\\r\\n\", \"output\": [\"9726\"]}, {\"input\": \"6 3\\r\\n\", \"output\": [\"50916\"]}, {\"input\": \"6 4\\r\\n\", \"output\": [\"296856\"]}, {\"input\": \"6 5\\r\\n\", \"output\": [\"1789776\"]}, {\"input\": \"6 6\\r\\n\", \"output\": [\"10755936\"]}, {\"input\": \"6 7\\r\\n\", \"output\": [\"64535616\"]}, {\"input\": \"6 8\\r\\n\", \"output\": [\"387213696\"]}, {\"input\": \"7 2\\r\\n\", \"output\": [\"68425\"]}, {\"input\": \"7 3\\r\\n\", \"output\": [\"366625\"]}, {\"input\": \"7 4\\r\\n\", \"output\": [\"2290855\"]}, {\"input\": \"7 5\\r\\n\", \"output\": [\"15673105\"]}, {\"input\": \"7 6\\r\\n\", \"output\": [\"109953655\"]}, {\"input\": \"7 7\\r\\n\", \"output\": [\"770280385\"]}, {\"input\": \"7 8\\r\\n\", \"output\": [\"391962660\"]}, {\"input\": \"8 2\\r\\n\", \"output\": [\"547912\"]}, {\"input\": \"8 3\\r\\n\", \"output\": [\"2953952\"]}, {\"input\": \"8 4\\r\\n\", \"output\": [\"18951136\"]}, {\"input\": \"8 5\\r\\n\", \"output\": [\"138867968\"]}, {\"input\": \"8 6\\r\\n\", \"output\": [\"92073977\"]}, {\"input\": \"8 7\\r\\n\", \"output\": [\"746268616\"]}, {\"input\": \"8 8\\r\\n\", \"output\": [\"999179293\"]}, {\"input\": \"999999 1000001\\r\\n\", \"output\": [\"134450642\"]}, {\"input\": \"1000000 1000001\\r\\n\", \"output\": [\"142931557\"]}, {\"input\": \"1000000 999999\\r\\n\", \"output\": [\"250496915\"]}, {\"input\": \"1000000 999998\\r\\n\", \"output\": [\"129080538\"]}, {\"input\": \"1000000 999997\\r\\n\", \"output\": [\"769225275\"]}, {\"input\": \"1000000 1000002\\r\\n\", \"output\": [\"555999483\"]}, {\"input\": \"1000000 1000003\\r\\n\", \"output\": [\"479108007\"]}, {\"input\": \"983039 939524096\\r\\n\", \"output\": [\"604697498\"]}, {\"input\": \"998999 3\\r\\n\", \"output\": [\"356230103\"]}, {\"input\": \"987899 555555\\r\\n\", \"output\": [\"229752266\"]}, {\"input\": \"999009 55\\r\\n\", \"output\": [\"484803676\"]}, {\"input\": \"999009 818243\\r\\n\", \"output\": [\"282452206\"]}, {\"input\": \"999009 999004\\r\\n\", \"output\": [\"614735788\"]}, {\"input\": \"999009 999005\\r\\n\", \"output\": [\"945978791\"]}, {\"input\": \"999009 999006\\r\\n\", \"output\": [\"175954096\"]}, {\"input\": \"999009 999007\\r\\n\", \"output\": [\"318397869\"]}, {\"input\": \"999009 999008\\r\\n\", \"output\": [\"751039945\"]}, {\"input\": \"999009 999009\\r\\n\", \"output\": [\"187298386\"]}, {\"input\": \"999010 72\\r\\n\", \"output\": [\"131671481\"]}, {\"input\": \"999010 808035\\r\\n\", \"output\": [\"568832480\"]}, {\"input\": \"999010 999005\\r\\n\", \"output\": [\"898095114\"]}, {\"input\": \"999010 999006\\r\\n\", \"output\": [\"100649860\"]}, {\"input\": \"999010 999007\\r\\n\", \"output\": [\"292072410\"]}, {\"input\": \"999010 999008\\r\\n\", \"output\": [\"253072162\"]}, {\"input\": \"999010 999009\\r\\n\", \"output\": [\"808216351\"]}, {\"input\": \"999010 999010\\r\\n\", \"output\": [\"493965177\"]}, {\"input\": \"999011 64\\r\\n\", \"output\": [\"197612280\"]}, {\"input\": \"999011 133617\\r\\n\", \"output\": [\"471490419\"]}, {\"input\": \"999011 999006\\r\\n\", \"output\": [\"537424009\"]}, {\"input\": \"999011 999007\\r\\n\", \"output\": [\"932469897\"]}, {\"input\": \"999011 999008\\r\\n\", \"output\": [\"712314569\"]}, {\"input\": \"999011 999009\\r\\n\", \"output\": [\"272668831\"]}, {\"input\": \"999011 999010\\r\\n\", \"output\": [\"926206743\"]}, {\"input\": \"999011 999011\\r\\n\", \"output\": [\"68819519\"]}]"}
{"prob_desc_description":"Life is not easy for the perfectly common variable named Vasya. Wherever it goes, it is either assigned a value, or simply ignored, or is being used!Vasya's life goes in states of a program. In each state, Vasya can either be used (for example, to calculate the value of another variable), or be assigned a value, or ignored. Between some states are directed (oriented) transitions.A path is a sequence of states v1,\u2009v2,\u2009...,\u2009vx, where for any 1\u2009\u2264\u2009i\u2009<\u2009x exists a transition from vi to vi\u2009+\u20091.Vasya's value in state v is interesting to the world, if exists path p1,\u2009p2,\u2009...,\u2009pk such, that pi\u2009=\u2009v for some i (1\u2009\u2264\u2009i\u2009\u2264\u2009k), in state p1 Vasya gets assigned a value, in state pk Vasya is used and there is no state pi (except for p1) where Vasya gets assigned a value.Help Vasya, find the states in which Vasya's value is interesting to the world.","prob_desc_output_spec":"Print n integers r1,\u2009r2,\u2009...,\u2009rn, separated by spaces or new lines. Number ri should equal 1, if Vasya's value in state i is interesting to the world and otherwise, it should equal 0. The states are numbered from 1 to n in the order, in which they are described in the input.","lang_cluster":"","src_uid":"87d869a0fd4a510c5e7e310886b86a57","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["graphs"],"prob_desc_created_at":"1333897500","prob_desc_sample_inputs":"[\"4 3\\n1 0 0 2\\n1 2\\n2 3\\n3 4\", \"3 1\\n1 0 2\\n1 3\", \"3 1\\n2 0 1\\n1 3\"]","prob_desc_notes":"NoteIn the first sample the program states can be used to make the only path in which the value of Vasya interests the world, 1  2  3  4; it includes all the states, so in all of them Vasya's value is interesting to the world.The second sample the only path in which Vasya's value is interesting to the world is , \u2014 1  3; state 2 is not included there.In the third sample we cannot make from the states any path in which the value of Vasya would be interesting to the world, so the value of Vasya is never interesting to the world.","exec_outcome":"","difficulty":1700.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains two space-separated integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009105) \u2014 the numbers of states and transitions, correspondingly. The second line contains space-separated n integers f1,\u2009f2,\u2009...,\u2009fn (0\u2009\u2264\u2009fi\u2009\u2264\u20092), fi described actions performed upon Vasya in state i: 0 represents ignoring, 1 \u2014 assigning a value, 2 \u2014 using. Next m lines contain space-separated pairs of integers ai,\u2009bi (1\u2009\u2264\u2009ai,\u2009bi\u2009\u2264\u2009n, ai\u2009\u2260\u2009bi), each pair represents the transition from the state number ai to the state number bi. Between two states can be any number of transitions.","prob_desc_sample_outputs":"[\"1\\n1\\n1\\n1\", \"1\\n0\\n1\", \"0\\n0\\n0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"4 3\\r\\n1 0 0 2\\r\\n1 2\\r\\n2 3\\r\\n3 4\\r\\n\", \"output\": [\"1\\r\\n1\\r\\n1\\r\\n1\"]}, {\"input\": \"3 1\\r\\n1 0 2\\r\\n1 3\\r\\n\", \"output\": [\"1\\r\\n0\\r\\n1\"]}, {\"input\": \"3 1\\r\\n2 0 1\\r\\n1 3\\r\\n\", \"output\": [\"0\\r\\n0\\r\\n0\"]}, {\"input\": \"4 4\\r\\n1 0 2 0\\r\\n1 2\\r\\n2 3\\r\\n3 4\\r\\n4 1\\r\\n\", \"output\": [\"1\\r\\n1\\r\\n1\\r\\n0\"]}, {\"input\": \"10000 10000\\r\\n0 1 2 2 2 0 1 0 1 0 0 0 1 2 2 0 0 0 2 1 2 0 1 0 2 1 1 1 1 0 1 1 0 2 1 2 0 1 0 1 2 2 0 0 0 1 0 0 0 2 2 2 1 2 2 1 0 2 2 1 1 2 0 2 1 1 2 2 1 0 0 2 1 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 2 0 0 0 1 2 2 2 1 2 2 1 2 1 1 1 0 1 2 0 2 2 0 0 1 0 0 0 1 0 2 2 1 ...\", \"output\": 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1...\", \"output\": [\"0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n0\\r\\n...\"]}]"}
{"prob_desc_description":"To get money for a new aeonic blaster, ranger Qwerty decided to engage in trade for a while. He wants to buy some number of items (or probably not to buy anything at all) on one of the planets, and then sell the bought items on another planet. Note that this operation is not repeated, that is, the buying and the selling are made only once. To carry out his plan, Qwerty is going to take a bank loan that covers all expenses and to return the loaned money at the end of the operation (the money is returned without the interest). At the same time, Querty wants to get as much profit as possible.The system has n planets in total. On each of them Qwerty can buy or sell items of m types (such as food, medicine, weapons, alcohol, and so on). For each planet i and each type of items j Qwerty knows the following: aij \u2014 the cost of buying an item;  bij \u2014 the cost of selling an item;  cij \u2014 the number of remaining items.It is not allowed to buy more than cij items of type j on planet i, but it is allowed to sell any number of items of any kind.Knowing that the hold of Qwerty's ship has room for no more than k items, determine the maximum profit which Qwerty can get.","prob_desc_output_spec":"Print a single number \u2014 the maximum profit Qwerty can get.","lang_cluster":"","src_uid":"7419c4268a9815282fadca6581f28ec1","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["games","graph matchings","greedy"],"prob_desc_created_at":"1334934300","prob_desc_sample_inputs":"[\"3 3 10\\nVenus\\n6 5 3\\n7 6 5\\n8 6 10\\nEarth\\n10 9 0\\n8 6 4\\n10 9 3\\nMars\\n4 3 0\\n8 4 12\\n7 2 5\"]","prob_desc_notes":"NoteIn the first test case you should fly to planet Venus, take a loan on 74 units of money and buy three items of the first type and 7 items of the third type (3\u00b76\u2009+\u20097\u00b78\u2009=\u200974). Then the ranger should fly to planet Earth and sell there all the items he has bought. He gets 3\u00b79\u2009+\u20097\u00b79\u2009=\u200990 units of money for the items, he should give 74 of them for the loan. The resulting profit equals 16 units of money. We cannot get more profit in this case.","exec_outcome":"","difficulty":1200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains three space-separated integers n, m and k (2\u2009\u2264\u2009n\u2009\u2264\u200910, 1\u2009\u2264\u2009m,\u2009k\u2009\u2264\u2009100) \u2014 the number of planets, the number of question types and the capacity of Qwerty's ship hold, correspondingly. Then follow n blocks describing each planet. The first line of the i-th block has the planet's name as a string with length from 1 to 10 Latin letters. The first letter of the name is uppercase, the rest are lowercase. Then in the i-th block follow m lines, the j-th of them contains three integers aij, bij and cij (1\u2009\u2264\u2009bij\u2009<\u2009aij\u2009\u2264\u20091000, 0\u2009\u2264\u2009cij\u2009\u2264\u2009100) \u2014 the numbers that describe money operations with the j-th item on the i-th planet. The numbers in the lines are separated by spaces. It is guaranteed that the names of all planets are different.","prob_desc_sample_outputs":"[\"16\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3 3 10\\r\\nVenus\\r\\n6 5 3\\r\\n7 6 5\\r\\n8 6 10\\r\\nEarth\\r\\n10 9 0\\r\\n8 6 4\\r\\n10 9 3\\r\\nMars\\r\\n4 3 0\\r\\n8 4 12\\r\\n7 2 5\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"2 1 5\\r\\nA\\r\\n6 5 5\\r\\nB\\r\\n10 9 0\\r\\n\", \"output\": [\"15\"]}, {\"input\": \"2 2 5\\r\\nAbcdefghij\\r\\n20 15 20\\r\\n10 5 13\\r\\nKlmopqrstu\\r\\n19 16 20\\r\\n12 7 14\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 1 5\\r\\nTomato\\r\\n10 7 20\\r\\nBanana\\r\\n13 11 0\\r\\nApple\\r\\n15 14 10\\r\\n\", \"output\": [\"20\"]}, {\"input\": \"3 2 11\\r\\nMars\\r\\n15 10 4\\r\\n7 6 3\\r\\nSnickers\\r\\n20 17 2\\r\\n10 8 0\\r\\nBounty\\r\\n21 18 5\\r\\n9 7 3\\r\\n\", \"output\": [\"12\"]}, {\"input\": \"5 7 30\\r\\nBzbmwey\\r\\n61 2 6\\r\\n39 20 2\\r\\n76 15 7\\r\\n12 1 5\\r\\n62 38 1\\r\\n84 22 7\\r\\n52 31 3\\r\\nDyfw\\r\\n77 22 8\\r\\n88 21 4\\r\\n48 21 7\\r\\n82 81 2\\r\\n49 2 7\\r\\n57 38 10\\r\\n99 98 8\\r\\nG\\r\\n91 2 4\\r\\n84 60 4\\r\\n9 6 5\\r\\n69 45 1\\r\\n81 27 4\\r\\n93 22 9\\r\\n73 14 5\\r\\nUpwb\\r\\n72 67 10\\r\\n18 9 7\\r\\n80 13 2\\r\\n66 30 2\\r\\n88 61 7\\r\\n98 13 6\\r\\n90 12 1\\r\\nYiadtlcoue\\r\\n95 57 1\\r\\n99 86 10\\r\\n59 20 6\\r\\n98 95 1\\r\\n36 5 1\\r\\n42 14 1\\r\\n91 11 7\\r\\n\", \"output\": [\"534\"]}, {\"input\": \"2 1 1\\r\\nIeyxawsao\\r\\n2 1 0\\r\\nJhmsvvy\\r\\n2 1 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 1 1\\r\\nCcn\\r\\n2 1 1\\r\\nOxgzx\\r\\n2 1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 1 1\\r\\nG\\r\\n2 1 9\\r\\nRdepya\\r\\n2 1 8\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 10 10\\r\\nB\\r\\n9 1 0\\r\\n7 6 0\\r\\n10 3 0\\r\\n4 3 0\\r\\n10 7 0\\r\\n7 6 0\\r\\n6 5 0\\r\\n3 2 0\\r\\n5 4 0\\r\\n6 2 0\\r\\nFffkk\\r\\n7 6 0\\r\\n6 3 0\\r\\n8 7 0\\r\\n9 2 0\\r\\n4 3 0\\r\\n10 2 0\\r\\n9 2 0\\r\\n3 1 0\\r\\n10 9 0\\r\\n10 1 0\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"2 10 10\\r\\nQdkeso\\r\\n7 4 7\\r\\n2 1 0\\r\\n9 2 6\\r\\n9 8 1\\r\\n3 2 0\\r\\n7 5 7\\r\\n5 2 0\\r\\n6 3 4\\r\\n7 4 5\\r\\n8 4 0\\r\\nRzh\\r\\n3 1 9\\r\\n10 3 0\\r\\n8 1 0\\r\\n10 9 6\\r\\n10 7 4\\r\\n10 3 3\\r\\n10 3 1\\r\\n9 2 7\\r\\n10 9 0\\r\\n10 6 6\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"2 17 100\\r\\nFevvyt\\r\\n35 34 4\\r\\n80 50 7\\r\\n88 85 1\\r\\n60 45 9\\r\\n48 47 9\\r\\n63 47 9\\r\\n81 56 1\\r\\n25 23 5\\r\\n100 46 1\\r\\n25 7 9\\r\\n29 12 6\\r\\n36 2 8\\r\\n49 27 10\\r\\n35 20 5\\r\\n92 64 2\\r\\n60 3 8\\r\\n72 28 3\\r\\nOfntgr\\r\\n93 12 4\\r\\n67 38 6\\r\\n28 21 2\\r\\n86 29 5\\r\\n23 3 4\\r\\n81 69 6\\r\\n79 12 3\\r\\n64 43 5\\r\\n81 38 9\\r\\n62 25 2\\r\\n54 1 1\\r\\n95 78 8\\r\\n78 23 5\\r\\n96 90 10\\r\\n95 38 8\\r\\n84 20 5\\r\\n80 77 5\\r\\n\", \"output\": [\"770\"]}, {\"input\": \"2 23 97\\r\\nAfgickc\\r\\n737 670 3\\r\\n554 515 2\\r\\n725 568 1\\r\\n365 77 2\\r\\n951 183 0\\r\\n902 833 3\\r\\n326 146 1\\r\\n876 299 2\\r\\n484 151 1\\r\\n753 406 2\\r\\n415 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0\\r\\n665 354 15\\r\\n573 541 4\\r\\n370 205 1\\r\\n473 74 14\\r\\n347 301 12\\r\\n613 176 14\\r\\n626 529 1\\r\\n435 51 6\\r\\n273 266 5\\r\\n696 536 6\\r\\n483 435 14\\r\\n441 236 8\\r\\n278 201 14\\r\\n620 349 1\\r\\n639 107 8\\r\\n391 120 13\\r\\n149 23 6\\r\\n...\", \"output\": [\"10526\"]}, {\"input\": \"2 79 81\\r\\nMacvhxgfcn\\r\\n483 34 49\\r\\n438 60 19\\r\\n271 54 13\\r\\n416 361 29\\r\\n365 76 21\\r\\n583 230 2\\r\\n580 159 18\\r\\n253 56 27\\r\\n561 110 11\\r\\n511 322 12\\r\\n493 352 36\\r\\n305 165 3\\r\\n572 336 8\\r\\n93 8 42\\r\\n263 208 42\\r\\n479 397 47\\r\\n568 428 34\\r\\n497 370 49\\r\\n352 250 31\\r\\n68 48 33\\r\\n356 278 29\\r\\n246 175 0\\r\\n313 186 14\\r\\n333 35 1\\r\\n205 186 49\\r\\n403 162 25\\r\\n539 174 38\\r\\n562 555 38\\r\\n575 570 28\\r\\n181 21 44\\r\\n343 201 16\\r\\n348 57 17\\r\\n471 74 2\\r\\n469 323 42\\r\\n552 347 49\\r\\n402 291 35\\r\\n265 82 46\\r\\n344 142 36\\r\\n361 242 32\\r\\n160 134 50\\r\\n486 404 12\\r\\n522 134 44\\r\\n515 16 ...\", \"output\": [\"31581\"]}, {\"input\": \"2 100 1\\r\\nLjmpcxrzul\\r\\n695 271 1\\r\\n723 720 1\\r\\n152 10 1\\r\\n966 757 0\\r\\n486 279 1\\r\\n229 145 1\\r\\n440 8 1\\r\\n798 294 1\\r\\n671 595 0\\r\\n96 7 0\\r\\n510 65 0\\r\\n637 56 0\\r\\n621 174 1\\r\\n76 55 1\\r\\n770 114 1\\r\\n123 38 0\\r\\n337 216 1\\r\\n152 141 0\\r\\n535 253 1\\r\\n696 170 1\\r\\n332 228 1\\r\\n412 198 0\\r\\n628 459 0\\r\\n837 335 1\\r\\n830 332 0\\r\\n519 104 1\\r\\n975 87 0\\r\\n69 26 1\\r\\n356 82 1\\r\\n700 138 0\\r\\n842 186 0\\r\\n975 48 0\\r\\n779 728 1\\r\\n440 247 1\\r\\n245 92 1\\r\\n606 31 0\\r\\n817 192 0\\r\\n468 39 0\\r\\n993 542 1\\r\\n708 616 1\\r\\n911 256 0\\r\\n868 821 0\\r\\n948 491 0\\r\\n781 442 0\\r\\n158 125 0\\r\\n178 65 0\\r\\n589 ...\", \"output\": [\"597\"]}, {\"input\": \"2 100 1\\r\\nD\\r\\n742 643 21\\r\\n394 113 53\\r\\n969 856 8\\r\\n544 535 99\\r\\n715 456 36\\r\\n442 434 15\\r\\n368 354 51\\r\\n518 219 97\\r\\n816 412 60\\r\\n552 536 59\\r\\n406 241 37\\r\\n728 644 70\\r\\n551 54 52\\r\\n875 847 36\\r\\n591 311 5\\r\\n122 26 75\\r\\n741 382 25\\r\\n791 347 55\\r\\n465 395 96\\r\\n835 135 33\\r\\n362 48 3\\r\\n826 767 96\\r\\n759 704 18\\r\\n262 59 11\\r\\n838 70 39\\r\\n345 148 37\\r\\n563 503 96\\r\\n50 8 68\\r\\n870 759 35\\r\\n881 336 48\\r\\n604 299 61\\r\\n889 50 20\\r\\n863 345 58\\r\\n148 104 91\\r\\n811 123 42\\r\\n696 474 31\\r\\n481 473 22\\r\\n644 611 28\\r\\n846 699 97\\r\\n867 434 14\\r\\n208 11 89\\r\\n778 767 44\\r\\n884 365 ...\", \"output\": [\"435\"]}, {\"input\": \"2 100 100\\r\\nRzhggggh\\r\\n323 53 1\\r\\n788 434 0\\r\\n675 369 1\\r\\n575 46 0\\r\\n60 42 0\\r\\n745 625 1\\r\\n76 49 1\\r\\n662 548 0\\r\\n673 432 0\\r\\n402 272 0\\r\\n904 328 0\\r\\n616 6 0\\r\\n474 272 1\\r\\n164 28 1\\r\\n749 692 0\\r\\n833 228 0\\r\\n188 160 0\\r\\n728 190 1\\r\\n946 280 0\\r\\n321 180 0\\r\\n853 705 0\\r\\n621 256 0\\r\\n654 419 1\\r\\n984 32 1\\r\\n441 50 0\\r\\n537 483 1\\r\\n786 772 0\\r\\n900 217 0\\r\\n504 212 1\\r\\n802 46 1\\r\\n874 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[\"35342\"]}, {\"input\": \"10 100 100\\r\\nIepcfjlv\\r\\n532 378 62\\r\\n720 252 4\\r\\n891 7 99\\r\\n432 384 86\\r\\n927 813 6\\r\\n571 120 89\\r\\n300 149 31\\r\\n639 627 39\\r\\n597 136 94\\r\\n463 72 37\\r\\n713 300 93\\r\\n210 8 59\\r\\n362 98 12\\r\\n923 813 29\\r\\n329 9 100\\r\\n986 807 54\\r\\n788 109 94\\r\\n647 612 5\\r\\n867 94 77\\r\\n359 158 61\\r\\n585 ...\", \"output\": [\"78153\"]}, {\"input\": \"10 100 100\\r\\nElgr\\r\\n897 340 43\\r\\n975 666 54\\r\\n469 125 87\\r\\n595 534 99\\r\\n619 415 22\\r\\n997 312 34\\r\\n391 306 2\\r\\n702 630 26\\r\\n499 426 31\\r\\n185 181 31\\r\\n661 599 99\\r\\n934 283 99\\r\\n666 84 23\\r\\n413 167 56\\r\\n641 139 19\\r\\n886 852 27\\r\\n625 47 65\\r\\n838 68 34\\r\\n866 428 87\\r\\n410 276 32\\r\\n6...\", \"output\": [\"72354\"]}, {\"input\": \"10 100 100\\r\\nEol\\r\\n959 955 61\\r\\n859 160 94\\r\\n641 405 63\\r\\n795 414 70\\r\\n326 61 51\\r\\n854 810 22\\r\\n732 668 24\\r\\n782 321 51\\r\\n150 93 3\\r\\n516 293 67\\r\\n698 159 86\\r\\n435 109 59\\r\\n972 154 70\\r\\n246 152 62\\r\\n891 603 37\\r\\n660 369 61\\r\\n490 110 41\\r\\n889 438 33\\r\\n776 471 56\\r\\n345 57 20\\r\\n70...\", \"output\": [\"73440\"]}, {\"input\": \"10 100 100\\r\\nAaxx\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 ...\", \"output\": [\"99700\"]}, {\"input\": \"10 100 100\\r\\nAbxx\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 0\\r\\n1000 1 ...\", \"output\": [\"0\"]}, {\"input\": \"10 100 100\\r\\nAaxx\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 100\\r\\n100 1 ...\", \"output\": [\"80100\"]}, {\"input\": \"10 10 100\\r\\nAdzzzzk\\r\\n100 1 10\\r\\n100 1 10\\r\\n100 1 10\\r\\n100 1 10\\r\\n100 1 10\\r\\n100 1 10\\r\\n100 1 10\\r\\n100 1 10\\r\\n100 1 10\\r\\n100 1 10\\r\\nBdzzzzk\\r\\n200 101 10\\r\\n200 101 10\\r\\n200 101 10\\r\\n200 101 10\\r\\n200 101 10\\r\\n200 101 10\\r\\n200 101 10\\r\\n200 101 10\\r\\n200 101 10\\r\\n200 101 10\\r\\nCdzzzz...\", \"output\": [\"80100\"]}, {\"input\": \"10 100 100\\r\\nAbbbzzk\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 999 1\\r\\n1000 9...\", \"output\": [\"0\"]}, {\"input\": \"10 100 100\\r\\nCap\\r\\n998 2 1\\r\\n997 3 1\\r\\n996 4 1\\r\\n995 5 1\\r\\n994 6 1\\r\\n993 7 1\\r\\n992 8 1\\r\\n991 9 1\\r\\n990 10 1\\r\\n989 11 1\\r\\n988 12 1\\r\\n987 13 1\\r\\n986 14 1\\r\\n985 15 1\\r\\n984 16 1\\r\\n983 17 1\\r\\n982 18 1\\r\\n981 19 1\\r\\n980 20 1\\r\\n979 21 1\\r\\n978 22 1\\r\\n977 23 1\\r\\n976 24 1\\r\\n975 25 1\\r\\n974 26...\", \"output\": [\"0\"]}, {\"input\": \"2 100 100\\r\\nAasdsad\\r\\n783 451 77\\r\\n796 790 58\\r\\n838 835 86\\r\\n640 454 27\\r\\n566 473 38\\r\\n750 421 86\\r\\n417 155 23\\r\\n838 637 51\\r\\n854 779 9\\r\\n893 522 45\\r\\n973 62 31\\r\\n534 453 76\\r\\n835 154 36\\r\\n749 187 43\\r\\n951 644 15\\r\\n444 237 51\\r\\n891 769 7\\r\\n551 315 55\\r\\n822 334 73\\r\\n199 52 18\\r...\", \"output\": [\"50640\"]}]"}
{"prob_desc_description":"Several ages ago Berland was a kingdom. The King of Berland adored math. That's why, when he first visited one of his many palaces, he first of all paid attention to the floor in one hall. The floor was tiled with hexagonal tiles.The hall also turned out hexagonal in its shape. The King walked along the perimeter of the hall and concluded that each of the six sides has a, b, c, a, b and c adjacent tiles, correspondingly.To better visualize the situation, look at the picture showing a similar hexagon for a\u2009=\u20092, b\u2009=\u20093 and c\u2009=\u20094.  According to the legend, as the King of Berland obtained the values a, b and c, he almost immediately calculated the total number of tiles on the hall floor. Can you do the same?","prob_desc_output_spec":"Print a single number \u2014 the total number of tiles on the hall floor.","lang_cluster":"","src_uid":"8ab25ed4955d978fe20f6872cb94b0da","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math","implementation"],"prob_desc_created_at":"1344958200","prob_desc_sample_inputs":"[\"2 3 4\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1200.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains three integers: a, b and c (2\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u20091000).","prob_desc_sample_outputs":"[\"18\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 3 4\\r\\n\", \"output\": [\"18\"]}, {\"input\": \"2 2 2\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"7 8 13\\r\\n\", \"output\": [\"224\"]}, {\"input\": \"14 7 75\\r\\n\", \"output\": [\"1578\"]}, {\"input\": \"201 108 304\\r\\n\", \"output\": [\"115032\"]}, {\"input\": \"999 998 996\\r\\n\", \"output\": [\"2983022\"]}, {\"input\": \"2 2 3\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"2 3 2\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"3 2 2\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"2 3 3\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"3 2 3\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"3 3 2\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"3 3 3\\r\\n\", \"output\": [\"19\"]}, {\"input\": \"4 5 3\\r\\n\", \"output\": [\"36\"]}, {\"input\": \"2 2 856\\r\\n\", \"output\": [\"2569\"]}, {\"input\": \"2 986 2\\r\\n\", \"output\": [\"2959\"]}, {\"input\": \"985 2 2\\r\\n\", \"output\": [\"2956\"]}, {\"input\": \"2 958 983\\r\\n\", \"output\": [\"943654\"]}, {\"input\": \"992 2 912\\r\\n\", \"output\": [\"906607\"]}, {\"input\": \"789 894 2\\r\\n\", \"output\": [\"707048\"]}, {\"input\": \"1000 1000 1000\\r\\n\", \"output\": [\"2997001\"]}, {\"input\": \"384 458 284\\r\\n\", \"output\": [\"413875\"]}, {\"input\": \"709 14 290\\r\\n\", \"output\": [\"218584\"]}, {\"input\": \"485 117 521\\r\\n\", \"output\": [\"369265\"]}, {\"input\": \"849 333 102\\r\\n\", \"output\": [\"401998\"]}, {\"input\": \"998 999 1000\\r\\n\", \"output\": [\"2991006\"]}, {\"input\": \"2 2 1000\\r\\n\", \"output\": [\"3001\"]}, {\"input\": \"2 1000 2\\r\\n\", \"output\": [\"3001\"]}, {\"input\": \"1000 2 2\\r\\n\", \"output\": [\"3001\"]}, {\"input\": \"1000 2 1000\\r\\n\", \"output\": [\"1001999\"]}, {\"input\": \"865 291 383\\r\\n\", \"output\": [\"692925\"]}, {\"input\": \"41 49 28\\r\\n\", \"output\": [\"4412\"]}, {\"input\": \"34 86 90\\r\\n\", \"output\": [\"13515\"]}, {\"input\": \"39 23 56\\r\\n\", \"output\": [\"4252\"]}, {\"input\": \"14 99 81\\r\\n\", \"output\": [\"10346\"]}, {\"input\": \"48 38 193\\r\\n\", \"output\": [\"18144\"]}, {\"input\": \"395 85 22\\r\\n\", \"output\": [\"43634\"]}, {\"input\": \"38 291 89\\r\\n\", \"output\": [\"39922\"]}, {\"input\": \"7 23 595\\r\\n\", \"output\": [\"17387\"]}, {\"input\": \"948 48 3\\r\\n\", \"output\": [\"47494\"]}]"}
{"prob_desc_description":"Polycarpus is an amateur businessman. Recently he was surprised to find out that the market for paper scissors is completely free! Without further ado, Polycarpus decided to start producing and selling such scissors.Polycaprus calculated that the optimal celling price for such scissors would be p bourles. However, he read somewhere that customers are attracted by prices that say something like \"Special Offer! Super price 999 bourles!\". So Polycarpus decided to lower the price a little if it leads to the desired effect.Polycarpus agrees to lower the price by no more than d bourles so that the number of nines at the end of the resulting price is maximum. If there are several ways to do it, he chooses the maximum possible price.Note, Polycarpus counts only the trailing nines in a price.","prob_desc_output_spec":"Print the required price \u2014 the maximum price that ends with the largest number of nines and that is less than p by no more than d. The required number shouldn't have leading zeroes.","lang_cluster":"","src_uid":"c706cfcd4c37fbc1b1631aeeb2c02b6a","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["implementation"],"prob_desc_created_at":"1346081400","prob_desc_sample_inputs":"[\"1029 102\", \"27191 17\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1400.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains two integers p and d (1\u2009\u2264\u2009p\u2009\u2264\u20091018; 0\u2009\u2264\u2009d\u2009<\u2009p) \u2014 the initial price of scissors and the maximum possible price reduction. Please, do not use the %lld specifier to read or write 64-bit integers in \u0421++. It is preferred to use cin, cout streams or the %I64d specifier.","prob_desc_sample_outputs":"[\"999\", \"27189\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1029 102\\r\\n\", \"output\": [\"999\"]}, {\"input\": \"27191 17\\r\\n\", \"output\": [\"27189\"]}, {\"input\": \"1 0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"9 0\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"20 1\\r\\n\", \"output\": [\"19\"]}, {\"input\": \"100 23\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"10281 1\\r\\n\", \"output\": [\"10281\"]}, {\"input\": \"2111 21\\r\\n\", \"output\": [\"2099\"]}, {\"input\": \"3021 112\\r\\n\", \"output\": [\"2999\"]}, {\"input\": \"1000000000000000000 999999999999999999\\r\\n\", \"output\": [\"999999999999999999\"]}, {\"input\": \"29287101 301\\r\\n\", \"output\": [\"29286999\"]}, {\"input\": \"302918113 8113\\r\\n\", \"output\": [\"302917999\"]}, {\"input\": \"23483247283432 47283432\\r\\n\", \"output\": [\"23483239999999\"]}, {\"input\": \"47283432 7283432\\r\\n\", 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{\"input\": \"559198116944738707 844709\\r\\n\", \"output\": [\"559198116943999999\"]}, {\"input\": \"559198116944738707 84470\\r\\n\", \"output\": [\"559198116944699999\"]}, {\"input\": \"559198116944738707 8447\\r\\n\", \"output\": [\"559198116944737999\"]}, {\"input\": \"559198116944738707 844\\r\\n\", \"output\": [\"559198116944737999\"]}, {\"input\": \"559198116944738707 84\\r\\n\", \"output\": [\"559198116944738699\"]}, {\"input\": \"559198116944738707 8\\r\\n\", \"output\": [\"559198116944738699\"]}, {\"input\": \"559198116944738707 7\\r\\n\", \"output\": [\"559198116944738707\"]}, {\"input\": \"559198116944738707 6\\r\\n\", \"output\": [\"559198116944738707\"]}, {\"input\": \"559198116944738707 1\\r\\n\", \"output\": [\"559198116944738707\"]}, {\"input\": \"559198116944738707 0\\r\\n\", \"output\": [\"559198116944738707\"]}, {\"input\": \"559198116944738700 1\\r\\n\", \"output\": [\"559198116944738699\"]}, {\"input\": \"559198116944738700 0\\r\\n\", \"output\": [\"559198116944738700\"]}, {\"input\": \"559198116944738999 0\\r\\n\", \"output\": [\"559198116944738999\"]}, {\"input\": \"559198116944738999 1\\r\\n\", \"output\": [\"559198116944738999\"]}, {\"input\": \"199 100\\r\\n\", \"output\": [\"199\"]}, {\"input\": \"99 10\\r\\n\", \"output\": [\"99\"]}, {\"input\": \"10 1\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"18 17\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"199 198\\r\\n\", \"output\": [\"199\"]}, {\"input\": \"1000000000000000000 0\\r\\n\", \"output\": [\"1000000000000000000\"]}, {\"input\": \"59 3\\r\\n\", \"output\": [\"59\"]}, {\"input\": \"9999 10\\r\\n\", \"output\": [\"9999\"]}, {\"input\": \"999999999999999998 999999999999999997\\r\\n\", \"output\": [\"899999999999999999\"]}, {\"input\": \"8 7\\r\\n\", \"output\": [\"8\"]}]"}
{"prob_desc_description":"The Little Elephant is playing with the Cartesian coordinates' system. Most of all he likes playing with integer points. The Little Elephant defines an integer point as a pair of integers (x;\u00a0y), such that 0\u2009\u2264\u2009x\u2009\u2264\u2009w and 0\u2009\u2264\u2009y\u2009\u2264\u2009h. Thus, the Little Elephant knows only (w\u2009+\u20091)\u00b7(h\u2009+\u20091) distinct integer points.The Little Elephant wants to paint a triangle with vertexes at integer points, the triangle's area must be a positive integer. For that, he needs to find the number of groups of three points that form such triangle. At that, the order of points in a group matters, that is, the group of three points (0;0), (0;2), (2;2) isn't equal to the group (0;2), (0;0), (2;2).Help the Little Elephant to find the number of groups of three integer points that form a nondegenerate triangle with integer area.","prob_desc_output_spec":"In a single output line print an integer \u2014 the remainder of dividing the answer to the problem by 1000000007 (109\u2009+\u20097).","lang_cluster":"","src_uid":"984788e4b4925c15c9c6f31e42f2f8fa","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["geometry","math"],"prob_desc_created_at":"1346427000","prob_desc_sample_inputs":"[\"2 1\", \"2 2\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":2500.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"3 seconds","prob_desc_input_spec":"A single line contains two integers w and h (1\u2009\u2264\u2009w,\u2009h\u2009\u2264\u20094000).","prob_desc_sample_outputs":"[\"36\", \"240\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 1\\r\\n\", \"output\": [\"36\"]}, {\"input\": \"2 2\\r\\n\", \"output\": [\"240\"]}, {\"input\": \"4 4\\r\\n\", \"output\": [\"7488\"]}, {\"input\": \"1 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"1 2\\r\\n\", \"output\": [\"36\"]}, {\"input\": \"3 3\\r\\n\", \"output\": [\"1560\"]}, {\"input\": \"1 3\\r\\n\", \"output\": [\"96\"]}, {\"input\": \"1000 1\\r\\n\", \"output\": [\"2999979\"]}, {\"input\": \"1 4\\r\\n\", \"output\": [\"240\"]}, {\"input\": \"1 10\\r\\n\", \"output\": [\"3300\"]}, {\"input\": \"10 1\\r\\n\", \"output\": [\"3300\"]}, {\"input\": \"1000 1000\\r\\n\", \"output\": [\"569772966\"]}, {\"input\": \"47 74\\r\\n\", \"output\": [\"45773261\"]}, {\"input\": \"1 1000\\r\\n\", \"output\": [\"2999979\"]}, {\"input\": \"999 1\\r\\n\", \"output\": [\"993999986\"]}, {\"input\": \"2 10\\r\\n\", \"output\": [\"17520\"]}, {\"input\": \"2 4\\r\\n\", \"output\": [\"1392\"]}, {\"input\": \"10 10\\r\\n\", \"output\": [\"1032528\"]}, {\"input\": \"9 9\\r\\n\", \"output\": [\"568512\"]}, {\"input\": \"8 8\\r\\n\", \"output\": [\"301248\"]}, {\"input\": \"7 11\\r\\n\", \"output\": [\"500472\"]}, {\"input\": \"3 25\\r\\n\", \"output\": [\"601632\"]}, {\"input\": \"25 25\\r\\n\", \"output\": [\"189684480\"]}, {\"input\": \"100 25\\r\\n\", \"output\": [\"247915499\"]}, {\"input\": \"100 99\\r\\n\", \"output\": [\"968021874\"]}, {\"input\": \"512 1000\\r\\n\", \"output\": [\"722505988\"]}, {\"input\": \"999 999\\r\\n\", \"output\": [\"290889748\"]}, {\"input\": \"987 895\\r\\n\", \"output\": [\"888141259\"]}, {\"input\": \"597 574\\r\\n\", \"output\": [\"789630913\"]}, {\"input\": \"975 157\\r\\n\", \"output\": [\"484861614\"]}, {\"input\": \"976 485\\r\\n\", \"output\": [\"672226096\"]}, {\"input\": \"999 689\\r\\n\", \"output\": [\"323811885\"]}, {\"input\": \"888 999\\r\\n\", \"output\": [\"421953459\"]}, {\"input\": \"999 2\\r\\n\", \"output\": [\"978999902\"]}, {\"input\": \"998 1000\\r\\n\", \"output\": [\"300694183\"]}, {\"input\": \"990 1000\\r\\n\", \"output\": [\"256938752\"]}, {\"input\": \"990 990\\r\\n\", \"output\": [\"437439079\"]}, {\"input\": \"950 851\\r\\n\", \"output\": [\"805992327\"]}, {\"input\": \"2 5\\r\\n\", \"output\": [\"2484\"]}, {\"input\": \"3 7\\r\\n\", \"output\": [\"15480\"]}, {\"input\": \"13 11\\r\\n\", \"output\": [\"2790408\"]}, {\"input\": \"2000 2000\\r\\n\", \"output\": [\"537764217\"]}, {\"input\": \"3000 3000\\r\\n\", \"output\": [\"235619250\"]}, {\"input\": \"4000 4000\\r\\n\", \"output\": [\"255288322\"]}, {\"input\": \"1001 1000\\r\\n\", \"output\": [\"916251534\"]}, {\"input\": \"1001 1007\\r\\n\", \"output\": [\"59378872\"]}, {\"input\": \"1000 4000\\r\\n\", \"output\": [\"796436035\"]}, {\"input\": \"2001 3999\\r\\n\", \"output\": [\"287223043\"]}, {\"input\": \"3999 3998\\r\\n\", \"output\": [\"146043529\"]}, {\"input\": \"3997 2584\\r\\n\", \"output\": [\"304397084\"]}, {\"input\": \"2000 2578\\r\\n\", \"output\": [\"729387043\"]}, {\"input\": \"3000 2000\\r\\n\", \"output\": [\"44275416\"]}, {\"input\": \"3545 3942\\r\\n\", \"output\": [\"683342945\"]}, {\"input\": \"2888 3999\\r\\n\", \"output\": [\"944142552\"]}, {\"input\": \"1 4000\\r\\n\", \"output\": [\"47998656\"]}, {\"input\": \"2 3999\\r\\n\", \"output\": [\"663993287\"]}, {\"input\": \"7 3777\\r\\n\", \"output\": [\"614855828\"]}, {\"input\": \"47 3747\\r\\n\", \"output\": [\"191757978\"]}, {\"input\": \"3757 256\\r\\n\", \"output\": [\"814200976\"]}, {\"input\": \"100 2000\\r\\n\", \"output\": [\"570798722\"]}, {\"input\": \"4000 500\\r\\n\", \"output\": [\"792193190\"]}]"}
{"prob_desc_description":"Polycarpus loves lucky numbers. Everybody knows that lucky numbers are positive integers, whose decimal representation (without leading zeroes) contain only the lucky digits x and y. For example, if x\u2009=\u20094, and y\u2009=\u20097, then numbers 47, 744, 4 are lucky.Let's call a positive integer a undoubtedly lucky, if there are such digits x and y (0\u2009\u2264\u2009x,\u2009y\u2009\u2264\u20099), that the decimal representation of number a (without leading zeroes) contains only digits x and y.Polycarpus has integer n. He wants to know how many positive integers that do not exceed n, are undoubtedly lucky. Help him, count this number.","prob_desc_output_spec":"Print a single integer that says, how many positive integers that do not exceed n are undoubtedly lucky.","lang_cluster":"","src_uid":"0f7f10557602c8c2f2eb80762709ffc4","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","bitmasks","dfs and similar"],"prob_desc_created_at":"1353079800","prob_desc_sample_inputs":"[\"10\", \"123\"]","prob_desc_notes":"NoteIn the first test sample all numbers that do not exceed 10 are undoubtedly lucky.In the second sample numbers 102, 103, 104, 105, 106, 107, 108, 109, 120, 123 are not undoubtedly lucky.","exec_outcome":"","difficulty":1600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009109) \u2014 Polycarpus's number.","prob_desc_sample_outputs":"[\"10\", \"113\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"10\\r\\n\", \"output\": [\"10\"]}, {\"input\": \"123\\r\\n\", \"output\": [\"113\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1000\\r\\n\", \"output\": [\"352\"]}, {\"input\": \"1000000000\\r\\n\", \"output\": [\"40744\"]}, {\"input\": \"999999999\\r\\n\", \"output\": [\"40743\"]}, {\"input\": \"999999998\\r\\n\", \"output\": [\"40742\"]}, {\"input\": \"999999997\\r\\n\", \"output\": [\"40741\"]}, {\"input\": \"909090901\\r\\n\", \"output\": [\"38532\"]}, {\"input\": \"142498040\\r\\n\", \"output\": [\"21671\"]}, {\"input\": \"603356456\\r\\n\", \"output\": [\"31623\"]}, {\"input\": \"64214872\\r\\n\", \"output\": [\"15759\"]}, {\"input\": \"820040584\\r\\n\", \"output\": [\"36407\"]}, {\"input\": \"442198\\r\\n\", \"output\": [\"3071\"]}, {\"input\": \"784262\\r\\n\", \"output\": [\"4079\"]}, {\"input\": \"642678\\r\\n\", \"output\": [\"3615\"]}, {\"input\": \"468390\\r\\n\", \"output\": [\"3223\"]}, {\"input\": \"326806\\r\\n\", \"output\": [\"2759\"]}, {\"input\": \"940\\r\\n\", \"output\": [\"331\"]}, {\"input\": \"356\\r\\n\", \"output\": [\"175\"]}, {\"input\": \"68\\r\\n\", \"output\": [\"68\"]}, {\"input\": \"132\\r\\n\", \"output\": [\"114\"]}, {\"input\": \"72\\r\\n\", \"output\": [\"72\"]}, {\"input\": \"89\\r\\n\", \"output\": [\"89\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"4\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"5\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"8\\r\\n\", \"output\": [\"8\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"101\\r\\n\", \"output\": [\"101\"]}, {\"input\": \"102\\r\\n\", \"output\": [\"101\"]}]"}
{"prob_desc_description":"One hot summer day Pete and his friend Billy decided to buy a watermelon. They chose the biggest and the ripest one, in their opinion. After that the watermelon was weighed, and the scales showed w kilos. They rushed home, dying of thirst, and decided to divide the berry, however they faced a hard problem.Pete and Billy are great fans of even numbers, that's why they want to divide the watermelon in such a way that each of the two parts weighs even number of kilos, at the same time it is not obligatory that the parts are equal. The boys are extremely tired and want to start their meal as soon as possible, that's why you should help them and find out, if they can divide the watermelon in the way they want. For sure, each of them should get a part of positive weight.","prob_desc_output_spec":"Print YES, if the boys can divide the watermelon into two parts, each of them weighing even number of kilos; and NO in the opposite case.","lang_cluster":"","src_uid":"230a3c4d7090401e5fa3c6b9d994cdf2","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"64 megabytes","file_name":"prog_syn_val.jsonl","tags":["brute force","math"],"prob_desc_created_at":"1268395200","prob_desc_sample_inputs":"[\"8\"]","prob_desc_notes":"NoteFor example, the boys can divide the watermelon into two parts of 2 and 6 kilos respectively (another variant \u2014 two parts of 4 and 4 kilos).","exec_outcome":"","difficulty":800.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first (and the only) input line contains integer number w (1\u2009\u2264\u2009w\u2009\u2264\u2009100) \u2014 the weight of the watermelon bought by the boys.","prob_desc_sample_outputs":"[\"YES\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"8\\r\\n\", \"output\": [\"YES\", \"Yes\", \"yes\"]}, {\"input\": \"5\\r\\n\", \"output\": [\"No\", \"NO\", \"no\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"YES\", \"Yes\", \"yes\"]}, {\"input\": \"3\\r\\n\", \"output\": [\"No\", \"NO\", \"no\"]}, {\"input\": \"2\\r\\n\", \"output\": [\"No\", \"NO\", \"no\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"No\", \"NO\", \"no\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"No\", \"NO\", \"no\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"YES\", \"Yes\", \"yes\"]}, {\"input\": \"10\\r\\n\", \"output\": [\"YES\", \"Yes\", \"yes\"]}, {\"input\": \"9\\r\\n\", \"output\": [\"No\", \"NO\", \"no\"]}, {\"input\": \"53\\r\\n\", \"output\": [\"No\", \"NO\", \"no\"]}, {\"input\": \"77\\r\\n\", \"output\": [\"No\", \"NO\", \"no\"]}, {\"input\": \"32\\r\\n\", \"output\": [\"YES\", \"Yes\", \"yes\"]}, {\"input\": \"44\\r\\n\", \"output\": [\"YES\", \"Yes\", \"yes\"]}, {\"input\": \"98\\r\\n\", \"output\": [\"YES\", \"Yes\", \"yes\"]}, {\"input\": \"99\\r\\n\", \"output\": [\"No\", \"NO\", \"no\"]}, {\"input\": \"90\\r\\n\", \"output\": [\"YES\", \"Yes\", \"yes\"]}, {\"input\": \"67\\r\\n\", \"output\": [\"No\", \"NO\", \"no\"]}, {\"input\": \"100\\r\\n\", \"output\": [\"YES\", \"Yes\", \"yes\"]}, {\"input\": \"88\\r\\n\", \"output\": [\"YES\", \"Yes\", \"yes\"]}]"}
{"prob_desc_description":"Bob likes to draw camels: with a single hump, two humps, three humps, etc. He draws a camel by connecting points on a coordinate plane. Now he's drawing camels with t humps, representing them as polylines in the plane. Each polyline consists of n vertices with coordinates (x1,\u2009y1), (x2,\u2009y2), ..., (xn,\u2009yn). The first vertex has a coordinate x1\u2009=\u20091, the second \u2014 x2\u2009=\u20092, etc. Coordinates yi might be any, but should satisfy the following conditions:  there should be t humps precisely, i.e. such indexes j (2\u2009\u2264\u2009j\u2009\u2264\u2009n\u2009-\u20091), so that yj\u2009-\u20091\u2009<\u2009yj\u2009>\u2009yj\u2009+\u20091,  there should be precisely t\u2009-\u20091 such indexes j (2\u2009\u2264\u2009j\u2009\u2264\u2009n\u2009-\u20091), so that yj\u2009-\u20091\u2009>\u2009yj\u2009<\u2009yj\u2009+\u20091,  no segment of a polyline should be parallel to the Ox-axis,  all yi are integers between 1 and 4. For a series of his drawings of camels with t humps Bob wants to buy a notebook, but he doesn't know how many pages he will need. Output the amount of different polylines that can be drawn to represent camels with t humps for a given number n.","prob_desc_output_spec":"Output the required amount of camels with t humps.","lang_cluster":"","src_uid":"6d67559744583229455c5eafe68f7952","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"64 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp"],"prob_desc_created_at":"1274283000","prob_desc_sample_inputs":"[\"6 1\", \"4 2\"]","prob_desc_notes":"NoteIn the first sample test sequences of y-coordinates for six camels are: 123421, 123431, 123432, 124321, 134321 \u0438 234321 (each digit corresponds to one value of yi).","exec_outcome":"","difficulty":1900.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains a pair of integers n and t (3\u2009\u2264\u2009n\u2009\u2264\u200920, 1\u2009\u2264\u2009t\u2009\u2264\u200910).","prob_desc_sample_outputs":"[\"6\", \"0\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"6 1\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"4 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 1\\r\\n\", \"output\": [\"14\"]}, {\"input\": \"3 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"3 10\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 1\\r\\n\", \"output\": [\"22\"]}, {\"input\": \"4 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"4 9\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5 1\\r\\n\", \"output\": [\"16\"]}, {\"input\": \"5 2\\r\\n\", \"output\": [\"70\"]}, {\"input\": \"5 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5 5\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5 9\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"5 10\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"6 1\\r\\n\", \"output\": [\"6\"]}, {\"input\": \"6 2\\r\\n\", \"output\": [\"232\"]}, {\"input\": \"6 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"6 4\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"6 10\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"19 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"19 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"19 3\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"19 4\\r\\n\", \"output\": [\"32632\"]}, {\"input\": \"19 5\\r\\n\", \"output\": [\"4594423\"]}, {\"input\": \"19 6\\r\\n\", \"output\": [\"69183464\"]}, {\"input\": \"19 7\\r\\n\", \"output\": [\"197939352\"]}, {\"input\": \"19 8\\r\\n\", \"output\": [\"109824208\"]}, {\"input\": \"19 9\\r\\n\", \"output\": [\"5846414\"]}, {\"input\": \"19 10\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"20 1\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"20 2\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"20 3\\r\\n\", \"output\": [\"0\"]}, {\"input\": \"20 4\\r\\n\", \"output\": [\"12628\"]}, {\"input\": \"20 5\\r\\n\", \"output\": [\"3715462\"]}, {\"input\": \"20 6\\r\\n\", \"output\": [\"96046590\"]}, {\"input\": \"20 7\\r\\n\", \"output\": [\"468541040\"]}, {\"input\": \"20 8\\r\\n\", \"output\": [\"503245466\"]}, {\"input\": \"20 9\\r\\n\", \"output\": [\"90700276\"]}, {\"input\": \"20 10\\r\\n\", \"output\": [\"0\"]}]"}
{"prob_desc_description":"A car moves from point A to point B at speed v meters per second. The action takes place on the X-axis. At the distance d meters from A there are traffic lights. Starting from time 0, for the first g seconds the green light is on, then for the following r seconds the red light is on, then again the green light is on for the g seconds, and so on.The car can be instantly accelerated from 0 to v and vice versa, can instantly slow down from the v to 0. Consider that it passes the traffic lights at the green light instantly. If the car approaches the traffic lights at the moment when the red light has just turned on, it doesn't have time to pass it. But if it approaches the traffic lights at the moment when the green light has just turned on, it can move. The car leaves point A at the time 0.What is the minimum time for the car to get from point A to point B without breaking the traffic rules?","prob_desc_output_spec":"Output a single number \u2014 the minimum time that the car needs to get from point A to point B. Your output must have relative or absolute error less than 10\u2009-\u20096.","lang_cluster":"","src_uid":"e4a4affb439365c843c9f9828d81b42c","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["implementation"],"prob_desc_created_at":"1284994800","prob_desc_sample_inputs":"[\"2 1 3 4 5\", \"5 4 3 1 1\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1500.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains integers l, d, v, g, r (1\u2009\u2264\u2009l,\u2009d,\u2009v,\u2009g,\u2009r\u2009\u2264\u20091000,\u2009d\u2009<\u2009l) \u2014 the distance between A and B (in meters), the distance from A to the traffic lights, car's speed, the duration of green light and the duration of red light.","prob_desc_sample_outputs":"[\"0.66666667\", \"2.33333333\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"2 1 3 4 5\\r\\n\", \"output\": [\"0.66666667\", \"0.6666666666666666\", \"0.666666666667\", \"0.666667\", \"0.6666666667\"]}, {\"input\": \"5 4 3 1 1\\r\\n\", \"output\": [\"2.333333\", \"2.33333333\", \"2.3333333333\", \"2.333333333333\", \"2.33333333333\", \"2.3333333333333335\"]}, {\"input\": \"862 33 604 888 704\\r\\n\", \"output\": [\"1.42715232\", \"1.427152317881\", \"1.427152\", \"1.42715231788\", \"1.4271523179\", \"1.4271523178807948\"]}, {\"input\": \"458 251 49 622 472\\r\\n\", \"output\": [\"9.346938775510203\", \"9.346939\", \"9.3469387755\", \"9.34693877551\", \"9.34693878\", \"9.346938775510\"]}, {\"input\": \"772 467 142 356 889\\r\\n\", \"output\": [\"5.436619718309859\", \"5.436619718310\", \"5.43661971831\", \"5.43661972\", \"5.4366197183\", \"5.436620\"]}, {\"input\": \"86 64 587 89 657\\r\\n\", \"output\": [\"0.14650767\", \"0.146507666099\", \"0.1465076660988075\", \"0.1465076661\", \"0.146508\"]}, {\"input\": \"400 333 31 823 74\\r\\n\", \"output\": [\"12.903226\", \"12.90322581\", \"12.903225806452\", \"12.903225806451612\", \"12.9032258065\"]}, {\"input\": \"714 474 124 205 491\\r\\n\", \"output\": [\"5.7580645161\", \"5.758064516129032\", \"5.758064516129\", \"5.75806452\", \"5.75806451613\", \"5.758065\"]}, {\"input\": \"29 12 569 939 259\\r\\n\", \"output\": [\"0.050966608084\", \"0.0509666081\", \"0.0509666080844\", \"0.050967\", \"0.050966608084358524\", \"0.05096661\"]}, {\"input\": \"65 24 832 159 171\\r\\n\", \"output\": [\"0.0781250000\", \"0.078125\", \"0.078125000000\", \"0.07812500\"]}, {\"input\": \"2 1 1 1 1\\r\\n\", \"output\": [\"3.0000000000\", \"3.000000\", \"3.0\", \"3.000000000000\", \"3.00000000\", \"3\"]}, {\"input\": \"2 1 1 1 1000\\r\\n\", \"output\": [\"1002\", \"1002.0000000000\", \"1002.000000\", \"1002.000000000000\", \"1002.00000000\", \"1002.0\"]}, {\"input\": \"2 1 1 1000 1\\r\\n\", \"output\": [\"2\", \"2.0\", \"2.00000000\", \"2.000000000000\", \"2.0000000000\", \"2.000000\"]}, {\"input\": \"2 1 1 1000 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{"prob_desc_description":"Volodya is an odd boy and his taste is strange as well. It seems to him that a positive integer number is beautiful if and only if it is divisible by each of its nonzero digits. We will not argue with this and just count the quantity of beautiful numbers in given ranges.","prob_desc_output_spec":"Output should contain t numbers \u2014 answers to the queries, one number per line \u2014 quantities of beautiful numbers in given intervals (from li to ri, inclusively).","lang_cluster":"","src_uid":"37feadce373f728ba2a560b198ca4bc9","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["dp","number theory"],"prob_desc_created_at":"1294992000","prob_desc_sample_inputs":"[\"1\\n1 9\", \"1\\n12 15\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":2500.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"4 seconds","prob_desc_input_spec":"The first line of the input contains the number of cases t (1\u2009\u2264\u2009t\u2009\u2264\u200910). Each of the next t lines contains two natural numbers li and ri (1\u2009\u2264\u2009li\u2009\u2264\u2009ri\u2009\u2264\u20099\u2009\u00b71018). Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cin (also you may use %I64d).","prob_desc_sample_outputs":"[\"9\", \"2\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"1\\r\\n1 9\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"1\\r\\n12 15\\r\\n\", \"output\": [\"2\"]}, {\"input\": \"1\\r\\n25 53\\r\\n\", \"output\": [\"7\"]}, {\"input\": \"1\\r\\n1 1000\\r\\n\", \"output\": [\"138\"]}, {\"input\": \"1\\r\\n1 100000\\r\\n\", \"output\": [\"4578\"]}, {\"input\": \"2\\r\\n234 59843\\r\\n46 3243\\r\\n\", \"output\": [\"3378\\r\\n381\"]}, {\"input\": \"4\\r\\n55 55\\r\\n1234 2348\\r\\n620 620\\r\\n4 1000\\r\\n\", \"output\": [\"1\\r\\n135\\r\\n0\\r\\n135\"]}, {\"input\": \"1\\r\\n1 9000000000000000000\\r\\n\", \"output\": [\"15957349671845566\"]}, {\"input\": \"5\\r\\n5397562498 1230483490253448\\r\\n39218765 5293867493184739\\r\\n99 999999999999\\r\\n546234 2394748365397856\\r\\n67 801834\\r\\n\", \"output\": [\"3974776165902\\r\\n15977172601197\\r\\n5429986145\\r\\n7654830993719\\r\\n26117\"]}, {\"input\": 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{"prob_desc_description":"Vasya has recently learned to type and log on to the Internet. He immediately entered a chat room and decided to say hello to everybody. Vasya typed the word s. It is considered that Vasya managed to say hello if several letters can be deleted from the typed word so that it resulted in the word \"hello\". For example, if Vasya types the word \"ahhellllloou\", it will be considered that he said hello, and if he types \"hlelo\", it will be considered that Vasya got misunderstood and he didn't manage to say hello. Determine whether Vasya managed to say hello by the given word s.","prob_desc_output_spec":"If Vasya managed to say hello, print \"YES\", otherwise print \"NO\".","lang_cluster":"","src_uid":"c5d19dc8f2478ee8d9cba8cc2e4cd838","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["strings","greedy"],"prob_desc_created_at":"1296489600","prob_desc_sample_inputs":"[\"ahhellllloou\", \"hlelo\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1000.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first and only line contains the word s, which Vasya typed. This word consisits of small Latin letters, its length is no less that 1 and no more than 100 letters.","prob_desc_sample_outputs":"[\"YES\", \"NO\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"ahhellllloou\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"hlelo\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"helhcludoo\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"hehwelloho\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"pnnepelqomhhheollvlo\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"tymbzjyqhymedasloqbq\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"yehluhlkwo\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"hatlevhhalrohairnolsvocafgueelrqmlqlleello\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"hhhtehdbllnhwmbyhvelqqyoulretpbfokflhlhreeflxeftelziclrwllrpflflbdtotvlqgoaoqldlroovbfsq\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"rzlvihhghnelqtwlexmvdjjrliqllolhyewgozkuovaiezgcilelqapuoeglnwmnlftxxiigzczlouooi\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"pfhhwctyqdlkrwhebfqfelhyebwllhemtrmeblgrynmvyhioesqklclocxmlffuormljszllpoo\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"lqllcolohwflhfhlnaow\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"heheeellollvoo\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"hellooo\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"o\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"hhqhzeclohlehljlhtesllylrolmomvuhcxsobtsckogdv\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"yoegfuzhqsihygnhpnukluutocvvwuldiighpogsifealtgkfzqbwtmgghmythcxflebrkctlldlkzlagovwlstsghbouk\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"uatqtgbvrnywfacwursctpagasnhydvmlinrcnqrry\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"tndtbldbllnrwmbyhvqaqqyoudrstpbfokfoclnraefuxtftmgzicorwisrpfnfpbdtatvwqgyalqtdtrjqvbfsq\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"rzlvirhgemelnzdawzpaoqtxmqucnahvqnwldklrmjiiyageraijfivigvozgwngiulttxxgzczptusoi\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"kgyelmchocojsnaqdsyeqgnllytbqietpdlgknwwumqkxrexgdcnwoldicwzwofpmuesjuxzrasscvyuqwspm\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"pnyvrcotjvgynbeldnxieghfltmexttuxzyac\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"dtwhbqoumejligbenxvzhjlhosqojetcqsynlzyhfaevbdpekgbtjrbhlltbceobcok\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"crrfpfftjwhhikwzeedrlwzblckkteseofjuxjrktcjfsylmlsvogvrcxbxtffujqshslemnixoeezivksouefeqlhhokwbqjz\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"jhfbndhyzdvhbvhmhmefqllujdflwdpjbehedlsqfdsqlyelwjtyloxwsvasrbqosblzbowlqjmyeilcvotdlaouxhdpoeloaovb\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"hwlghueoemiqtjhhpashjsouyegdlvoyzeunlroypoprnhlyiwiuxrghekaylndhrhllllwhbebezoglydcvykllotrlaqtvmlla\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"wshiaunnqnqxodholbipwhhjmyeblhgpeleblklpzwhdunmpqkbuzloetmwwxmeltkrcomulxauzlwmlklldjodozxryghsnwgcz\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"shvksednttggehroewuiptvvxtrzgidravtnjwuqrlnnkxbplctzkckinpkgjopjfoxdbojtcvsuvablcbkrzajrlhgobkcxeqti\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"hyyhddqhxhekehkwfhlnlsihzefwchzerevcjtokefplholrbvxlltdlafjxrfhleglrvlolojoqaolagtbeyogxlbgfolllslli\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"iaagrdhhelxpdegueiulflquvlzidoprzkehthkldaytrjwhyhprwjxlltinxvuilxohqgjqcvkkdcuoliekcnlilwgqlnlzouoo\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"wfluaeseldgxyvxpwuhkptdmlflnlhktwxiabsvkolsquymrmhzczzoybvlilhmvsuunggvgxzgyyffk\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"loee\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"izdipwylefqmjbuoznfglgcfvedeouflkeehxbasaqmiooppfsqlhprospqgxvzrcpwlfdddngoqvpwvggsnvvxhmjoslwjudjlo\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"pplynflbjlseflaegzqpdxswgunhnlglqhycrbcwdfhclmcrwekkzsoosmfblljeenwfjyifcvxihhhbyhmhlkvtskeglaovjnsi\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"xqjqmenkodmlhzyzmmvofdngktygbbxbzpluzcohohmalkoeuwfikblltaaigv\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"hello\\r\\n\", \"output\": [\"YES\"]}, {\"input\": \"oohell\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"hell\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"eloellohoelo\\r\\n\", \"output\": [\"NO\"]}, {\"input\": \"helllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllo\\r\\n\", \"output\": [\"YES\"]}]"}
{"prob_desc_description":"Sometimes one has to spell email addresses over the phone. Then one usually pronounces a dot as dot, an at sign as at. As a result, we get something like vasyaatgmaildotcom. Your task is to transform it into a proper email address (vasya@gmail.com). It is known that a proper email address contains only such symbols as . @ and lower-case Latin letters, doesn't start with and doesn't end with a dot. Also, a proper email address doesn't start with and doesn't end with an at sign. Moreover, an email address contains exactly one such symbol as @, yet may contain any number (possible, zero) of dots. You have to carry out a series of replacements so that the length of the result was as short as possible and it was a proper email address. If the lengths are equal, you should print the lexicographically minimal result. Overall, two variants of replacement are possible: dot can be replaced by a dot, at can be replaced by an at. ","prob_desc_output_spec":"Print the shortest email address, from which the given line could be made by the described above replacements. If there are several solutions to that problem, print the lexicographically minimal one (the lexicographical comparison of the lines are implemented with an operator < in modern programming languages). In the ASCII table the symbols go in this order: . @ ab...z","lang_cluster":"","src_uid":"a11c9679d8e2dca51be17d466202df6e","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["expression parsing","implementation"],"prob_desc_created_at":"1289232000","prob_desc_sample_inputs":"[\"vasyaatgmaildotcom\", \"dotdotdotatdotdotat\", \"aatt\"]","prob_desc_notes":null,"exec_outcome":"","difficulty":1300.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"The first line contains the email address description. It is guaranteed that that is a proper email address with all the dots replaced by dot an the at signs replaced by at. The line is not empty and its length does not exceed 100 symbols.","prob_desc_sample_outputs":"[\"vasya@gmail.com\", \"dot..@..at\", \"a@t\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"vasyaatgmaildotcom\\r\\n\", \"output\": [\"vasya@gmail.com\"]}, {\"input\": \"dotdotdotatdotdotat\\r\\n\", \"output\": [\"dot..@..at\"]}, {\"input\": \"aatt\\r\\n\", \"output\": [\"a@t\"]}, {\"input\": \"zdotdotatdotz\\r\\n\", \"output\": [\"z..@.z\"]}, {\"input\": \"dotdotdotdotatdotatatatdotdotdot\\r\\n\", \"output\": [\"dot...@.atatat..dot\"]}, {\"input\": \"taatta\\r\\n\", \"output\": [\"ta@ta\"]}, {\"input\": \"doatdt\\r\\n\", \"output\": [\"do@dt\"]}, {\"input\": \"catdotdotdotatatdotdotdotnatjdotatdotdotdoteatatoatatatoatatatdotdotatdotdotwxrdotatfatgfdotuatata\\r\\n\", \"output\": [\"c@...atat...natj.at...eatatoatatatoatatat..at..wxr.atfatgf.uatata\"]}, {\"input\": \"hmatcxatxatdotatlyucjatdothatdotcatatatdotqatatdotdotdotdotatjddotdotdotqdotdotattdotdotatddotatatat\\r\\n\", \"output\": [\"hm@cxatxat.atlyucjat.hat.catatat.qatat....atjd...q..att..atd.atatat\"]}, {\"input\": \"xatvdotrjatatatdotatatdotdotdotdotndothidotatdotdotdotqyxdotdotatdotdotdotdotdotdotduatgdotdotaatdot\\r\\n\", \"output\": [\"x@v.rjatatat.atat....n.hi.at...qyx..at......duatg..aatdot\"]}, {\"input\": \"attdotdotatdotzsedotdotatcyatdotpndotdotdotatuwatatatatatwdotdotqsatatrqatatsatqndotjcdotatnatxatoq\\r\\n\", \"output\": [\"att..@.zse..atcyat.pn...atuwatatatatatw..qsatatrqatatsatqn.jc.atnatxatoq\"]}, {\"input\": \"atdotatsatatiatatnatudotdotdotatdotdotddotdotdotwatxdotdotdotdotdoteatatfattatatdotatatdotidotzkvnat\\r\\n\", \"output\": [\"at.@satatiatatnatu...at..d...watx.....eatatfattatat.atat.i.zkvnat\"]}, {\"input\": \"atdotdotatatdottatdotatatatatdotdotdotatdotdotatucrdotdotatatdotdatatatusgdatatdotatdotdotpdotatdot\\r\\n\", \"output\": [\"at..@at.tat.atatatat...at..atucr..atat.datatatusgdatat.at..p.atdot\"]}, {\"input\": \"dotdotdotdotatdotatdoteatdotatatatatatneatatdotmdotdotatsatdotdotdotndotatjatdotatdotdotatatdotdotgp\\r\\n\", \"output\": [\"dot...@.at.eat.atatatatatneatat.m..atsat...n.atjat.at..atat..gp\"]}, {\"input\": \"dotatjdotqcratqatidotatdotudotqulatdotdotdotatatdotdotdotdotdotatatdotdotatdotdotdotymdotdotwvdotat\\r\\n\", \"output\": [\"dot@j.qcratqati.at.u.qulat...atat.....atat..at...ym..wv.at\"]}, {\"input\": \"dotatatcdotxdotatgatatatkqdotrspatdotatodotqdotbdotdotnndotatatgatatudotdotatlatatdotatbjdotdotatdot\\r\\n\", \"output\": [\"dot@atc.x.atgatatatkq.rspat.ato.q.b..nn.atatgatatu..atlatat.atbj..atdot\"]}, {\"input\": \"xqbdotatuatatdotatatatidotdotdotbatpdotdotatatatdotatbptatdotatigdotdotdotdotatatatatatdotdotdotdotl\\r\\n\", \"output\": [\"xqb.@uatat.atatati...batp..atatat.atbptat.atig....atatatatat....l\"]}, {\"input\": \"hatatatdotcatqatdotwhvdotatdotsatattatatcdotddotdotvasatdottxdotatatdotatmdotvvatkatdotxatcdotdotzsx\\r\\n\", \"output\": [\"h@atat.catqat.whv.at.satattatatc.d..vasat.tx.atat.atm.vvatkat.xatc..zsx\"]}, {\"input\": \"dotxcdotdottdotdotatdotybdotqdotatdotatdotatatpndotljethatdotdotlrdotdotdottgdotgkdotkatatdotdotzat\\r\\n\", \"output\": [\"dotxc..t..@.yb.q.at.at.atatpn.ljethat..lr...tg.gk.katat..zat\"]}, {\"input\": \"dotkatudotatdotatatwlatiwatatdotwdotatcdotatdotatatatdotdotidotdotbatldotoxdotatdotdotudotdotvatatat\\r\\n\", \"output\": [\"dotk@u.at.atatwlatiwatat.w.atc.at.atatat..i..batl.ox.at..u..vatatat\"]}, {\"input\": \"edotdotdotsatoatedotatpdotatatfatpmdotdotdotatyatdotzjdoteuldotdottatdotatmtidotdotdotadotratqisat\\r\\n\", \"output\": [\"e...s@oate.atp.atatfatpm...atyat.zj.eul..tat.atmti...a.ratqisat\"]}, {\"input\": \"atcatiatdotncbdotatedotatoiataatydotoatihzatdotdotcatkdotdotudotodotxatatatatdotatdotnhdotdotatatat\\r\\n\", \"output\": [\"atc@iat.ncb.ate.atoiataaty.oatihzat..catk..u.o.xatatatat.at.nh..atatat\"]}, {\"input\": \"atodotdotatdotatdotvpndotatdotatdotadotatdotattnysatqdotatdotdotsdotcmdotdotdotdotywateatdotatgsdot\\r\\n\", \"output\": [\"ato..@.at.vpn.at.at.a.at.attnysatq.at..s.cm....ywateat.atgsdot\"]}, {\"input\": \"dotdotatlatnatdotjatxdotdotdotudotcdotdotatdotgdotatdotatdotatdotsatatcdatzhatdotatkdotbmidotdotudot\\r\\n\", \"output\": [\"dot.@latnat.jatx...u.c..at.g.at.at.at.satatcdatzhat.atk.bmi..udot\"]}, {\"input\": \"fatdotatdotydotatdotdotatdotdotdottatatdotdotatdotatatdotatadotdotqdotatatatidotdotatkecdotdotatdot\\r\\n\", \"output\": [\"f@.at.y.at..at...tatat..at.atat.ata..q.atatati..atkec..atdot\"]}, {\"input\": \"zdotatdotatatatiatdotrdotatatcatatatdotatmaatdottatatcmdotdotatdotatdotdottnuatdotfatatdotnathdota\\r\\n\", \"output\": [\"z.@.atatatiat.r.atatcatatat.atmaat.tatatcm..at.at..tnuat.fatat.nath.a\"]}, {\"input\": \"dotatdotatvdotjatatjsdotdotdotatsdotatatcdotatldottrdotoctvhatdotdotxeatdotfatdotratdotatfatatatdot\\r\\n\", \"output\": [\"dot@.atv.jatatjs...ats.atatc.atl.tr.octvhat..xeat.fat.rat.atfatatatdot\"]}, {\"input\": \"jdotypatdotatqatdothdotdqatadotkdotodotdotatdotdotdotdotdottdotdotatatatdotzndotodotdotkdotfdotatat\\r\\n\", \"output\": [\"j.yp@.atqat.h.dqata.k.o..at.....t..atatat.zn.o..k.f.atat\"]}, {\"input\": \"batatatgldotatatpatsatrdotatjdotatdotatfndotdotatzatuatrdotxiwatvhdatdatsyatatatratatxdothdotadotaty\\r\\n\", \"output\": [\"b@atatgl.atatpatsatr.atj.at.atfn..atzatuatr.xiwatvhdatdatsyatatatratatx.h.a.aty\"]}, {\"input\": \"atdotpgatgnatatatdotfoatdotatwatdotatmdotdotdotjnhatatdotatatdotatpdotatadotatatdotdotdotatdotdotdot\\r\\n\", \"output\": [\"at.pg@gnatatat.foat.atwat.atm...jnhatat.atat.atp.ata.atat...at..dot\"]}, {\"input\": \"atatat\\r\\n\", \"output\": [\"at@at\"]}, {\"input\": \"dotdotdotdotdatotdotdotdotatdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdot\\r\\n\", \"output\": [\"dot...d@ot...at...............dot\"]}, {\"input\": \"dotatdot\\r\\n\", \"output\": [\"dot@dot\"]}, {\"input\": \"dotatat\\r\\n\", \"output\": [\"dot@at\"]}, {\"input\": \"atatdot\\r\\n\", \"output\": [\"at@dot\"]}, {\"input\": \"atatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatat\\r\\n\", \"output\": [\"at@atatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatatat\"]}, {\"input\": \"dotdotdotdotdotdotdotdotdotdotdotdoatdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdot\\r\\n\", \"output\": [\"dot..........do@....................dot\"]}, {\"input\": \"dotdotdotdotdotdotdotdotdotdotdotdotdotatdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdotdot\\r\\n\", \"output\": [\"dot............@..................dot\"]}, {\"input\": \"sdfuiopguoidfbhuihsregftuioheguoatsfhgvuherasuihfsduphguphewruheruopsghuiofhbvjudfbdpiuthrupwrkgfhda\\r\\n\", \"output\": [\"sdfuiopguoidfbhuihsregftuioheguo@sfhgvuherasuihfsduphguphewruheruopsghuiofhbvjudfbdpiuthrupwrkgfhda\"]}, {\"input\": \"sdfuiopguoidfbhuihsregftuioheguodpsfhgvuherasuihfsduphguatwruheruopsghuiofhbvjudfbdpiuthrupwrkgfhdat\\r\\n\", \"output\": [\"sdfuiopguoidfbhuihsregftuioheguodpsfhgvuherasuihfsduphgu@wruheruopsghuiofhbvjudfbdpiuthrupwrkgfhdat\"]}, {\"input\": \"atatatat\\r\\n\", \"output\": [\"at@atat\"]}, {\"input\": \"atatatdot\\r\\n\", \"output\": [\"at@atdot\"]}, {\"input\": \"atatdotat\\r\\n\", \"output\": [\"at@.at\"]}, {\"input\": \"atatdotdot\\r\\n\", \"output\": [\"at@.dot\"]}, {\"input\": \"atdotatat\\r\\n\", \"output\": [\"at.@at\"]}, {\"input\": \"atdotatdot\\r\\n\", \"output\": [\"at.@dot\"]}, {\"input\": \"dotatatat\\r\\n\", \"output\": [\"dot@atat\"]}, {\"input\": \"dotatatdot\\r\\n\", \"output\": [\"dot@atdot\"]}, {\"input\": \"dotatdotat\\r\\n\", \"output\": [\"dot@.at\"]}, {\"input\": \"dotatdotdot\\r\\n\", \"output\": [\"dot@.dot\"]}, {\"input\": \"dotdotatat\\r\\n\", \"output\": [\"dot.@at\"]}, {\"input\": \"dotdotatdot\\r\\n\", \"output\": [\"dot.@dot\"]}]"}
{"prob_desc_description":"Fangy collects cookies. Once he decided to take a box and put cookies into it in some way. If we take a square k\u2009\u00d7\u2009k in size, divided into blocks 1\u2009\u00d7\u20091 in size and paint there the main diagonal together with cells, which lie above it, then the painted area will be equal to the area occupied by one cookie k in size. Fangy also has a box with a square base 2n\u2009\u00d7\u20092n, divided into blocks 1\u2009\u00d7\u20091 in size. In a box the cookies should not overlap, and they should not be turned over or rotated. See cookies of sizes 2 and 4 respectively on the figure:    To stack the cookies the little walrus uses the following algorithm. He takes out of the repository the largest cookie which can fit in some place in the box and puts it there. Everything could be perfect but alas, in the repository the little walrus has infinitely many cookies of size 2 and larger, and there are no cookies of size 1, therefore, empty cells will remain in the box. Fangy wants to know how many empty cells will be left in the end.","prob_desc_output_spec":"Print the single number, equal to the number of empty cells in the box. The answer should be printed modulo 106\u2009+\u20093.","lang_cluster":"","src_uid":"1a335a9638523ca0315282a67e18eec7","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math"],"prob_desc_created_at":"1301155200","prob_desc_sample_inputs":"[\"3\"]","prob_desc_notes":"NoteIf the box possesses the base of 23\u2009\u00d7\u200923 (as in the example), then the cookies will be put there in the following manner: ","exec_outcome":"","difficulty":1300.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"1 second","prob_desc_input_spec":"The first line contains a single integer n (0\u2009\u2264\u2009n\u2009\u2264\u20091000).","prob_desc_sample_outputs":"[\"9\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3\\r\\n\", \"output\": [\"9\"]}, {\"input\": \"1\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"2\\r\\n\", \"output\": [\"3\"]}, {\"input\": \"4\\r\\n\", \"output\": [\"27\"]}, {\"input\": \"6\\r\\n\", \"output\": [\"243\"]}, {\"input\": \"11\\r\\n\", \"output\": [\"59049\"]}, {\"input\": \"14\\r\\n\", \"output\": [\"594320\"]}, {\"input\": \"15\\r\\n\", \"output\": [\"782957\"]}, {\"input\": \"7\\r\\n\", \"output\": [\"729\"]}, {\"input\": \"0\\r\\n\", \"output\": [\"1\"]}, {\"input\": \"1000\\r\\n\", \"output\": [\"691074\"]}, {\"input\": \"657\\r\\n\", \"output\": [\"874011\"]}, {\"input\": \"561\\r\\n\", \"output\": [\"842553\"]}, {\"input\": \"823\\r\\n\", \"output\": [\"858672\"]}, {\"input\": \"850\\r\\n\", \"output\": [\"557186\"]}, {\"input\": \"298\\r\\n\", \"output\": [\"999535\"]}, {\"input\": \"262\\r\\n\", \"output\": [\"946384\"]}, {\"input\": \"910\\r\\n\", \"output\": [\"678945\"]}, {\"input\": \"617\\r\\n\", \"output\": [\"247876\"]}, {\"input\": \"857\\r\\n\", \"output\": [\"562128\"]}, {\"input\": \"69\\r\\n\", \"output\": [\"327984\"]}, {\"input\": \"589\\r\\n\", \"output\": [\"889192\"]}, {\"input\": \"928\\r\\n\", \"output\": [\"794863\"]}, {\"input\": \"696\\r\\n\", \"output\": [\"695035\"]}, {\"input\": \"226\\r\\n\", \"output\": [\"376094\"]}]"}
{"prob_desc_description":"For each positive integer n consider the integer \u03c8(n) which is obtained from n by replacing every digit a in the decimal notation of n with the digit (9\u2009\u2009-\u2009\u2009a). We say that \u03c8(n) is the reflection of n. For example, reflection of 192 equals 807. Note that leading zeros (if any) should be omitted. So reflection of 9 equals 0, reflection of 91 equals 8.Let us call the weight of the number the product of the number and its reflection. Thus, the weight of the number 10 is equal to 10\u00b789\u2009=\u2009890.Your task is to find the maximum weight of the numbers in the given range [l,\u2009r] (boundaries are included).","prob_desc_output_spec":"Output should contain single integer number: maximum value of the product n\u00b7\u03c8(n), where l\u2009\u2264\u2009n\u2009\u2264\u2009r. Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preferred to use cout (also you may use %I64d).","lang_cluster":"","src_uid":"2c4b2a162563242cb2f43f6209b59d5e","code_uid":"","lang":"","prob_desc_output_to":"standard output","prob_desc_memory_limit":"256 megabytes","file_name":"prog_syn_val.jsonl","tags":["math"],"prob_desc_created_at":"1306077000","prob_desc_sample_inputs":"[\"3 7\", \"1 1\", \"8 10\"]","prob_desc_notes":"NoteIn the third sample weight of 8 equals 8\u00b71\u2009=\u20098, weight of 9 equals 9\u00b70\u2009=\u20090, weight of 10 equals 890.Thus, maximum value of the product is equal to 890.","exec_outcome":"","difficulty":1600.0,"prob_desc_input_from":"standard input","prob_desc_time_limit":"2 seconds","prob_desc_input_spec":"Input contains two space-separated integers l and r (1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009109) \u2014 bounds of the range.","prob_desc_sample_outputs":"[\"20\", \"8\", \"890\"]","source_code":"","hidden_unit_tests":"[{\"input\": \"3 7\\r\\n\", \"output\": [\"20\"]}, 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