message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4 | instruction | 0 | 5,646 | 16 | 11,292 |
"Correct Solution:
```
n, k = map(int, input().split())
print((n-1)//(k-1)+1 if (n-1)%(k-1) else (n-1)//(k-1))
``` | output | 1 | 5,646 | 16 | 11,293 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4 | instruction | 0 | 5,647 | 16 | 11,294 |
"Correct Solution:
```
N,K = map(int,input().split())
answer = (N-2)//(K-1)+1
print(answer)
``` | output | 1 | 5,647 | 16 | 11,295 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4 | instruction | 0 | 5,648 | 16 | 11,296 |
"Correct Solution:
```
N, K, *a = map(int, open(0).read().split())
print((N - 2) // (K - 1) + 1)
``` | output | 1 | 5,648 | 16 | 11,297 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4 | instruction | 0 | 5,649 | 16 | 11,298 |
"Correct Solution:
```
print(eval('0--~-'+input().replace(' ','//~-')))
``` | output | 1 | 5,649 | 16 | 11,299 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4 | instruction | 0 | 5,650 | 16 | 11,300 |
"Correct Solution:
```
n,k=map(int,input().split())
print((n-1)//(k-1)+((n-1)%(k-1)!=0))
``` | output | 1 | 5,650 | 16 | 11,301 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4 | instruction | 0 | 5,651 | 16 | 11,302 |
"Correct Solution:
```
import math
N,K = map(int, input().split())
ans = math.ceil((N-1) / (K-1))
print(ans)
``` | output | 1 | 5,651 | 16 | 11,303 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4 | instruction | 0 | 5,652 | 16 | 11,304 |
"Correct Solution:
```
n,k=map(int,input().split())
i=1
cnt=0
while i<n:
i+=k-1
cnt+=1
print(cnt)
``` | output | 1 | 5,652 | 16 | 11,305 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4
Submitted Solution:
```
N, K = [int(s) for s in input().split()]
print(1 -(-(N-K)//(K-1)))
``` | instruction | 0 | 5,653 | 16 | 11,306 |
Yes | output | 1 | 5,653 | 16 | 11,307 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4
Submitted Solution:
```
n,k=map(int,input().split());print((n+k-3)//~-k)
``` | instruction | 0 | 5,654 | 16 | 11,308 |
Yes | output | 1 | 5,654 | 16 | 11,309 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4
Submitted Solution:
```
N, K = map(int, input().split())
A = [int(x) for x in input().split()]
print((N+K-3)//(K-1))
``` | instruction | 0 | 5,655 | 16 | 11,310 |
Yes | output | 1 | 5,655 | 16 | 11,311 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4
Submitted Solution:
```
n, k = map(int, input().split())
d = k - 1
print((n + d - 2) // d)
``` | instruction | 0 | 5,656 | 16 | 11,312 |
Yes | output | 1 | 5,656 | 16 | 11,313 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4
Submitted Solution:
```
from math import ceil
N, K = map(int, input().split())
A = list(map(int, input().split()))
if N == K:
print(1)
if K == 2:
print(N-1)
else:
ans = ceil(N/(K-1))
print(ans)
``` | instruction | 0 | 5,657 | 16 | 11,314 |
No | output | 1 | 5,657 | 16 | 11,315 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4
Submitted Solution:
```
N, K = map(int, input().split())
A = [int(x) for x in input().split()]
minIndex = A.index(min(A))
cnt1 = (minIndex+1)//(K-1)
cnt2 = (len(A)-minIndex)//(K-1)
print(cnt1 + cnt2)
``` | instruction | 0 | 5,658 | 16 | 11,316 |
No | output | 1 | 5,658 | 16 | 11,317 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4
Submitted Solution:
```
def getN():
return int(input())
def getNM():
return map(int, input().split())
def getList():
return list(map(int, input().split()))
def getArray(intn):
return [int(input()) for i in range(intn)]
def input():
return sys.stdin.readline().rstrip()
from collections import defaultdict, deque, Counter
from sys import exit
import heapq
import math
import fractions
import copy
from itertools import permutations
from operator import mul
from functools import reduce
from bisect import bisect_left, bisect_right
import sys
sys.setrecursionlimit(1000000000)
mod = 10 ** 9 + 7
from itertools import permutations
from math import factorial, hypot
N, K = getNM()
A = getList()
mi = min(A)
miindex = []
for i in range(N):
if A[i] == mi:
miindex.append(i)
ans = 1000000
for i in miindex:
rang = K - 1
opt1 = (i + rang - 1) // rang
opt2 = ((N - i - 1) + rang - 1) // rang
ans = min(ans, opt1 + opt2)
print(ans)
``` | instruction | 0 | 5,659 | 16 | 11,318 |
No | output | 1 | 5,659 | 16 | 11,319 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.
On this sequence, Snuke can perform the following operation:
* Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.
Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times. Find the minimum number of operations required. It can be proved that, Under the constraints of this problem, this objective is always achievable.
Constraints
* 2 \leq K \leq N \leq 100000
* A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
Print the minimum number of operations required.
Examples
Input
4 3
2 3 1 4
Output
2
Input
3 3
1 2 3
Output
1
Input
8 3
7 3 1 8 4 6 2 5
Output
4
Submitted Solution:
```
info = list(map(int, input().split(' ')))
array = list(map(int, input().split(' ')))
print(info[0]//(info[1]-1))
``` | instruction | 0 | 5,660 | 16 | 11,320 |
No | output | 1 | 5,660 | 16 | 11,321 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Snuke came up with a game that uses a number sequence, as follows:
* Prepare a sequence of length M consisting of integers between 0 and 2^N-1 (inclusive): a = a_1, a_2, \ldots, a_M.
* Snuke first does the operation below as many times as he likes:
* Choose a positive integer d, and for each i (1 \leq i \leq M), in binary, set the d-th least significant bit of a_i to 0. (Here the least significant bit is considered the 1-st least significant bit.)
* After Snuke finishes doing operations, Takahashi tries to sort a in ascending order by doing the operation below some number of times. Here a is said to be in ascending order when a_i \leq a_{i + 1} for all i (1 \leq i \leq M - 1).
* Choose two adjacent elements of a: a_i and a_{i + 1}. If, in binary, these numbers differ in exactly one bit, swap a_i and a_{i + 1}.
There are 2^{NM} different sequences of length M consisting of integers between 0 and 2^N-1 that can be used in the game.
How many among them have the following property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations? Find the count modulo (10^9 + 7).
Constraints
* All values in input are integers.
* 1 \leq N \leq 5000
* 2 \leq M \leq 5000
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number, modulo (10^9 + 7), of sequences with the property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations.
Examples
Input
2 5
Output
352
Input
2020 530
Output
823277409
Submitted Solution:
```
input()
print(1)
``` | instruction | 0 | 7,298 | 16 | 14,596 |
No | output | 1 | 7,298 | 16 | 14,597 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Snuke came up with a game that uses a number sequence, as follows:
* Prepare a sequence of length M consisting of integers between 0 and 2^N-1 (inclusive): a = a_1, a_2, \ldots, a_M.
* Snuke first does the operation below as many times as he likes:
* Choose a positive integer d, and for each i (1 \leq i \leq M), in binary, set the d-th least significant bit of a_i to 0. (Here the least significant bit is considered the 1-st least significant bit.)
* After Snuke finishes doing operations, Takahashi tries to sort a in ascending order by doing the operation below some number of times. Here a is said to be in ascending order when a_i \leq a_{i + 1} for all i (1 \leq i \leq M - 1).
* Choose two adjacent elements of a: a_i and a_{i + 1}. If, in binary, these numbers differ in exactly one bit, swap a_i and a_{i + 1}.
There are 2^{NM} different sequences of length M consisting of integers between 0 and 2^N-1 that can be used in the game.
How many among them have the following property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations? Find the count modulo (10^9 + 7).
Constraints
* All values in input are integers.
* 1 \leq N \leq 5000
* 2 \leq M \leq 5000
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number, modulo (10^9 + 7), of sequences with the property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations.
Examples
Input
2 5
Output
352
Input
2020 530
Output
823277409
Submitted Solution:
```
class comb():
F = [1, 1]
Fi = [1, 1]
I = [0, 1]
def __init__(self, num, mod):
self.MOD = mod
for i in range(2, num + 1):
self.F.append((self.F[-1] * i) % mod)
self.I.append(mod - self.I[mod % i] * (mod // i) % mod)
self.Fi.append(self.Fi[-1] * self.I[i] % mod)
def com(self, n, k):
if n < k: return 0
if n < 0 or k < 0: return 0
return self.F[n] * (self.Fi[k] * self.Fi[n - k] % self.MOD) % self.MOD
M, N = list(map(int, input().split()))
MOD = 10 ** 9 + 7
DP = [[[0] * 2 for i in range(M + 1)] for _ in range(N)]
com = comb(M + 1, MOD)
L = [0] * (M + 1)
for i in range(M + 1):
L[i] = com.com(M, i)
for i in range(M + 1):
DP[0][i][0] = 1
for i in range(1, N):
for j in range(M + 1):
if j != 0:
DP[i][j][0] += (DP[i - 1][j - 1][0] + DP[i - 1][j - 1][1]) * L[j - 1] % MOD
DP[i][j][0] += DP[i - 1][j][0] * L[j] % MOD
DP[i][j][0] %= MOD
if j != M:
DP[i][j][1] += (DP[i - 1][j + 1][0]) * L[j + 1] % MOD
DP[i][j][1] += DP[i - 1][j][1] * L[j] % MOD
ans = 0
for i in range(M + 1):
ans = (ans + DP[-1][i][0] + DP[-1][i][1]) % MOD
print(ans)
``` | instruction | 0 | 7,299 | 16 | 14,598 |
No | output | 1 | 7,299 | 16 | 14,599 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Snuke came up with a game that uses a number sequence, as follows:
* Prepare a sequence of length M consisting of integers between 0 and 2^N-1 (inclusive): a = a_1, a_2, \ldots, a_M.
* Snuke first does the operation below as many times as he likes:
* Choose a positive integer d, and for each i (1 \leq i \leq M), in binary, set the d-th least significant bit of a_i to 0. (Here the least significant bit is considered the 1-st least significant bit.)
* After Snuke finishes doing operations, Takahashi tries to sort a in ascending order by doing the operation below some number of times. Here a is said to be in ascending order when a_i \leq a_{i + 1} for all i (1 \leq i \leq M - 1).
* Choose two adjacent elements of a: a_i and a_{i + 1}. If, in binary, these numbers differ in exactly one bit, swap a_i and a_{i + 1}.
There are 2^{NM} different sequences of length M consisting of integers between 0 and 2^N-1 that can be used in the game.
How many among them have the following property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations? Find the count modulo (10^9 + 7).
Constraints
* All values in input are integers.
* 1 \leq N \leq 5000
* 2 \leq M \leq 5000
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number, modulo (10^9 + 7), of sequences with the property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations.
Examples
Input
2 5
Output
352
Input
2020 530
Output
823277409
Submitted Solution:
```
import itertools
N = int(input())
A = [int(_) for _ in input().split()]
if A[0] != 0:
if N == 0 and A[0] == 1:
print(1)
else:
print(-1)
exit()
ans = 1
n = 1
if A[0] > 1:
print(-1)
exit()
cumr = list(itertools.accumulate(A[::-1]))[::-1]
for i in range(1, N + 1):
n = min(2 * (n - A[i - 1]), cumr[i])
ans += n
if n < 0:
print(-1)
exit()
print(ans)
``` | instruction | 0 | 7,300 | 16 | 14,600 |
No | output | 1 | 7,300 | 16 | 14,601 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Snuke came up with a game that uses a number sequence, as follows:
* Prepare a sequence of length M consisting of integers between 0 and 2^N-1 (inclusive): a = a_1, a_2, \ldots, a_M.
* Snuke first does the operation below as many times as he likes:
* Choose a positive integer d, and for each i (1 \leq i \leq M), in binary, set the d-th least significant bit of a_i to 0. (Here the least significant bit is considered the 1-st least significant bit.)
* After Snuke finishes doing operations, Takahashi tries to sort a in ascending order by doing the operation below some number of times. Here a is said to be in ascending order when a_i \leq a_{i + 1} for all i (1 \leq i \leq M - 1).
* Choose two adjacent elements of a: a_i and a_{i + 1}. If, in binary, these numbers differ in exactly one bit, swap a_i and a_{i + 1}.
There are 2^{NM} different sequences of length M consisting of integers between 0 and 2^N-1 that can be used in the game.
How many among them have the following property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations? Find the count modulo (10^9 + 7).
Constraints
* All values in input are integers.
* 1 \leq N \leq 5000
* 2 \leq M \leq 5000
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number, modulo (10^9 + 7), of sequences with the property: if used in the game, there is always a way for Takahashi to sort the sequence in ascending order regardless of Snuke's operations.
Examples
Input
2 5
Output
352
Input
2020 530
Output
823277409
Submitted Solution:
```
#!/usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
from bisect import bisect_left, bisect_right
import sys, random, itertools, math
sys.setrecursionlimit(10**5)
input = sys.stdin.readline
sqrt = math.sqrt
def LI(): return list(map(int, input().split()))
def LF(): return list(map(float, input().split()))
def LI_(): return list(map(lambda x: int(x)-1, input().split()))
def II(): return int(input())
def IF(): return float(input())
def S(): return input().rstrip()
def LS(): return S().split()
def IR(n): return [II() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def FR(n): return [IF() for _ in range(n)]
def LFR(n): return [LI() for _ in range(n)]
def LIR_(n): return [LI_() for _ in range(n)]
def SR(n): return [S() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]
mod = 1000000007
inf = float('INF')
fact = [i for i in range(10**5+1)]
fact[0] = 1
for i in range(10**5):
fact[i+1]*=fact[i]
fact[i+1]%=mod
invfact=[None]*(10**5+1)
invfact[-1]=pow(fact[-1],mod-2,mod)
for i in range(10**5):
invfact[-i-2]=(invfact[-i-1]*(10**5-i))%mod
def cmb(n,k):
return fact[n]*invfact[k]*invfact[n-k]%mod
#solve
def solve():
n, m = LI()
dp = [[0, 0] for i in range(n + 1)]
dp[0][0] = 1
dp[1][0] = n
dp[1][1] = n
for i in range(1,n):
dp[i + 1][0] = cmb(n,i)
dp[i + 1][1] = cmb(n,i)*(i+1)%mod
ans = pow(2, m, mod)
tmp = 0
for d1, d2 in dp:
tmp += d1 + d2
tmp %= mod
print(ans * tmp % mod)
return
#main
if __name__ == '__main__':
solve()
``` | instruction | 0 | 7,301 | 16 | 14,602 |
No | output | 1 | 7,301 | 16 | 14,603 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two sequences a and b, both of length 2N. The i-th elements in a and b are a_i and b_i, respectively. Using these sequences, Snuke is doing the job of calculating the beauty of pairs of balanced sequences of parentheses (defined below) of length 2N. The beauty of a pair (s,t) is calculated as follows:
* Let X=0.
* For each i between 1 and 2N (inclusive), increment X by a_i if s_i = t_i, and increment X by b_i otherwise.
* The beauty of (s,t) is the final value of X.
You will be given Q queries. Process them in order. In the i-th query, update the value of a_{p_i} to x_i, and the value of b_{p_i} to y_i. Then, find the maximum possible beauty of a pair of balanced sequences of parentheses.
In this problem, only the sequences below are defined to be balanced sequences of parentheses.
* An empty string
* The concatenation of `(`, s, `)` in this order, where s is a balanced sequence of parentheses
* The concatenation of s, t in this order, where s and t are balanced sequences of parentheses
Constraints
* 1 \leq N,Q \leq 10^{5}
* -10^{9} \leq a_i,b_i,x_i,y_i \leq 10^{9}
* 1 \leq p_i \leq 2N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N Q
a_1 a_2 ... a_{2N}
b_1 b_2 ... b_{2N}
p_1 x_1 y_1
:
p_Q x_Q y_Q
Output
Print Q lines. The i-th line should contain the response to the i-th query.
Examples
Input
2 2
1 1 7 3
4 2 3 3
2 4 6
3 2 5
Output
15
15
Input
7 7
34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29
46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17
7 27 34
12 -2 22
4 -50 -12
3 -32 15
8 -7 23
3 -30 11
4 -2 23
Output
311
312
260
286
296
292
327 | instruction | 0 | 7,382 | 16 | 14,764 |
"Correct Solution:
```
import sys
from heapq import heappop, heappush, heapify
def main():
input = sys.stdin.readline
N, Q = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
ls = [b-a for a, b in zip(A, B)]
q_m = [-v for v in ls[1:-1] if v < 0]
q_p = [v for v in ls[1:-1] if v >= 0]
heapify(q_m)
heapify(q_p)
sum_A = sum(A)
sum_q_p = sum(q_p)
to_remove = set()
odd = len(q_p) % 2
Ans = []
ans = sum_A + sum_q_p - (min(q_p[0], q_m[0]) if odd else 0)
for _ in range(Q):
p, x, y = map(int, input().split())
p -= 1
v = y-x
sum_A += x - A[p]
if p==0 or p==2*N-1:
ans += x - A[p]
Ans.append(ans)
A[p] = x
continue
A[p] = x
odd ^= (ls[p] >= 0) ^ (v >= 0)
if v >= 0:
sum_q_p += v
if ls[p] >= 0:
sum_q_p -= ls[p]
to_remove.add(ls[p])
ls[p] = v
if v >= 0:
heappush(q_p, v)
else:
heappush(q_m, -v)
ans = sum_q_p + sum_A
if odd:
while q_p[0] in to_remove:
to_remove.remove(heappop(q_p))
while -q_m[0] in to_remove:
to_remove.remove(-heappop(q_m))
ans -= min(q_p[0], q_m[0])
Ans.append(ans)
print("\n".join(map(str, Ans)))
main()
``` | output | 1 | 7,382 | 16 | 14,765 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two sequences a and b, both of length 2N. The i-th elements in a and b are a_i and b_i, respectively. Using these sequences, Snuke is doing the job of calculating the beauty of pairs of balanced sequences of parentheses (defined below) of length 2N. The beauty of a pair (s,t) is calculated as follows:
* Let X=0.
* For each i between 1 and 2N (inclusive), increment X by a_i if s_i = t_i, and increment X by b_i otherwise.
* The beauty of (s,t) is the final value of X.
You will be given Q queries. Process them in order. In the i-th query, update the value of a_{p_i} to x_i, and the value of b_{p_i} to y_i. Then, find the maximum possible beauty of a pair of balanced sequences of parentheses.
In this problem, only the sequences below are defined to be balanced sequences of parentheses.
* An empty string
* The concatenation of `(`, s, `)` in this order, where s is a balanced sequence of parentheses
* The concatenation of s, t in this order, where s and t are balanced sequences of parentheses
Constraints
* 1 \leq N,Q \leq 10^{5}
* -10^{9} \leq a_i,b_i,x_i,y_i \leq 10^{9}
* 1 \leq p_i \leq 2N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N Q
a_1 a_2 ... a_{2N}
b_1 b_2 ... b_{2N}
p_1 x_1 y_1
:
p_Q x_Q y_Q
Output
Print Q lines. The i-th line should contain the response to the i-th query.
Examples
Input
2 2
1 1 7 3
4 2 3 3
2 4 6
3 2 5
Output
15
15
Input
7 7
34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29
46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17
7 27 34
12 -2 22
4 -50 -12
3 -32 15
8 -7 23
3 -30 11
4 -2 23
Output
311
312
260
286
296
292
327
Submitted Solution:
```
import sys
from heapq import heappop, heappush, heapify
def main():
input = sys.stdin.readline
N, Q = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
ls = [b-a for a, b in zip(A, B)]
st = set(ls[1:-1])
q_m = [-v for v in ls[1:-1] if v < 0]
q_p = [v for v in ls[1:-1] if v >= 0]
heapify(q_m)
heapify(q_p)
sum_A = sum(A)
sum_q_p = sum(q_p)
to_remove = set()
odd = len(q_p) % 2
Ans = []
ans = sum_A + sum_q_p - (min(q_p[0], q_m[0]) if odd else 0)
for _ in range(Q):
p, x, y = map(int, input().split())
p -= 1
v = y-x
sum_A += x - A[p]
if p==0 or p==2*N-1:
ans += x - A[p]
Ans.append(ans)
A[p] = x
continue
A[p] = x
odd ^= (ls[p] >= 0) ^ (v >= 0)
if v >= 0:
sum_q_p += v
if ls[p] >= 0:
sum_q_p -= ls[p]
to_remove.add(ls[p])
ls[p] = v
if v >= 0:
heappush(q_p, v)
else:
heappush(q_m, -v)
ans = sum_q_p + sum_A
if odd:
while q_p[0] in to_remove:
heappop(q_p)
while -q_m[0] in to_remove:
heappop(q_m)
ans -= min(q_p[0], q_m[0])
Ans.append(ans)
print("\n".join(map(str, Ans)))
main()
``` | instruction | 0 | 7,383 | 16 | 14,766 |
No | output | 1 | 7,383 | 16 | 14,767 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two sequences a and b, both of length 2N. The i-th elements in a and b are a_i and b_i, respectively. Using these sequences, Snuke is doing the job of calculating the beauty of pairs of balanced sequences of parentheses (defined below) of length 2N. The beauty of a pair (s,t) is calculated as follows:
* Let X=0.
* For each i between 1 and 2N (inclusive), increment X by a_i if s_i = t_i, and increment X by b_i otherwise.
* The beauty of (s,t) is the final value of X.
You will be given Q queries. Process them in order. In the i-th query, update the value of a_{p_i} to x_i, and the value of b_{p_i} to y_i. Then, find the maximum possible beauty of a pair of balanced sequences of parentheses.
In this problem, only the sequences below are defined to be balanced sequences of parentheses.
* An empty string
* The concatenation of `(`, s, `)` in this order, where s is a balanced sequence of parentheses
* The concatenation of s, t in this order, where s and t are balanced sequences of parentheses
Constraints
* 1 \leq N,Q \leq 10^{5}
* -10^{9} \leq a_i,b_i,x_i,y_i \leq 10^{9}
* 1 \leq p_i \leq 2N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N Q
a_1 a_2 ... a_{2N}
b_1 b_2 ... b_{2N}
p_1 x_1 y_1
:
p_Q x_Q y_Q
Output
Print Q lines. The i-th line should contain the response to the i-th query.
Examples
Input
2 2
1 1 7 3
4 2 3 3
2 4 6
3 2 5
Output
15
15
Input
7 7
34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29
46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17
7 27 34
12 -2 22
4 -50 -12
3 -32 15
8 -7 23
3 -30 11
4 -2 23
Output
311
312
260
286
296
292
327
Submitted Solution:
```
import sys
from heapq import heappop, heappush, heapify
def main():
input = sys.stdin.readline
N, Q = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
ls = [b-a for a, b in zip(A, B)]
st = set(ls[1:-1])
q_m = [-v for v in ls[1:-1] if v < 0]
q_p = [v for v in ls[1:-1] if v >= 0]
heapify(q_m)
heapify(q_p)
sum_A = sum(A)
sum_q_p = sum(q_p)
to_remove = set()
odd = len(q_p) % 2
Ans = []
ans = sum_A + sum_q_p - (min(q_p[0], q_m[0]) if odd else 0)
for _ in range(Q):
p, x, y = map(int, input().split())
p -= 1
v = y-x
sum_A += x - A[p]
if p==0 or p==2*N-1:
ans += x - A[p]
Ans.append(ans)
A[p] = x
continue
A[p] = x
odd ^= (ls[p] >= 0) ^ (v >= 0)
if v >= 0:
sum_q_p += v
if ls[p] >= 0:
sum_q_p -= ls[p]
to_remove.add(ls[p])
ls[p] = v
if v >= 0:
heappush(q_p, v)
else:
heappush(q_m, -v)
ans = sum_q_p + sum_A
if odd:
while q_p[0] in to_remove:
heappop(q_p)
while q_m[0] in to_remove:
heappop(q_m)
ans -= min(q_p[0], q_m[0])
Ans.append(ans)
print("\n".join(map(str, Ans)))
main()
``` | instruction | 0 | 7,384 | 16 | 14,768 |
No | output | 1 | 7,384 | 16 | 14,769 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two sequences a and b, both of length 2N. The i-th elements in a and b are a_i and b_i, respectively. Using these sequences, Snuke is doing the job of calculating the beauty of pairs of balanced sequences of parentheses (defined below) of length 2N. The beauty of a pair (s,t) is calculated as follows:
* Let X=0.
* For each i between 1 and 2N (inclusive), increment X by a_i if s_i = t_i, and increment X by b_i otherwise.
* The beauty of (s,t) is the final value of X.
You will be given Q queries. Process them in order. In the i-th query, update the value of a_{p_i} to x_i, and the value of b_{p_i} to y_i. Then, find the maximum possible beauty of a pair of balanced sequences of parentheses.
In this problem, only the sequences below are defined to be balanced sequences of parentheses.
* An empty string
* The concatenation of `(`, s, `)` in this order, where s is a balanced sequence of parentheses
* The concatenation of s, t in this order, where s and t are balanced sequences of parentheses
Constraints
* 1 \leq N,Q \leq 10^{5}
* -10^{9} \leq a_i,b_i,x_i,y_i \leq 10^{9}
* 1 \leq p_i \leq 2N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N Q
a_1 a_2 ... a_{2N}
b_1 b_2 ... b_{2N}
p_1 x_1 y_1
:
p_Q x_Q y_Q
Output
Print Q lines. The i-th line should contain the response to the i-th query.
Examples
Input
2 2
1 1 7 3
4 2 3 3
2 4 6
3 2 5
Output
15
15
Input
7 7
34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29
46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17
7 27 34
12 -2 22
4 -50 -12
3 -32 15
8 -7 23
3 -30 11
4 -2 23
Output
311
312
260
286
296
292
327
Submitted Solution:
```
N,Q =list(map(int,input().split()))
a= list(map(int,input().split()))
b=list(map(int,input().split()))
INF=-1E10
def calc(s,t):
X=0
for i in range(2*N):
if s[i]==t[i]:
X+=a[i]
else:
X+=b[i]
return X
for p,x,y in [list(map(int,input().split())) for _ in range(Q)]:
a[p-1]=x
b[p-1]=y
def get_dp(i,j):
if 0<=i<2*N and 0 <=j<=i:
return dp[i][j]
return INF
dp = [-INF for _ in range(2*N)]
dp[0]=a[0]
flag=False
tmp=0
X =a[0]+a[-1]
for i in range(1,2*N-1):
X+=max(a[i],b[i])
if a[i]>b[i]:
tmp+=1
if a[i]==b[i]:
flag=True
if flag or tmp%2==0:
print(X)
else:
print(X- min(abs(a[i]-b[i]) for i in range(1,2*N-1)))
``` | instruction | 0 | 7,385 | 16 | 14,770 |
No | output | 1 | 7,385 | 16 | 14,771 |
Provide a correct Python 3 solution for this coding contest problem.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad | instruction | 0 | 8,876 | 16 | 17,752 |
"Correct Solution:
```
s=input()
a=0
for i in range(3):
if s[i]==s[i+1]:
a+=1
print('Bad' if a>0 else 'Good')
``` | output | 1 | 8,876 | 16 | 17,753 |
Provide a correct Python 3 solution for this coding contest problem.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad | instruction | 0 | 8,877 | 16 | 17,754 |
"Correct Solution:
```
s=input()
print(["Good","Bad"][s[0]==s[1] or s[1]==s[2] or s[2]==s[3]])
``` | output | 1 | 8,877 | 16 | 17,755 |
Provide a correct Python 3 solution for this coding contest problem.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad | instruction | 0 | 8,878 | 16 | 17,756 |
"Correct Solution:
```
N=input()
print("Bad" if N[0]==N[1] or N[1]==N[2] or N[2]==N[3] else "Good")
``` | output | 1 | 8,878 | 16 | 17,757 |
Provide a correct Python 3 solution for this coding contest problem.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad | instruction | 0 | 8,879 | 16 | 17,758 |
"Correct Solution:
```
w=input()
print("BGaodo d"[w[0]!=w[1]!=w[2]!=w[3]::2])
``` | output | 1 | 8,879 | 16 | 17,759 |
Provide a correct Python 3 solution for this coding contest problem.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad | instruction | 0 | 8,880 | 16 | 17,760 |
"Correct Solution:
```
S = input()
A = 'Good'
for i in range(3):
if S[i] == S[i+1]:
A = 'Bad'
print(A)
``` | output | 1 | 8,880 | 16 | 17,761 |
Provide a correct Python 3 solution for this coding contest problem.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad | instruction | 0 | 8,881 | 16 | 17,762 |
"Correct Solution:
```
a = input()
print('Good' if a[0] != a[1] !=a[2] !=a[3] else 'Bad')
``` | output | 1 | 8,881 | 16 | 17,763 |
Provide a correct Python 3 solution for this coding contest problem.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad | instruction | 0 | 8,882 | 16 | 17,764 |
"Correct Solution:
```
s=input()
if not any(s[i]==s[i+1] for i in range(3)):
print('Good')
else:
print('Bad')
``` | output | 1 | 8,882 | 16 | 17,765 |
Provide a correct Python 3 solution for this coding contest problem.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad | instruction | 0 | 8,883 | 16 | 17,766 |
"Correct Solution:
```
S=input()
if S[0]!=S[1] and S[1]!=S[2] and S[2]!=S[3]:
print("Good")
else:
print("Bad")
``` | output | 1 | 8,883 | 16 | 17,767 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad
Submitted Solution:
```
S = input()
print("Bad") if S[0] == S[1] or S[1] == S[2] or S[2] == S[3] else print("Good")
``` | instruction | 0 | 8,884 | 16 | 17,768 |
Yes | output | 1 | 8,884 | 16 | 17,769 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad
Submitted Solution:
```
a, b, c, d = list(input())
print('Bad' if a==b or b==c or c==d else 'Good')
``` | instruction | 0 | 8,885 | 16 | 17,770 |
Yes | output | 1 | 8,885 | 16 | 17,771 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad
Submitted Solution:
```
import re;print(re.search(r'(.)\1',input())and'Bad'or'Good')
``` | instruction | 0 | 8,886 | 16 | 17,772 |
Yes | output | 1 | 8,886 | 16 | 17,773 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad
Submitted Solution:
```
S = input()
print("Good" if S[0] != S[1] != S[2] != S[3] else "Bad")
``` | instruction | 0 | 8,887 | 16 | 17,774 |
Yes | output | 1 | 8,887 | 16 | 17,775 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad
Submitted Solution:
```
s=input()
for i in range(3):
if s[i]==s[i+1]:
ans=1
else:
ans=0
print("Bad" if ans==1 else "Good")
``` | instruction | 0 | 8,888 | 16 | 17,776 |
No | output | 1 | 8,888 | 16 | 17,777 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad
Submitted Solution:
```
import re
def judge(S):
S_list = list(str(S)) #list化
i_pure = None
for i in S_list:
if i == i_pure:
return 'Bad'
i_pure = i
return 'Good'
S = ['3776','8080','1333','0024']
for s in S:
print(judge(s))
``` | instruction | 0 | 8,889 | 16 | 17,778 |
No | output | 1 | 8,889 | 16 | 17,779 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad
Submitted Solution:
```
a=input()
b=False
for i in range(3):
if a[i+1]==a[i]:
b=True
if b:
print(“Bad”)
else:
print(“Good”)
``` | instruction | 0 | 8,890 | 16 | 17,780 |
No | output | 1 | 8,890 | 16 | 17,781 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The door of Snuke's laboratory is locked with a security code.
The security code is a 4-digit number. We say the security code is hard to enter when it contains two consecutive digits that are the same.
You are given the current security code S. If S is hard to enter, print `Bad`; otherwise, print `Good`.
Constraints
* S is a 4-character string consisting of digits.
Input
Input is given from Standard Input in the following format:
S
Output
If S is hard to enter, print `Bad`; otherwise, print `Good`.
Examples
Input
3776
Output
Bad
Input
8080
Output
Good
Input
1333
Output
Bad
Input
0024
Output
Bad
Submitted Solution:
```
S = str(input())
ans = 'Good'
for i in range(2):
if S[i] == S[i+1]:
ans = 'Bad'
Print(ans)
``` | instruction | 0 | 8,891 | 16 | 17,782 |
No | output | 1 | 8,891 | 16 | 17,783 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959 | instruction | 0 | 8,892 | 16 | 17,784 |
"Correct Solution:
```
mod = 998244353
def cmb(n, r, mod=mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] * g2[n-r] % mod
NN = 10**5 # 使うデータによって変える
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル
for i in range( 2, NN + 1 ):
g1.append( ( g1[-1] * i ) % mod )
inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
g2.append( (g2[-1] * inverse[-1]) % mod )
import sys
input = sys.stdin.readline
S = list(input().rstrip())
L = len(S)
dp = [[0]*(L+1) for _ in range(L+1)]
dp[0][0] = 1
rmax = [0, 0]
rmin = [0, 0]
rsum = 0
for i, s in enumerate(S):
p = int(s)
rsum += p
if p == 0:
rmin[1] += 2
elif p == 1:
rmax[1] += 1
rmin[1] += 1
else:
rmax[1] += 2
if rmax[1] > 0:
rmax[0] += 1
rmax[1] -= 1
if rmin[1] > 0:
rmin[0] += 1
rmin[1] -= 1
for j in range(i+1):
if rmax[0] >= j+1:
dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % mod
if rmin[0] >= (i+1) - j:
dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % mod
ans = 0
for j in range(L+1):
ans = (ans + dp[L][j] * cmb(L, rsum-j)) % mod
print(ans)
``` | output | 1 | 8,892 | 16 | 17,785 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959 | instruction | 0 | 8,893 | 16 | 17,786 |
"Correct Solution:
```
S = input()
N = len(S)
from collections import defaultdict
reddic = defaultdict(int)
bludic = defaultdict(int)
redarray = [0] * (N+1)
bluarray = [0] * (N+1)
for e,c in enumerate(S):
if c == "2":
bludic[e+1] += 2
bluarray[e+1] += 2
elif c == "1":
reddic[e+1] += 1
bludic[e+1] += 1
redarray[e+1] += 1
bluarray[e+1] += 1
elif c == "0":
reddic[e+1] += 2
redarray[e+1] += 2
for i in range(1,N+1):
redarray[i] += redarray[i-1]
bluarray[i] += bluarray[i-1]
# print("redarray: ", redarray)
# print("bluarray: ", bluarray)
dp = [ [0] * (2*N+1) for _ in range(2*N+1)]
dp[0][0] = 1
MOD = 998244353
for p in range(1, 2*N+1):
for r in range(0, p):
idx = p if p <= N else N
if r < redarray[idx]:
dp[p][r+1] += dp[p-1][r] % MOD
if p-1-r < bluarray[idx]:
dp[p][r] += dp[p-1][r] % MOD
# print("{:3d}".format(p), dp[p])
print(dp[2*N][redarray[N]]%MOD)
``` | output | 1 | 8,893 | 16 | 17,787 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959 | instruction | 0 | 8,894 | 16 | 17,788 |
"Correct Solution:
```
# 数え上げで制約が 2 乗っぽいのでどうせ dp だろという気持ちになる
# なんで入力が数字で与えられるのかを考えるとちょっと視界が開ける
# よく考えると、できる列の制約は
# 「赤い/青いボールはできる列の i 個目までに A[i]/B[i] 個使える」
# と表せることがわかる
# これに気付けばあとは
# dp[i][j] := i 個目まで並べたとき赤いボールを j 個使う場合の数
# とした dp が自然と思いつく
from itertools import accumulate
def main():
mod = 998244353
B = list(map(int, input()))
N = len(B)
A = [2-b for b in B] + [0]*N
B += [0] * N
a = b = 0
for i in range(2*N):
b += B[i]
if b > 0:
b -= 1
B[i] = 1
a += A[i]
if a > 0:
a -= 1
A[i] = 1
A = list(accumulate(A))
B = list(accumulate(B))
dp = [[0]*(2*N+2) for _ in range(2*N+1)]
dp[0][0] = 1
for i, (a, b) in enumerate(zip(A, B), 1):
for j in range(2*N+1):
if i - b <= j <= a:
dp[i][j] = (dp[i-1][j-1] + dp[i-1][j]) % mod
print(sum(dp[2*N]) % mod)
main()
``` | output | 1 | 8,894 | 16 | 17,789 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959 | instruction | 0 | 8,895 | 16 | 17,790 |
"Correct Solution:
```
M=998244353
S=input()
N=len(S)
d=[[0]*4001 for _ in range(4001)]
d[0][0]=1
x=0
for i in range(2*N):
if i<N:
x+=int(S[i])
y=2*i+2-x
for j in range(i+1):
for k in range(2):d[j+1-k][i-j+k]+=i-y<=j-k<x and d[j][i-j]%M
print(d[x][y]%M)
``` | output | 1 | 8,895 | 16 | 17,791 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959 | instruction | 0 | 8,896 | 16 | 17,792 |
"Correct Solution:
```
S=input()
N=len(S)
C=[0]
for i in range(N):
C.append(C[i]+int(S[i]))
for i in range(N):
C.append(C[N])
B=C[N]
DP=[[0]*(B+1) for i in range(2*N+1)]
DP[0][0]=1
mod=998244353
for i in range(2*N):
for j in range(B+1):
if 2*min(i+1,N)-C[i+1]>=i+1-j:
DP[i+1][j]=(DP[i+1][j]+DP[i][j])%mod
if j<C[i+1]:
DP[i+1][j+1]=DP[i][j]
print(DP[2*N][B])
``` | output | 1 | 8,896 | 16 | 17,793 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959 | instruction | 0 | 8,897 | 16 | 17,794 |
"Correct Solution:
```
s=input()
N=len(s)
table=[]
mod=998244353
if s[0]=="0":
table.append((2,0))
elif s[0]=="1":
table.append((1,1))
elif s[0]=="2":
table.append((0,2))
for i in range(1,N):
r,b=table[-1]
if s[i]=="0":
r,b=table[-1]
table.append((r+2,b))
elif s[i]=="1":
r,b=table[-1]
table.append((r+1,b+1))
elif s[i]=="2":
r,b=table[-1]
table.append((r,b+2))
for i in range(N):
table.append(table[-1])
dp=[[0]*(2*N+1) for i in range(2*N+1)]
dp[0][0]=1
for i in range(2*N):
for k in range(2*N):
if k+1<=table[i][0]:
dp[i+1][k+1]=(dp[i+1][k+1]+dp[i][k])%mod
if i+1-k<=table[i][1]:
dp[i+1][k]=(dp[i+1][k]+dp[i][k])%mod
ans=0
for k in range(2*N+1):
ans=(ans+dp[2*N][k])%mod
print(ans)
``` | output | 1 | 8,897 | 16 | 17,795 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959 | instruction | 0 | 8,898 | 16 | 17,796 |
"Correct Solution:
```
from itertools import accumulate
import sys
input = sys.stdin.readline
mod = 998244353
S = list(map(int, input().rstrip()))
N = len(S)
front = [0] * N
back = [0] * N
cum = list(accumulate(S))
for i in range(N-1):
front[i+1] = max(front[i], i + 1 - cum[i])
back[i+1] = max(back[i], cum[i] - (i + 1))
cnt = cum[-1]
dp = [1] * (2 * N - cnt + 1)
for i in range(N - 1, -1, -1):
for c in range(S[i]):
f = front[i]
b = 2 * N - cum[-1]
for j in range(N):
if back[j] == cnt:
b = 2 * j - cum[j-1]
break
for j in range(b - 1, f - 1, -1):
dp[j] = (dp[j] + dp[j+1]) % mod
for j in range(f - 1, -1, -1):
dp[j] = dp[j+1]
cnt -= 1
print(dp[0])
``` | output | 1 | 8,898 | 16 | 17,797 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959 | instruction | 0 | 8,899 | 16 | 17,798 |
"Correct Solution:
```
S=input()
N=len(S)
mod=998244353
red=[0]*N
blue=[0]*N
for i in range(N):
if S[i]=="0":
red[i]+=2
elif S[i]=="1":
red[i]+=1
blue[i]+=1
else:
blue[i]+=2
if i!=0:
red[i]+=red[i-1]
blue[i]+=blue[i-1]
R=red[-1]
B=blue[-1]
dp=[[0 for i in range(2*N+1)] for i in range(2*N+1)]
dp[2*N][R]=1
for i in range(2*N-1,-1,-1):
for j in range(2*N+1):
if i>=N:
r=R-j
b=B-(i-j)
if r and 2*N>=j+1:
dp[i][j]+=dp[i+1][j+1]
dp[i][j]%=mod
if b:
dp[i][j]+=dp[i+1][j]
dp[i][j]%=mod
else:
r=red[i]-j
b=blue[i]-(i-j)
if r and 2*N>=j+1:
dp[i][j]+=dp[i+1][j+1]
dp[i][j]%=mod
if b:
dp[i][j]+=dp[i+1][j]
dp[i][j]%=mod
print(dp[0][0])
``` | output | 1 | 8,899 | 16 | 17,799 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959
Submitted Solution:
```
import sys
input = sys.stdin.readline
S = input()[:-1]
N = len(S)
dp = [[0]*(2*N+1) for _ in range(2*N+1)]
dp[0][0] = 1
MOD = 998244353
r, b = 0, 0
for i in range(2*N):
if i<N:
if S[i]=='0':
r += 2
elif S[i]=='1':
r += 1
b += 1
else:
b += 2
for j in range(2*N+1):
rc = r-j
bc = b-(i-j)
if rc>0:
dp[i+1][j+1] += dp[i][j]
dp[i+1][j+1] %= MOD
if bc>0:
dp[i+1][j] += dp[i][j]
dp[i+1][j] %= MOD
print(sum(dp[2*N]))
``` | instruction | 0 | 8,900 | 16 | 17,800 |
Yes | output | 1 | 8,900 | 16 | 17,801 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959
Submitted Solution:
```
S=input()
N=len(S)
d=[[0]*4001 for _ in range(4001)]
d[0][0]=1
x=0
y=0
for i in range(2*N):
if i<N:
x+=int(S[i])
y=2*i+2-x
for j in range(i+1):
for k in range(2):
if j+1-k<=x and i-j+k<=y:
d[j+1-k][i-j+k]+=d[j][i-j]
d[j+1-k][i-j+k]%=998244353
print(d[x][y])
``` | instruction | 0 | 8,901 | 16 | 17,802 |
Yes | output | 1 | 8,901 | 16 | 17,803 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Snukes lining up in a row. You are given a string S of length N. The i-th Snuke from the front has two red balls if the i-th character in S is `0`; one red ball and one blue ball if the i-th character in S is `1`; two blue balls if the i-th character in S is `2`.
Takahashi has a sequence that is initially empty. Find the number of the possible sequences he may have after repeating the following procedure 2N times, modulo 998244353:
* Each Snuke who has one or more balls simultaneously chooses one of his balls and hand it to the Snuke in front of him, or hand it to Takahashi if he is the first Snuke in the row.
* Takahashi receives the ball and put it to the end of his sequence.
Constraints
* 1 \leq |S| \leq 2000
* S consists of `0`,`1` and `2`.
Note that the integer N is not directly given in input; it is given indirectly as the length of the string S.
Input
Input is given from Standard Input in the following format:
S
Output
Print the number of the possible sequences Takahashi may have after repeating the procedure 2N times, modulo 998244353.
Examples
Input
02
Output
3
Input
1210
Output
55
Input
12001021211100201020
Output
543589959
Submitted Solution:
```
M=998244353
S=input()
N=len(S)
d=[[0]*4001 for _ in range(4001)]
d[0][0]=1
x=0
for i in range(2*N):
if i<N:
x+=int(S[i])
y=2*i+2-x
for j in range(i+1):
for k in range(2):
if i-y<=j-k<x:d[j+1-k][i-j+k]+=d[j][i-j]%M
print(d[x][y]%M)
``` | instruction | 0 | 8,902 | 16 | 17,804 |
Yes | output | 1 | 8,902 | 16 | 17,805 |
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