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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n integers a_1, a_2, ..., a_n, such that for each 1≤ i ≤ n holds i-n≤ a_i≤ i-1. Find some nonempty subset of these integers, whose sum is equal to 0. It can be shown that such a s...
instruction
0
47,133
5
94,266
No
output
1
47,133
5
94,267
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n integers a_1, a_2, ..., a_n, such that for each 1≤ i ≤ n holds i-n≤ a_i≤ i-1. Find some nonempty subset of these integers, whose sum is equal to 0. It can be shown that such a s...
instruction
0
47,134
5
94,268
No
output
1
47,134
5
94,269
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n integers a_1, a_2, ..., a_n, such that for each 1≤ i ≤ n holds i-n≤ a_i≤ i-1. Find some nonempty subset of these integers, whose sum is equal to 0. It can be shown that such a s...
instruction
0
47,135
5
94,270
No
output
1
47,135
5
94,271
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given n integers a_1, a_2, ..., a_n, such that for each 1≤ i ≤ n holds i-n≤ a_i≤ i-1. Find some nonempty subset of these integers, whose sum is equal to 0. It can be shown that such a s...
instruction
0
47,136
5
94,272
No
output
1
47,136
5
94,273
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik s...
instruction
0
47,326
5
94,652
Yes
output
1
47,326
5
94,653
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik s...
instruction
0
47,327
5
94,654
Yes
output
1
47,327
5
94,655
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik s...
instruction
0
47,328
5
94,656
Yes
output
1
47,328
5
94,657
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik s...
instruction
0
47,329
5
94,658
No
output
1
47,329
5
94,659
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik s...
instruction
0
47,330
5
94,660
No
output
1
47,330
5
94,661
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik s...
instruction
0
47,331
5
94,662
No
output
1
47,331
5
94,663
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik s...
instruction
0
47,332
5
94,664
No
output
1
47,332
5
94,665
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each ...
instruction
0
47,341
5
94,682
Yes
output
1
47,341
5
94,683
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each ...
instruction
0
47,342
5
94,684
Yes
output
1
47,342
5
94,685
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each ...
instruction
0
47,343
5
94,686
Yes
output
1
47,343
5
94,687
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each ...
instruction
0
47,344
5
94,688
Yes
output
1
47,344
5
94,689
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each ...
instruction
0
47,345
5
94,690
No
output
1
47,345
5
94,691
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each ...
instruction
0
47,346
5
94,692
No
output
1
47,346
5
94,693
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each ...
instruction
0
47,347
5
94,694
No
output
1
47,347
5
94,695
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each ...
instruction
0
47,348
5
94,696
No
output
1
47,348
5
94,697
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For each positive integer n consider the integer ψ(n) which is obtained from n by replacing every digit a in the decimal notation of n with the digit (9 - a). We say that ψ(n) is the reflection ...
instruction
0
47,614
5
95,228
Yes
output
1
47,614
5
95,229
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For each positive integer n consider the integer ψ(n) which is obtained from n by replacing every digit a in the decimal notation of n with the digit (9 - a). We say that ψ(n) is the reflection ...
instruction
0
47,615
5
95,230
Yes
output
1
47,615
5
95,231
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For each positive integer n consider the integer ψ(n) which is obtained from n by replacing every digit a in the decimal notation of n with the digit (9 - a). We say that ψ(n) is the reflection ...
instruction
0
47,616
5
95,232
Yes
output
1
47,616
5
95,233
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For each positive integer n consider the integer ψ(n) which is obtained from n by replacing every digit a in the decimal notation of n with the digit (9 - a). We say that ψ(n) is the reflection ...
instruction
0
47,617
5
95,234
Yes
output
1
47,617
5
95,235
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For each positive integer n consider the integer ψ(n) which is obtained from n by replacing every digit a in the decimal notation of n with the digit (9 - a). We say that ψ(n) is the reflection ...
instruction
0
47,618
5
95,236
No
output
1
47,618
5
95,237
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For each positive integer n consider the integer ψ(n) which is obtained from n by replacing every digit a in the decimal notation of n with the digit (9 - a). We say that ψ(n) is the reflection ...
instruction
0
47,619
5
95,238
No
output
1
47,619
5
95,239
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For each positive integer n consider the integer ψ(n) which is obtained from n by replacing every digit a in the decimal notation of n with the digit (9 - a). We say that ψ(n) is the reflection ...
instruction
0
47,620
5
95,240
No
output
1
47,620
5
95,241
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For each positive integer n consider the integer ψ(n) which is obtained from n by replacing every digit a in the decimal notation of n with the digit (9 - a). We say that ψ(n) is the reflection ...
instruction
0
47,621
5
95,242
No
output
1
47,621
5
95,243
Provide a correct Python 3 solution for this coding contest problem. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_i \neq B_i, for every i such that 1\leq i\leq N. * A_i \...
instruction
0
47,688
5
95,376
"Correct Solution: ``` MOD = 10 ** 9 + 7 N,M = map(int,input().split()) ans1 = 1 for i in range(N): ans1 *= M - i ans1 %= MOD ans2 = [1,M-N] for i in range(2,N+1): ans2.append((ans2[-2] * (i -1) + ans2[-1] * (M - N + i - 1))% MOD) print(ans1 * ans2[N] % MOD) ```
output
1
47,688
5
95,377
Provide a correct Python 3 solution for this coding contest problem. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_i \neq B_i, for every i such that 1\leq i\leq N. * A_i \...
instruction
0
47,689
5
95,378
"Correct Solution: ``` n, m = map(int, input().split()) N = m + 100 MOD = 10 ** 9 + 7 fact = [0 for _ in range(N)] invfact = [0 for _ in range(N)] fact[0] = 1 for i in range(1, N): fact[i] = i * fact[i - 1] % MOD invfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD) for i in range(N - 2, -1, -1): invfact[i] = invf...
output
1
47,689
5
95,379
Provide a correct Python 3 solution for this coding contest problem. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_i \neq B_i, for every i such that 1\leq i\leq N. * A_i \...
instruction
0
47,690
5
95,380
"Correct Solution: ``` def prepare(n, MOD): # n! の計算 f = 1 fn=[1]*(n+1) for m in range(1, n + 1): f *= m f %= MOD fn[m]=f # n!^-1 の計算 inv = pow(f, MOD - 2, MOD) # n!^-1 - 1!^-1 の計算 invs = [1] * (n + 1) invs[n] = inv for m in range(n, 1, -1): ...
output
1
47,690
5
95,381
Provide a correct Python 3 solution for this coding contest problem. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_i \neq B_i, for every i such that 1\leq i\leq N. * A_i \...
instruction
0
47,691
5
95,382
"Correct Solution: ``` import sys def input(): return sys.stdin.readline().strip() def mapint(): return map(int, input().split()) sys.setrecursionlimit(10**9) N, M = mapint() mod = 10**9+7 pos = [1]+[0]*M neg = [1]+[0]*M n = 1 for i in range(1, M+1): n = n*i%mod pos[i] = n neg[i] = pow(n, mod-2, mod) ans =...
output
1
47,691
5
95,383
Provide a correct Python 3 solution for this coding contest problem. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_i \neq B_i, for every i such that 1\leq i\leq N. * A_i \...
instruction
0
47,692
5
95,384
"Correct Solution: ``` n, m = map(int, input().split()) mod = 10**9 + 7 factorial = [1] inverse = [1] for i in range(1, m+1): factorial.append(factorial[-1] * i % mod) inverse.append(pow(factorial[-1], mod - 2, mod)) def comb(n, r, mod): if n < r or r < 0: return 0 elif r == 0: return 1 return fact...
output
1
47,692
5
95,385
Provide a correct Python 3 solution for this coding contest problem. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_i \neq B_i, for every i such that 1\leq i\leq N. * A_i \...
instruction
0
47,693
5
95,386
"Correct Solution: ``` n,m = map(int,input().split()) mod = 10 ** 9 + 7 g1 = [1,1] ### g1[i]はiの階乗の逆数 g2 = [0,1] ###g2[i]はiの逆数 for i in range(2,m + 1): g2.append((-g2[mod % i] * (mod//i))% mod) g1.append(g1[-1] * g2[-1] % mod) g3 = [1,m - n + 1] for i in range(n - 1): g3.append((g3[-1] * (m - n + i + 2))%mod...
output
1
47,693
5
95,387
Provide a correct Python 3 solution for this coding contest problem. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_i \neq B_i, for every i such that 1\leq i\leq N. * A_i \...
instruction
0
47,694
5
95,388
"Correct Solution: ``` MOD=10**9+7 N, M = map(int, input().split()) FCT = [1] for i in range(1, M+1): FCT.append((FCT[-1] * i)%MOD) def pmu(n, r, mod=MOD): return (FCT[n] * pow(FCT[n-r], mod-2, mod)) % mod def cmb(n, r, mod=MOD): return (pmu(n, r) * pow(FCT[r], mod-2, mod)) % mod def solve(): # {the...
output
1
47,694
5
95,389
Provide a correct Python 3 solution for this coding contest problem. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_i \neq B_i, for every i such that 1\leq i\leq N. * A_i \...
instruction
0
47,695
5
95,390
"Correct Solution: ``` N,M=map(int,input().split()) mod=10**9+7 def cmb(n,r): global mod if r<0 or r>n: return 0 return (g1[n]*g2[r]*g2[n-r])%mod def perm(n,r): global mod if r<0 or r>n: return 0 return (g1[n]*g2[n-r])%mod g1=[1,1] g2=[1,1] inv=[0,1] for i in range(2,N+M+10): g1.append((g1[-1]*...
output
1
47,695
5
95,391
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_...
instruction
0
47,696
5
95,392
Yes
output
1
47,696
5
95,393
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_...
instruction
0
47,697
5
95,394
Yes
output
1
47,697
5
95,395
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_...
instruction
0
47,698
5
95,396
Yes
output
1
47,698
5
95,397
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_...
instruction
0
47,699
5
95,398
Yes
output
1
47,699
5
95,399
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_...
instruction
0
47,700
5
95,400
No
output
1
47,700
5
95,401
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_...
instruction
0
47,701
5
95,402
No
output
1
47,701
5
95,403
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_...
instruction
0
47,702
5
95,404
No
output
1
47,702
5
95,405
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions: * A_...
instruction
0
47,703
5
95,406
No
output
1
47,703
5
95,407
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a three-digit positive integer N. Determine whether N is a palindromic number. Here, a palindromic number is an integer that reads the same backward as forward in decimal notation....
instruction
0
47,808
5
95,616
Yes
output
1
47,808
5
95,617
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a three-digit positive integer N. Determine whether N is a palindromic number. Here, a palindromic number is an integer that reads the same backward as forward in decimal notation....
instruction
0
47,812
5
95,624
No
output
1
47,812
5
95,625
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You have a set of items, each having some integer weight not greater than 8. You denote that a subset of items is good if total weight of items in the subset does not exceed W. You want to calc...
instruction
0
47,987
5
95,974
No
output
1
47,987
5
95,975
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You have a set of items, each having some integer weight not greater than 8. You denote that a subset of items is good if total weight of items in the subset does not exceed W. You want to calc...
instruction
0
47,988
5
95,976
No
output
1
47,988
5
95,977
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a permutation of numbers from 1 to n. Determine whether there's a pair of integers a, b (1 ≤ a, b ≤ n; a ≠ b) such that the element <image> (note, that it is usual division, not in...
instruction
0
48,301
5
96,602
No
output
1
48,301
5
96,603
Provide tags and a correct Python 3 solution for this coding contest problem. You have two variables a and b. Consider the following sequence of actions performed with these variables: 1. If a = 0 or b = 0, end the process. Otherwise, go to step 2; 2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat ste...
instruction
0
48,530
5
97,060
Tags: math, number theory Correct Solution: ``` a, b = map(int, input().split(' ')) while 1: if a == 0 or b == 0: break elif a >= 2 * b: a %= 2 * b continue elif b >= 2 * a: b %= 2 * a continue else: break print(a, b) ```
output
1
48,530
5
97,061
Provide tags and a correct Python 3 solution for this coding contest problem. You have two variables a and b. Consider the following sequence of actions performed with these variables: 1. If a = 0 or b = 0, end the process. Otherwise, go to step 2; 2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat ste...
instruction
0
48,531
5
97,062
Tags: math, number theory Correct Solution: ``` a,b=map(int,input().split()) while 1: if a==0 or b==0: break if a>=2*b: a-=(a//(b*2))*(b*2) else: if b>=2*a: b-=(b//(a*2))*(a*2) else: break print(a,b) ```
output
1
48,531
5
97,063