message stringlengths 2 44.5k | message_type stringclasses 2
values | message_id int64 0 1 | conversation_id int64 42 109k | cluster float64 5 5 | __index_level_0__ int64 84 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer n let's define a function f:
f(n) = - 1 + 2 - 3 + .. + ( - 1)nn
Your task is to calculate f(n) for a given integer n.
Input
The single line contains the positive integer n (1 ≤ n ≤ 1015).
Output
Print f(n) in a single line.
Examples
Input
4
Output
2
Input
5
Output
-3
Note
f(4) = - 1 + 2 - 3 + 4 = 2
f(5) = - 1 + 2 - 3 + 4 - 5 = - 3
Submitted Solution:
```
import math
n=int(input())
if n%2==0:
print(n//2)
else:
print(-math.ceil(n/2))
``` | instruction | 0 | 68,522 | 5 | 137,044 |
Yes | output | 1 | 68,522 | 5 | 137,045 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer n let's define a function f:
f(n) = - 1 + 2 - 3 + .. + ( - 1)nn
Your task is to calculate f(n) for a given integer n.
Input
The single line contains the positive integer n (1 ≤ n ≤ 1015).
Output
Print f(n) in a single line.
Examples
Input
4
Output
2
Input
5
Output
-3
Note
f(4) = - 1 + 2 - 3 + 4 = 2
f(5) = - 1 + 2 - 3 + 4 - 5 = - 3
Submitted Solution:
```
n = int(input())
o = e = 0
for i in range(1, n+1, -1):
o += i
print(o)
``` | instruction | 0 | 68,523 | 5 | 137,046 |
No | output | 1 | 68,523 | 5 | 137,047 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer n let's define a function f:
f(n) = - 1 + 2 - 3 + .. + ( - 1)nn
Your task is to calculate f(n) for a given integer n.
Input
The single line contains the positive integer n (1 ≤ n ≤ 1015).
Output
Print f(n) in a single line.
Examples
Input
4
Output
2
Input
5
Output
-3
Note
f(4) = - 1 + 2 - 3 + 4 = 2
f(5) = - 1 + 2 - 3 + 4 - 5 = - 3
Submitted Solution:
```
n=int(input())
a=0
if n%2==0:
a=n/2
else:
a=(n-1)/2-n
print(a)
``` | instruction | 0 | 68,524 | 5 | 137,048 |
No | output | 1 | 68,524 | 5 | 137,049 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer n let's define a function f:
f(n) = - 1 + 2 - 3 + .. + ( - 1)nn
Your task is to calculate f(n) for a given integer n.
Input
The single line contains the positive integer n (1 ≤ n ≤ 1015).
Output
Print f(n) in a single line.
Examples
Input
4
Output
2
Input
5
Output
-3
Note
f(4) = - 1 + 2 - 3 + 4 = 2
f(5) = - 1 + 2 - 3 + 4 - 5 = - 3
Submitted Solution:
```
n=int(input())
fuck=-1**n&1
print(fuck*(n+1)//2)
``` | instruction | 0 | 68,525 | 5 | 137,050 |
No | output | 1 | 68,525 | 5 | 137,051 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer n let's define a function f:
f(n) = - 1 + 2 - 3 + .. + ( - 1)nn
Your task is to calculate f(n) for a given integer n.
Input
The single line contains the positive integer n (1 ≤ n ≤ 1015).
Output
Print f(n) in a single line.
Examples
Input
4
Output
2
Input
5
Output
-3
Note
f(4) = - 1 + 2 - 3 + 4 = 2
f(5) = - 1 + 2 - 3 + 4 - 5 = - 3
Submitted Solution:
```
n=int(input())
if n%2==0:
f=(n/2)*((n/2)+1)-(n/2)**2
else:
f=((n-1)/2)*(((n-1)/2)+1) - ((n+1)/2)**2
print(int(f))
``` | instruction | 0 | 68,526 | 5 | 137,052 |
No | output | 1 | 68,526 | 5 | 137,053 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.
Input
The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.
Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
Output
Print the only integer s — the value g(n)(x) modulo 109 + 7.
Examples
Input
3 4 1 1
Output
7
Input
3 4 2 1
Output
25
Input
3 4 3 1
Output
79
Submitted Solution:
```
A, B, M = 0, 0, 10**9 + 7
def GP(A,n):
if n == 0:
return 1
if A == 1:
return (n * A) % M
res = (pow(A,n,M)-1) * pow(A-1,M-2,M)
return res % M
def f(n,x):
res = pow(A,n,M) * x + B * GP(A,n)
return res % M
def g(n,x):
if n == 0:
return x
elif n == 1:
return (A*x + B) % M
return f(n,x) % M
A, B, n, x = map(int,input().split())
print(g(n,x))
``` | instruction | 0 | 68,583 | 5 | 137,166 |
Yes | output | 1 | 68,583 | 5 | 137,167 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.
Input
The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.
Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
Output
Print the only integer s — the value g(n)(x) modulo 109 + 7.
Examples
Input
3 4 1 1
Output
7
Input
3 4 2 1
Output
25
Input
3 4 3 1
Output
79
Submitted Solution:
```
a,b,n,x = map(int,input().split())
md = 10**9+7
mult = lambda u,v : 0 if v==0 else (u+mult(u,v-1))%md if v % 2 == 1 else (2*mult(u,v//2))%md
get_prog = lambda a,b,n : mult(pow(a,n,md)-1+md,pow(a-1+md,md-2,md)) if a!=1 else n
res = mult(pow(a,n,md),x)+mult(get_prog(a,b,n),b)
res%=md
print(res)
``` | instruction | 0 | 68,584 | 5 | 137,168 |
Yes | output | 1 | 68,584 | 5 | 137,169 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.
Input
The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.
Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
Output
Print the only integer s — the value g(n)(x) modulo 109 + 7.
Examples
Input
3 4 1 1
Output
7
Input
3 4 2 1
Output
25
Input
3 4 3 1
Output
79
Submitted Solution:
```
def mod(a, m) :
return pow(a, m - 2, m)
a,b,n,x=list(map(int,input().split()))
m=10**9+7
if a==1:
print((x+b*n)%m)
else:
print(int((pow(a,n,m)*x+(b*(pow(a,n,m)-1)*mod(a-1,m)))%m))
``` | instruction | 0 | 68,585 | 5 | 137,170 |
Yes | output | 1 | 68,585 | 5 | 137,171 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.
Input
The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.
Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
Output
Print the only integer s — the value g(n)(x) modulo 109 + 7.
Examples
Input
3 4 1 1
Output
7
Input
3 4 2 1
Output
25
Input
3 4 3 1
Output
79
Submitted Solution:
```
def egcd(a, b):
x = v = 0
y = u = 1
while a:
q, r = divmod(b, a)
a, b, x, y, u, v = r, a, u, v, x - u * q, y - v * q
return x, y, b
def main():
a, b, n, x = map(int, input().split())
mod = 1000000007
print(((x + b * n) if a == 1 else (pow(a, n, mod) * x + (pow(a, n, mod) - 1) * b * egcd(a - 1, mod)[0])) % mod)
if __name__ == '__main__':
main()
``` | instruction | 0 | 68,586 | 5 | 137,172 |
Yes | output | 1 | 68,586 | 5 | 137,173 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.
Input
The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.
Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
Output
Print the only integer s — the value g(n)(x) modulo 109 + 7.
Examples
Input
3 4 1 1
Output
7
Input
3 4 2 1
Output
25
Input
3 4 3 1
Output
79
Submitted Solution:
```
line = input().split(' ')
A = int(line[0])
B = int(line[1])
n = int(line[2])
x = int(line[3])
ans = B
for i in range(1, n+1):
if i == n :
ans += (pow(A, n) * x)
else :
ans += (pow(A, i) * B)
print(ans)
``` | instruction | 0 | 68,587 | 5 | 137,174 |
No | output | 1 | 68,587 | 5 | 137,175 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.
Input
The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.
Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
Output
Print the only integer s — the value g(n)(x) modulo 109 + 7.
Examples
Input
3 4 1 1
Output
7
Input
3 4 2 1
Output
25
Input
3 4 3 1
Output
79
Submitted Solution:
```
mod = 1000000007
def mul(x, y):
return (x * y) % mod
a, b, n, x = [int(tmp) for tmp in input().strip().split(' ')]
mi_list = [n]
while mi_list[-1] > 1:
if mi_list[-1] % 2 == 0:
mi_list.append(int(mi_list[-1] / 2 + 0.5))
else:
mi_list.append(int((mi_list[-1] - 1) / 2 + 0.5))
mi_list.reverse()
mi_value = [a]
for i in range(1, len(mi_list)):
mi_value.append((mi_value[-1] ** 2) % mod)
if mi_list[i] != mi_list[i - 1] * 2:
mi_value[-1] = (mi_value[-1] * a) % mod
res1 = (mi_value[-1] * x) % mod
tmp = 1
for i in range(1, len(mi_list)):
if mi_list[i] == mi_list[i - 1] * 2:
tmp = (mul(tmp, mi_value[i - 1]) + tmp) % mod
else:
tmp = (mul(mul(mi_value[i - 1], a), tmp) + mul(tmp, a) + 1) % mod
tmp = mul(tmp, b)
res = (res1 + tmp) % mod
print(res)
``` | instruction | 0 | 68,588 | 5 | 137,176 |
No | output | 1 | 68,588 | 5 | 137,177 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.
Input
The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.
Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
Output
Print the only integer s — the value g(n)(x) modulo 109 + 7.
Examples
Input
3 4 1 1
Output
7
Input
3 4 2 1
Output
25
Input
3 4 3 1
Output
79
Submitted Solution:
```
'''
Name : Jaymeet Mehta
codeforces id :mj_13
Problem : Iterated linear function
'''
from sys import stdin,stdout
mod=10**9+7
A,B,n,x = map(int,stdin.readline().split())
if n==1:
print((A*x+B)%mod)
else:
ans=((pow(A,n,mod)*x)%mod+(B*((pow(A,n,mod)-1)*pow(A-1,mod-2,mod)))%mod)%mod
print(ans%mod)
``` | instruction | 0 | 68,589 | 5 | 137,178 |
No | output | 1 | 68,589 | 5 | 137,179 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.
Input
The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.
Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.
Output
Print the only integer s — the value g(n)(x) modulo 109 + 7.
Examples
Input
3 4 1 1
Output
7
Input
3 4 2 1
Output
25
Input
3 4 3 1
Output
79
Submitted Solution:
```
import sys
A, B, n, x = map(int, input().split())
mod = 10**9 + 7
def matmul(matA, matB):
x, y, z = len(matA), len(matB[0]), len(matA[0])
res = [[0]*y for _ in range(x)]
for i in range(x):
for j in range(y):
for k in range(z):
res[i][j] += matA[i][k] * matB[k][j]
res[i][j] %= mod
return res
matA = [
[A*x + B, 1],
[x, 1]
]
matB = [
[A, 0],
[B, 1]
]
n -= 1
while n:
if n & 1:
matA = matmul(matA, matB)
matB = matmul(matB, matB)
n >>= 1
print(matA[0][0])
``` | instruction | 0 | 68,590 | 5 | 137,180 |
No | output | 1 | 68,590 | 5 | 137,181 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK | instruction | 0 | 68,697 | 5 | 137,394 |
"Correct Solution:
```
K=int(input())
A,B=map(int,input().split())
print('OK' if A<=B//K*K else 'NG')
``` | output | 1 | 68,697 | 5 | 137,395 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK | instruction | 0 | 68,698 | 5 | 137,396 |
"Correct Solution:
```
k,a,b = map(int,open(0).read().split())
print('NOGK'[b%k<=b-a::2])
``` | output | 1 | 68,698 | 5 | 137,397 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK | instruction | 0 | 68,699 | 5 | 137,398 |
"Correct Solution:
```
k =int(input())
a, b =map(int, input().split())
if a <= b//k*k:
print('OK')
else:
print('NG')
``` | output | 1 | 68,699 | 5 | 137,399 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK | instruction | 0 | 68,700 | 5 | 137,400 |
"Correct Solution:
```
K = int(input())
A, B = map(int,input().split())
if B%K <= B-A:
print('OK')
else:
print('NG')
``` | output | 1 | 68,700 | 5 | 137,401 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK | instruction | 0 | 68,701 | 5 | 137,402 |
"Correct Solution:
```
k=int(input())
a,b=map(int,input().split())
print("OK") if a<=b//k*k else print("NG")
``` | output | 1 | 68,701 | 5 | 137,403 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK | instruction | 0 | 68,702 | 5 | 137,404 |
"Correct Solution:
```
K=int(input())
a,b=map(int, input().split())
print(['NG','OK'][b//K-(a-1)//K>0])
#print(b//K-(a-1)//K)
``` | output | 1 | 68,702 | 5 | 137,405 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK | instruction | 0 | 68,703 | 5 | 137,406 |
"Correct Solution:
```
k=int(input())
a,b=map(int,input().split())
n=1
while k*n<=b:
n+=1
print('OK' if a<=(n-1)*k<=b else 'NG')
``` | output | 1 | 68,703 | 5 | 137,407 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK | instruction | 0 | 68,704 | 5 | 137,408 |
"Correct Solution:
```
k=int(input())
a,b=map(int,input().split())
print('OK' if -(-a//k)<=b//k else 'NG')
``` | output | 1 | 68,704 | 5 | 137,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK
Submitted Solution:
```
K=int(input())
a,b=map(int,input().split())
print("OK" if b%K<b-a+1 else "OK" if K==1 else "NG")
``` | instruction | 0 | 68,705 | 5 | 137,410 |
Yes | output | 1 | 68,705 | 5 | 137,411 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK
Submitted Solution:
```
#!/usr/bin/env python3
k = int(input())
a, b = map(int, input().split())
print(["NG", "OK"][b // k * k >= a])
``` | instruction | 0 | 68,706 | 5 | 137,412 |
Yes | output | 1 | 68,706 | 5 | 137,413 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK
Submitted Solution:
```
k=int(input())
a,b=map(int,input().split())
kmax=b//k*k
if kmax>=a:
ans="OK"
else:
ans="NG"
print(ans)
``` | instruction | 0 | 68,707 | 5 | 137,414 |
Yes | output | 1 | 68,707 | 5 | 137,415 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK
Submitted Solution:
```
k=int(input())
a,b=map(int,input().split())
print('OK' if b//k-a//k>=1 or a%k==0 else 'NG')
``` | instruction | 0 | 68,708 | 5 | 137,416 |
Yes | output | 1 | 68,708 | 5 | 137,417 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK
Submitted Solution:
```
k= int(input())
x,y = map(int,input().split())
if 1<=x<=y<=1000 and 1<=k<=1000:
pass
if x%k>>0 :
if x<= (x/k+1)*k <=y :
print('OK')
else:
print('NG')
else:
print('OK')
``` | instruction | 0 | 68,709 | 5 | 137,418 |
No | output | 1 | 68,709 | 5 | 137,419 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK
Submitted Solution:
```
S = input("")
if S == 'ABC':
print('ARC')
else:
print('ABC')
``` | instruction | 0 | 68,710 | 5 | 137,420 |
No | output | 1 | 68,710 | 5 | 137,421 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK
Submitted Solution:
```
a, b, n = map(int, input().split())
temp_prev = 0
temp_curr = 0
x = min(n, b-1)
while x <= n:
temp_prev = temp_curr
temp_curr = int(a * x / b) - a * int(x / b)
x += 1.0
if temp_curr <= temp_prev:
break
print(max(temp_curr, temp_prev))
``` | instruction | 0 | 68,711 | 5 | 137,422 |
No | output | 1 | 68,711 | 5 | 137,423 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi the Jumbo will practice golf.
His objective is to get a carry distance that is a multiple of K, while he can only make a carry distance of between A and B (inclusive).
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Constraints
* All values in input are integers.
* 1 \leq A \leq B \leq 1000
* 1 \leq K \leq 1000
Input
Input is given from Standard Input in the following format:
K
A B
Output
If he can achieve the objective, print `OK`; if he cannot, print `NG`.
Examples
Input
7
500 600
Output
OK
Input
4
5 7
Output
NG
Input
1
11 11
Output
OK
Submitted Solution:
```
K=int(input())
A, B = map(int, input().split())
for i in range(i*K):
if i*K>=A and i*K<=B:
print('OK')
break
for i in range(i*K):
if i*K<A or i*K>B:
print('NG')
break
``` | instruction | 0 | 68,712 | 5 | 137,424 |
No | output | 1 | 68,712 | 5 | 137,425 |
Provide a correct Python 3 solution for this coding contest problem.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169 | instruction | 0 | 68,781 | 5 | 137,562 |
"Correct Solution:
```
import math
t=int(input())
a=int(math.sqrt(t))
print(a*a)
``` | output | 1 | 68,781 | 5 | 137,563 |
Provide a correct Python 3 solution for this coding contest problem.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169 | instruction | 0 | 68,782 | 5 | 137,564 |
"Correct Solution:
```
N = int(input())
a = int(N**0.5)
print(a**2)
``` | output | 1 | 68,782 | 5 | 137,565 |
Provide a correct Python 3 solution for this coding contest problem.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169 | instruction | 0 | 68,783 | 5 | 137,566 |
"Correct Solution:
```
from math import sqrt
print(int(sqrt(int(input())))**2)
``` | output | 1 | 68,783 | 5 | 137,567 |
Provide a correct Python 3 solution for this coding contest problem.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169 | instruction | 0 | 68,784 | 5 | 137,568 |
"Correct Solution:
```
n=int(input())
print(int(n**(1/2))**(2))
``` | output | 1 | 68,784 | 5 | 137,569 |
Provide a correct Python 3 solution for this coding contest problem.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169 | instruction | 0 | 68,785 | 5 | 137,570 |
"Correct Solution:
```
N=int(input())
import math
print(int(math.sqrt(N))**2)
``` | output | 1 | 68,785 | 5 | 137,571 |
Provide a correct Python 3 solution for this coding contest problem.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169 | instruction | 0 | 68,786 | 5 | 137,572 |
"Correct Solution:
```
import math
n = int(input())
print((math.floor(n**0.5)**2))
``` | output | 1 | 68,786 | 5 | 137,573 |
Provide a correct Python 3 solution for this coding contest problem.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169 | instruction | 0 | 68,787 | 5 | 137,574 |
"Correct Solution:
```
from math import sqrt
N=int(sqrt(int(input())))
print(N*N)
``` | output | 1 | 68,787 | 5 | 137,575 |
Provide a correct Python 3 solution for this coding contest problem.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169 | instruction | 0 | 68,788 | 5 | 137,576 |
"Correct Solution:
```
n=int(input())
print(int((int(n**(1/2)))**2))
``` | output | 1 | 68,788 | 5 | 137,577 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169
Submitted Solution:
```
N = int(input())
print((int(N**0.5)**2))
``` | instruction | 0 | 68,789 | 5 | 137,578 |
Yes | output | 1 | 68,789 | 5 | 137,579 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169
Submitted Solution:
```
import math
print(math.floor(int(input())**0.5)**2)
``` | instruction | 0 | 68,790 | 5 | 137,580 |
Yes | output | 1 | 68,790 | 5 | 137,581 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169
Submitted Solution:
```
N=int(input())
n=int(N**0.5)
print(n**2)
``` | instruction | 0 | 68,791 | 5 | 137,582 |
Yes | output | 1 | 68,791 | 5 | 137,583 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169
Submitted Solution:
```
import math
print(int(math.sqrt(int(input())))**2)
``` | instruction | 0 | 68,792 | 5 | 137,584 |
Yes | output | 1 | 68,792 | 5 | 137,585 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169
Submitted Solution:
```
n = int(input())
i = 1
while True:
if i ** 2 > n:
print(i-1)
break
i += 1
if i >= 10000:
break
``` | instruction | 0 | 68,793 | 5 | 137,586 |
No | output | 1 | 68,793 | 5 | 137,587 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169
Submitted Solution:
```
n = int(input())
if n == 1:
print(0)
exit()
for i in range(n + 1):
if i ** 2 <= n < (i + 1) ** 2:
print(i ** 2)
exit()
``` | instruction | 0 | 68,794 | 5 | 137,588 |
No | output | 1 | 68,794 | 5 | 137,589 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169
Submitted Solution:
```
n=int(input())
for i in range(1,10**9):
print(i)
if i*i > n:
break
print((i-1)*(i-1))
``` | instruction | 0 | 68,795 | 5 | 137,590 |
No | output | 1 | 68,795 | 5 | 137,591 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.
Constraints
* 1 \leq N \leq 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the largest square number not exceeding N.
Examples
Input
10
Output
9
Input
81
Output
81
Input
271828182
Output
271821169
Submitted Solution:
```
import math
n=int(input())
k=0
for i in range(math.sqrt(n)):
while (i+1)**2 < n:
k+=1
print((k+1)**2)
``` | instruction | 0 | 68,796 | 5 | 137,592 |
No | output | 1 | 68,796 | 5 | 137,593 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki are going to together construct a sequence of integers.
First, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:
* The length of a is N.
* Each element in a is an integer between 1 and K, inclusive.
* a is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.
Then, Aoki will perform the following operation an arbitrary number of times:
* Move the first element in a to the end of a.
How many sequences a can be obtained after this procedure, modulo 10^9+7?
Constraints
* 1≤N≤10^9
* 1≤K≤10^9
Input
The input is given from Standard Input in the following format:
N K
Output
Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.
Examples
Input
4 2
Output
6
Input
1 10
Output
10
Input
6 3
Output
75
Input
1000000000 1000000000
Output
875699961 | instruction | 0 | 68,813 | 5 | 137,626 |
"Correct Solution:
```
M=10**9+7;D=[];i=1;r=0;N,K=map(int,input().split())
while i*i<=N:
if N%i==0:D.append(i);i*i<N and D.append(N//i)
i+=1
D.sort();N=[]
for i in range(len(D)):
N.append(pow(K,-~D[i]//2,M))
for j in range(i):
if D[i]%D[j]==0:N[i]=(N[i]-N[j])%M
r=(r+(N[i]*D[i]*pow(2,M-2+D[i]%2,M)))%M
print(r)
``` | output | 1 | 68,813 | 5 | 137,627 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki are going to together construct a sequence of integers.
First, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:
* The length of a is N.
* Each element in a is an integer between 1 and K, inclusive.
* a is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.
Then, Aoki will perform the following operation an arbitrary number of times:
* Move the first element in a to the end of a.
How many sequences a can be obtained after this procedure, modulo 10^9+7?
Constraints
* 1≤N≤10^9
* 1≤K≤10^9
Input
The input is given from Standard Input in the following format:
N K
Output
Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.
Examples
Input
4 2
Output
6
Input
1 10
Output
10
Input
6 3
Output
75
Input
1000000000 1000000000
Output
875699961 | instruction | 0 | 68,817 | 5 | 137,634 |
"Correct Solution:
```
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline
n,k = map(int,readline().split())
MOD = 10**9+7
def divisor_list(N): #約数のリスト
if N == 1: return [1]
res = []
for i in range(1,N):
if i*i >= N: break
if N%i == 0:
res.append(i)
res.append(N//i)
if i*i == N: res.append(i)
return sorted(res)
if n&1:
p = [i for i in divisor_list(n)]
r = {pi:pow(k,(pi+1)//2,MOD) for pi in p}
#print(r)
for pi in p:
for pj in p:
if pj >= pi: break
if pi%pj==0:
r[pi] -= r[pj]
#print(r)
ans = 0
for pi,v in r.items():
ans += v*(pi)
ans %= MOD
print(ans)
else:
p = [1] + [i for i in divisor_list(n) if i%2==0 and i!=2]
r = {pi:pow(k,(pi+1)//2,MOD) for pi in p}
for pi in p:
for pj in p:
if pj >= pi: break
if pi%pj==0:
r[pi] -= r[pj]
#print(r)
ans = 0
for pi,v in r.items():
if pi==1:
ans += v
else:
ans += v*(pi//2)
ans %= MOD
print(ans)
``` | output | 1 | 68,817 | 5 | 137,635 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki are going to together construct a sequence of integers.
First, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:
* The length of a is N.
* Each element in a is an integer between 1 and K, inclusive.
* a is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.
Then, Aoki will perform the following operation an arbitrary number of times:
* Move the first element in a to the end of a.
How many sequences a can be obtained after this procedure, modulo 10^9+7?
Constraints
* 1≤N≤10^9
* 1≤K≤10^9
Input
The input is given from Standard Input in the following format:
N K
Output
Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.
Examples
Input
4 2
Output
6
Input
1 10
Output
10
Input
6 3
Output
75
Input
1000000000 1000000000
Output
875699961 | instruction | 0 | 68,818 | 5 | 137,636 |
"Correct Solution:
```
N, K = map(int, input().split())
MOD = 10 ** 9 + 7
i = 1
M = N
div = []
while i * i <= N:
if N % i == 0:
div.append(i)
if N // i != i:
div.append(N // i)
i += 1
div = sorted(div)
N1 = len(div)
num = [0] * (N1 + 1)
ans = 0
for i in range(N1):
num[i] = pow(K, (div[i] + 1) // 2, MOD)
for j in range(i):
if div[i] % div[j] == 0:
num[i] = num[i] - num[j] + MOD
num[i] %= MOD
if div[i] % 2 == 0:
ans += div[i] * num[i] // 2
ans %= MOD
else:
ans += div[i] * num[i]
ans %= MOD
print(ans)
``` | output | 1 | 68,818 | 5 | 137,637 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki are going to together construct a sequence of integers.
First, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:
* The length of a is N.
* Each element in a is an integer between 1 and K, inclusive.
* a is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.
Then, Aoki will perform the following operation an arbitrary number of times:
* Move the first element in a to the end of a.
How many sequences a can be obtained after this procedure, modulo 10^9+7?
Constraints
* 1≤N≤10^9
* 1≤K≤10^9
Input
The input is given from Standard Input in the following format:
N K
Output
Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.
Examples
Input
4 2
Output
6
Input
1 10
Output
10
Input
6 3
Output
75
Input
1000000000 1000000000
Output
875699961 | instruction | 0 | 68,819 | 5 | 137,638 |
"Correct Solution:
```
N, K = map(int, input().split())
S = []; T = []
for x in range(1, int(N**.5)+1):
if N % x == 0:
S.append(x)
if x*x < N:
T.append(N//x)
T.reverse()
S += T
M = len(S)
U = []
MOD = 10**9 + 7
ans = 0
v = 0
for i in range(M):
x = S[i]
v = pow(K, (x+1)//2, MOD)
for j in range(i):
y = S[j]
if x % y == 0:
v -= U[j]
U.append(v % MOD)
ans = (ans + (v * x if x & 1 else v * (x//2))) % MOD
print(ans)
``` | output | 1 | 68,819 | 5 | 137,639 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki are going to together construct a sequence of integers.
First, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:
* The length of a is N.
* Each element in a is an integer between 1 and K, inclusive.
* a is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.
Then, Aoki will perform the following operation an arbitrary number of times:
* Move the first element in a to the end of a.
How many sequences a can be obtained after this procedure, modulo 10^9+7?
Constraints
* 1≤N≤10^9
* 1≤K≤10^9
Input
The input is given from Standard Input in the following format:
N K
Output
Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.
Examples
Input
4 2
Output
6
Input
1 10
Output
10
Input
6 3
Output
75
Input
1000000000 1000000000
Output
875699961 | instruction | 0 | 68,820 | 5 | 137,640 |
"Correct Solution:
```
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")
n,k = list(map(int, input().split()))
M = 10**9+7
### 約数列挙
def fs(n):
s = set()
for i in range(1,int(n**0.5)+2):
if n%i==0:
s.add(i)
s.add(n//i)
l = sorted(list(s))
return l
ds = fs(n)
m = len(ds)
nums = [None]*m
for i in range(m):
val = pow(k, (ds[i]+1)//2, M)
for j in range(i):
if ds[i]%ds[j]==0:
val -= nums[j]
val %= M
nums[i] = val%M
ans = 0
inv2 = pow(2, M-2, M)
for i in range(m):
if ds[i]%2==0:
ans += ds[i]*nums[i]*inv2
else:
ans += ds[i]*nums[i]
ans %= M
print(ans%M)
``` | output | 1 | 68,820 | 5 | 137,641 |
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