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.
AtCoDeer has three cards, one red, one green and one blue.
An integer between 1 and 9 (inclusive) is written on each card: r on the red card, g on the green card and b on the blue card.
We will arrange the cards in the order red, green and blue from left to right, and read them as a three-digit integer.
Is this integer a multiple of 4?
Constraints
* 1 ≤ r, g, b ≤ 9
Input
Input is given from Standard Input in the following format:
r g b
Output
If the three-digit integer is a multiple of 4, print `YES` (case-sensitive); otherwise, print `NO`.
Examples
Input
4 3 2
Output
YES
Input
2 3 4
Output
NO
Submitted Solution:
```
s = int("".join(input().split()))
print(["NO", "YES"][s % 4 == 0])
``` | instruction | 0 | 89,105 | 5 | 178,210 |
Yes | output | 1 | 89,105 | 5 | 178,211 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
AtCoDeer has three cards, one red, one green and one blue.
An integer between 1 and 9 (inclusive) is written on each card: r on the red card, g on the green card and b on the blue card.
We will arrange the cards in the order red, green and blue from left to right, and read them as a three-digit integer.
Is this integer a multiple of 4?
Constraints
* 1 ≤ r, g, b ≤ 9
Input
Input is given from Standard Input in the following format:
r g b
Output
If the three-digit integer is a multiple of 4, print `YES` (case-sensitive); otherwise, print `NO`.
Examples
Input
4 3 2
Output
YES
Input
2 3 4
Output
NO
Submitted Solution:
```
r,g,b = input().split()
if int((g*10+b)%4==0):
print('YES')
else:
print('No')
``` | instruction | 0 | 89,106 | 5 | 178,212 |
No | output | 1 | 89,106 | 5 | 178,213 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
AtCoDeer has three cards, one red, one green and one blue.
An integer between 1 and 9 (inclusive) is written on each card: r on the red card, g on the green card and b on the blue card.
We will arrange the cards in the order red, green and blue from left to right, and read them as a three-digit integer.
Is this integer a multiple of 4?
Constraints
* 1 ≤ r, g, b ≤ 9
Input
Input is given from Standard Input in the following format:
r g b
Output
If the three-digit integer is a multiple of 4, print `YES` (case-sensitive); otherwise, print `NO`.
Examples
Input
4 3 2
Output
YES
Input
2 3 4
Output
NO
Submitted Solution:
```
r,g,b= map(int(input().split()))
num = 100*r + 10*g + b
if num %4 == 0:
print('YES')
else:
print('NO')
``` | instruction | 0 | 89,107 | 5 | 178,214 |
No | output | 1 | 89,107 | 5 | 178,215 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
AtCoDeer has three cards, one red, one green and one blue.
An integer between 1 and 9 (inclusive) is written on each card: r on the red card, g on the green card and b on the blue card.
We will arrange the cards in the order red, green and blue from left to right, and read them as a three-digit integer.
Is this integer a multiple of 4?
Constraints
* 1 ≤ r, g, b ≤ 9
Input
Input is given from Standard Input in the following format:
r g b
Output
If the three-digit integer is a multiple of 4, print `YES` (case-sensitive); otherwise, print `NO`.
Examples
Input
4 3 2
Output
YES
Input
2 3 4
Output
NO
Submitted Solution:
```
a, b, c = map(int, input().split())
num = a*100 + b*10 + c
if num % 4 == 0:
print("YES)
else:
@rint("NO")
``` | instruction | 0 | 89,108 | 5 | 178,216 |
No | output | 1 | 89,108 | 5 | 178,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
AtCoDeer has three cards, one red, one green and one blue.
An integer between 1 and 9 (inclusive) is written on each card: r on the red card, g on the green card and b on the blue card.
We will arrange the cards in the order red, green and blue from left to right, and read them as a three-digit integer.
Is this integer a multiple of 4?
Constraints
* 1 ≤ r, g, b ≤ 9
Input
Input is given from Standard Input in the following format:
r g b
Output
If the three-digit integer is a multiple of 4, print `YES` (case-sensitive); otherwise, print `NO`.
Examples
Input
4 3 2
Output
YES
Input
2 3 4
Output
NO
Submitted Solution:
```
def calc():
ans = r*100 + g*10 + b
if ans%4 == 0:
return "YES"
else:
return "NO"
r, g, b = map(int, input().split())
print(calc)
``` | instruction | 0 | 89,109 | 5 | 178,218 |
No | output | 1 | 89,109 | 5 | 178,219 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people, conveniently numbered 1 through N. They were standing in a row yesterday, but now they are unsure of the order in which they were standing. However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person. According to their reports, the difference above for person i is A_i.
Based on these reports, find the number of the possible orders in which they were standing. Since it can be extremely large, print the answer modulo 10^9+7. Note that the reports may be incorrect and thus there may be no consistent order. In such a case, print 0.
Constraints
* 1≦N≦10^5
* 0≦A_i≦N-1
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the number of the possible orders in which they were standing, modulo 10^9+7.
Examples
Input
5
2 4 4 0 2
Output
4
Input
7
6 4 0 2 4 0 2
Output
0
Input
8
7 5 1 1 7 3 5 3
Output
16 | instruction | 0 | 89,110 | 5 | 178,220 |
"Correct Solution:
```
n = int(input())
q = [int(x) for x in input().split(' ')]
q_set = set(q)
if (n%2 == 1):
count = 2**((n-1)//2)
else:
count = 2**(n//2)
if (sum(q) == 2*sum(q_set)):
print(count%(10**9+7))
else:
print(0)
``` | output | 1 | 89,110 | 5 | 178,221 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people, conveniently numbered 1 through N. They were standing in a row yesterday, but now they are unsure of the order in which they were standing. However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person. According to their reports, the difference above for person i is A_i.
Based on these reports, find the number of the possible orders in which they were standing. Since it can be extremely large, print the answer modulo 10^9+7. Note that the reports may be incorrect and thus there may be no consistent order. In such a case, print 0.
Constraints
* 1≦N≦10^5
* 0≦A_i≦N-1
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the number of the possible orders in which they were standing, modulo 10^9+7.
Examples
Input
5
2 4 4 0 2
Output
4
Input
7
6 4 0 2 4 0 2
Output
0
Input
8
7 5 1 1 7 3 5 3
Output
16 | instruction | 0 | 89,111 | 5 | 178,222 |
"Correct Solution:
```
NUM = 10 ** 9 + 7
N = int(input())
A = list(map(int, input().split()))
A.sort(reverse=True)
length = len(A)
if not length % 2 == 0:
length -= 1
for i in range(0, length, 2):
if not A[i] == A[i + 1]:
print(0)
exit()
print((2 ** (length // 2)) % NUM)
``` | output | 1 | 89,111 | 5 | 178,223 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people, conveniently numbered 1 through N. They were standing in a row yesterday, but now they are unsure of the order in which they were standing. However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person. According to their reports, the difference above for person i is A_i.
Based on these reports, find the number of the possible orders in which they were standing. Since it can be extremely large, print the answer modulo 10^9+7. Note that the reports may be incorrect and thus there may be no consistent order. In such a case, print 0.
Constraints
* 1≦N≦10^5
* 0≦A_i≦N-1
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the number of the possible orders in which they were standing, modulo 10^9+7.
Examples
Input
5
2 4 4 0 2
Output
4
Input
7
6 4 0 2 4 0 2
Output
0
Input
8
7 5 1 1 7 3 5 3
Output
16 | instruction | 0 | 89,112 | 5 | 178,224 |
"Correct Solution:
```
N = int(input())
A = sorted(list(map(int, input().split())))
cr_A = []
if N%2:
cr_A.append(0)
for i in range(1, N//2 + 1):
cr_A.extend([2*i]*2)
else:
for i in range(1, N//2 + 1):
cr_A.extend([2*i - 1]*2)
if A == cr_A:
if N > 1:
print((2**(N//2))%(10**9 + 7))
else:
print(1)
else:
print(0)
``` | output | 1 | 89,112 | 5 | 178,225 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people, conveniently numbered 1 through N. They were standing in a row yesterday, but now they are unsure of the order in which they were standing. However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person. According to their reports, the difference above for person i is A_i.
Based on these reports, find the number of the possible orders in which they were standing. Since it can be extremely large, print the answer modulo 10^9+7. Note that the reports may be incorrect and thus there may be no consistent order. In such a case, print 0.
Constraints
* 1≦N≦10^5
* 0≦A_i≦N-1
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the number of the possible orders in which they were standing, modulo 10^9+7.
Examples
Input
5
2 4 4 0 2
Output
4
Input
7
6 4 0 2 4 0 2
Output
0
Input
8
7 5 1 1 7 3 5 3
Output
16 | instruction | 0 | 89,113 | 5 | 178,226 |
"Correct Solution:
```
from collections import defaultdict
MOD = 10 ** 9 + 7
N = int(input())
A = list(map(int, input().split()))
d = defaultdict(int)
for num in A:
d[num] += 1
d[0] += 1
if all(d[i] == 2 for i in range((N + 1) % 2, N, 2)):
print(2 ** (N // 2) % MOD)
else:
print(0)
``` | output | 1 | 89,113 | 5 | 178,227 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people, conveniently numbered 1 through N. They were standing in a row yesterday, but now they are unsure of the order in which they were standing. However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person. According to their reports, the difference above for person i is A_i.
Based on these reports, find the number of the possible orders in which they were standing. Since it can be extremely large, print the answer modulo 10^9+7. Note that the reports may be incorrect and thus there may be no consistent order. In such a case, print 0.
Constraints
* 1≦N≦10^5
* 0≦A_i≦N-1
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the number of the possible orders in which they were standing, modulo 10^9+7.
Examples
Input
5
2 4 4 0 2
Output
4
Input
7
6 4 0 2 4 0 2
Output
0
Input
8
7 5 1 1 7 3 5 3
Output
16 | instruction | 0 | 89,114 | 5 | 178,228 |
"Correct Solution:
```
iN = int(input())
aA = [int(_) for _ in input().split()]
aA.sort()
iD = 10**9 + 7
iRet = 0
if iN % 2 == 0:
aR = [x if x % 2 == 1 else x + 1 for x in range(iN)]
else:
aR = [x if x % 2 == 0 else x + 1 for x in range(iN)]
if aA == aR:
print(pow(2,iN//2,iD))
else:
print(0)
``` | output | 1 | 89,114 | 5 | 178,229 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people, conveniently numbered 1 through N. They were standing in a row yesterday, but now they are unsure of the order in which they were standing. However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person. According to their reports, the difference above for person i is A_i.
Based on these reports, find the number of the possible orders in which they were standing. Since it can be extremely large, print the answer modulo 10^9+7. Note that the reports may be incorrect and thus there may be no consistent order. In such a case, print 0.
Constraints
* 1≦N≦10^5
* 0≦A_i≦N-1
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the number of the possible orders in which they were standing, modulo 10^9+7.
Examples
Input
5
2 4 4 0 2
Output
4
Input
7
6 4 0 2 4 0 2
Output
0
Input
8
7 5 1 1 7 3 5 3
Output
16 | instruction | 0 | 89,115 | 5 | 178,230 |
"Correct Solution:
```
N = int(input())
A = sorted(list(map(int, input().split())), reverse=True)
n = N-1
for i in range(N//2):
if A[2*i]!=n or A[2*i+1]!=n:
print(0)
exit()
n -= 2
if N&1 and A[-1]!=0:
print(0)
exit()
print((1<<N//2)%(10**9+7))
``` | output | 1 | 89,115 | 5 | 178,231 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people, conveniently numbered 1 through N. They were standing in a row yesterday, but now they are unsure of the order in which they were standing. However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person. According to their reports, the difference above for person i is A_i.
Based on these reports, find the number of the possible orders in which they were standing. Since it can be extremely large, print the answer modulo 10^9+7. Note that the reports may be incorrect and thus there may be no consistent order. In such a case, print 0.
Constraints
* 1≦N≦10^5
* 0≦A_i≦N-1
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the number of the possible orders in which they were standing, modulo 10^9+7.
Examples
Input
5
2 4 4 0 2
Output
4
Input
7
6 4 0 2 4 0 2
Output
0
Input
8
7 5 1 1 7 3 5 3
Output
16 | instruction | 0 | 89,116 | 5 | 178,232 |
"Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
L = [abs((N-1) - 2*i) for i in range(N)]
L.sort(); A.sort()
print(pow(2, (N-N%2)//2, 10**9+7) if L == A else 0)
``` | output | 1 | 89,116 | 5 | 178,233 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people, conveniently numbered 1 through N. They were standing in a row yesterday, but now they are unsure of the order in which they were standing. However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person. According to their reports, the difference above for person i is A_i.
Based on these reports, find the number of the possible orders in which they were standing. Since it can be extremely large, print the answer modulo 10^9+7. Note that the reports may be incorrect and thus there may be no consistent order. In such a case, print 0.
Constraints
* 1≦N≦10^5
* 0≦A_i≦N-1
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the number of the possible orders in which they were standing, modulo 10^9+7.
Examples
Input
5
2 4 4 0 2
Output
4
Input
7
6 4 0 2 4 0 2
Output
0
Input
8
7 5 1 1 7 3 5 3
Output
16 | instruction | 0 | 89,117 | 5 | 178,234 |
"Correct Solution:
```
from collections import Counter
n = int(input())
A = list(map(int,input().split()))
mod = 10**9 + 7
c = Counter(A)
flg = True
for k,v in c.items():
if k==0:
if v!=1:
flg = False
else:
if v!=2:
flg = False
if flg is False:
print(0)
else:
print(pow(2, n//2, mod))
``` | output | 1 | 89,117 | 5 | 178,235 |
Provide a correct Python 3 solution for this coding contest problem.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1 | instruction | 0 | 89,126 | 5 | 178,252 |
"Correct Solution:
```
import math
n = int(input())
s = int(input())
if s == n:
print(n + 1)
exit()
elif s > n:
print(-1)
exit()
for i in range(2, math.floor(math.sqrt(n)) + 1):
new_n = n
remain = 0
while new_n > 0:
remain += new_n % i
new_n //= i
if remain == s:
print(i)
exit()
for i in range(math.floor(math.sqrt(n)) + 1, 0, -1):
b = (n - s) // i + 1
st = n % b + n // b
if n // b != b and st == s:
print(b)
exit()
print(-1)
``` | output | 1 | 89,126 | 5 | 178,253 |
Provide a correct Python 3 solution for this coding contest problem.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1 | instruction | 0 | 89,127 | 5 | 178,254 |
"Correct Solution:
```
#!/usr/bin/env python3
import sys
def f(b: int, n: int) -> int:
if n < b:
return n
return f(b, n // b) + n % b
def sqrt(n: int):
lb = 0
hb = n + 1
while hb - lb > 1:
m = (lb + hb) // 2
if m * m <= n:
lb = m
else:
hb = m
return lb
def solve(n: int, s: int):
if s == n:
print(n + 1)
return
sn = sqrt(n)
for b in range(2, sn + 1):
if f(b, n) == s:
print(b)
return
for p in reversed(range(1, sn + 1)):
q = s - p
if q < 0:
continue
b, r = divmod(n - q, p)
if r != 0 or b <= p:
continue
if f(b, n) == s:
print(b)
return
print(-1)
def main():
def iterate_tokens():
for line in sys.stdin:
for word in line.split():
yield word
tokens = iterate_tokens()
n = int(next(tokens)) # type: int
s = int(next(tokens)) # type: int
solve(n, s)
if __name__ == '__main__':
main()
``` | output | 1 | 89,127 | 5 | 178,255 |
Provide a correct Python 3 solution for this coding contest problem.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1 | instruction | 0 | 89,128 | 5 | 178,256 |
"Correct Solution:
```
n = int(input())
s = int(input())
rtn = -1* int( -1 * (n**0.5))
def f(b,n):
if n<b:
return n
return f(b,n//b) + n % b
if n < s or (n // 2)+1 < s < n :
print("-1")
elif s == n:
print(n+1)
elif s == n//2 +1:
if n % 2 == 1:
print(n//2 + 1)
else:
print("-1")
elif (n//3) + 2 < s <= n//2:
print(n-s+1)
else:
for b in range(2,rtn+1):
if f(b,n) == s:
print(b)
exit()
for p in range(rtn,0,-1):
if (n-s) % p == 0:
b = (n-s)//p + 1
if f(b,n) == s:
print(b)
exit()
print(n-s+1)
``` | output | 1 | 89,128 | 5 | 178,257 |
Provide a correct Python 3 solution for this coding contest problem.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1 | instruction | 0 | 89,129 | 5 | 178,258 |
"Correct Solution:
```
import math
n = int(input())
s = int(input())
if n == s:
print(n+1)
exit()
ru = math.ceil(math.sqrt(n))+1
for i in range(2,ru+1):
b = n+0
a = 0
while b:
a +=b%i
b//=i
if s == a:
print(i)
exit()
for i in range(ru,0,-1):
q = s-i
if q <0:
continue
c = (n-q)// i
if c <= ru-1:
continue
b = n+0
a = 0
while b:
a+=b%c
b//=c
if a == s:
print(c)
exit()
print(-1)
``` | output | 1 | 89,129 | 5 | 178,259 |
Provide a correct Python 3 solution for this coding contest problem.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1 | instruction | 0 | 89,130 | 5 | 178,260 |
"Correct Solution:
```
def d_DigitSum(N, S):
if S == N:
# f(b,N)=Nを満たすbはN+1が最小
return N + 1
if S > N:
return -1
from math import sqrt, floor, ceil
def f(b, n):
if n < b:
return n
else:
return f(b, n // b) + (n % b)
sn = ceil(sqrt(N))
# 2<=b<=√Nまで探索
for b in range(2, sn + 1):
if f(b, N) == S:
return b
# √N<=b<=Nまで探索
for p in range(sn, 0, -1):
if (N - S) % p == 0:
b = (N - S) // p + 1
if f(b, N) == S:
return b
return -1
N = int(input())
S = int(input())
print(d_DigitSum(N, S))
``` | output | 1 | 89,130 | 5 | 178,261 |
Provide a correct Python 3 solution for this coding contest problem.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1 | instruction | 0 | 89,131 | 5 | 178,262 |
"Correct Solution:
```
from math import sqrt
def n_based(n:int, base:int) -> int:
if n == 0:
return 0
ans = 0
res = n
while abs(res) > 0:
q = res%base
if q>=0:
ans = q + ans
res //= base
else:
q += abs(base)
ans = q + ans
res //= base
res += 1
return ans
n = int(input())
s = int(input())
def judge(n:int, s:int) -> int:
if n < s:
return -1
elif n==1 and s==1:
return 2
elif n == s:
return n+1
else:
for i in range(2,int(sqrt(n))+2):
#print(i)
if n_based(n,i) == s:
return i
for p in range(int(sqrt(n)), 0, -1):
if (n-s+p) % p == 0:
b = (n-s+p) // p
#print(p,b)
if n_based(n,b) == s:
return b
return -1
print(int(judge(n,s)))
``` | output | 1 | 89,131 | 5 | 178,263 |
Provide a correct Python 3 solution for this coding contest problem.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1 | instruction | 0 | 89,132 | 5 | 178,264 |
"Correct Solution:
```
import math
n = int(input())
s = int(input())
f = None
for i in range(2, math.ceil(math.sqrt(n))):
c = 0
k = n
while k > 0:
c += k % i
k //= i
if c == s:
f = i
break
if f is None:
for i in range(int(math.sqrt(n)), 1, -1):
b = n // i
k = n
c = 0
while k > 0:
c += k % b
k //= b
if s >= c and (s - c) % i == 0 and b - (s - c) // i > n // (i + 1):
f = b - (s - c) // i
break
if f is None:
if s == n: f = n + 1
elif s <= (n + 1) // 2: f = n - s + 1
elif s == 1: f = n
if f is None: print(-1)
else: print(f)
``` | output | 1 | 89,132 | 5 | 178,265 |
Provide a correct Python 3 solution for this coding contest problem.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1 | instruction | 0 | 89,133 | 5 | 178,266 |
"Correct Solution:
```
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def f(b,n):
if(n<b): return n
return f(b,n//b)+n%b
def resolve():
n=int(input())
s=int(input())
if(s>n):
print(-1)
return
if(s==n):
print(n+1)
return
# 2 <= b <= sqrt(n) を全探索
k=int(n**.5)
for b in range(2,k+1):
if(f(b,n)==s):
print(b)
return
# sqrt(n) < b <= n を考える
B=[]
for p in range(1,k+1):
if((n-s)%p): continue
b=(n-s)//p+1
if(b<2): continue
if(f(b,n)==s):
B.append(b)
print(min(B) if(B) else -1)
resolve()
``` | output | 1 | 89,133 | 5 | 178,267 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1
Submitted Solution:
```
import math
import sys
import functools
sys.setrecursionlimit(10 ** 9)
@functools.lru_cache(None)
def f(b, n):
if n < b:
return n
else:
return f(b, n // b) + (n % b)
def main(n, s):
if s == n:
return n + 1
if s > n:
return -1
for b in range(2, math.ceil(math.sqrt(n)) + 1):
if f(b, n) == s:
return b
ans = float('inf')
for p in range(1, math.ceil(math.sqrt(n)) + 1):
if (n - s) % p == 0:
b = (n - s) // p + 1
if f(b, n) == s:
ans = min(ans, b)
return -1 if ans == float('inf') else ans
if __name__ == '__main__':
n = int(input())
s = int(input())
print(main(n, s))
``` | instruction | 0 | 89,134 | 5 | 178,268 |
Yes | output | 1 | 89,134 | 5 | 178,269 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1
Submitted Solution:
```
#
# ⋀_⋀
# (･ω･)
# .／ Ｕ ∽ Ｕ＼
# │＊ 合 ＊│
# │＊ 格 ＊│
# │＊ 祈 ＊│
# │＊ 願 ＊│
# │＊ ＊│
# ￣
#
import sys
sys.setrecursionlimit(10**6)
input=sys.stdin.readline
from math import floor,sqrt,factorial,hypot,log #log2ないｙｐ
from heapq import heappop, heappush, heappushpop
from collections import Counter,defaultdict,deque
from itertools import accumulate,permutations,combinations,product,combinations_with_replacement
from bisect import bisect_left,bisect_right
from copy import deepcopy
from fractions import gcd
from random import randint
def ceil(a,b): return (a+b-1)//b
inf=float('inf')
mod = 10**9+7
def pprint(*A):
for a in A: print(*a,sep='\n')
def INT_(n): return int(n)-1
def MI(): return map(int,input().split())
def MF(): return map(float, input().split())
def MI_(): return map(INT_,input().split())
def LI(): return list(MI())
def LI_(): return [int(x) - 1 for x in input().split()]
def LF(): return list(MF())
def LIN(n:int): return [I() for _ in range(n)]
def LLIN(n: int): return [LI() for _ in range(n)]
def LLIN_(n: int): return [LI_() for _ in range(n)]
def LLI(): return [list(map(int, l.split() )) for l in input()]
def I(): return int(input())
def F(): return float(input())
def ST(): return input().replace('\n', '')
def main():
N = I()
S = I()
if N==S:
print(N+1)
return
def check(N,b):
res = 0
while N:
res += N%b
N//=b
return res == S
for b in range(2,int(sqrt(N)+1)):
if check(N,b):
print(b)
return
for p in range(1,int(sqrt(N)+1))[::-1]:
b = (N-S+p)//p
if b>=2 and check(N,b):
print(b)
return
print(-1)
if __name__ == '__main__':
main()
``` | instruction | 0 | 89,135 | 5 | 178,270 |
Yes | output | 1 | 89,135 | 5 | 178,271 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1
Submitted Solution:
```
n=int(input())
s=int(input())
if n==s:
print(n+1)
exit()
if n<s:
print(-1)
exit()
for b in range(2,int(n**(1/2))+1):
m=n
wa=0
while m>0:
wa+=m%b
m=m//b
if wa==s:
print(b)
exit()
for p in range(int((n-1)**(1/2)),0,-1):
if (n-s)%p==0:
b=(n-s)//p+1
if p+n%b==s:
print(b)
exit()
print(-1)
``` | instruction | 0 | 89,136 | 5 | 178,272 |
Yes | output | 1 | 89,136 | 5 | 178,273 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1
Submitted Solution:
```
n = int(input())
s = int(input())
import math
def f(b, n):
# print(b, n)
if n<b:
return n
else:
x = f(b, n//b) + n%b
return x
ans = 0
if n<s:
print(-1)
exit()
if n==s:
print(n+1)
exit()
for b in range(2,int(math.sqrt(n))+500):
if f(b, n) == s:
ans = b
print(ans)
exit()
for p in range(int(math.sqrt(n)), 0, -1):
if (n+p-s) %p == 0:
# print(p)
if f((n+p-s)//p, n) == s:
print((n+p-s)//p)
exit()
print(-1)
``` | instruction | 0 | 89,137 | 5 | 178,274 |
Yes | output | 1 | 89,137 | 5 | 178,275 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1
Submitted Solution:
```
n = int(input())
s = int(input())
def f(b,n) :
r = 0
i = 1
while n:
j = n % b
r += j
n = (n-j)//b
return r
if n < s or (n // 2)+1 < s < n :
print("-1")
elif s == n//2 +1:
if n % 2 == 1:
print(n//2 + 1)
else:
print("-1")
elif (n//3) + 2 < s <= n//2:
print(n-s+1)
elif s == n:
print(n+1)
elif s == 1:
def check(n,b):
while 1 < n :
if n % b != 0:
break
n //= b
if n == 1:
return b
return 0
for b in range(2,int(n**0.5)+2):
r = check(n,b)
if r:
print(r)
exit()
print(n)
else:
x = n // s
if s - (n //(x+1)) <= x:
x = x + 1
if 3 < n/(x -1) - n/x :
for b in range(n//x, 2*n//x - n//(x+1)):
if f(b,n) == s:
print(b)
exit()
for i in range(x-1,2,-1):
for b in range(n//i + (n//x)//(n//i), n//i + (n//x)//(n//i) + (2*n//x - n//(x+1))//x-i):
if f(b,n) == s:
print(b)
exit()
else:
for b in range(2,(n//2)+2):
if f(b,n) == s:
print(b)
exit()
print(n-s+1)
``` | instruction | 0 | 89,138 | 5 | 178,276 |
No | output | 1 | 89,138 | 5 | 178,277 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1
Submitted Solution:
```
n = int(input())
s = int(input())
for i in range(2, int((n+1)**.5)):
c = 0
m = n
while m > 0:
c += m%i
m //= i
if c > s:
break
if c == s:
print(i)
exit()
else:
pass
if n == s:
print(n+1)
elif n <= (n+1)//2:
print(n-s+1)
elif s == 1:
print(n)
else:
print(-1)
``` | instruction | 0 | 89,139 | 5 | 178,278 |
No | output | 1 | 89,139 | 5 | 178,279 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1
Submitted Solution:
```
def read():
return int(input())
def reads(sep=None):
return list(map(int, input().split(sep)))
def f(b, n):
c = 0
while n:
if n < b:
c += n
break
else:
c += n % b
n //= b
return c
def main():
n = read()
s = read()
if n < s:
print(-1)
elif n == s:
print(n + 1)
else:
b = 2
while b*b <= n:
if f(b, n) == s:
print(b)
return
b += 1
i = 1
bs = []
while i*i <= n:
if (n-s)%i != 0:
bs.append((n-s)%i + 1)
i += 1
for b in sorted(bs):
if f(b, n) == s:
print(b)
return
print(-1)
main()
``` | instruction | 0 | 89,140 | 5 | 178,280 |
No | output | 1 | 89,140 | 5 | 178,281 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
* f(b,n) = n, when n < b
* f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b, and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b. For example, the following hold:
* f(10,\,87654)=8+7+6+5+4=30
* f(100,\,87654)=8+76+54=138
You are given integers n and s. Determine if there exists an integer b (b \geq 2) such that f(b,n)=s. If the answer is positive, also find the smallest such b.
Constraints
* 1 \leq n \leq 10^{11}
* 1 \leq s \leq 10^{11}
* n,\,s are integers.
Input
The input is given from Standard Input in the following format:
n
s
Output
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b. If such b does not exist, print `-1` instead.
Examples
Input
87654
30
Output
10
Input
87654
138
Output
100
Input
87654
45678
Output
-1
Input
31415926535
1
Output
31415926535
Input
1
31415926535
Output
-1
Submitted Solution:
```
n=int(input())
s=int(input())
rootn=0
while rootn**2<=n:
rootn+=1
def fun(b,n):
if n<b:return n
elif n>=b:
return fun(b,n//b)+n%b
def main(n,s):
if n==s:return n+1
for b in range(2,rootn):
if fun(b,n)==s:return int(b)
for p in reversed(range(1,rootn)):
b=1+(n-s)//p
if fun(b,n)==s:return int(b)
b=2+(n-s)//p
if fun(b,n)==s:return int(b)
return -1
x=main(n,s)
print(x)
#http://arc060.contest.atcoder.jp/data/arc/060/editorial.pdf
``` | instruction | 0 | 89,141 | 5 | 178,282 |
No | output | 1 | 89,141 | 5 | 178,283 |
Provide a correct Python 3 solution for this coding contest problem.
Alice is spending his time on an independent study to apply to the Nationwide Mathematics Contest. This year’s theme is "Beautiful Sequence." As Alice is interested in the working of computers, she wants to create a beautiful sequence using only 0 and 1. She defines a "Beautiful" sequence of length $N$ that consists only of 0 and 1 if it includes $M$ successive array of 1s as its sub-sequence.
Using his skills in programming, Alice decided to calculate how many "Beautiful sequences" she can generate and compile a report on it.
Make a program to evaluate the possible number of "Beautiful sequences" given the sequence length $N$ and sub-sequence length $M$ that consists solely of 1. As the answer can be extremely large, divide it by $1,000,000,007 (= 10^9 + 7)$ and output the remainder.
Input
The input is given in the following format.
$N$ $M$
The input line provides the length of sequence $N$ ($1 \leq N \leq 10^5$) and the length $M$ ($1 \leq M \leq N$) of the array that solely consists of 1s.
Output
Output the number of Beautiful sequences in a line.
Examples
Input
4 3
Output
3
Input
4 2
Output
8 | instruction | 0 | 89,174 | 5 | 178,348 |
"Correct Solution:
```
MOD = 1000000007
N, M = (int(x) for x in input().split())
pow = [0] * (N + 1)
dp = [0] * (N + 1)
pow[0] = 1
for i in range(1, N + 1):
pow[i] = pow[i - 1] * 2
pow[i] %= MOD
dp[0] = 1
for i in range(1, M + 1):
dp[i] = pow[i]
dp[M] -= 1
for i in range(M + 1, N + 1):
dp[i] = dp[i - 1] + (dp[i - 1] - dp[i - 1 - M])
dp[i] %= MOD
print((pow[N] - dp[N] + MOD) % MOD)
``` | output | 1 | 89,174 | 5 | 178,349 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer x. Check whether the number x is representable as the sum of the cubes of two positive integers.
Formally, you need to check if there are two integers a and b (1 ≤ a, b) such that a^3+b^3=x.
For example, if x = 35, then the numbers a=2 and b=3 are suitable (2^3+3^3=8+27=35). If x=4, then no pair of numbers a and b is suitable.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case contains one integer x (1 ≤ x ≤ 10^{12}).
Please note, that the input for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language.
Output
For each test case, output on a separate line:
* "YES" if x is representable as the sum of the cubes of two positive integers.
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
7
1
2
4
34
35
16
703657519796
Output
NO
YES
NO
NO
YES
YES
YES
Note
The number 1 is not representable as the sum of two cubes.
The number 2 is represented as 1^3+1^3.
The number 4 is not representable as the sum of two cubes.
The number 34 is not representable as the sum of two cubes.
The number 35 is represented as 2^3+3^3.
The number 16 is represented as 2^3+2^3.
The number 703657519796 is represented as 5779^3+7993^3.
Submitted Solution:
```
import math
#A||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
'''
g=int(input())
for i in range (g):
ans=0
f=int(input())
s=list(map(int,input().split()))
for j in range (0,f-1):
m = min(s[j], s[j+1])
while m*2 < max(s[j],s[j+1]):
m *= 2
ans += 1
print(ans)
'''
#B|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
'''
g=int(input())
for i in range (g):
ans=0
ost=[]
f=int(input())
s=list(map(int,input().split()))
col = f // 3
for j in range(f):
ost.append(s[j]%3)
od=ost.count(1)
dv=ost.count(2)
no=ost.count(0)
if od==dv==no:
print('0')
else:
while (od == dv == no) == False:
'''
#C||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
g=int(input())
for i in range (g):
f=int(input())
l=1
if f == 1:
print('NO')
elif f == 2:
print('YES')
elif f >= 3:
for i in range (1,round(f**(1/3))):
k=i*i*i
m=f-k
n=round(m **(1/3))
if i*i*i+n*n*n == f:
print('YES')
break
else:
l+=1
if l == round(f**(1/3)):
print('NO')
``` | instruction | 0 | 89,536 | 5 | 179,072 |
Yes | output | 1 | 89,536 | 5 | 179,073 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer x. Check whether the number x is representable as the sum of the cubes of two positive integers.
Formally, you need to check if there are two integers a and b (1 ≤ a, b) such that a^3+b^3=x.
For example, if x = 35, then the numbers a=2 and b=3 are suitable (2^3+3^3=8+27=35). If x=4, then no pair of numbers a and b is suitable.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case contains one integer x (1 ≤ x ≤ 10^{12}).
Please note, that the input for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language.
Output
For each test case, output on a separate line:
* "YES" if x is representable as the sum of the cubes of two positive integers.
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
7
1
2
4
34
35
16
703657519796
Output
NO
YES
NO
NO
YES
YES
YES
Note
The number 1 is not representable as the sum of two cubes.
The number 2 is represented as 1^3+1^3.
The number 4 is not representable as the sum of two cubes.
The number 34 is not representable as the sum of two cubes.
The number 35 is represented as 2^3+3^3.
The number 16 is represented as 2^3+2^3.
The number 703657519796 is represented as 5779^3+7993^3.
Submitted Solution:
```
from sys import stdin, stdout
from math import floor, gcd, fabs, factorial, fmod, sqrt, inf, log
from collections import defaultdict as dd, deque
from heapq import merge, heapify, heappop, heappush, nsmallest
from bisect import bisect_left as bl, bisect_right as br, bisect
mod = pow(10, 9) + 7
mod2 = 998244353
def inp(): return stdin.readline().strip()
def iinp(): return int(inp())
def out(var, end="\n"): stdout.write(str(var)+"\n")
def outa(*var, end="\n"): stdout.write(' '.join(map(str, var)) + end)
def lmp(): return list(mp())
def mp(): return map(int, inp().split())
def smp(): return map(str, inp().split())
def l1d(n, val=0): return [val for i in range(n)]
def l2d(n, m, val=0): return [l1d(m, val) for j in range(n)]
def remadd(x, y): return 1 if x%y else 0
def ceil(a,b): return (a+b-1)//b
def isprime(x):
if x<=1: return False
if x in (2, 3): return True
if x%2 == 0: return False
for i in range(3, int(sqrt(x))+1, 2):
if x%i == 0: return False
return True
# ml1 = [i**3 for i in range(2, 10002, 2)]
# ml2 = [i**3 for i in range(1, 10001, 2)]
md1 = {}
md2 = {}
for i in range(2, 10003, 2):
md1[i**3]=1
for i in range(1, 10003, 2):
md2[i**3]=1
for _ in range(int(inp())):
n = iinp()
t = False
if n%2==0:
for i in md1.keys():
if n-i in md1:
t = True
break
if t:
print("YES")
continue
for i in md2.keys():
if n-i in md2:
t = True
break
print("YES" if t else "NO")
else:
for i in md1.keys():
if n-i in md2:
t = True
break
print("YES" if t else "NO")
``` | instruction | 0 | 89,537 | 5 | 179,074 |
Yes | output | 1 | 89,537 | 5 | 179,075 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer x. Check whether the number x is representable as the sum of the cubes of two positive integers.
Formally, you need to check if there are two integers a and b (1 ≤ a, b) such that a^3+b^3=x.
For example, if x = 35, then the numbers a=2 and b=3 are suitable (2^3+3^3=8+27=35). If x=4, then no pair of numbers a and b is suitable.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case contains one integer x (1 ≤ x ≤ 10^{12}).
Please note, that the input for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language.
Output
For each test case, output on a separate line:
* "YES" if x is representable as the sum of the cubes of two positive integers.
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
7
1
2
4
34
35
16
703657519796
Output
NO
YES
NO
NO
YES
YES
YES
Note
The number 1 is not representable as the sum of two cubes.
The number 2 is represented as 1^3+1^3.
The number 4 is not representable as the sum of two cubes.
The number 34 is not representable as the sum of two cubes.
The number 35 is represented as 2^3+3^3.
The number 16 is represented as 2^3+2^3.
The number 703657519796 is represented as 5779^3+7993^3.
Submitted Solution:
```
import sys
input = sys.stdin.readline
import bisect
C=[i**3 for i in range(1,10**4+1)]
t=int(input())
for tests in range(t):
x=int(input())
flag=0
for c in C:
if c>x:
break
k=bisect.bisect(C,x-c)
if C[k-1]==x-c:
print("YES")
flag=1
break
if flag==0:
print("NO")
``` | instruction | 0 | 89,538 | 5 | 179,076 |
Yes | output | 1 | 89,538 | 5 | 179,077 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer x. Check whether the number x is representable as the sum of the cubes of two positive integers.
Formally, you need to check if there are two integers a and b (1 ≤ a, b) such that a^3+b^3=x.
For example, if x = 35, then the numbers a=2 and b=3 are suitable (2^3+3^3=8+27=35). If x=4, then no pair of numbers a and b is suitable.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case contains one integer x (1 ≤ x ≤ 10^{12}).
Please note, that the input for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language.
Output
For each test case, output on a separate line:
* "YES" if x is representable as the sum of the cubes of two positive integers.
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
7
1
2
4
34
35
16
703657519796
Output
NO
YES
NO
NO
YES
YES
YES
Note
The number 1 is not representable as the sum of two cubes.
The number 2 is represented as 1^3+1^3.
The number 4 is not representable as the sum of two cubes.
The number 34 is not representable as the sum of two cubes.
The number 35 is represented as 2^3+3^3.
The number 16 is represented as 2^3+2^3.
The number 703657519796 is represented as 5779^3+7993^3.
Submitted Solution:
```
import math
def checkCube(x):
try:
if x==0:
return False
croot=round(x**(1/3))
if (croot*croot*croot)==x:
return True
return False
except:
return False
for t in range(int(input())):
n=int(input())
end=math.ceil(n**(1/3))
flag=0
for i in range(1,end+1):
z=math.floor(i**3)
if checkCube(n-z):
flag=1
break
if flag==0:
print("NO")
else:
print("YES")
``` | instruction | 0 | 89,539 | 5 | 179,078 |
Yes | output | 1 | 89,539 | 5 | 179,079 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer x. Check whether the number x is representable as the sum of the cubes of two positive integers.
Formally, you need to check if there are two integers a and b (1 ≤ a, b) such that a^3+b^3=x.
For example, if x = 35, then the numbers a=2 and b=3 are suitable (2^3+3^3=8+27=35). If x=4, then no pair of numbers a and b is suitable.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case contains one integer x (1 ≤ x ≤ 10^{12}).
Please note, that the input for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language.
Output
For each test case, output on a separate line:
* "YES" if x is representable as the sum of the cubes of two positive integers.
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
7
1
2
4
34
35
16
703657519796
Output
NO
YES
NO
NO
YES
YES
YES
Note
The number 1 is not representable as the sum of two cubes.
The number 2 is represented as 1^3+1^3.
The number 4 is not representable as the sum of two cubes.
The number 34 is not representable as the sum of two cubes.
The number 35 is represented as 2^3+3^3.
The number 16 is represented as 2^3+2^3.
The number 703657519796 is represented as 5779^3+7993^3.
Submitted Solution:
```
r = int(input())
l=[]
for i in range(r):
q =int(input())
l.append(q)
def is_perfect_cube(n):
c = int(n**(1/3.))
return (c**3 == n) or ((c+1)**3 == n)
for n in l:
a='NO'
if n==1:
print("NO")
continue
for i in range(1,int((((n)**(1/3))+1))):
if is_perfect_cube(n-(i**3))**(1/3):
a='YES'
break
print(a)
``` | instruction | 0 | 89,540 | 5 | 179,080 |
No | output | 1 | 89,540 | 5 | 179,081 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer x. Check whether the number x is representable as the sum of the cubes of two positive integers.
Formally, you need to check if there are two integers a and b (1 ≤ a, b) such that a^3+b^3=x.
For example, if x = 35, then the numbers a=2 and b=3 are suitable (2^3+3^3=8+27=35). If x=4, then no pair of numbers a and b is suitable.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case contains one integer x (1 ≤ x ≤ 10^{12}).
Please note, that the input for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language.
Output
For each test case, output on a separate line:
* "YES" if x is representable as the sum of the cubes of two positive integers.
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
7
1
2
4
34
35
16
703657519796
Output
NO
YES
NO
NO
YES
YES
YES
Note
The number 1 is not representable as the sum of two cubes.
The number 2 is represented as 1^3+1^3.
The number 4 is not representable as the sum of two cubes.
The number 34 is not representable as the sum of two cubes.
The number 35 is represented as 2^3+3^3.
The number 16 is represented as 2^3+2^3.
The number 703657519796 is represented as 5779^3+7993^3.
Submitted Solution:
```
for _ in range(int(input())):
xxx=int(input())
x=xxx**(1/3)
flag=False
for i in range(1,int(x)):
y=(xxx-i**3)**(1/3)
z=int(y)
if(y-z==0 and z!=0):
flag=True
if(flag==True):
print("YES")
else:
print("NO")
``` | instruction | 0 | 89,541 | 5 | 179,082 |
No | output | 1 | 89,541 | 5 | 179,083 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer x. Check whether the number x is representable as the sum of the cubes of two positive integers.
Formally, you need to check if there are two integers a and b (1 ≤ a, b) such that a^3+b^3=x.
For example, if x = 35, then the numbers a=2 and b=3 are suitable (2^3+3^3=8+27=35). If x=4, then no pair of numbers a and b is suitable.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case contains one integer x (1 ≤ x ≤ 10^{12}).
Please note, that the input for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language.
Output
For each test case, output on a separate line:
* "YES" if x is representable as the sum of the cubes of two positive integers.
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
7
1
2
4
34
35
16
703657519796
Output
NO
YES
NO
NO
YES
YES
YES
Note
The number 1 is not representable as the sum of two cubes.
The number 2 is represented as 1^3+1^3.
The number 4 is not representable as the sum of two cubes.
The number 34 is not representable as the sum of two cubes.
The number 35 is represented as 2^3+3^3.
The number 16 is represented as 2^3+2^3.
The number 703657519796 is represented as 5779^3+7993^3.
Submitted Solution:
```
import sys
data = [int(x.rstrip()) for x in sys.stdin]
del data[0]
def findCubes(num):
if num == 1:
return "NO"
if num > 50000000:
return "YES"
for a in range(round(num)):
for b in range(round(num)):
if a**3 + b**3 == data[i]:
return "YES"
return "NO"
results = []
for i in range(len(data)):
results.append(findCubes(data[i]))
for i in results:
print(i)
``` | instruction | 0 | 89,542 | 5 | 179,084 |
No | output | 1 | 89,542 | 5 | 179,085 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer x. Check whether the number x is representable as the sum of the cubes of two positive integers.
Formally, you need to check if there are two integers a and b (1 ≤ a, b) such that a^3+b^3=x.
For example, if x = 35, then the numbers a=2 and b=3 are suitable (2^3+3^3=8+27=35). If x=4, then no pair of numbers a and b is suitable.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case contains one integer x (1 ≤ x ≤ 10^{12}).
Please note, that the input for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language.
Output
For each test case, output on a separate line:
* "YES" if x is representable as the sum of the cubes of two positive integers.
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
7
1
2
4
34
35
16
703657519796
Output
NO
YES
NO
NO
YES
YES
YES
Note
The number 1 is not representable as the sum of two cubes.
The number 2 is represented as 1^3+1^3.
The number 4 is not representable as the sum of two cubes.
The number 34 is not representable as the sum of two cubes.
The number 35 is represented as 2^3+3^3.
The number 16 is represented as 2^3+2^3.
The number 703657519796 is represented as 5779^3+7993^3.
Submitted Solution:
```
for i in range(int(input())):
x=int(input())
a=0
b=0
solu=False
xx=int(x**(1/3))+1
p=0
for i in range(1, xx):
b = x-i**3
#a= x-i**3
if int((b**(1 / 3))) ** 3 == b and b!=0:
solu=True
break
if solu:
print("YES")
else:
print("NO")
``` | instruction | 0 | 89,543 | 5 | 179,086 |
No | output | 1 | 89,543 | 5 | 179,087 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}.
In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.
Input
The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.
Output
If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.
Examples
Input
1 2 3 4
Output
Impossible
Input
1 2 2 1
Output
0110
Submitted Solution:
```
root = lambda k : int((1 + (1 + 8*k) ** 0.5)/2)
def check(k):
n = root(k)
return n*(n-1)/2 == k
def solve(a00, a01, a10, a11):
s = a00 + a01 + a10 + a11
if not check(a00) or not check(a11) or not check(s):
return None
x, y, z = root(a00), root(a11), root(s)
if a00 == 0 or a11 == 0:
if s == 0:
return '0'
elif a10 == 0 and a01 == 0:
return '0'*z if a00 > 0 else '1'*z
elif a10 + a01 == z -1:
return '1'*a10 + '0' + '1'*a01 if a11 > 0 else '0'*a01 + '1' + '0'*a10
else:
return None
if x + y != z:
return None
if x == 0:
if a00 == 0 and a01 == 0 and a10 == 0:
return '1'*z
else:
return None
t, k = a10//x, a10%x
if z-t-x > 0:
return '1'*t + '0'*(x-k) + '1' + '0'*k + '1'*(z-t-x-1)
else:
return '1'*t + x*'0'
a00, a01, a10, a11 = [int(x) for x in input().split()]
ans = solve(a00, a01, a10, a11)
if ans is None:
print('Impossible')
else:
print(ans)
``` | instruction | 0 | 89,749 | 5 | 179,498 |
Yes | output | 1 | 89,749 | 5 | 179,499 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}.
In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.
Input
The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.
Output
If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.
Examples
Input
1 2 3 4
Output
Impossible
Input
1 2 2 1
Output
0110
Submitted Solution:
```
a00, a01, a10, a11 = map(int, input().split())
numZeros = 0
numOnes = 0
ans = True
for n0 in range(1, 2*a00 + 1):
if n0 * (n0 - 1) == 2 * a00:
numZeros = n0
break
elif n0 * (n0 - 1) > 2 * a00:
ans = False
break;
for n1 in range(1, 2*a11 + 1):
if n1 * (n1 - 1) == 2 * a11:
numOnes = n1
break
elif n1 * (n1 - 1) > 2 * a11:
ans = False
break;
res = []
def generateResult(x,a01, a10, n0, n1):
while n0 > 0 or n1 > 0:
if a01 >= n1 and n1 > 0:
if n0 >= 1:
res.append(0)
a01 = a01 - n1
n0 = n0-1
else:
return
elif a10 >= n0 and n0 > 0:
if n1 >= 1:
res.append(1)
a10 = a10 - n0
n1 = n1-1
else:
return
elif n0 > 0 and n1 > 0:
return
elif 0 < n0 == a01 + a10 + n0 + n1:
for i in range(n0):
res.append(0)
n0 = 0
elif 0 < n1 == a01 + a10 + n0 + n1:
for i in range(n1):
res.append(1)
n1 = 0
else:
return
if a01 > 0 or a10 > 0:
numOnes = max(numOnes, 1)
numZeros = max(numZeros, 1)
if a00 == a01 == a10 == a11 == 0:
print(1)
elif a11 == 0 and a00 == 0 and a10 == 1 and a01 == 0:
print("10")
elif a11 == 0 and a00 == 0 and a01 == 1 and a10 == 0:
print("01")
elif ans:
generateResult(res, a01, a10, numZeros, numOnes)
if len(res) == numZeros + numOnes:
print("".join(map(str, res)))
else:
print("Impossible")
else:
print("Impossible")
``` | instruction | 0 | 89,750 | 5 | 179,500 |
Yes | output | 1 | 89,750 | 5 | 179,501 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}.
In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.
Input
The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.
Output
If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.
Examples
Input
1 2 3 4
Output
Impossible
Input
1 2 2 1
Output
0110
Submitted Solution:
```
a00, a01, a10, a11 = map(int, input().split())
numZeros = 0
numOnes = 0
ans = True
for n0 in range(1, 2*a00 + 1):
if n0 * (n0 - 1) == 2 * a00:
numZeros = n0
break
elif n0 * (n0 - 1) > 2 * a00:
ans = False
break;
for n1 in range(1, 2*a11 + 1):
if n1 * (n1 - 1) == 2 * a11:
numOnes = n1
break
elif n1 * (n1 - 1) > 2 * a11:
ans = False
break;
res = []
def generateResult(x,a01, a10, n0, n1):
while n0 > 0 or n1 > 0:
if a01 >= n1 and n1 > 0:
if n0 >= 1:
res.append(0)
a01 = a01 - n1
n0 = n0-1
else:
return
elif a10 >= n0 and n0 > 0:
if n1 >= 1:
res.append(1)
a10 = a10 - n0
n1 = n1-1
else:
return
elif n0 > 0 and n1 > 0:
return
elif 0 < n0 == a01 + a10 + n0 + n1:
for i in range(n0):
res.append(0)
n0 = 0
elif 0 < n1 == a01 + a10 + n0 + n1:
for i in range(n1):
res.append(1)
n1 = 0
else:
return
if a11 == 0 and a01 > 0:
numOnes = 1
if a00 == 0 and a10 > 0:
numZeros = 1
if a00 == a01 == a10 == a11 == 0:
print(1)
elif a11 == 0 and a00 == 0 and a10 == 1 and a01 == 0:
print("10")
elif a11 == 0 and a00 == 0 and a01 == 1 and a10 == 0:
print("01")
elif ans:
generateResult(res, a01, a10, numZeros, numOnes)
if len(res) == numZeros + numOnes:
print("".join(map(str, res)))
else:
print("Impossible")
else:
print("Impossible")
``` | instruction | 0 | 89,753 | 5 | 179,506 |
No | output | 1 | 89,753 | 5 | 179,507 |
Provide a correct Python 3 solution for this coding contest problem.
You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits "1974".
Constraints
* 0 \leq N_1, N_2, N_3, N_4 \leq 9
* N_1, N_2, N_3 and N_4 are integers.
Input
Input is given from Standard Input in the following format:
N_1 N_2 N_3 N_4
Output
If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits "1974", print `YES`; if they cannot, print `NO`.
Examples
Input
1 7 9 4
Output
YES
Input
1 9 7 4
Output
YES
Input
1 2 9 1
Output
NO
Input
4 9 0 8
Output
NO | instruction | 0 | 89,929 | 5 | 179,858 |
"Correct Solution:
```
l = sorted(list(map(int,input().split())))
if l == [1, 4, 7, 9]:
print('YES')
else:
print('NO')
``` | output | 1 | 89,929 | 5 | 179,859 |
Provide a correct Python 3 solution for this coding contest problem.
You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits "1974".
Constraints
* 0 \leq N_1, N_2, N_3, N_4 \leq 9
* N_1, N_2, N_3 and N_4 are integers.
Input
Input is given from Standard Input in the following format:
N_1 N_2 N_3 N_4
Output
If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits "1974", print `YES`; if they cannot, print `NO`.
Examples
Input
1 7 9 4
Output
YES
Input
1 9 7 4
Output
YES
Input
1 2 9 1
Output
NO
Input
4 9 0 8
Output
NO | instruction | 0 | 89,930 | 5 | 179,860 |
"Correct Solution:
```
print("YES" if [1, 4, 7, 9] == sorted(map(int, input().split())) else "NO")
``` | output | 1 | 89,930 | 5 | 179,861 |
Provide a correct Python 3 solution for this coding contest problem.
You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits "1974".
Constraints
* 0 \leq N_1, N_2, N_3, N_4 \leq 9
* N_1, N_2, N_3 and N_4 are integers.
Input
Input is given from Standard Input in the following format:
N_1 N_2 N_3 N_4
Output
If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits "1974", print `YES`; if they cannot, print `NO`.
Examples
Input
1 7 9 4
Output
YES
Input
1 9 7 4
Output
YES
Input
1 2 9 1
Output
NO
Input
4 9 0 8
Output
NO | instruction | 0 | 89,931 | 5 | 179,862 |
"Correct Solution:
```
s = input()
print("YES" * (s.count("1") * s.count("9") * s.count("7") * s.count("4")) or "NO")
``` | output | 1 | 89,931 | 5 | 179,863 |
Provide a correct Python 3 solution for this coding contest problem.
You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits "1974".
Constraints
* 0 \leq N_1, N_2, N_3, N_4 \leq 9
* N_1, N_2, N_3 and N_4 are integers.
Input
Input is given from Standard Input in the following format:
N_1 N_2 N_3 N_4
Output
If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits "1974", print `YES`; if they cannot, print `NO`.
Examples
Input
1 7 9 4
Output
YES
Input
1 9 7 4
Output
YES
Input
1 2 9 1
Output
NO
Input
4 9 0 8
Output
NO | instruction | 0 | 89,932 | 5 | 179,864 |
"Correct Solution:
```
print("YNEOS"[sorted(input())!=list(" 1479")::2])
``` | output | 1 | 89,932 | 5 | 179,865 |
Provide a correct Python 3 solution for this coding contest problem.
You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits "1974".
Constraints
* 0 \leq N_1, N_2, N_3, N_4 \leq 9
* N_1, N_2, N_3 and N_4 are integers.
Input
Input is given from Standard Input in the following format:
N_1 N_2 N_3 N_4
Output
If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits "1974", print `YES`; if they cannot, print `NO`.
Examples
Input
1 7 9 4
Output
YES
Input
1 9 7 4
Output
YES
Input
1 2 9 1
Output
NO
Input
4 9 0 8
Output
NO | instruction | 0 | 89,933 | 5 | 179,866 |
"Correct Solution:
```
a=list(map(int,input().split()))
a.sort()
b=[1,4,7,9]
if a==b:
print('YES')
else: print('NO')
``` | output | 1 | 89,933 | 5 | 179,867 |
Provide a correct Python 3 solution for this coding contest problem.
You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits "1974".
Constraints
* 0 \leq N_1, N_2, N_3, N_4 \leq 9
* N_1, N_2, N_3 and N_4 are integers.
Input
Input is given from Standard Input in the following format:
N_1 N_2 N_3 N_4
Output
If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits "1974", print `YES`; if they cannot, print `NO`.
Examples
Input
1 7 9 4
Output
YES
Input
1 9 7 4
Output
YES
Input
1 2 9 1
Output
NO
Input
4 9 0 8
Output
NO | instruction | 0 | 89,934 | 5 | 179,868 |
"Correct Solution:
```
N = input().split()
if set(N) == set("1794"):
print("YES")
else:
print("NO")
``` | output | 1 | 89,934 | 5 | 179,869 |
Provide a correct Python 3 solution for this coding contest problem.
You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits "1974".
Constraints
* 0 \leq N_1, N_2, N_3, N_4 \leq 9
* N_1, N_2, N_3 and N_4 are integers.
Input
Input is given from Standard Input in the following format:
N_1 N_2 N_3 N_4
Output
If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits "1974", print `YES`; if they cannot, print `NO`.
Examples
Input
1 7 9 4
Output
YES
Input
1 9 7 4
Output
YES
Input
1 2 9 1
Output
NO
Input
4 9 0 8
Output
NO | instruction | 0 | 89,935 | 5 | 179,870 |
"Correct Solution:
```
a=set(list(map(int,input().split())))
if a=={1,9,7,4}:
print("YES")
else:
print("NO")
``` | output | 1 | 89,935 | 5 | 179,871 |
Provide a correct Python 3 solution for this coding contest problem.
You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits "1974".
Constraints
* 0 \leq N_1, N_2, N_3, N_4 \leq 9
* N_1, N_2, N_3 and N_4 are integers.
Input
Input is given from Standard Input in the following format:
N_1 N_2 N_3 N_4
Output
If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits "1974", print `YES`; if they cannot, print `NO`.
Examples
Input
1 7 9 4
Output
YES
Input
1 9 7 4
Output
YES
Input
1 2 9 1
Output
NO
Input
4 9 0 8
Output
NO | instruction | 0 | 89,936 | 5 | 179,872 |
"Correct Solution:
```
print('YES' if set(input().split())=={'1','9','7','4'} else 'NO')
``` | output | 1 | 89,936 | 5 | 179,873 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given four digits N_1, N_2, N_3 and N_4. Determine if these can be arranged into the sequence of digits "1974".
Constraints
* 0 \leq N_1, N_2, N_3, N_4 \leq 9
* N_1, N_2, N_3 and N_4 are integers.
Input
Input is given from Standard Input in the following format:
N_1 N_2 N_3 N_4
Output
If N_1, N_2, N_3 and N_4 can be arranged into the sequence of digits "1974", print `YES`; if they cannot, print `NO`.
Examples
Input
1 7 9 4
Output
YES
Input
1 9 7 4
Output
YES
Input
1 2 9 1
Output
NO
Input
4 9 0 8
Output
NO
Submitted Solution:
```
print('YES' if set(input().split()) == set(['1', '9', '7', '4']) else 'NO')
``` | instruction | 0 | 89,937 | 5 | 179,874 |
Yes | output | 1 | 89,937 | 5 | 179,875 |
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