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 |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120 | instruction | 0 | 82,482 | 5 | 164,964 |
"Correct Solution:
```
def main():
n = int(input())
for x in range(1, n):
n *= x
print(n)
if __name__ == "__main__":
main()
``` | output | 1 | 82,482 | 5 | 164,965 |
Provide a correct Python 3 solution for this coding contest problem.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120 | instruction | 0 | 82,483 | 5 | 164,966 |
"Correct Solution:
```
user = input()
n = int(user)
kai = 1
for i in range(1, n+1):
kai *= i
print(kai)
``` | output | 1 | 82,483 | 5 | 164,967 |
Provide a correct Python 3 solution for this coding contest problem.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120 | instruction | 0 | 82,484 | 5 | 164,968 |
"Correct Solution:
```
n = int(input())
s = 1
for i in range(1,n+1):
s=s*i
print(s)
``` | output | 1 | 82,484 | 5 | 164,969 |
Provide a correct Python 3 solution for this coding contest problem.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120 | instruction | 0 | 82,485 | 5 | 164,970 |
"Correct Solution:
```
import math
if __name__ == '__main__':
n = int(input())
print(math.factorial(n))
``` | output | 1 | 82,485 | 5 | 164,971 |
Provide a correct Python 3 solution for this coding contest problem.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120 | instruction | 0 | 82,486 | 5 | 164,972 |
"Correct Solution:
```
s = int(input())
k = 1
for i in range(2,s+1):
k *= i
print(k)
``` | output | 1 | 82,486 | 5 | 164,973 |
Provide a correct Python 3 solution for this coding contest problem.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120 | instruction | 0 | 82,487 | 5 | 164,974 |
"Correct Solution:
```
n = int(input())
def f(n):
if n == 0 : return 1
else : return f(n - 1) * n
print(f(n))
``` | output | 1 | 82,487 | 5 | 164,975 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120
Submitted Solution:
```
n = int(input())
factorial = 1
for i in range(2, n + 1):
factorial *= i
print(factorial)
``` | instruction | 0 | 82,488 | 5 | 164,976 |
Yes | output | 1 | 82,488 | 5 | 164,977 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120
Submitted Solution:
```
n = int(input())
ans = 1
while n > 1:
ans *= n
n -= 1
print(ans)
``` | instruction | 0 | 82,489 | 5 | 164,978 |
Yes | output | 1 | 82,489 | 5 | 164,979 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120
Submitted Solution:
```
def fact(n):
if(n==0):
return 1
return n * fact(n-1)
if __name__ == '__main__':
n = int(input())
print(fact(n))
``` | instruction | 0 | 82,490 | 5 | 164,980 |
Yes | output | 1 | 82,490 | 5 | 164,981 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120
Submitted Solution:
```
from math import factorial
if __name__ == '__main__':
# ??????????????\???
num = int(input())
# ??????????¨????
result = factorial(num)
# ???????????¨???
print(result)
``` | instruction | 0 | 82,491 | 5 | 164,982 |
Yes | output | 1 | 82,491 | 5 | 164,983 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120
Submitted Solution:
```
from math import factorial
print(factorial(int(input()))
``` | instruction | 0 | 82,492 | 5 | 164,984 |
No | output | 1 | 82,492 | 5 | 164,985 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120
Submitted Solution:
```
x=input()
def f(n):
if n==0:return 1
return f(n-1)*n
print(f(int(n)))
``` | instruction | 0 | 82,493 | 5 | 164,986 |
No | output | 1 | 82,493 | 5 | 164,987 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120
Submitted Solution:
```
ret = 1
for i in range(2, int(input())):
ret *= i
print(ret)
``` | instruction | 0 | 82,494 | 5 | 164,988 |
No | output | 1 | 82,494 | 5 | 164,989 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and prints the factorial of n. You can assume that n ≤ 20.
Input
An integer n (1 ≤ n ≤ 20) in a line.
Output
Print the factorial of n in a line.
Example
Input
5
Output
120
Submitted Solution:
```
def f(x):return 1if x<2else x*f(x-1)
print(f(int(input())))
``` | instruction | 0 | 82,495 | 5 | 164,990 |
No | output | 1 | 82,495 | 5 | 164,991 |
Provide a correct Python 3 solution for this coding contest problem.
Example
Input
3 3 1 2 4
1 2
2 3
3 1
Output
IMPOSSIBLE | instruction | 0 | 82,520 | 5 | 165,040 |
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
rr = []
def f(n,m,a):
t = [LI() for _ in range(m)]
e = collections.defaultdict(set)
for b,c in t:
e[b].add(c)
sm = max(a)
ed = {}
for i in range(1, n+1):
t = {}
q = set([i])
for j in range(sm):
nq = set()
for c in q:
nq |= e[c]
if (j+1) in a:
t[j+1] = nq
q = nq
ed[i] = t
d = collections.defaultdict(lambda: None)
d[n] = 0
def ff(i):
if not d[i] is None:
return d[i]
d[i] = inf
mr = 0
for n in a:
mi = inf
for ni in ed[i][n]:
t = ff(ni)
if mi > t:
mi = t
if mr < mi:
mr = mi
d[i] = mr + 1
return mr + 1
res = ff(1)
for tt in range(n):
for ti in range(1,n+1):
if (not d[ti] is None) and d[ti] > tt:
d[ti] = None
res = ff(1)
if res >= inf:
return 'IMPOSSIBLE'
return res
while 1:
n,m,a,b,c = LI()
if n == 0:
break
rr.append(f(n,m,[a,b,c]))
break
return '\n'.join(map(str, rr))
print(main())
``` | output | 1 | 82,520 | 5 | 165,041 |
Provide a correct Python 3 solution for this coding contest problem.
Example
Input
3 3 1 2 4
1 2
2 3
3 1
Output
IMPOSSIBLE | instruction | 0 | 82,521 | 5 | 165,042 |
"Correct Solution:
```
from collections import deque
import sys
def solve():
readline = sys.stdin.readline
write = sys.stdout.write
N, M, *V = map(int, readline().split())
G = [[] for i in range(N)]
for i in range(M):
u, v = map(int, readline().split())
G[u-1].append(v-1)
def matmul(A, B):
C = [[0]*N for i in range(N)]
for i in range(N):
for j in range(N):
C[i][j] = +(sum(A[i][k] & B[k][j] for k in range(N)) > 0)
return C
def fast_pow(X, k):
R = [[0]*N for i in range(N)]
for i in range(N):
R[i][i] = 1
while k:
if k & 1:
R = matmul(R, X)
X = matmul(X, X)
k >>= 1
return R
V.sort()
prv = 0
ES = [[0]*N for i in range(N)]
for v in range(N):
for w in G[v]:
ES[v][w] = 1
EE = []
ds = []
rgs = []
for i, k in enumerate(V):
d = [0]*N
rg = [[] for i in range(N)]
ek = fast_pow(ES, k)
EE.append(ek)
for v in range(N):
ts = ek[v]
for w in range(N):
if ts[w]:
d[v] += 1
rg[w].append(v)
ds.append(d)
rgs.append(rg)
D = [0]*N
for i in range(3):
d = ds[i]
for v in range(N):
if d[v]:
D[v] += 1
U = [-1]*N
U[N-1] = 0
que = deque([N-1])
while que:
v = que.popleft()
u = U[v]
for i, rg in enumerate(rgs):
d = ds[i]
for w in rg[v]:
if d[w] == 0:
continue
d[w] = 0
D[w] -= 1
if D[w] == 0:
if U[w] == -1:
U[w] = u+1
que.append(w)
write("%d\n" % U[0] if U[0] != -1 else "IMPOSSIBLE\n")
solve()
``` | output | 1 | 82,521 | 5 | 165,043 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Try guessing the statement from this picture:
<image>
You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.
Input
The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.
Each test case contains one integer d (0 ≤ d ≤ 10^3).
Output
For each test print one line.
If there is an answer for the i-th test, print "Y", and then the numbers a and b.
If there is no answer for the i-th test, print "N".
Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.
Example
Input
7
69
0
1
4
5
999
1000
Output
Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005
Submitted Solution:
```
t = int(input())
itog = []
for _ in range(t):
n = int(input())
if n == 0:
itog.append(['Y', 0.000000, 0.000000])
else:
l = -1
r = n + 1
while l + 1 != r:
mid = (l + r)//2
if mid * (n - mid) >= n:
r = mid
else:
l = mid
for i in range(100):
mid = (l + r)/2
if mid * (n - mid) > n:
r = mid
else:
l = mid
if round(l * (n - l)) == n and round(l + (n - l)) == n:
itog.append(['Y', n - l, l])
else:
itog.append(['N'])
for i in itog:
print(*i)
``` | instruction | 0 | 82,604 | 5 | 165,208 |
Yes | output | 1 | 82,604 | 5 | 165,209 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Try guessing the statement from this picture:
<image>
You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.
Input
The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.
Each test case contains one integer d (0 ≤ d ≤ 10^3).
Output
For each test print one line.
If there is an answer for the i-th test, print "Y", and then the numbers a and b.
If there is no answer for the i-th test, print "N".
Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.
Example
Input
7
69
0
1
4
5
999
1000
Output
Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005
Submitted Solution:
```
import math
t=int(input())
for i in range(t):
k=float(input())
r=k*k-4*k
if k*k-4*k<0:
print("N")
else:
print("Y",end=" ")
l=(k+math.sqrt(r))/2.0
print("%.9f"%(l),end=" ")
print("%.9f"%(k-l))
``` | instruction | 0 | 82,605 | 5 | 165,210 |
Yes | output | 1 | 82,605 | 5 | 165,211 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Try guessing the statement from this picture:
<image>
You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.
Input
The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.
Each test case contains one integer d (0 ≤ d ≤ 10^3).
Output
For each test print one line.
If there is an answer for the i-th test, print "Y", and then the numbers a and b.
If there is no answer for the i-th test, print "N".
Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.
Example
Input
7
69
0
1
4
5
999
1000
Output
Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005
Submitted Solution:
```
t = int(input())
for i in range(t):
x = int(input())
if x == 0 or x >= 4:
d = (x * x - 4 * x) ** 0.5
a = 0.5 * (x - d)
b = 0.5 * (x + d)
print("Y", b, a)
else:
print("N")
``` | instruction | 0 | 82,606 | 5 | 165,212 |
Yes | output | 1 | 82,606 | 5 | 165,213 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Try guessing the statement from this picture:
<image>
You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.
Input
The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.
Each test case contains one integer d (0 ≤ d ≤ 10^3).
Output
For each test print one line.
If there is an answer for the i-th test, print "Y", and then the numbers a and b.
If there is no answer for the i-th test, print "N".
Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.
Example
Input
7
69
0
1
4
5
999
1000
Output
Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005
Submitted Solution:
```
import math
for i in range(int(input())):
d=int(input())
D=d*d-4*d
if D<0:
print('N')
else:
a=(d+math.sqrt(D))/2
b=(d-math.sqrt(D))/2
print('Y','%.10f'%a,'%.10f'%b,sep=' ')
``` | instruction | 0 | 82,607 | 5 | 165,214 |
Yes | output | 1 | 82,607 | 5 | 165,215 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Try guessing the statement from this picture:
<image>
You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.
Input
The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.
Each test case contains one integer d (0 ≤ d ≤ 10^3).
Output
For each test print one line.
If there is an answer for the i-th test, print "Y", and then the numbers a and b.
If there is no answer for the i-th test, print "N".
Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.
Example
Input
7
69
0
1
4
5
999
1000
Output
Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005
Submitted Solution:
```
T = int(input())
for t in range(T):
d = int(input())
if 0 < d < 4:
print('N')
continue
d = float(d)
left, right = 1.0000000, 2.000000
for i in range(100):
mid = (left + right) / 2
if mid * mid - mid * d + d > 0:
left = mid
else:
right = mid
print('Y')
print(left, d - left)
``` | instruction | 0 | 82,608 | 5 | 165,216 |
No | output | 1 | 82,608 | 5 | 165,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Try guessing the statement from this picture:
<image>
You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.
Input
The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.
Each test case contains one integer d (0 ≤ d ≤ 10^3).
Output
For each test print one line.
If there is an answer for the i-th test, print "Y", and then the numbers a and b.
If there is no answer for the i-th test, print "N".
Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.
Example
Input
7
69
0
1
4
5
999
1000
Output
Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005
Submitted Solution:
```
import math
t = int(input())
while t> 0:
d = int(input())
if d*d - 4*d < 0:
print('N')
t-=1
continue
if d!=0:
a = (d + math.sqrt( d*d - 4*d ) ) / 2
b = d / a
else:
a=0
b=0
print('Y %.8f %.8f'%(a,b))
t-=1
``` | instruction | 0 | 82,609 | 5 | 165,218 |
No | output | 1 | 82,609 | 5 | 165,219 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Try guessing the statement from this picture:
<image>
You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.
Input
The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.
Each test case contains one integer d (0 ≤ d ≤ 10^3).
Output
For each test print one line.
If there is an answer for the i-th test, print "Y", and then the numbers a and b.
If there is no answer for the i-th test, print "N".
Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.
Example
Input
7
69
0
1
4
5
999
1000
Output
Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005
Submitted Solution:
```
e = 1e-9
def prob( n ):
if n == 1:
print( "N" )
elif n == 0:
print( "Y 0.000000000 0.000000000")
else:
l = 0
r = n
while r - l > e:
a = ( r + l ) / 2
b = n - a
if a * b < n:
l = ( r + l ) / 2
else:
r = ( r + l ) / 2
print( "Y {:.9f} {:.9f}".format( l, n - l ) )
t = int( input() )
for i in range( t ):
prob( int( input() ) )
``` | instruction | 0 | 82,610 | 5 | 165,220 |
No | output | 1 | 82,610 | 5 | 165,221 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Try guessing the statement from this picture:
<image>
You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.
Input
The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.
Each test case contains one integer d (0 ≤ d ≤ 10^3).
Output
For each test print one line.
If there is an answer for the i-th test, print "Y", and then the numbers a and b.
If there is no answer for the i-th test, print "N".
Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.
Example
Input
7
69
0
1
4
5
999
1000
Output
Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005
Submitted Solution:
```
T = int(input())
for _ in range(T):
d = int(input())
if d==0:
print("Y 0.000000000 0.000000000")
continue
l = 0.0
h = d
EPS = 0.0000001
b = True
while h-l>EPS and b:
m = (l+h)/2
if abs(d-(m+(d/m)))<EPS and abs((m*(d/m))-(m+(d/m)))<EPS:
print('Y {0} {1}'.format(m,(d-m)))
b = not b
elif (m+(d/m))<d:
l = m
else:
h = m
if b:
print("N")
``` | instruction | 0 | 82,611 | 5 | 165,222 |
No | output | 1 | 82,611 | 5 | 165,223 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
To become the king of Codeforces, Kuroni has to solve the following problem.
He is given n numbers a_1, a_2, ..., a_n. Help Kuroni to calculate ∏_{1≤ i<j≤ n} |a_i - a_j|. As result can be very big, output it modulo m.
If you are not familiar with short notation, ∏_{1≤ i<j≤ n} |a_i - a_j| is equal to |a_1 - a_2|⋅|a_1 - a_3|⋅ ... ⋅|a_1 - a_n|⋅|a_2 - a_3|⋅|a_2 - a_4|⋅ ... ⋅|a_2 - a_n| ⋅ ... ⋅ |a_{n-1} - a_n|. In other words, this is the product of |a_i - a_j| for all 1≤ i < j ≤ n.
Input
The first line contains two integers n, m (2≤ n ≤ 2⋅ 10^5, 1≤ m ≤ 1000) — number of numbers and modulo.
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Output the single number — ∏_{1≤ i<j≤ n} |a_i - a_j| mod m.
Examples
Input
2 10
8 5
Output
3
Input
3 12
1 4 5
Output
0
Input
3 7
1 4 9
Output
1
Note
In the first sample, |8 - 5| = 3 ≡ 3 mod 10.
In the second sample, |1 - 4|⋅|1 - 5|⋅|4 - 5| = 3⋅ 4 ⋅ 1 = 12 ≡ 0 mod 12.
In the third sample, |1 - 4|⋅|1 - 9|⋅|4 - 9| = 3 ⋅ 8 ⋅ 5 = 120 ≡ 1 mod 7.
Submitted Solution:
```
n,m = map(int,input().split())
a = list(map(int,input().split()))
ans=1
if n > m:
print('0')
else:
for i in range(n):
for j in range(i+1,n):
ans*=abs(a[i]-a[j])
ans%=m
print(ans)
``` | instruction | 0 | 82,733 | 5 | 165,466 |
Yes | output | 1 | 82,733 | 5 | 165,467 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
To become the king of Codeforces, Kuroni has to solve the following problem.
He is given n numbers a_1, a_2, ..., a_n. Help Kuroni to calculate ∏_{1≤ i<j≤ n} |a_i - a_j|. As result can be very big, output it modulo m.
If you are not familiar with short notation, ∏_{1≤ i<j≤ n} |a_i - a_j| is equal to |a_1 - a_2|⋅|a_1 - a_3|⋅ ... ⋅|a_1 - a_n|⋅|a_2 - a_3|⋅|a_2 - a_4|⋅ ... ⋅|a_2 - a_n| ⋅ ... ⋅ |a_{n-1} - a_n|. In other words, this is the product of |a_i - a_j| for all 1≤ i < j ≤ n.
Input
The first line contains two integers n, m (2≤ n ≤ 2⋅ 10^5, 1≤ m ≤ 1000) — number of numbers and modulo.
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Output the single number — ∏_{1≤ i<j≤ n} |a_i - a_j| mod m.
Examples
Input
2 10
8 5
Output
3
Input
3 12
1 4 5
Output
0
Input
3 7
1 4 9
Output
1
Note
In the first sample, |8 - 5| = 3 ≡ 3 mod 10.
In the second sample, |1 - 4|⋅|1 - 5|⋅|4 - 5| = 3⋅ 4 ⋅ 1 = 12 ≡ 0 mod 12.
In the third sample, |1 - 4|⋅|1 - 9|⋅|4 - 9| = 3 ⋅ 8 ⋅ 5 = 120 ≡ 1 mod 7.
Submitted Solution:
```
def main():
n,m =list(map(int,input().split()))
a =list(map(int,input().split()))
s=1
if(n>m):
s=0
else:
for i in range(n):
for j in range(i+1,n):
if(s!=0):
s=(s*abs(a[i]-a[j]))%m
else:
break
print(s)
main()
``` | instruction | 0 | 82,734 | 5 | 165,468 |
Yes | output | 1 | 82,734 | 5 | 165,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
To become the king of Codeforces, Kuroni has to solve the following problem.
He is given n numbers a_1, a_2, ..., a_n. Help Kuroni to calculate ∏_{1≤ i<j≤ n} |a_i - a_j|. As result can be very big, output it modulo m.
If you are not familiar with short notation, ∏_{1≤ i<j≤ n} |a_i - a_j| is equal to |a_1 - a_2|⋅|a_1 - a_3|⋅ ... ⋅|a_1 - a_n|⋅|a_2 - a_3|⋅|a_2 - a_4|⋅ ... ⋅|a_2 - a_n| ⋅ ... ⋅ |a_{n-1} - a_n|. In other words, this is the product of |a_i - a_j| for all 1≤ i < j ≤ n.
Input
The first line contains two integers n, m (2≤ n ≤ 2⋅ 10^5, 1≤ m ≤ 1000) — number of numbers and modulo.
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Output the single number — ∏_{1≤ i<j≤ n} |a_i - a_j| mod m.
Examples
Input
2 10
8 5
Output
3
Input
3 12
1 4 5
Output
0
Input
3 7
1 4 9
Output
1
Note
In the first sample, |8 - 5| = 3 ≡ 3 mod 10.
In the second sample, |1 - 4|⋅|1 - 5|⋅|4 - 5| = 3⋅ 4 ⋅ 1 = 12 ≡ 0 mod 12.
In the third sample, |1 - 4|⋅|1 - 9|⋅|4 - 9| = 3 ⋅ 8 ⋅ 5 = 120 ≡ 1 mod 7.
Submitted Solution:
```
# problem 1305 c
N,mod=map(int,input().split())
a=list(map(int,input().split()))
if N>=mod:
print(0)
elif N<mod:
ans=1
for i in range(N):
for j in range(i+1,N):
ans*=abs(a[j]-a[i])
ans%=mod
print(ans)
``` | instruction | 0 | 82,737 | 5 | 165,474 |
No | output | 1 | 82,737 | 5 | 165,475 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
To become the king of Codeforces, Kuroni has to solve the following problem.
He is given n numbers a_1, a_2, ..., a_n. Help Kuroni to calculate ∏_{1≤ i<j≤ n} |a_i - a_j|. As result can be very big, output it modulo m.
If you are not familiar with short notation, ∏_{1≤ i<j≤ n} |a_i - a_j| is equal to |a_1 - a_2|⋅|a_1 - a_3|⋅ ... ⋅|a_1 - a_n|⋅|a_2 - a_3|⋅|a_2 - a_4|⋅ ... ⋅|a_2 - a_n| ⋅ ... ⋅ |a_{n-1} - a_n|. In other words, this is the product of |a_i - a_j| for all 1≤ i < j ≤ n.
Input
The first line contains two integers n, m (2≤ n ≤ 2⋅ 10^5, 1≤ m ≤ 1000) — number of numbers and modulo.
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Output the single number — ∏_{1≤ i<j≤ n} |a_i - a_j| mod m.
Examples
Input
2 10
8 5
Output
3
Input
3 12
1 4 5
Output
0
Input
3 7
1 4 9
Output
1
Note
In the first sample, |8 - 5| = 3 ≡ 3 mod 10.
In the second sample, |1 - 4|⋅|1 - 5|⋅|4 - 5| = 3⋅ 4 ⋅ 1 = 12 ≡ 0 mod 12.
In the third sample, |1 - 4|⋅|1 - 9|⋅|4 - 9| = 3 ⋅ 8 ⋅ 5 = 120 ≡ 1 mod 7.
Submitted Solution:
```
n,m=map(int,input().split())
a=[int(i) for i in input().split()]
p=1
for i in range(n-1):
for j in range(i+1,n):
p*=a[i]-a[j]
print(p%m)
``` | instruction | 0 | 82,739 | 5 | 165,478 |
No | output | 1 | 82,739 | 5 | 165,479 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes.
Input
The single line of the input contains a pair of integers m, s (1 ≤ m ≤ 100, 0 ≤ s ≤ 900) — the length and the sum of the digits of the required numbers.
Output
In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers "-1 -1" (without the quotes).
Examples
Input
2 15
Output
69 96
Input
3 0
Output
-1 -1
Submitted Solution:
```
n,s=map(int,input().split())
flag=False
smallest=[]
longest=[]
i,p=n,s
while i>0:
if p==0:
longest.append('0')
else:
longest.append(str(min(p,9)))
p-=int(longest[len(longest)-1])
i-=1
if n>1 and s==0:
#print("pointed at line 14")
flag=True
if p>0:
#print("pointed at line 17")
flag=True
i,p=n,s
p-=1
while i>1:
smallest.append(str(min(p,9)))
p-=int(smallest[len(smallest)-1])
i-=1
smallest.append(str(1+p))
p-=int(smallest[len(smallest)-1])
if p>0:
#print("pointed at line 30")
flag=True
if not flag:
print(''.join(smallest[::-1]),''.join(longest))
else:
print(-1,-1)
``` | instruction | 0 | 82,934 | 5 | 165,868 |
Yes | output | 1 | 82,934 | 5 | 165,869 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes.
Input
The single line of the input contains a pair of integers m, s (1 ≤ m ≤ 100, 0 ≤ s ≤ 900) — the length and the sum of the digits of the required numbers.
Output
In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers "-1 -1" (without the quotes).
Examples
Input
2 15
Output
69 96
Input
3 0
Output
-1 -1
Submitted Solution:
```
m, s = list(map(int, input().split()))
def find_min(m, s):
result = []
s -= 1
for k in range(m):
if s >= 9:
result.append(9)
s -= 9
else:
result.append(s % 9)
s -= s % 9
result[-1] += 1
return "".join(list(map(str, reversed(result))))
def find_max(m, s):
result = []
for k in range(m):
if s >= 9:
result.append(9)
s -= 9
else:
result.append(s % 9)
s -= s % 9
return "".join(list(map(str, result)))
if m * 9 < s:
print(-1, -1)
else:
if s == 0:
if m == 1:
minimal, maximal = 0, 0
else:
minimal, maximal = -1, -1
else:
minimal = find_min(m, s)
maximal = find_max(m, s)
print(minimal, maximal)
``` | instruction | 0 | 82,935 | 5 | 165,870 |
Yes | output | 1 | 82,935 | 5 | 165,871 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes.
Input
The single line of the input contains a pair of integers m, s (1 ≤ m ≤ 100, 0 ≤ s ≤ 900) — the length and the sum of the digits of the required numbers.
Output
In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers "-1 -1" (without the quotes).
Examples
Input
2 15
Output
69 96
Input
3 0
Output
-1 -1
Submitted Solution:
```
m, s = map(int, input().split())
if s == 0 and m == 1:
print(0, 0)
elif s == 0:
print(-1, -1)
elif m * 9 < s:
print(-1, -1)
else:
nums = []
while len(nums) < m:
nums.append(min(9, s))
s = s - min(9, s)
max_nums = [str(i) for i in nums]
max_num = ''.join(max_nums)
min_nums = nums[::-1]
if min_nums[0] == 0:
for j, num in enumerate(min_nums):
if num != 0:
min_nums[j] = num - 1
break
min_nums[0] = 1
min_nums = [str(i) for i in min_nums]
min_num = ''.join(min_nums)
print(min_num, max_num)
``` | instruction | 0 | 82,936 | 5 | 165,872 |
Yes | output | 1 | 82,936 | 5 | 165,873 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes.
Input
The single line of the input contains a pair of integers m, s (1 ≤ m ≤ 100, 0 ≤ s ≤ 900) — the length and the sum of the digits of the required numbers.
Output
In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers "-1 -1" (without the quotes).
Examples
Input
2 15
Output
69 96
Input
3 0
Output
-1 -1
Submitted Solution:
```
#from collections import Counter,defaultdict,deque
#alph = 'abcdefghijklmnopqrstuvwxyz'
#from math import factorial as fact
#import math
t = 1#int(input())
#total=0
#n = int(input())
#n,m,k = [int(x) for x in input().split()]
for i in range(t):
m,s = [int(x) for x in input().split()]
nines = s//9
if m==1 and s==0:
print(0,0)
continue
if nines>m or s==0 or m*9<s:
print('-1 -1')
continue
if s<10:
if m==1:
print(s,s)
else:
mn = '1'+'0'*(m-2)+str(s-1)
mx = str(s)+'0'*(m-1)
print(mn,mx)
continue
if m*9==s:
print('9'*m,'9'*m)
continue
rem = s%9
if nines+1 == m and rem!=0:
mn = str(rem)+'9'*nines
else:
if rem ==0:
mn = '1'+ '0'*(m-nines-1) + '8'+ '9'*(nines-1)
else:
mn = '1'+ '0'*(m-nines-2) + str(rem-1)+ '9'*nines
mx = (nines*'9'+str(rem)+'0'*101)[:m]
print(mn,mx)
``` | instruction | 0 | 82,937 | 5 | 165,874 |
Yes | output | 1 | 82,937 | 5 | 165,875 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes.
Input
The single line of the input contains a pair of integers m, s (1 ≤ m ≤ 100, 0 ≤ s ≤ 900) — the length and the sum of the digits of the required numbers.
Output
In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers "-1 -1" (without the quotes).
Examples
Input
2 15
Output
69 96
Input
3 0
Output
-1 -1
Submitted Solution:
```
import sys
def rs(): return sys.stdin.readline().rstrip()
def ri(): return int(sys.stdin.readline())
def ria(): return list(map(int, sys.stdin.readline().split()))
def ws(s): sys.stdout.write(s + '\n')
def wi(n): sys.stdout.write(str(n) + '\n')
def wia(a): sys.stdout.write(' '.join([str(x) for x in a]) + '\n')
import math
from collections import defaultdict
n,s=ria()
if s==0:print(-1,-1)
else:
m=''
k=s//9
m=m+'9'*k
s=s%9
m+=str(s)
l=len(m)
if l>n:
print(-1,-1)
else:
m=m+'0'*(n-l)
print(int(m[::-1]),m)
``` | instruction | 0 | 82,938 | 5 | 165,876 |
No | output | 1 | 82,938 | 5 | 165,877 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes.
Input
The single line of the input contains a pair of integers m, s (1 ≤ m ≤ 100, 0 ≤ s ≤ 900) — the length and the sum of the digits of the required numbers.
Output
In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers "-1 -1" (without the quotes).
Examples
Input
2 15
Output
69 96
Input
3 0
Output
-1 -1
Submitted Solution:
```
"""
Author : co_devil Chirag Garg
Institute : JIIT
"""
from __future__ import division, print_function
import itertools, os, sys, threading
from collections import deque, Counter, OrderedDict, defaultdict
import heapq
from math import ceil,floor,log,sqrt,factorial,pow,pi
# from bisect import bisect_left,bisect_right
# from decimal import *,threading
"""from io import BytesIO, IOBase
if sys.version_info[0] < 3:
from __builtin__ import xrange as range
from future_builtins import ascii, filter, hex, map, oct, zip
else:
from builtins import str as __str__
str = lambda x=b'': x if type(x) is bytes else __str__(x).encode()
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._buffer = BytesIO()
self._fd = file.fileno()
self._writable = 'x' in file.mode or 'r' not in file.mode
self.write = self._buffer.write if self._writable else None
def read(self):
return self._buffer.read() if self._buffer.tell() else os.read(self._fd, os.fstat(self._fd).st_size)
def readline(self):
while self.newlines == 0:
b, ptr = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)), self._buffer.tell()
self._buffer.seek(0, 2), self._buffer.write(b), self._buffer.seek(ptr)
self.newlines += b.count(b'\n') + (not b)
self.newlines -= 1
return self._buffer.readline()
def flush(self):
if self._writable:
os.write(self._fd, self._buffer.getvalue())
self._buffer.truncate(0), self._buffer.seek(0)
sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
input = lambda: sys.stdin.readline().rstrip(b'\r\n')
def print(*args, **kwargs):
sep, file = kwargs.pop('sep', b' '), kwargs.pop('file', sys.stdout)
at_start = True
for x in args:
if not at_start:
file.write(sep)
file.write(str(x))
at_start = False
file.write(kwargs.pop('end', b'\n'))
if kwargs.pop('flush', False):
file.flush()
"""
def ii(): return int(input())
def si(): return str(input())
def mi(): return map(int,input().split())
def li(): return list(mi())
abc = 'abcdefghijklmnopqrstuvwxyz'
abd = {'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12,
'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24,
'z': 25}
mod = 1000000007
dx, dy = [-1, 1, 0, 0], [0, 0, 1, -1]
def getKey(item): return item[0]
def sort2(l): return sorted(l, key=getKey)
def d2(n, m, num): return [[num for x in range(m)] for y in range(n)]
def isPowerOfTwo(x): return (x and (not (x & (x - 1))))
def decimalToBinary(n): return bin(n).replace("0b", "")
def ntl(n): return [int(i) for i in str(n)]
def powerMod(x, y, p):
res = 1
x %= p
while y > 0:
if y & 1:
res = (res * x) % p
y = y >> 1
x = (x * x) % p
return res
def gcd(x, y):
while y:
x, y = y, x % y
return x
# For getting input from input.txt file
# sys.stdin = open('input.txt', 'r')
# Printing the Output to output.txt file
# sys.stdout = open('output.txt', 'w')
graph = defaultdict(list)
visited = [0] * 1000000
col = [-1] * 1000000
def dfs(v, c):
if visited[v]:
if col[v] != c:
print('-1')
exit()
return
col[v] = c
visited[v] = 1
for i in graph[v]:
dfs(i, c ^ 1)
def bfs(d,v):
q=[]
q.append(v)
visited[v]=1
while len(q)!=0:
x=q[0]
q.pop(0)
for i in d[x]:
if visited[i]!=1:
visited[i]=1
q.append(i)
print(x)
print(l)
def make_graph(e):
d={}
for i in range(e):
x,y=mi()
if x not in d.keys():
d[x]=[y]
else:
d[x].append(y)
if y not in d.keys():
d[y] = [x]
else:
d[y].append(x)
return d
def gr2(n):
d={}
for i in range(n):
x,y=mi()
if x not in d.keys():
d[x]=[y]
else:
d[x].append(y)
return d
def connected_components(graph):
seen = set()
def dfs(v):
vs = set([v])
component=[]
while vs:
v = vs.pop()
seen.add(v)
vs |= set(graph[v]) - seen
component.append(v)
return component
ans=[]
for v in graph:
if v not in seen:
d=dfs(v)
ans.append(d)
return ans
m,s=mi()
x=''
while s>0:
if s>=9:
z=9
else:
z=s
x+=str(z)
s-=z
if len(x)==m:
y=str(int(x[::-1]))
x=str(int(x))
if len(x)==m and len(y)==m:
print(y,x)
elif len(x)==m and len(y)!=m:
print(x,x)
elif len(x)!=m and len(y)==m:
print(y,y)
else:
print(-1,-1)
elif len(x)>0:
z=m-len(x)
x=list(map(int,list(x)))
for i in range(z):
x[-1]-=1
x.append(1)
x=''.join(map(str,x))
y=str(int(x[::-1]))
x=str(int(x))
if len(x)==m and len(y)==m:
print(y,x)
elif len(x)==m and len(y)!=m:
print(x,x)
elif len(x)!=m and len(y)==m:
print(y,y)
else:
print(-1,-1)
else:
print(-1,-1)
``` | instruction | 0 | 82,939 | 5 | 165,878 |
No | output | 1 | 82,939 | 5 | 165,879 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes.
Input
The single line of the input contains a pair of integers m, s (1 ≤ m ≤ 100, 0 ≤ s ≤ 900) — the length and the sum of the digits of the required numbers.
Output
In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers "-1 -1" (without the quotes).
Examples
Input
2 15
Output
69 96
Input
3 0
Output
-1 -1
Submitted Solution:
```
a=input()
m,s=a.split()
m=int(m)
s=int(s)
small=[0]*m
big=[0]*m
t=s//9
if s>9*m or s==0:
print('-1 -1')
else:
if s>9:
for i in range(t):
small[m-1-i]=9
if small[1]==9 and small[0]==0:
small[0]=s%9
elif small[1]==0:
small[0]=1
small[m-1-t]=s%9-1
elif m>1:
small[0]=1
small[m-1]=s-1
else:
small[0]=s
if s<=9*m and s!=0:
if s>9:
for i in range(t):
big[i]=9
big[t]=s%9
else:
big[0]=s
smallStr=''
bigStr=''
for i in range(m):
smallStr+=str(small[i])
bigStr+=str(big[i])
print(smallStr+' '+bigStr)
``` | instruction | 0 | 82,940 | 5 | 165,880 |
No | output | 1 | 82,940 | 5 | 165,881 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes.
Input
The single line of the input contains a pair of integers m, s (1 ≤ m ≤ 100, 0 ≤ s ≤ 900) — the length and the sum of the digits of the required numbers.
Output
In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers "-1 -1" (without the quotes).
Examples
Input
2 15
Output
69 96
Input
3 0
Output
-1 -1
Submitted Solution:
```
def maximal(m,s):
if s > 9*m:
return '*'
if s == 0:
if m == 1:
return str(0)
else:
return '*'
if m==1:
if s in range(0,10):
return str(s)
else:
return '*'
else:
if s < 10:
return str(s*10**(m-1))
else:
return str(9) + maximal(m-1,s-9)
'''
def minimal(m,s):
temp_out = maximal(m,s)
if '*' in list(temp_out):
return '*'
else:
if temp_out == '0':
return str(0)
else:
index_ = 1
while(temp_out[-index_] == str('0')):
index_ +=1
if index_ > 1:
return temp_out[-index_] + ''.join([str(0) for i in range(1,index_)]) + temp_out[:-index_][::-1]
else:
return temp_out[::-1]
'''
def minimal(m,s,m_start):
if s > 9*m:
return '*'
if s == 0:
if m == 1:
return str(0)
else:
return '*'
if m == 1:
if s in range(0,10):
return str(s)
else:
if m == m_start:
index_list = [s - i <= 9*(m-1) for i in range(1,10)]
if True in index_list:
index_ = index_list.index(True) + 1
return str(index_) + minimal(m-1,s-index_,m_start)
else:
return '*'
else:
index_list = [s - i <= 9*(m-1) for i in range(10)]
if True in index_list:
index_ = index_list.index(True)
return str(index_) + minimal(m-1,s-index_,m_start)
else:
return '*'
input_ = list(map(int, input().split()))
m, s = input_[0], input_[1]
out_1, out_2 = maximal(m,s), minimal(m,s,m)
if '*' in list(out_1) or '*' in list(out_2):
print (str(-1) + ' ' + str(-1))
else:
print(out_2, end = ' ')
print(out_1)
``` | instruction | 0 | 82,941 | 5 | 165,882 |
No | output | 1 | 82,941 | 5 | 165,883 |
Provide a correct Python 3 solution for this coding contest problem.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO | instruction | 0 | 83,254 | 5 | 166,508 |
"Correct Solution:
```
a, b, c = map(int, input().split())
for i in range(a):
if (b*i+c)%a == 0:
print('YES')
exit()
print('NO')
``` | output | 1 | 83,254 | 5 | 166,509 |
Provide a correct Python 3 solution for this coding contest problem.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO | instruction | 0 | 83,255 | 5 | 166,510 |
"Correct Solution:
```
A, B, C = map(int,input().split())
ans = "NO"
for i in range(1,B+1):
if A*i%B == C:
ans = "YES"
print(ans)
``` | output | 1 | 83,255 | 5 | 166,511 |
Provide a correct Python 3 solution for this coding contest problem.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO | instruction | 0 | 83,256 | 5 | 166,512 |
"Correct Solution:
```
a, b, c = map(int, input().split())
print('YES' if any((a*i)%b == c for i in range(1,b+1)) else 'NO')
``` | output | 1 | 83,256 | 5 | 166,513 |
Provide a correct Python 3 solution for this coding contest problem.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO | instruction | 0 | 83,257 | 5 | 166,514 |
"Correct Solution:
```
A,B,C = map(int,input().split())
print('YES' if any([1 if (A*i)%B == C else 0 for i in range(1,B+1)]) else 'NO')
``` | output | 1 | 83,257 | 5 | 166,515 |
Provide a correct Python 3 solution for this coding contest problem.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO | instruction | 0 | 83,258 | 5 | 166,516 |
"Correct Solution:
```
A, B, C = map(int, input().split())
r = [(A * k) % B for k in range(B)]
print(["NO", "YES"][C in r])
``` | output | 1 | 83,258 | 5 | 166,517 |
Provide a correct Python 3 solution for this coding contest problem.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO | instruction | 0 | 83,259 | 5 | 166,518 |
"Correct Solution:
```
A, B, C = list(map(int, input().split()))
if A>B: A,B=B,A
while A:
A,B = B%A, A
print('YES' if C%B==0 else 'NO')
``` | output | 1 | 83,259 | 5 | 166,519 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO
Submitted Solution:
```
A,B,C=map(int,input().split())
for i in range(B):
if(i+1)*A%B==C:print('YES');exit()
print('NO')
``` | instruction | 0 | 83,260 | 5 | 166,520 |
Yes | output | 1 | 83,260 | 5 | 166,521 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO
Submitted Solution:
```
A,B,C = map(int,input().split())
for i in range(1,B+1):
if(A*i%B == C):
print("YES")
exit()
print("NO")
``` | instruction | 0 | 83,261 | 5 | 166,522 |
Yes | output | 1 | 83,261 | 5 | 166,523 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO
Submitted Solution:
```
a,b,c = map(int,input().split())
ans = 'NO'
for i in range(b):
if a*(i+1)%b==c:
ans = 'YES'
print(ans)
``` | instruction | 0 | 83,262 | 5 | 166,524 |
Yes | output | 1 | 83,262 | 5 | 166,525 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO
Submitted Solution:
```
a,b,c=map(int,input().split())
print('YNEOS'[c not in [a*i%b for i in range(b)]::2])
``` | instruction | 0 | 83,263 | 5 | 166,526 |
Yes | output | 1 | 83,263 | 5 | 166,527 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO
Submitted Solution:
```
ABC = input().split()
A=ABC[0]
B=ABC[1]
C=ABC[2]
count = 50
N=0
for index in range(count+1):
if (A*N-C)%B ==0:
print("Yes")
elif index == (count):
print("NO")
else:
N+=1
``` | instruction | 0 | 83,264 | 5 | 166,528 |
No | output | 1 | 83,264 | 5 | 166,529 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO
Submitted Solution:
```
a, b, c = map(int, input().split())
ans = 'NO'
total = 0
if a < b and c%a == 0:
ans = 'YES'
else:
for i in range(1, 100000):
total += a*i
if total%b == c:
ans = 'YES'
break
print(ans)
``` | instruction | 0 | 83,266 | 5 | 166,532 |
No | output | 1 | 83,266 | 5 | 166,533 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We ask you to select some number of positive integers, and calculate the sum of them.
It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.
Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.
If the objective is achievable, print `YES`. Otherwise, print `NO`.
Constraints
* 1 ≤ A ≤ 100
* 1 ≤ B ≤ 100
* 0 ≤ C < B
Input
Input is given from Standard Input in the following format:
A B C
Output
Print `YES` or `NO`.
Examples
Input
7 5 1
Output
YES
Input
2 2 1
Output
NO
Input
1 100 97
Output
YES
Input
40 98 58
Output
YES
Input
77 42 36
Output
NO
Submitted Solution:
```
a,b,c=map(int,input().split())
moda=a%k
keep=0
for i in range(0,10**8):
if (moda*i)%k==c:
keep=1
print("YES")
break
if keep==0:
print("No")
``` | instruction | 0 | 83,267 | 5 | 166,534 |
No | output | 1 | 83,267 | 5 | 166,535 |
Provide a correct Python 3 solution for this coding contest problem.
Write a program which prints multiplication tables in the following format:
1x1=1
1x2=2
.
.
9x8=72
9x9=81
Input
No input.
Output
1x1=1
1x2=2
.
.
9x8=72
9x9=81
Example
Input
Output | instruction | 0 | 83,278 | 5 | 166,556 |
"Correct Solution:
```
numbers = list(range(1, 10))
for i in numbers:
for j in numbers:
print("{}x{}={}".format(i, j, i*j))
``` | output | 1 | 83,278 | 5 | 166,557 |
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