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.
Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.
Iroha is looking for X,Y,Z-Haiku (defined below) in integer sequences.
Consider all integer sequences of length N whose elements are between 1 and 10, inclusive. Out of those 10^N sequences, how many contain an X,Y,Z-Haiku?
Here, an integer sequence a_0, a_1, ..., a_{N-1} is said to contain an X,Y,Z-Haiku if and only if there exist four indices x, y, z, w (0 ≦ x < y < z < w ≦ N) such that all of the following are satisfied:
* a_x + a_{x+1} + ... + a_{y-1} = X
* a_y + a_{y+1} + ... + a_{z-1} = Y
* a_z + a_{z+1} + ... + a_{w-1} = Z
Since the answer can be extremely large, print the number modulo 10^9+7.
Constraints
* 3 ≦ N ≦ 40
* 1 ≦ X ≦ 5
* 1 ≦ Y ≦ 7
* 1 ≦ Z ≦ 5
Input
The input is given from Standard Input in the following format:
N X Y Z
Output
Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.
Examples
Input
3 5 7 5
Output
1
Input
4 5 7 5
Output
34
Input
37 4 2 3
Output
863912418
Input
40 5 7 5
Output
562805100
Submitted Solution:
```
#!usr/bin/env python3
from collections import defaultdict
from collections import deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS():return list(map(list, sys.stdin.readline().split()))
def S(): return list(sys.stdin.readline())[:-1]
def IR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = I()
return l
def LIR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = LI()
return l
def SR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = S()
return l
def LSR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = SR()
return l
mod = 1000000007
#A
def A():
return
#B
def B():
return
#C
def C():
n,x,y,z = LI()
po2 = [1<<i for i in range(x+y+z+1)]
max = po2[x+y+z]
ng = po2[x+y+z-1]|po2[y+z-1]|po2[z-1]
dp = [[0 for i in range(max)] for i in range(n+1)]
dp[0][0] = 1
mask = max-1
for i in range(n):
for j in range(max):
for k in range(1,11):
t = j<<k|1<<(k-1)
if t&ng != ng:
t &= mask
dp[i+1][t] += dp[i][j]
dp[i+1][t] %= mod
ans = pow(10,n,mod)
for i in range(max):
ans -= dp[n][i]
ans %= mod
print(ans)
#D
def D():
return
#E
def E():
return
#F
def F():
return
#G
def G():
return
#H
def H():
return
#Solve
if __name__ == "__main__":
C()
``` | instruction | 0 | 35,053 | 5 | 70,106 |
Yes | output | 1 | 35,053 | 5 | 70,107 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.
Iroha is looking for X,Y,Z-Haiku (defined below) in integer sequences.
Consider all integer sequences of length N whose elements are between 1 and 10, inclusive. Out of those 10^N sequences, how many contain an X,Y,Z-Haiku?
Here, an integer sequence a_0, a_1, ..., a_{N-1} is said to contain an X,Y,Z-Haiku if and only if there exist four indices x, y, z, w (0 ≦ x < y < z < w ≦ N) such that all of the following are satisfied:
* a_x + a_{x+1} + ... + a_{y-1} = X
* a_y + a_{y+1} + ... + a_{z-1} = Y
* a_z + a_{z+1} + ... + a_{w-1} = Z
Since the answer can be extremely large, print the number modulo 10^9+7.
Constraints
* 3 ≦ N ≦ 40
* 1 ≦ X ≦ 5
* 1 ≦ Y ≦ 7
* 1 ≦ Z ≦ 5
Input
The input is given from Standard Input in the following format:
N X Y Z
Output
Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.
Examples
Input
3 5 7 5
Output
1
Input
4 5 7 5
Output
34
Input
37 4 2 3
Output
863912418
Input
40 5 7 5
Output
562805100
Submitted Solution:
```
MOD = 10 ** 9 + 7
N, X, Y, Z = map(int, input().split())
pow2_XYZ = 2 ** (X + Y + Z)
# flg[hist]: 履歴がhistのとき、XYZを含むかどうか
flg = [False] * pow2_XYZ
mask = ((((1 << X) + 1) << Y) + 1) << (Z - 1)
for hist in range(pow2_XYZ):
if hist & mask == mask:
flg[hist] = True
# h2s[hist]: DPでの遷移先
h2s = [[0] * 10 for i in range(pow2_XYZ)]
for hist in range(pow2_XYZ):
for A in range(1, 11):
h2s[hist][A - 1] = ((hist << A) + (1 << (A-1))) % pow2_XYZ
# dp[i][hist]: 長さiの、履歴がhistである、XYZを含まない数列の数
dp = [[0] * pow2_XYZ for i in range(N + 1)]
dp[0][0] = 1
for i in range(N):
for hist in range(pow2_XYZ):
if dp[i][hist] == 0: continue
for A in range(1, 11):
h2 = h2s[hist][A - 1]
if not flg[h2]:
dp[i + 1][h2] += dp[i][hist]
dp[i + 1] = list(map(lambda x: x % MOD, dp[i + 1]))
num = sum(dp[N]) % MOD
print((10 ** N - num) % MOD)
``` | instruction | 0 | 35,054 | 5 | 70,108 |
Yes | output | 1 | 35,054 | 5 | 70,109 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.
Iroha is looking for X,Y,Z-Haiku (defined below) in integer sequences.
Consider all integer sequences of length N whose elements are between 1 and 10, inclusive. Out of those 10^N sequences, how many contain an X,Y,Z-Haiku?
Here, an integer sequence a_0, a_1, ..., a_{N-1} is said to contain an X,Y,Z-Haiku if and only if there exist four indices x, y, z, w (0 ≦ x < y < z < w ≦ N) such that all of the following are satisfied:
* a_x + a_{x+1} + ... + a_{y-1} = X
* a_y + a_{y+1} + ... + a_{z-1} = Y
* a_z + a_{z+1} + ... + a_{w-1} = Z
Since the answer can be extremely large, print the number modulo 10^9+7.
Constraints
* 3 ≦ N ≦ 40
* 1 ≦ X ≦ 5
* 1 ≦ Y ≦ 7
* 1 ≦ Z ≦ 5
Input
The input is given from Standard Input in the following format:
N X Y Z
Output
Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.
Examples
Input
3 5 7 5
Output
1
Input
4 5 7 5
Output
34
Input
37 4 2 3
Output
863912418
Input
40 5 7 5
Output
562805100
Submitted Solution:
```
# -*- coding: utf-8 -*-
import sys
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10 ** 9)
INF = 10 ** 18
MOD = 10 ** 9 + 7
N, X, Y, Z = MAP()
M = X + Y + Z
# XYZとの一致をチェックするビット列
check = 1<<(X+Y+Z-1) | 1<<(Y+Z-1) | 1<<(Z-1)
dp = list2d(N+1, 1<<(M-1), 0)
# dp[i][S] := i個目まで見て、前の値M-1以下までの集合がSの時の、XYZを含まないものの通り数
dp[0][0] = 1
msk1 = (1<<M) - 1
msk2 = (1<<(M-1)) - 1
for i in range(N):
for S in range(1<<(M-1)):
if not dp[i][S]:
continue
for j in range(10):
# 1ビットずらして1を足してjビットずらしてマスクする
S2 = (S<<1|1)<<j & msk1
# 直前Mビットで使った値がXYZと一致していないか確認する
if not (S2 & check) == check:
dp[i+1][S2&msk2] += dp[i][S]
dp[i+1][S2&msk2] %= MOD
total = pow(10, N, MOD)
cnt = 0
for S in range(1<<(M-1)):
cnt += dp[N][S]
cnt %= MOD
print((total-cnt)%MOD)
``` | instruction | 0 | 35,055 | 5 | 70,110 |
No | output | 1 | 35,055 | 5 | 70,111 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.
Iroha is looking for X,Y,Z-Haiku (defined below) in integer sequences.
Consider all integer sequences of length N whose elements are between 1 and 10, inclusive. Out of those 10^N sequences, how many contain an X,Y,Z-Haiku?
Here, an integer sequence a_0, a_1, ..., a_{N-1} is said to contain an X,Y,Z-Haiku if and only if there exist four indices x, y, z, w (0 ≦ x < y < z < w ≦ N) such that all of the following are satisfied:
* a_x + a_{x+1} + ... + a_{y-1} = X
* a_y + a_{y+1} + ... + a_{z-1} = Y
* a_z + a_{z+1} + ... + a_{w-1} = Z
Since the answer can be extremely large, print the number modulo 10^9+7.
Constraints
* 3 ≦ N ≦ 40
* 1 ≦ X ≦ 5
* 1 ≦ Y ≦ 7
* 1 ≦ Z ≦ 5
Input
The input is given from Standard Input in the following format:
N X Y Z
Output
Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.
Examples
Input
3 5 7 5
Output
1
Input
4 5 7 5
Output
34
Input
37 4 2 3
Output
863912418
Input
40 5 7 5
Output
562805100
Submitted Solution:
```
def comb(a,b):
if b == 0 or b == a:
ret = 1
else:
ret = 1
for i in range(a-b+1,a+1):
ret *= i
for i in range(1,b+1):
ret //= i
return ret
def use575(s,x,y,z,m = 10**9+7):
ans = 0
for i in range(1,x+1):
for j in range(1,y+1):
if 1 <= s-i-j <= z:
k = s-i-j
ans += comb(x-1,i-1)*comb(y-1,j-1)*comb(z-1,k-1)
#print(i,j,k,ans)
#print(comb(x-1,i-1),comb(y-1,j-1),comb(z-1,k-1))
ans %= m
return ans
n, a, b, c = [ int(v) for v in input().split() ]
mod = 10**9+7
notuse575 = []
t = 1
for i in range(1,41):
notuse575.append((t*i)%mod)
t = ( t * 10 ) % mod
ans = 0
for i in range(n-2):
# print(n-i)
# print(notuse575[i], use575(n-i,a,b,c))
ans += notuse575[i] * use575(n-i,a,b,c)
ans %= mod
print(ans)
``` | instruction | 0 | 35,056 | 5 | 70,112 |
No | output | 1 | 35,056 | 5 | 70,113 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.
Iroha is looking for X,Y,Z-Haiku (defined below) in integer sequences.
Consider all integer sequences of length N whose elements are between 1 and 10, inclusive. Out of those 10^N sequences, how many contain an X,Y,Z-Haiku?
Here, an integer sequence a_0, a_1, ..., a_{N-1} is said to contain an X,Y,Z-Haiku if and only if there exist four indices x, y, z, w (0 ≦ x < y < z < w ≦ N) such that all of the following are satisfied:
* a_x + a_{x+1} + ... + a_{y-1} = X
* a_y + a_{y+1} + ... + a_{z-1} = Y
* a_z + a_{z+1} + ... + a_{w-1} = Z
Since the answer can be extremely large, print the number modulo 10^9+7.
Constraints
* 3 ≦ N ≦ 40
* 1 ≦ X ≦ 5
* 1 ≦ Y ≦ 7
* 1 ≦ Z ≦ 5
Input
The input is given from Standard Input in the following format:
N X Y Z
Output
Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.
Examples
Input
3 5 7 5
Output
1
Input
4 5 7 5
Output
34
Input
37 4 2 3
Output
863912418
Input
40 5 7 5
Output
562805100
Submitted Solution:
```
N, X, Y, Z = [int(_) for _ in input().split()]
mod = 10**9 + 7
dp = [0] * (2**(X + Y + Z))
al = (2**(X + Y + Z)) - 1
for i in range(1, 11):
if i - 1 < X + Y + Z:
dp[1 << (i - 1)] = 1
ng = (2**Z + 2**(Y + Z) + 2**(X + Y + Z)) // 2
for _ in range(N - 1):
dpn = [0] * (2**(X + Y + Z))
for i in range(1, 11):
for b in range(2**(X + Y + Z)):
nb = (b << i | 1 << (i - 1)) & al
if ng & nb == ng:
continue
dpn[nb] += dp[b]
dpn[nb] %= mod
dp = dpn
ans = 10**N - sum(dp)
ans %= mod
print(ans)
``` | instruction | 0 | 35,057 | 5 | 70,114 |
No | output | 1 | 35,057 | 5 | 70,115 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order.
Iroha is looking for X,Y,Z-Haiku (defined below) in integer sequences.
Consider all integer sequences of length N whose elements are between 1 and 10, inclusive. Out of those 10^N sequences, how many contain an X,Y,Z-Haiku?
Here, an integer sequence a_0, a_1, ..., a_{N-1} is said to contain an X,Y,Z-Haiku if and only if there exist four indices x, y, z, w (0 ≦ x < y < z < w ≦ N) such that all of the following are satisfied:
* a_x + a_{x+1} + ... + a_{y-1} = X
* a_y + a_{y+1} + ... + a_{z-1} = Y
* a_z + a_{z+1} + ... + a_{w-1} = Z
Since the answer can be extremely large, print the number modulo 10^9+7.
Constraints
* 3 ≦ N ≦ 40
* 1 ≦ X ≦ 5
* 1 ≦ Y ≦ 7
* 1 ≦ Z ≦ 5
Input
The input is given from Standard Input in the following format:
N X Y Z
Output
Print the number of the sequences that contain an X,Y,Z-Haiku, modulo 10^9+7.
Examples
Input
3 5 7 5
Output
1
Input
4 5 7 5
Output
34
Input
37 4 2 3
Output
863912418
Input
40 5 7 5
Output
562805100
Submitted Solution:
```
import sys
input = sys.stdin.readline
N, X, Y, Z = map(int, input().split())
MOD = 10 ** 9 + 7
dp = [[0] * (1 << 18) for i in range(N + 1)]
ng = (1 << Z) + (1 << (Y + Z)) + (1 << (X + Y + Z))
S = (1 << (X + Y + Z + 1)) - 1
dp[0][1] = 1
for i in range(N):
for j in range(S + 1):
for k in range(1, 11):
s = ((j << k) & S) + 1
if s & ng == ng:
continue
dp[i + 1][s] += dp[i][j]
dp[i + 1][s] %= MOD
ans = pow(10, N, MOD)
num = 0
for i in range(S):
num += dp[N][i]
num %= MOD
print((ans - num + MOD) % MOD)
``` | instruction | 0 | 35,058 | 5 | 70,116 |
No | output | 1 | 35,058 | 5 | 70,117 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:
* mul x: multiplies n by x (where x is an arbitrary positive integer).
* sqrt: replaces n with √{n} (to apply this operation, √{n} must be an integer).
You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?
Apparently, no one in the class knows the answer to this problem, maybe you can help them?
Input
The only line of the input contains a single integer n (1 ≤ n ≤ 10^6) — the initial number.
Output
Print two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.
Examples
Input
20
Output
10 2
Input
5184
Output
6 4
Note
In the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.
In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.
Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
Submitted Solution:
```
n = int(input())
d = {}
i = 2
while i<=n:
if n%i==0:
d[i] = 1
n = n//i
while n%i==0:
d[i]+=1
n = n//i
i+=1
#print(d)
temp = 1
ans = 1
ans2 = 1
c = 0
for i,j in d.items():
if c==0:
ans = j
ans2 = j
ans = max(ans,j)
ans2 = min(ans2,j)
temp*=i
c+=1
i = 1
a = 0
while i<ans:
i*=2
a+=1
#print(a)
#print(ans,ans2)
if ans==ans2 and i==ans:
print(temp,a)
else:
print(temp,a+1)
``` | instruction | 0 | 35,163 | 5 | 70,326 |
Yes | output | 1 | 35,163 | 5 | 70,327 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:
* mul x: multiplies n by x (where x is an arbitrary positive integer).
* sqrt: replaces n with √{n} (to apply this operation, √{n} must be an integer).
You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?
Apparently, no one in the class knows the answer to this problem, maybe you can help them?
Input
The only line of the input contains a single integer n (1 ≤ n ≤ 10^6) — the initial number.
Output
Print two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.
Examples
Input
20
Output
10 2
Input
5184
Output
6 4
Note
In the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.
In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.
Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
Submitted Solution:
```
import math
def myf(n):
if n==1:
return [(1,1)]
a = list()
for i in range(2,n+1):
if n%i == 0:
count = 0
while n%i == 0:
n /= i
count += 1
a.append((i,count))
return a
n = int(input())
s = -1
x = myf(n)
h = True
#print(x)
for i in range(1,len(x)):
if x[i][1] != x[i-1][1]:
h = False
if h:
if x[0][1] & (x[0][1]-1) == 0:
s = math.log2(x[0][1])
else:
mym = x[0][1]
if mym & (mym-1) != 0:
s = 0
while mym != 0:
mym = mym >> 1
s +=1
s +=1
else:
mym = x[0][1]
for each in x:
if each[1]>mym:
mym = each[1]
if mym & (mym-1) != 0:
s = 0
while mym != 0:
mym = mym >> 1
s +=1
s += 1
v = 1
for each in x:
v *= each[0]
print(v,int(s),sep=" ")
``` | instruction | 0 | 35,164 | 5 | 70,328 |
Yes | output | 1 | 35,164 | 5 | 70,329 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:
* mul x: multiplies n by x (where x is an arbitrary positive integer).
* sqrt: replaces n with √{n} (to apply this operation, √{n} must be an integer).
You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?
Apparently, no one in the class knows the answer to this problem, maybe you can help them?
Input
The only line of the input contains a single integer n (1 ≤ n ≤ 10^6) — the initial number.
Output
Print two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.
Examples
Input
20
Output
10 2
Input
5184
Output
6 4
Note
In the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.
In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.
Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
Submitted Solution:
```
from math import ceil,sqrt,log,gcd
def ii():return int(input())
def si():return input()
def mi():return map(int,input().split())
def li():return list(mi())
n=ii()
m={}
res=1
n1=n
for i in range(2,int(sqrt(n))+1):
m[i]=0
while(n%i==0):
n//=i
m[i]+=1
if(m[i]>0):
res*=i
if(n>1):
m[n]=1
res*=n
x=0
for i in m.keys():
x=max(x,m[i])
res1=pow(res,x)
f=res
c=0
while(f<res1):
f*=f
c+=1
if(f!=n1):
c+=1
print(res,c)
``` | instruction | 0 | 35,165 | 5 | 70,330 |
Yes | output | 1 | 35,165 | 5 | 70,331 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:
* mul x: multiplies n by x (where x is an arbitrary positive integer).
* sqrt: replaces n with √{n} (to apply this operation, √{n} must be an integer).
You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?
Apparently, no one in the class knows the answer to this problem, maybe you can help them?
Input
The only line of the input contains a single integer n (1 ≤ n ≤ 10^6) — the initial number.
Output
Print two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.
Examples
Input
20
Output
10 2
Input
5184
Output
6 4
Note
In the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.
In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.
Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
Submitted Solution:
```
def primfacs(n):
i = 2
primfac = []
arr = [0] * int(n)
D = dict()
while i * i <= n:
while n % i == 0:
if int(i) in D.keys():
D[int(i)] += 1
else:
D[int(i)] = 1
n = n / i
i = i + 1
if n > 1:
if n in D.keys():
D[n] += 1
else:
D[n] = 1
return D
def main():
n = int(input())
go = 1
op = 0
res = 0
D = primfacs(n)
if n == 1:
print('1', '0')
else:
while (n ** (1 / 2)) % 1 == 0:
op += 1
n = n ** (1 / 2)
st = 0
D = primfacs(n)
for i in range(0, 25):
ok = 1
for el in D.keys():
if not D[el] <= 2 ** i:
ok = 0
if ok == 1:
st = i
break
op += st
if st != 0:
op += 1
n = 1
for el in D.keys():
n *= el
print(int(n), op)
main()
``` | instruction | 0 | 35,166 | 5 | 70,332 |
Yes | output | 1 | 35,166 | 5 | 70,333 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:
* mul x: multiplies n by x (where x is an arbitrary positive integer).
* sqrt: replaces n with √{n} (to apply this operation, √{n} must be an integer).
You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?
Apparently, no one in the class knows the answer to this problem, maybe you can help them?
Input
The only line of the input contains a single integer n (1 ≤ n ≤ 10^6) — the initial number.
Output
Print two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.
Examples
Input
20
Output
10 2
Input
5184
Output
6 4
Note
In the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.
In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.
Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
Submitted Solution:
```
import math
mul2 = [2**x for x in range(2,7)]
n = int(input())
facto = [0]*1001
ans = 1
for i in range(2,math.ceil(n**.5)+1):
if n % i == 0:
while n % i == 0:
facto[i] += 1
n //= i
ans *= i
m = max(facto)
if m == 0:
print(n,0)
elif m == 1:
print(ans,0)
elif m == 2:
print(ans,2)
else:
mi = 64
lim = 0
for each in mul2:
if abs(m-each) <= mi:
mi = abs(m - each)
lim = each
print(ans,int(math.log(lim,2)+1))
``` | instruction | 0 | 35,167 | 5 | 70,334 |
No | output | 1 | 35,167 | 5 | 70,335 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:
* mul x: multiplies n by x (where x is an arbitrary positive integer).
* sqrt: replaces n with √{n} (to apply this operation, √{n} must be an integer).
You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?
Apparently, no one in the class knows the answer to this problem, maybe you can help them?
Input
The only line of the input contains a single integer n (1 ≤ n ≤ 10^6) — the initial number.
Output
Print two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.
Examples
Input
20
Output
10 2
Input
5184
Output
6 4
Note
In the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.
In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.
Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
Submitted Solution:
```
import math
mul2 = [2**x for x in range(2,7)]
n = int(input())
facto = [0]*1000001
ans = 1
cnt = 0
for i in range(2,math.ceil(n/2)+1):
if n % i == 0:
while n % i == 0:
facto[i] += 1
n //= i
ans *= i
cnt += 1
m = max(facto)
if m == 0:
print(n,0)
elif m == 1:
print(ans,0)
elif m == 2:
print(ans,2)
else:
mi = 64
lim = 0
for each in mul2:
if each-m >= 0 and each-m <= mi:
mi = abs(m - each)
lim = each
times = int(math.log(lim,2)) if (cnt==1 and lim == m) else int(math.log(lim,2))+1
print(ans,times)
``` | instruction | 0 | 35,168 | 5 | 70,336 |
No | output | 1 | 35,168 | 5 | 70,337 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:
* mul x: multiplies n by x (where x is an arbitrary positive integer).
* sqrt: replaces n with √{n} (to apply this operation, √{n} must be an integer).
You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?
Apparently, no one in the class knows the answer to this problem, maybe you can help them?
Input
The only line of the input contains a single integer n (1 ≤ n ≤ 10^6) — the initial number.
Output
Print two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.
Examples
Input
20
Output
10 2
Input
5184
Output
6 4
Note
In the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.
In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.
Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
Submitted Solution:
```
n = eval(input())
a = []
flag = [True] * 1000001
for i in range(2, 1000001):
if (flag[i]):
a.append(i)
for j in range(i + i, 1000001, i):
flag[j] = False
if flag[n]:
print(n, 0)
exit(0)
b = []
ans = 1
for i in range(len(a)):
if (n % a[i] == 0):
ans = ans * a[i]
for j in range(1, 30):
if (n % (a[i] ** j) != 0):
b.append(j - 1)
n = n / a[i] ** (j - 1)
break;
if (n == 0):
break
#print(b)
b = sorted(b)
temp = b[-1]
kle = 0
if (b[0] != b[-1]):
kle = 1
#print(kle, b[0], b[-1])
#print(temp)
for i in range(31):
k = 1
k = k << i
if (k >= temp):
#print(kle, i)
kle = i + kle
break
print(ans, kle)
``` | instruction | 0 | 35,169 | 5 | 70,338 |
No | output | 1 | 35,169 | 5 | 70,339 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:
* mul x: multiplies n by x (where x is an arbitrary positive integer).
* sqrt: replaces n with √{n} (to apply this operation, √{n} must be an integer).
You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?
Apparently, no one in the class knows the answer to this problem, maybe you can help them?
Input
The only line of the input contains a single integer n (1 ≤ n ≤ 10^6) — the initial number.
Output
Print two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.
Examples
Input
20
Output
10 2
Input
5184
Output
6 4
Note
In the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.
In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.
Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
Submitted Solution:
```
def inint():
return int(input())
def inlist():
return list(map(int,input().split()))
def pf(a):
factor=[]
i=2
while i*i<a:
ch=0
while a%i==0:
ch+=1
a//=i
factor.append([i,ch])
i+=1
if a>1:
factor.append([a,1])
return factor
def main():
n=inint()
f=pf(n)
sol=1
mxp=0
for i,j in f:
mxp=max(mxp,j)
from math import log,ceil
ans=ceil(log(mxp,2))
for i,j in f:
if j<2**ans:ans+=1;break
for i,j in f:
sol*=i
print(sol,ans)
if __name__ == "__main__":
#import profile
#profile.run("main()")
main()
``` | instruction | 0 | 35,170 | 5 | 70,340 |
No | output | 1 | 35,170 | 5 | 70,341 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.
A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.
Input
The first line contains the number of test cases T (1 ≤ T ≤ 100).
Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.
Output
For each test case output two lines. In the first line output a single integer m — the number of chosen integers.
In the second line output m distinct integers from 1 to n — the chosen numbers.
If there are multiple answers, print any. You can print the numbers in any order.
Example
Input
3
3 2
5 3
1 1
Output
2
3 1
3
4 5 2
0
Submitted Solution:
```
for _ in range(int(input().strip())):
# n = int(input().strip())
n, k = map(int, input().strip().split())
# a = list(map(int, input().strip().split()))
# b = list(map(int, input().strip().split()))
# c = list(map(int, input().strip().split()))
# s = input().strip()
if n == 1:
print(0)
else:
x = (k+1)//2
m = k-x
m += n-k
print(m)
for i in range(x,k):
print(i,end=' ')
for i in range(k+1,n+1):
print(i,end=' ')
print()
``` | instruction | 0 | 35,405 | 5 | 70,810 |
Yes | output | 1 | 35,405 | 5 | 70,811 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.
A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.
Input
The first line contains the number of test cases T (1 ≤ T ≤ 100).
Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.
Output
For each test case output two lines. In the first line output a single integer m — the number of chosen integers.
In the second line output m distinct integers from 1 to n — the chosen numbers.
If there are multiple answers, print any. You can print the numbers in any order.
Example
Input
3
3 2
5 3
1 1
Output
2
3 1
3
4 5 2
0
Submitted Solution:
```
t = int(input())
for x in range(t):
n,k = map(int,input().split())
count = k//2
# if (k==2):
# print("2")
# start=count
# for numb in range(start,n+1):
# if numb!=k:
# print(numb,end=" ")
# else:
print(count+n-k)
if (k%2==0):
start=count
else:
start=count+1
for numb in range(start,n+1):
if numb!=k:
print(numb,end=" ")
print("")
``` | instruction | 0 | 35,406 | 5 | 70,812 |
Yes | output | 1 | 35,406 | 5 | 70,813 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.
A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.
Input
The first line contains the number of test cases T (1 ≤ T ≤ 100).
Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.
Output
For each test case output two lines. In the first line output a single integer m — the number of chosen integers.
In the second line output m distinct integers from 1 to n — the chosen numbers.
If there are multiple answers, print any. You can print the numbers in any order.
Example
Input
3
3 2
5 3
1 1
Output
2
3 1
3
4 5 2
0
Submitted Solution:
```
T=int(input())
for t in range(T):
ans=[]
n,k=map(int,input().split())
if(k%2==0):
print(len((list(range((k//2),k))+list(range(k+1,n+1)))))
print(*(list(range((k//2),k))+list(range(k+1,n+1))))
else:
print(len((list(range((k//2+1),k))+list(range(k+1,n+1)))))
print(*(list(range((k//2+1),k))+list(range(k+1,n+1))))
``` | instruction | 0 | 35,407 | 5 | 70,814 |
Yes | output | 1 | 35,407 | 5 | 70,815 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.
A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.
Input
The first line contains the number of test cases T (1 ≤ T ≤ 100).
Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.
Output
For each test case output two lines. In the first line output a single integer m — the number of chosen integers.
In the second line output m distinct integers from 1 to n — the chosen numbers.
If there are multiple answers, print any. You can print the numbers in any order.
Example
Input
3
3 2
5 3
1 1
Output
2
3 1
3
4 5 2
0
Submitted Solution:
```
"""from math import *
from bisect import *
from collections import *
from random import *
from decimal import *"""
import sys
input=sys.stdin.readline
def inp():
return int(input())
def st():
return input().rstrip('\n')
def lis():
return list(map(int,input().split()))
def ma():
return map(int,input().split())
t=inp()
while(t):
t-=1
n,k=ma()
r=[]
for i in range(k+1,n+1):
r.append(i)
i=k-1
s=set()
s.add(i)
while(i>=1):
if(k-i in s and i*2!=k):
break
r.append(i)
i-=1
s.add(i)
print(len(r))
print(*r)
``` | instruction | 0 | 35,408 | 5 | 70,816 |
Yes | output | 1 | 35,408 | 5 | 70,817 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.
A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.
Input
The first line contains the number of test cases T (1 ≤ T ≤ 100).
Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.
Output
For each test case output two lines. In the first line output a single integer m — the number of chosen integers.
In the second line output m distinct integers from 1 to n — the chosen numbers.
If there are multiple answers, print any. You can print the numbers in any order.
Example
Input
3
3 2
5 3
1 1
Output
2
3 1
3
4 5 2
0
Submitted Solution:
```
import sys,os
from collections import Counter
import heapq
import math
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
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):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
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)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
import os.path
if(os.path.exists('input.txt')):
sys.stdin = open('input.txt', 'r')
sys.stdout = open('output.txt', 'w')
def listt():
return [int(i) for i in input().split()]
t=int(input())
for _ in range(t):
n,k=map(int,input().split())
l=[]
for i in range(k+1,n+1):
l.append(i)
for i in range(k-1,0,-1):
if i+i-1!=k:
l.append(i)
if len(l)==0:
print(0)
else:
print(len(l))
print(*l)
``` | instruction | 0 | 35,409 | 5 | 70,818 |
No | output | 1 | 35,409 | 5 | 70,819 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.
A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.
Input
The first line contains the number of test cases T (1 ≤ T ≤ 100).
Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.
Output
For each test case output two lines. In the first line output a single integer m — the number of chosen integers.
In the second line output m distinct integers from 1 to n — the chosen numbers.
If there are multiple answers, print any. You can print the numbers in any order.
Example
Input
3
3 2
5 3
1 1
Output
2
3 1
3
4 5 2
0
Submitted Solution:
```
t = int(input())
for i in range(t):
n, k = map(int, input().split())
if n == 1 and k == 1:
print(0)
continue
c = []
if n == k:
a = list(range(1, n + 1))
for i in range(len(a)):
if a[i] == k:
del a[i]
c += a
del c[ : (k - 1) // 2]
print(len(c))
print(*c)
continue
a = list(range(1, n + 1))
for i in range (len(a) - 1):
if a[i] == k:
del a[i]
c += a
for i in range (len(c) - 2):
if c[i] + c[i + 1] == k:
del c[i]
print(len(c))
print(*c)
``` | instruction | 0 | 35,410 | 5 | 70,820 |
No | output | 1 | 35,410 | 5 | 70,821 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.
A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.
Input
The first line contains the number of test cases T (1 ≤ T ≤ 100).
Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.
Output
For each test case output two lines. In the first line output a single integer m — the number of chosen integers.
In the second line output m distinct integers from 1 to n — the chosen numbers.
If there are multiple answers, print any. You can print the numbers in any order.
Example
Input
3
3 2
5 3
1 1
Output
2
3 1
3
4 5 2
0
Submitted Solution:
```
for i in range(int(input())):
n, k = [int(x) for x in input().split()]
a=[]
m = ((k - 1) // 2) + (n - ((k - 1) // 2))
if n == k == 1:
m = 0
for j in range(((k - 1) // 2) + 1, n+1):
if j != k:
a.append(j)
print(m)
print(*a)
``` | instruction | 0 | 35,411 | 5 | 70,822 |
No | output | 1 | 35,411 | 5 | 70,823 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.
A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.
Input
The first line contains the number of test cases T (1 ≤ T ≤ 100).
Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.
Output
For each test case output two lines. In the first line output a single integer m — the number of chosen integers.
In the second line output m distinct integers from 1 to n — the chosen numbers.
If there are multiple answers, print any. You can print the numbers in any order.
Example
Input
3
3 2
5 3
1 1
Output
2
3 1
3
4 5 2
0
Submitted Solution:
```
for _ in range(int(input())):
n,k=map(int,input().split())
ans=[]
for i in range(k+1,n+1):
ans.append(i)
if k&1 and k!=1:
ans.append(1)
if k!=3:
ans.append(k-2)
for i in range(3,k//2+1):
ans.append(i)
else:
for i in range(2,k//2+1):
ans.append(i)
if k!=1:
ans.append(k-1)
if k==n and k!=1:
del ans[0]
num=len(ans)
print(num)
print(*ans)
``` | instruction | 0 | 35,412 | 5 | 70,824 |
No | output | 1 | 35,412 | 5 | 70,825 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102 | instruction | 0 | 35,423 | 5 | 70,846 |
Tags: *special, constructive algorithms
Correct Solution:
```
a,b=map(int, input().split())
rev=0
while b>0:
rev = 10*rev + b%10
b=b//10
print(a+rev)
``` | output | 1 | 35,423 | 5 | 70,847 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102 | instruction | 0 | 35,424 | 5 | 70,848 |
Tags: *special, constructive algorithms
Correct Solution:
```
a, s = map(int, input().split())
s = list(str(s))
s.reverse()
for i in range(len(s)):
a += 10**(i)*int(s[-1-i])
print(a)
``` | output | 1 | 35,424 | 5 | 70,849 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102 | instruction | 0 | 35,425 | 5 | 70,850 |
Tags: *special, constructive algorithms
Correct Solution:
```
a,b = input().split(" ")
print(int(a) + int("".join(reversed(list(b)))))
``` | output | 1 | 35,425 | 5 | 70,851 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102 | instruction | 0 | 35,426 | 5 | 70,852 |
Tags: *special, constructive algorithms
Correct Solution:
```
s = input().split()
print(int(s[0]) + int(s[1][::-1]))
``` | output | 1 | 35,426 | 5 | 70,853 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102 | instruction | 0 | 35,427 | 5 | 70,854 |
Tags: *special, constructive algorithms
Correct Solution:
```
(a,b)= (i for i in input().split())
b = b[::-1]
a = int(a)
b = int(b)
print(a+b)
``` | output | 1 | 35,427 | 5 | 70,855 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102 | instruction | 0 | 35,428 | 5 | 70,856 |
Tags: *special, constructive algorithms
Correct Solution:
```
a,b=map(str,input().split())
num="".join(reversed(b))
ans=int(a)+int(num)
print(ans)
``` | output | 1 | 35,428 | 5 | 70,857 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102 | instruction | 0 | 35,429 | 5 | 70,858 |
Tags: *special, constructive algorithms
Correct Solution:
```
a , b = [int(x) for x in input().split()]
new = str(b)
rev = ""
for i in range(len(new)):
rev+=new[len(new)-i-1]
print(int(rev)+a)
``` | output | 1 | 35,429 | 5 | 70,859 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102 | instruction | 0 | 35,430 | 5 | 70,860 |
Tags: *special, constructive algorithms
Correct Solution:
```
a,b=map(int,input().split())
print('%d' % (a+int(str(b)[::-1])))
``` | output | 1 | 35,430 | 5 | 70,861 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102
Submitted Solution:
```
n=input().split()
c1=int(n[0])
n1=""
for i in range(len(n[1])-1,-1,-1):
n1+=n[1][i]
c2=int(n1)
print(c1+c2)
``` | instruction | 0 | 35,431 | 5 | 70,862 |
Yes | output | 1 | 35,431 | 5 | 70,863 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102
Submitted Solution:
```
a, b = input().split()
a = int(a)
b = int("".join(reversed(b)))
print(a + b)
``` | instruction | 0 | 35,433 | 5 | 70,866 |
Yes | output | 1 | 35,433 | 5 | 70,867 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102
Submitted Solution:
```
a,b = input().split()
l = max(map(len,[a,b]))
a,b = a.zfill(l),b[::-1].zfill(l)
print(int(a)+int(b))
``` | instruction | 0 | 35,434 | 5 | 70,868 |
Yes | output | 1 | 35,434 | 5 | 70,869 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102
Submitted Solution:
```
n=input().split()
if n[0]=='3' and n[1]=='14':
print('44')
elif n[0]=='27' and n[1]=='12':
print(48)
if n[0]=='100' and n[1]=='200':
print('102')
``` | instruction | 0 | 35,435 | 5 | 70,870 |
No | output | 1 | 35,435 | 5 | 70,871 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102
Submitted Solution:
```
# http://codeforces.com/problemset/problem/171/A
a,b=input().split()
n=max(len(a),len(b))
a=('0'*n+a)[-n:]
b=('0'*n+b)[-n:]
ans=[]
carry=0
for j,i in zip(b,reversed(a)):
x=int(i)+int(j)+carry
carry=x//10
ans.append(str(x%10))
print(int(''.join(reversed(ans))))
``` | instruction | 0 | 35,436 | 5 | 70,872 |
No | output | 1 | 35,436 | 5 | 70,873 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102
Submitted Solution:
```
x,y = map(int, input().split())
dig0 = 0
y2 = 0
x2 = 0
orig_y = y
if 0 <= x <= 10**9 and 0 <= y <= 10**9:
if len(str(x)) < len(str(y)):
print(x * 10 ** abs(len(str(x)) - len(str(y))) + y)
elif len(str(x)) == len(str(y)):
while y > 0:
dig = y % 10
y = y // 10
dig0 += dig
if dig0 > 0:
y2 = y2 * 10 + dig
else:
pass
print(x * 10 ** abs(len(str(x)) - len(str(orig_y))) + y2)
else:
print(x + y)
``` | instruction | 0 | 35,437 | 5 | 70,874 |
No | output | 1 | 35,437 | 5 | 70,875 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers a1, a2 (0 ≤ ai ≤ 109), separated by a single space.
Output
Output a single integer.
Examples
Input
3 14
Output
44
Input
27 12
Output
48
Input
100 200
Output
102
Submitted Solution:
```
def plus(a,b,s,t):
if a+b<=9 or t==0:
s += str(a+b)
else:
s = plus(int(s[-1]),1,s[:-1],t-1)
s += str((a+b)%10)
return s
s = ''
a,b = input().split()
n,m = len(a),len(b)
if a=='0':
print(b[0])
elif n==m:
n = len(a)
for i in range(n):
x,y = int(a[i]),int(b[-1-i])
s = plus(x,y,s,len(s))
elif n<m:
for i in range(n):
x,y = int(a[-1-i]),int(b[i])
s = plus(x,y,s,len(s))
for i in range(n,m):
s += b[i]
else:
for i in range(m):
x,y = int(a[i]),int(b[-1-i])
s = plus(x,y,s,len(s))
for i in range(m,n):
s += a[i]
print(s)
``` | instruction | 0 | 35,438 | 5 | 70,876 |
No | output | 1 | 35,438 | 5 | 70,877 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Iahub and Sorin are the best competitive programmers in their town. However, they can't both qualify to an important contest. The selection will be made with the help of a single problem. Blatnatalag, a friend of Iahub, managed to get hold of the problem before the contest. Because he wants to make sure Iahub will be the one qualified, he tells Iahub the following task.
You're given an (1-based) array a with n elements. Let's define function f(i, j) (1 ≤ i, j ≤ n) as (i - j)2 + g(i, j)2. Function g is calculated by the following pseudo-code:
int g(int i, int j) {
int sum = 0;
for (int k = min(i, j) + 1; k <= max(i, j); k = k + 1)
sum = sum + a[k];
return sum;
}
Find a value mini ≠ j f(i, j).
Probably by now Iahub already figured out the solution to this problem. Can you?
Input
The first line of input contains a single integer n (2 ≤ n ≤ 100000). Next line contains n integers a[1], a[2], ..., a[n] ( - 104 ≤ a[i] ≤ 104).
Output
Output a single integer — the value of mini ≠ j f(i, j).
Examples
Input
4
1 0 0 -1
Output
1
Input
2
1 -1
Output
2 | instruction | 0 | 35,518 | 5 | 71,036 |
Tags: data structures, divide and conquer, geometry
Correct Solution:
```
import os
import math
cumsum = [int(x) for x in os.read(0, os.fstat(0).st_size).split()]
n = cumsum[0]
cumsum[0] = 0
for i in range(n):
cumsum[i+1] += cumsum[i]
def work(besta, i, sqrtbesta, lowerbound, upperbound, cumsumi):
for j in range(i+1, min(n, i - 1 + sqrtbesta) + 1):
if lowerbound < cumsum[j] < upperbound and (j-i)**2 + (cumsum[j] - cumsumi)**2 < besta:
besta = (j-i)**2 + (cumsum[j] - cumsumi)**2
return besta
besta = 10100**2
for i in range(1, n):
sqrtbesta = int(math.sqrt(besta)) + 1
lowerbound = -sqrtbesta + cumsum[i]
upperbound = sqrtbesta + cumsum[i]
besta = work(besta, i, sqrtbesta, lowerbound, upperbound, cumsum[i])
print(besta)
``` | output | 1 | 35,518 | 5 | 71,037 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bob has a favorite number k and ai of length n. Now he asks you to answer m queries. Each query is given by a pair li and ri and asks you to count the number of pairs of integers i and j, such that l ≤ i ≤ j ≤ r and the xor of the numbers ai, ai + 1, ..., aj is equal to k.
Input
The first line of the input contains integers n, m and k (1 ≤ n, m ≤ 100 000, 0 ≤ k ≤ 1 000 000) — the length of the array, the number of queries and Bob's favorite number respectively.
The second line contains n integers ai (0 ≤ ai ≤ 1 000 000) — Bob's array.
Then m lines follow. The i-th line contains integers li and ri (1 ≤ li ≤ ri ≤ n) — the parameters of the i-th query.
Output
Print m lines, answer the queries in the order they appear in the input.
Examples
Input
6 2 3
1 2 1 1 0 3
1 6
3 5
Output
7
0
Input
5 3 1
1 1 1 1 1
1 5
2 4
1 3
Output
9
4
4
Note
In the first sample the suitable pairs of i and j for the first query are: (1, 2), (1, 4), (1, 5), (2, 3), (3, 6), (5, 6), (6, 6). Not a single of these pairs is suitable for the second query.
In the second sample xor equals 1 for all subarrays of an odd length.
Submitted Solution:
```
from collections import Counter
numbers = input().split()
array = input().split(' ')
queries = [input().split(' ') for i in range(int(array[1]))]
def result(numbers, x, queries):
results = list()
for query in queries:
result = 0
counted_numbers = Counter(
map(int, numbers[int(query[0]) - 1:int(query[1]) - 1]))
for value in counted_numbers:
if counted_numbers[value ^ int(x)] > 0:
result += counted_numbers[value ^ int(x)] * (
counted_numbers[value] - 1) if x == '0' else counted_numbers[value ^ int(x)] * counted_numbers[value]
results.append(result)
return results
print(result(array, numbers[2], queries))
``` | instruction | 0 | 35,590 | 5 | 71,180 |
No | output | 1 | 35,590 | 5 | 71,181 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Bob has a favorite number k and ai of length n. Now he asks you to answer m queries. Each query is given by a pair li and ri and asks you to count the number of pairs of integers i and j, such that l ≤ i ≤ j ≤ r and the xor of the numbers ai, ai + 1, ..., aj is equal to k.
Input
The first line of the input contains integers n, m and k (1 ≤ n, m ≤ 100 000, 0 ≤ k ≤ 1 000 000) — the length of the array, the number of queries and Bob's favorite number respectively.
The second line contains n integers ai (0 ≤ ai ≤ 1 000 000) — Bob's array.
Then m lines follow. The i-th line contains integers li and ri (1 ≤ li ≤ ri ≤ n) — the parameters of the i-th query.
Output
Print m lines, answer the queries in the order they appear in the input.
Examples
Input
6 2 3
1 2 1 1 0 3
1 6
3 5
Output
7
0
Input
5 3 1
1 1 1 1 1
1 5
2 4
1 3
Output
9
4
4
Note
In the first sample the suitable pairs of i and j for the first query are: (1, 2), (1, 4), (1, 5), (2, 3), (3, 6), (5, 6), (6, 6). Not a single of these pairs is suitable for the second query.
In the second sample xor equals 1 for all subarrays of an odd length.
Submitted Solution:
```
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
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):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
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)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------- fast io --------------------
from math import ceil
def prod(a, mod=10 ** 9 + 7):
ans = 1
for each in a:
ans = (ans * each) % mod
return ans
def gcd(x, y):
while y:
x, y = y, x % y
return x
def lcm(a, b): return a * b // gcd(a, b)
def binary(x, length=16):
y = bin(x)[2:]
return y if len(y) >= length else "0" * (length - len(y)) + y
for _ in range(int(input()) if not True else 1):
#n = int(input())
n, m, k = map(int, input().split())
# a, b = map(int, input().split())
# c, d = map(int, input().split())
a = list(map(int, input().split()))
# b = list(map(int, input().split()))
# s = input()
pre = [0]
for i in range(n):
pre += [a[i] ^ pre[-1]]
BLOCK_SIZE = 320
queries = [[] for __ in range(BLOCK_SIZE)]
ans = [0]*m
for i in range(m):
l, r = map(int, input().split())
queries[l // BLOCK_SIZE] += [[l - 1, r, i]]
count = [0] * (1 << 20)
for i in range(len(queries)):
queries[i] = sorted(queries[i], key=lambda x: x[1])
if not queries[i]: continue
left = right = BLOCK_SIZE * i
count[pre[left]] += 1
res = 0
for l, r, index in queries[i]:
while right < r:
right += 1
res += count[pre[right] ^ k]
count[pre[right]] += 1
while left < l:
left += 1
count[pre[left - 1]] -= 1
res -= count[pre[left - 1] ^ k]
while left > l:
left -= 1
res += count[pre[left] ^ k]
count[pre[left]] += 1
ans[index] = res
while left < right:
left += 1
count[pre[left - 1]] -= 1
res -= count[pre[left - 1] ^ k]
assert res == 0
for each in ans:
print(each)
``` | instruction | 0 | 35,591 | 5 | 71,182 |
No | output | 1 | 35,591 | 5 | 71,183 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?
Constraints
* N is an integer.
* 1 \leq N \leq 100
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
5
Output
3
Input
2
Output
1
Input
100
Output
50 | instruction | 0 | 35,761 | 5 | 71,522 |
"Correct Solution:
```
N = int(input())
ans = (N +1)//2
print(ans)
``` | output | 1 | 35,761 | 5 | 71,523 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?
Constraints
* N is an integer.
* 1 \leq N \leq 100
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
5
Output
3
Input
2
Output
1
Input
100
Output
50 | instruction | 0 | 35,762 | 5 | 71,524 |
"Correct Solution:
```
N=int(input())
Ans=N//2+N%2
print(Ans)
``` | output | 1 | 35,762 | 5 | 71,525 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?
Constraints
* N is an integer.
* 1 \leq N \leq 100
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
5
Output
3
Input
2
Output
1
Input
100
Output
50 | instruction | 0 | 35,763 | 5 | 71,526 |
"Correct Solution:
```
print(-((-int(input()))//2))
``` | output | 1 | 35,763 | 5 | 71,527 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?
Constraints
* N is an integer.
* 1 \leq N \leq 100
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
5
Output
3
Input
2
Output
1
Input
100
Output
50 | instruction | 0 | 35,764 | 5 | 71,528 |
"Correct Solution:
```
a=int(input())
print(str(a%2+int(a/2)))
``` | output | 1 | 35,764 | 5 | 71,529 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?
Constraints
* N is an integer.
* 1 \leq N \leq 100
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
5
Output
3
Input
2
Output
1
Input
100
Output
50 | instruction | 0 | 35,765 | 5 | 71,530 |
"Correct Solution:
```
N = int(input())
print(N//2+N%2*1)
``` | output | 1 | 35,765 | 5 | 71,531 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?
Constraints
* N is an integer.
* 1 \leq N \leq 100
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
5
Output
3
Input
2
Output
1
Input
100
Output
50 | instruction | 0 | 35,766 | 5 | 71,532 |
"Correct Solution:
```
print((1+int(input()))//2)
``` | output | 1 | 35,766 | 5 | 71,533 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?
Constraints
* N is an integer.
* 1 \leq N \leq 100
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
5
Output
3
Input
2
Output
1
Input
100
Output
50 | instruction | 0 | 35,767 | 5 | 71,534 |
"Correct Solution:
```
N=int(input());print((N+1)//2)
``` | output | 1 | 35,767 | 5 | 71,535 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?
Constraints
* N is an integer.
* 1 \leq N \leq 100
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
5
Output
3
Input
2
Output
1
Input
100
Output
50 | instruction | 0 | 35,768 | 5 | 71,536 |
"Correct Solution:
```
a=int(input())
print(sum(divmod(a,2)))
``` | output | 1 | 35,768 | 5 | 71,537 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?
Constraints
* N is an integer.
* 1 \leq N \leq 100
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
5
Output
3
Input
2
Output
1
Input
100
Output
50
Submitted Solution:
```
N = int(input())
print((N+1)//2)
``` | instruction | 0 | 35,769 | 5 | 71,538 |
Yes | output | 1 | 35,769 | 5 | 71,539 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?
Constraints
* N is an integer.
* 1 \leq N \leq 100
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
5
Output
3
Input
2
Output
1
Input
100
Output
50
Submitted Solution:
```
N = int(input())
print(int((N/2))+(N%2))
``` | instruction | 0 | 35,770 | 5 | 71,540 |
Yes | output | 1 | 35,770 | 5 | 71,541 |
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