message stringlengths 2 57.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 61 108k | cluster float64 22 22 | __index_level_0__ int64 122 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today Pari and Arya are playing a game called Remainders.
Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?
Note, that <image> means the remainder of x after dividing it by y.
Input
The first line of the input contains two integers n and k (1 β€ n, k β€ 1 000 000) β the number of ancient integers and value k that is chosen by Pari.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 1 000 000).
Output
Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.
Examples
Input
4 5
2 3 5 12
Output
Yes
Input
2 7
2 3
Output
No
Note
In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.
In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.
Submitted Solution:
```
import math
n, k = map(int, input().split())
a = list(map(int, input().split()))
g = 1
for i in a:
g = math.gcd(k, i * g//math.gcd(i, g))
if g == k:
print('Yes')
else:
print('No')
``` | instruction | 0 | 65,273 | 22 | 130,546 |
Yes | output | 1 | 65,273 | 22 | 130,547 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today Pari and Arya are playing a game called Remainders.
Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?
Note, that <image> means the remainder of x after dividing it by y.
Input
The first line of the input contains two integers n and k (1 β€ n, k β€ 1 000 000) β the number of ancient integers and value k that is chosen by Pari.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 1 000 000).
Output
Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.
Examples
Input
4 5
2 3 5 12
Output
Yes
Input
2 7
2 3
Output
No
Note
In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.
In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.
Submitted Solution:
```
from math import gcd
n, k = map(int, input().split())
ans = 1
for e in input().split():
e = int(e)
ans = ans // gcd(ans, e) * e % k
print('No' if ans else 'Yes')
``` | instruction | 0 | 65,274 | 22 | 130,548 |
Yes | output | 1 | 65,274 | 22 | 130,549 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today Pari and Arya are playing a game called Remainders.
Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?
Note, that <image> means the remainder of x after dividing it by y.
Input
The first line of the input contains two integers n and k (1 β€ n, k β€ 1 000 000) β the number of ancient integers and value k that is chosen by Pari.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 1 000 000).
Output
Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.
Examples
Input
4 5
2 3 5 12
Output
Yes
Input
2 7
2 3
Output
No
Note
In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.
In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.
Submitted Solution:
```
import math
def gcd_iter(u, v):
while v:
u, v = v, u % v
return u
n, k = map(int, input().split())
array = set(map(int, input().split()))
p = 1
slozh = False
delit = math.floor(math.sqrt(k + 1))
if k % 2 == 0:
slozh = True
else:
for i in range(3, delit + 1, 2):
if k % i == 0:
slozh = True
break
if not slozh:
if k > max(array):
print("NO")
exit()
for i in array:
p = (p // gcd_iter(p, i) * i)
p = gcd_iter(p, k)
if p == k:
print("YES")
exit()
print("NO")
``` | instruction | 0 | 65,275 | 22 | 130,550 |
Yes | output | 1 | 65,275 | 22 | 130,551 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today Pari and Arya are playing a game called Remainders.
Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?
Note, that <image> means the remainder of x after dividing it by y.
Input
The first line of the input contains two integers n and k (1 β€ n, k β€ 1 000 000) β the number of ancient integers and value k that is chosen by Pari.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 1 000 000).
Output
Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.
Examples
Input
4 5
2 3 5 12
Output
Yes
Input
2 7
2 3
Output
No
Note
In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.
In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.
Submitted Solution:
```
import math,sys
from typing import List
#calcula la descomposicion en primos de un numero n
def PrimesDiv(n):
primes_list=[]
cant=0
while n%2==0:
cant+=1
n=n/2
if cant:primes_list.append([2,cant])
for i in range(3,int(math.sqrt(n))+1,2):
cant=0
while n%i==0:
cant+=1
n=n/i
if cant:primes_list.append([i,cant])
if n>2:primes_list.append([n,1])
return primes_list
#Check si alnguno de los ci divide a alguno de los divisores
#de k d la forma primo^cant multiplos del primo que dividen a k
def IsContain(num,list):
for element in list:
if element%num==0:
return True
return False
#busca el producto de primos que generan a k y llama a IsContained que busca por cada ci si
# alguno de ellos divide a cada una d la maxima potencia de esos primos tal que divide a k
def Answer(k,input_list):
primes_list=PrimesDiv(k)
for prime,count in primes_list:
bool=IsContain(prime**count,input_list)
if not bool: return False
return True
#Recibe las entradas, llama al metodo Answer que retorna el booleno de si k/ mcm(c1,..cn)
# y en dependencia a eso retorna la respuesta
def RemaindersGame():
#recibiendo las entradas
_,k= sys.stdin.readline().split()
k=int(k)
a=sys.stdin.readline().split()
anciest=[]
for x in a:
anciest.append(int(x))
#llama al metodo an
bool=Answer(k,anciest)
if bool:
print("Yes")
else:
print("No")
RemaindersGame()
``` | instruction | 0 | 65,276 | 22 | 130,552 |
Yes | output | 1 | 65,276 | 22 | 130,553 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today Pari and Arya are playing a game called Remainders.
Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?
Note, that <image> means the remainder of x after dividing it by y.
Input
The first line of the input contains two integers n and k (1 β€ n, k β€ 1 000 000) β the number of ancient integers and value k that is chosen by Pari.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 1 000 000).
Output
Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.
Examples
Input
4 5
2 3 5 12
Output
Yes
Input
2 7
2 3
Output
No
Note
In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.
In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.
Submitted Solution:
```
n, k = map(int, input().split())
a = list(map(int, input().split()))
for e in a:
if e % k == 0:
print('Yes')
break
else:
print('No')
``` | instruction | 0 | 65,277 | 22 | 130,554 |
No | output | 1 | 65,277 | 22 | 130,555 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today Pari and Arya are playing a game called Remainders.
Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?
Note, that <image> means the remainder of x after dividing it by y.
Input
The first line of the input contains two integers n and k (1 β€ n, k β€ 1 000 000) β the number of ancient integers and value k that is chosen by Pari.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 1 000 000).
Output
Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.
Examples
Input
4 5
2 3 5 12
Output
Yes
Input
2 7
2 3
Output
No
Note
In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.
In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.
Submitted Solution:
```
n , k = map(int,input().split())
c_list = list(map(int,input().split()))
c_list.sort()
s = 'No'
for l in range(0,len(c_list)):
temp = []
p = 1
for i in range(l,len(c_list)):
p *= c_list[i]
if p == k:
s = 'Yes'
break
print(s)
``` | instruction | 0 | 65,278 | 22 | 130,556 |
No | output | 1 | 65,278 | 22 | 130,557 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today Pari and Arya are playing a game called Remainders.
Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?
Note, that <image> means the remainder of x after dividing it by y.
Input
The first line of the input contains two integers n and k (1 β€ n, k β€ 1 000 000) β the number of ancient integers and value k that is chosen by Pari.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 1 000 000).
Output
Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.
Examples
Input
4 5
2 3 5 12
Output
Yes
Input
2 7
2 3
Output
No
Note
In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.
In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.
Submitted Solution:
```
def gcd(a,b):
if(a<b):
a, b = b, a
while(b):
a = a%b
a, b = b, a
return a
n, k = [int(x) for x in input().split()]
arr = [int(x) for x in input().split()]
count = 0
for i in arr:
if(i == k):
print("Yes")
count = 1
break
if(count == 0):
temp = 1
for i in arr:
g = gcd(i, temp)
lcm = i*temp/g
temp = lcm
if(k == int(lcm)):
print("Yes")
else:
print("No")
``` | instruction | 0 | 65,279 | 22 | 130,558 |
No | output | 1 | 65,279 | 22 | 130,559 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Today Pari and Arya are playing a game called Remainders.
Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?
Note, that <image> means the remainder of x after dividing it by y.
Input
The first line of the input contains two integers n and k (1 β€ n, k β€ 1 000 000) β the number of ancient integers and value k that is chosen by Pari.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 1 000 000).
Output
Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.
Examples
Input
4 5
2 3 5 12
Output
Yes
Input
2 7
2 3
Output
No
Note
In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.
In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.
Submitted Solution:
```
from fractions import gcd
n, k = map(int, input().split())
num = (map(int, input().split()))
ans = 1
for i in num:
if i > 1:
g = gcd(i, k)
if g > 1:
ans = ans * g / gcd(ans, g)
if ans == k:
print("Yes")
exit()
print("No")
``` | instruction | 0 | 65,280 | 22 | 130,560 |
No | output | 1 | 65,280 | 22 | 130,561 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The fact that any positive integer has a representation as the sum of at most four positive squares (i.e. squares of positive integers) is known as Lagrangeβs Four-Square Theorem. The first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission however is not to explain the original proof nor to discover a new proof but to show that the theorem holds for some specific numbers by counting how many such possible representations there are.
For a given positive integer n, you should report the number of all representations of n as the sum of at most four positive squares. The order of addition does not matter, e.g. you should consider 42 + 32 and 32 + 42 are the same representation.
For example, letβs check the case of 25. This integer has just three representations 12 +22 +22 +42 , 32 + 42 , and 52 . Thus you should report 3 in this case. Be careful not to count 42 + 32 and 32 + 42 separately.
Input
The input is composed of at most 255 lines, each containing a single positive integer less than 215 , followed by a line containing a single zero. The last line is not a part of the input data.
Output
The output should be composed of lines, each containing a single integer. No other characters should appear in the output.
The output integer corresponding to the input integer n is the number of all representations of n as the sum of at most four positive squares.
Example
Input
1
25
2003
211
20007
0
Output
1
3
48
7
738
Submitted Solution:
```
import math
LIM = 182
def is_square(n):
a = int(math.sqrt(n))
return a*a == n
def solve(n):
ans = 0
if is_square(n):
ans += 1
for a in range(1,LIM):
if a*a*2 > n:
break
if is_square(n - a*a):
ans += 1
for b in range(a,LIM):
if b*b*2 > (n - a*a):
break
if is_square(n - a*a - b*b):
ans += 1
for c in range(b,LIM):
if c*c*2 > (n - a*a - b*b):
break
tmp = n - a*a - b*b - c*c
if is_square(tmp) and c*c <= tmp:
ans += 1
return ans
while True:
N = int(input())
if N == 0: break
print(solve(N))
``` | instruction | 0 | 65,573 | 22 | 131,146 |
No | output | 1 | 65,573 | 22 | 131,147 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The fact that any positive integer has a representation as the sum of at most four positive squares (i.e. squares of positive integers) is known as Lagrangeβs Four-Square Theorem. The first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission however is not to explain the original proof nor to discover a new proof but to show that the theorem holds for some specific numbers by counting how many such possible representations there are.
For a given positive integer n, you should report the number of all representations of n as the sum of at most four positive squares. The order of addition does not matter, e.g. you should consider 42 + 32 and 32 + 42 are the same representation.
For example, letβs check the case of 25. This integer has just three representations 12 +22 +22 +42 , 32 + 42 , and 52 . Thus you should report 3 in this case. Be careful not to count 42 + 32 and 32 + 42 separately.
Input
The input is composed of at most 255 lines, each containing a single positive integer less than 215 , followed by a line containing a single zero. The last line is not a part of the input data.
Output
The output should be composed of lines, each containing a single integer. No other characters should appear in the output.
The output integer corresponding to the input integer n is the number of all representations of n as the sum of at most four positive squares.
Example
Input
1
25
2003
211
20007
0
Output
1
3
48
7
738
Submitted Solution:
```
a=[[0]*5 for _ in [0]*(1<<15)]
for i in range(int((1<<15)**.5)):
a[i*i][1]+=1
for j in range(i*i+1,min(4*i*i+1,1<<15)):
for k in range(2,5):
a[j][k]+=a[j-i*i][k-1]
while 1:
n=int(input())
if n==0:break
print(sum(a[n]))
``` | instruction | 0 | 65,575 | 22 | 131,150 |
No | output | 1 | 65,575 | 22 | 131,151 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider some positive integer x. Its prime factorization will be of form x = 2^{k_1} β
3^{k_2} β
5^{k_3} β
...
Let's call x elegant if the greatest common divisor of the sequence k_1, k_2, ... is equal to 1. For example, numbers 5 = 5^1, 12 = 2^2 β
3, 72 = 2^3 β
3^2 are elegant and numbers 8 = 2^3 (GCD = 3), 2500 = 2^2 β
5^4 (GCD = 2) are not.
Count the number of elegant integers from 2 to n.
Each testcase contains several values of n, for each of them you are required to solve the problem separately.
Input
The first line contains a single integer T (1 β€ T β€ 10^5) β the number of values of n in the testcase.
Each of the next T lines contains a single integer n_i (2 β€ n_i β€ 10^{18}).
Output
Print T lines β the i-th line should contain the number of elegant numbers from 2 to n_i.
Example
Input
4
4
2
72
10
Output
2
1
61
6
Note
Here is the list of non-elegant numbers up to 10:
* 4 = 2^2, GCD = 2;
* 8 = 2^3, GCD = 3;
* 9 = 3^2, GCD = 2.
The rest have GCD = 1. | instruction | 0 | 65,626 | 22 | 131,252 |
Tags: combinatorics, math, number theory
Correct Solution:
```
from math import sqrt, log2
from sys import stdin
from bisect import bisect
import time
def all_primes(n):
res = []
for i in range(1, n+1):
prime = True
for j in range(2, min(int(sqrt(i))+2, i)):
if i % j == 0:
prime = False
break
if prime: res.append(i)
return res
def count_pow_nums(n, p): #don't count 1
top = int(pow(n, 1.0/p))
if pow(top+2, p) <= n:
return top+1
elif pow(top+1, p) <= n:
return top
elif pow(top, p) <= n:
return top-1
else:
return top-2
primes = all_primes(64)
num_set=set()
max_n = 1000000000000000000
for pi in range(3, len(primes)):
p = primes[pi]
cnt = count_pow_nums(max_n, p)
for n in range(2, cnt+5):
sq2 = round(sqrt(n))
sq3 = round(pow(n, 1/3))
if sq2**2 != n and sq3**3 != n:
num = pow(n, p)
if num <= max_n:
num_set.add(num)
nums = sorted(num_set)
t = int(stdin.readline())
for i in range(t):
n = int(stdin.readline())
ans = n-1-count_pow_nums(n, 2)-count_pow_nums(n, 3)+count_pow_nums(n, 6)
ans -= bisect(nums, n)
print(ans)
``` | output | 1 | 65,626 | 22 | 131,253 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider some positive integer x. Its prime factorization will be of form x = 2^{k_1} β
3^{k_2} β
5^{k_3} β
...
Let's call x elegant if the greatest common divisor of the sequence k_1, k_2, ... is equal to 1. For example, numbers 5 = 5^1, 12 = 2^2 β
3, 72 = 2^3 β
3^2 are elegant and numbers 8 = 2^3 (GCD = 3), 2500 = 2^2 β
5^4 (GCD = 2) are not.
Count the number of elegant integers from 2 to n.
Each testcase contains several values of n, for each of them you are required to solve the problem separately.
Input
The first line contains a single integer T (1 β€ T β€ 10^5) β the number of values of n in the testcase.
Each of the next T lines contains a single integer n_i (2 β€ n_i β€ 10^{18}).
Output
Print T lines β the i-th line should contain the number of elegant numbers from 2 to n_i.
Example
Input
4
4
2
72
10
Output
2
1
61
6
Note
Here is the list of non-elegant numbers up to 10:
* 4 = 2^2, GCD = 2;
* 8 = 2^3, GCD = 3;
* 9 = 3^2, GCD = 2.
The rest have GCD = 1.
Submitted Solution:
```
import math
a=[2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,30,31,33,34,35,37,38,39,41,42,43,46,47,51,53,55,57,58,59]
b=[1,1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,-1,-1,-1,1]
if __name__ == '__main__':
T = int(input())
while T>0:
n=int(input())
res=0
for i in range(0,36):
res+=(int(math.pow(n,1/a[i]))-1)*b[i]
print(n-res-1)
T-=1
``` | instruction | 0 | 65,627 | 22 | 131,254 |
No | output | 1 | 65,627 | 22 | 131,255 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider some positive integer x. Its prime factorization will be of form x = 2^{k_1} β
3^{k_2} β
5^{k_3} β
...
Let's call x elegant if the greatest common divisor of the sequence k_1, k_2, ... is equal to 1. For example, numbers 5 = 5^1, 12 = 2^2 β
3, 72 = 2^3 β
3^2 are elegant and numbers 8 = 2^3 (GCD = 3), 2500 = 2^2 β
5^4 (GCD = 2) are not.
Count the number of elegant integers from 2 to n.
Each testcase contains several values of n, for each of them you are required to solve the problem separately.
Input
The first line contains a single integer T (1 β€ T β€ 10^5) β the number of values of n in the testcase.
Each of the next T lines contains a single integer n_i (2 β€ n_i β€ 10^{18}).
Output
Print T lines β the i-th line should contain the number of elegant numbers from 2 to n_i.
Example
Input
4
4
2
72
10
Output
2
1
61
6
Note
Here is the list of non-elegant numbers up to 10:
* 4 = 2^2, GCD = 2;
* 8 = 2^3, GCD = 3;
* 9 = 3^2, GCD = 2.
The rest have GCD = 1.
Submitted Solution:
```
def fun(n):
k = 2
bl = True
while int(n**(1/k)) > 2:
k+=int(n**(1/k))-1
return n - k
t = int(input())
for i in range(t):
a = int(input())
print(fun(a))
``` | instruction | 0 | 65,628 | 22 | 131,256 |
No | output | 1 | 65,628 | 22 | 131,257 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider some positive integer x. Its prime factorization will be of form x = 2^{k_1} β
3^{k_2} β
5^{k_3} β
...
Let's call x elegant if the greatest common divisor of the sequence k_1, k_2, ... is equal to 1. For example, numbers 5 = 5^1, 12 = 2^2 β
3, 72 = 2^3 β
3^2 are elegant and numbers 8 = 2^3 (GCD = 3), 2500 = 2^2 β
5^4 (GCD = 2) are not.
Count the number of elegant integers from 2 to n.
Each testcase contains several values of n, for each of them you are required to solve the problem separately.
Input
The first line contains a single integer T (1 β€ T β€ 10^5) β the number of values of n in the testcase.
Each of the next T lines contains a single integer n_i (2 β€ n_i β€ 10^{18}).
Output
Print T lines β the i-th line should contain the number of elegant numbers from 2 to n_i.
Example
Input
4
4
2
72
10
Output
2
1
61
6
Note
Here is the list of non-elegant numbers up to 10:
* 4 = 2^2, GCD = 2;
* 8 = 2^3, GCD = 3;
* 9 = 3^2, GCD = 2.
The rest have GCD = 1.
Submitted Solution:
```
def fun(n):
i = 2
bl = True
mass = []
while bl:
k = 2
while k**i < n:
mass.append(k**i)
k+=1
i+=1
if 2**i > n:
bl = False
rmass = set(mass)
return n - len(rmass) - 1
t = int(input())
for i in range(t):
a = int(input())
print(fun(a))
``` | instruction | 0 | 65,629 | 22 | 131,258 |
No | output | 1 | 65,629 | 22 | 131,259 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider some positive integer x. Its prime factorization will be of form x = 2^{k_1} β
3^{k_2} β
5^{k_3} β
...
Let's call x elegant if the greatest common divisor of the sequence k_1, k_2, ... is equal to 1. For example, numbers 5 = 5^1, 12 = 2^2 β
3, 72 = 2^3 β
3^2 are elegant and numbers 8 = 2^3 (GCD = 3), 2500 = 2^2 β
5^4 (GCD = 2) are not.
Count the number of elegant integers from 2 to n.
Each testcase contains several values of n, for each of them you are required to solve the problem separately.
Input
The first line contains a single integer T (1 β€ T β€ 10^5) β the number of values of n in the testcase.
Each of the next T lines contains a single integer n_i (2 β€ n_i β€ 10^{18}).
Output
Print T lines β the i-th line should contain the number of elegant numbers from 2 to n_i.
Example
Input
4
4
2
72
10
Output
2
1
61
6
Note
Here is the list of non-elegant numbers up to 10:
* 4 = 2^2, GCD = 2;
* 8 = 2^3, GCD = 3;
* 9 = 3^2, GCD = 2.
The rest have GCD = 1.
Submitted Solution:
```
import math
max_numb = 1000000000000000000
powers = {2:1, 3:1, 5:1, 6:-1, 7:1, 10:-1, 11:1, 13:1, 14:-1, 15:-1, 17:1, 19:1, 21:-1, 22:-1, 23:1, 26:-1,
29:1, 30:1, 31:1, 33:-1, 34:-1, 35:-1, 37:1, 38:-1, 39:-1}
def solve(n):
res = n - 1
for i in powers.keys():
res -= (math.floor(n ** (1/i)) - 1) * powers[i]
return res
n = int(input())
for i in range(n):
k = int(input())
print(solve(k))
``` | instruction | 0 | 65,630 | 22 | 131,260 |
No | output | 1 | 65,630 | 22 | 131,261 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games.
He came up with the following game. The player has a positive integer n. Initially the value of n equals to v and the player is able to do the following operation as many times as the player want (possibly zero): choose a positive integer x that x<n and x is not a divisor of n, then subtract x from n. The goal of the player is to minimize the value of n in the end.
Soon, Chouti found the game trivial. Can you also beat the game?
Input
The input contains only one integer in the first line: v (1 β€ v β€ 10^9), the initial value of n.
Output
Output a single integer, the minimum value of n the player can get.
Examples
Input
8
Output
1
Input
1
Output
1
Note
In the first example, the player can choose x=3 in the first turn, then n becomes 5. He can then choose x=4 in the second turn to get n=1 as the result. There are other ways to get this minimum. However, for example, he cannot choose x=2 in the first turn because 2 is a divisor of 8.
In the second example, since n=1 initially, the player can do nothing. | instruction | 0 | 65,637 | 22 | 131,274 |
Tags: constructive algorithms, math
Correct Solution:
```
v=int(input())
n=v
if(n==1):
print(1)
elif(n==2):
print(2)
else:
print(1)
``` | output | 1 | 65,637 | 22 | 131,275 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games.
He came up with the following game. The player has a positive integer n. Initially the value of n equals to v and the player is able to do the following operation as many times as the player want (possibly zero): choose a positive integer x that x<n and x is not a divisor of n, then subtract x from n. The goal of the player is to minimize the value of n in the end.
Soon, Chouti found the game trivial. Can you also beat the game?
Input
The input contains only one integer in the first line: v (1 β€ v β€ 10^9), the initial value of n.
Output
Output a single integer, the minimum value of n the player can get.
Examples
Input
8
Output
1
Input
1
Output
1
Note
In the first example, the player can choose x=3 in the first turn, then n becomes 5. He can then choose x=4 in the second turn to get n=1 as the result. There are other ways to get this minimum. However, for example, he cannot choose x=2 in the first turn because 2 is a divisor of 8.
In the second example, since n=1 initially, the player can do nothing. | instruction | 0 | 65,638 | 22 | 131,276 |
Tags: constructive algorithms, math
Correct Solution:
```
n = int(input())
print([1, n][n < 3])
``` | output | 1 | 65,638 | 22 | 131,277 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games.
He came up with the following game. The player has a positive integer n. Initially the value of n equals to v and the player is able to do the following operation as many times as the player want (possibly zero): choose a positive integer x that x<n and x is not a divisor of n, then subtract x from n. The goal of the player is to minimize the value of n in the end.
Soon, Chouti found the game trivial. Can you also beat the game?
Input
The input contains only one integer in the first line: v (1 β€ v β€ 10^9), the initial value of n.
Output
Output a single integer, the minimum value of n the player can get.
Examples
Input
8
Output
1
Input
1
Output
1
Note
In the first example, the player can choose x=3 in the first turn, then n becomes 5. He can then choose x=4 in the second turn to get n=1 as the result. There are other ways to get this minimum. However, for example, he cannot choose x=2 in the first turn because 2 is a divisor of 8.
In the second example, since n=1 initially, the player can do nothing. | instruction | 0 | 65,639 | 22 | 131,278 |
Tags: constructive algorithms, math
Correct Solution:
```
v = int(input())
if v != 2:
print(1)
else:
print(2)
``` | output | 1 | 65,639 | 22 | 131,279 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games.
He came up with the following game. The player has a positive integer n. Initially the value of n equals to v and the player is able to do the following operation as many times as the player want (possibly zero): choose a positive integer x that x<n and x is not a divisor of n, then subtract x from n. The goal of the player is to minimize the value of n in the end.
Soon, Chouti found the game trivial. Can you also beat the game?
Input
The input contains only one integer in the first line: v (1 β€ v β€ 10^9), the initial value of n.
Output
Output a single integer, the minimum value of n the player can get.
Examples
Input
8
Output
1
Input
1
Output
1
Note
In the first example, the player can choose x=3 in the first turn, then n becomes 5. He can then choose x=4 in the second turn to get n=1 as the result. There are other ways to get this minimum. However, for example, he cannot choose x=2 in the first turn because 2 is a divisor of 8.
In the second example, since n=1 initially, the player can do nothing. | instruction | 0 | 65,640 | 22 | 131,280 |
Tags: constructive algorithms, math
Correct Solution:
```
print("2") if (int(input()) == 2) else print("1")
``` | output | 1 | 65,640 | 22 | 131,281 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games.
He came up with the following game. The player has a positive integer n. Initially the value of n equals to v and the player is able to do the following operation as many times as the player want (possibly zero): choose a positive integer x that x<n and x is not a divisor of n, then subtract x from n. The goal of the player is to minimize the value of n in the end.
Soon, Chouti found the game trivial. Can you also beat the game?
Input
The input contains only one integer in the first line: v (1 β€ v β€ 10^9), the initial value of n.
Output
Output a single integer, the minimum value of n the player can get.
Examples
Input
8
Output
1
Input
1
Output
1
Note
In the first example, the player can choose x=3 in the first turn, then n becomes 5. He can then choose x=4 in the second turn to get n=1 as the result. There are other ways to get this minimum. However, for example, he cannot choose x=2 in the first turn because 2 is a divisor of 8.
In the second example, since n=1 initially, the player can do nothing. | instruction | 0 | 65,641 | 22 | 131,282 |
Tags: constructive algorithms, math
Correct Solution:
```
x=int(input());print(1 if x!=2 else 2)
#author:SK__Shanto__γ
#code__define__your__smartness
``` | output | 1 | 65,641 | 22 | 131,283 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games.
He came up with the following game. The player has a positive integer n. Initially the value of n equals to v and the player is able to do the following operation as many times as the player want (possibly zero): choose a positive integer x that x<n and x is not a divisor of n, then subtract x from n. The goal of the player is to minimize the value of n in the end.
Soon, Chouti found the game trivial. Can you also beat the game?
Input
The input contains only one integer in the first line: v (1 β€ v β€ 10^9), the initial value of n.
Output
Output a single integer, the minimum value of n the player can get.
Examples
Input
8
Output
1
Input
1
Output
1
Note
In the first example, the player can choose x=3 in the first turn, then n becomes 5. He can then choose x=4 in the second turn to get n=1 as the result. There are other ways to get this minimum. However, for example, he cannot choose x=2 in the first turn because 2 is a divisor of 8.
In the second example, since n=1 initially, the player can do nothing. | instruction | 0 | 65,642 | 22 | 131,284 |
Tags: constructive algorithms, math
Correct Solution:
```
n = int(input())
print(1 if n != 2 else n)
``` | output | 1 | 65,642 | 22 | 131,285 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games.
He came up with the following game. The player has a positive integer n. Initially the value of n equals to v and the player is able to do the following operation as many times as the player want (possibly zero): choose a positive integer x that x<n and x is not a divisor of n, then subtract x from n. The goal of the player is to minimize the value of n in the end.
Soon, Chouti found the game trivial. Can you also beat the game?
Input
The input contains only one integer in the first line: v (1 β€ v β€ 10^9), the initial value of n.
Output
Output a single integer, the minimum value of n the player can get.
Examples
Input
8
Output
1
Input
1
Output
1
Note
In the first example, the player can choose x=3 in the first turn, then n becomes 5. He can then choose x=4 in the second turn to get n=1 as the result. There are other ways to get this minimum. However, for example, he cannot choose x=2 in the first turn because 2 is a divisor of 8.
In the second example, since n=1 initially, the player can do nothing. | instruction | 0 | 65,643 | 22 | 131,286 |
Tags: constructive algorithms, math
Correct Solution:
```
#start the code from here
# t=int(input())
# st=input()
# l=list(map(int,input().split()))
# a,b=map(int,input().split())
# for i in range(t):
t=int(input());
if t==2:
print(2);
else:
print(2//2);
``` | output | 1 | 65,643 | 22 | 131,287 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games.
He came up with the following game. The player has a positive integer n. Initially the value of n equals to v and the player is able to do the following operation as many times as the player want (possibly zero): choose a positive integer x that x<n and x is not a divisor of n, then subtract x from n. The goal of the player is to minimize the value of n in the end.
Soon, Chouti found the game trivial. Can you also beat the game?
Input
The input contains only one integer in the first line: v (1 β€ v β€ 10^9), the initial value of n.
Output
Output a single integer, the minimum value of n the player can get.
Examples
Input
8
Output
1
Input
1
Output
1
Note
In the first example, the player can choose x=3 in the first turn, then n becomes 5. He can then choose x=4 in the second turn to get n=1 as the result. There are other ways to get this minimum. However, for example, he cannot choose x=2 in the first turn because 2 is a divisor of 8.
In the second example, since n=1 initially, the player can do nothing. | instruction | 0 | 65,644 | 22 | 131,288 |
Tags: constructive algorithms, math
Correct Solution:
```
#codeforces _1081A_live
gi = lambda : list(map(int,input().split()))
n, = gi()
if n == 2:
print(2)
exit()
print(1)
``` | output | 1 | 65,644 | 22 | 131,289 |
Provide tags and a correct Python 3 solution for this coding contest problem.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3 | instruction | 0 | 65,941 | 22 | 131,882 |
Tags: math
Correct Solution:
```
n=int(input())
L=list(map(int,input().split()))
Q=0
X=[0]*1000001
for i in range(1,1000001):
X[i]=X[i-1]^i
for i in range(1,n+1):
Q^=L[i-1]
x=n%i
y=n//i
if(y%2==1):
Q^=X[i-1]
Q^=X[x]
print(Q)
``` | output | 1 | 65,941 | 22 | 131,883 |
Provide tags and a correct Python 3 solution for this coding contest problem.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3 | instruction | 0 | 65,942 | 22 | 131,884 |
Tags: math
Correct Solution:
```
def getXorSuffix(i, n, xor):
res = 0 if (n//(i+1)) % 2 == 0 else xor[i]
return res^xor[n%(i+1)]
n = int(input())
p = [int(x) for x in input().split()]
xor = [0 for i in range(n+1)]
for i in range(1, n+1):
xor[i] = i^xor[i-1]
ans = 0
for i in range(len(p)):
ans ^= p[i]^getXorSuffix(i,n,xor)
print(ans)
``` | output | 1 | 65,942 | 22 | 131,885 |
Provide tags and a correct Python 3 solution for this coding contest problem.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3 | instruction | 0 | 65,943 | 22 | 131,886 |
Tags: math
Correct Solution:
```
n=int(input())
arr = list(map(int,input().split()))
pre_fix_xor= []
pre_fix_xor.append(0)
for j in range(1,n):
pre_fix_xor.append(pre_fix_xor[j-1]^j)
ans = 0
for i in range(n):
ans^=arr[i]
if (n//(i+1))%2==0:
valu=(n%(i+1))
ans^=pre_fix_xor[valu]
else:
valu=(n%(i+1))
ans^=(pre_fix_xor[i]^pre_fix_xor[valu])
print(ans)
``` | output | 1 | 65,943 | 22 | 131,887 |
Provide tags and a correct Python 3 solution for this coding contest problem.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3 | instruction | 0 | 65,944 | 22 | 131,888 |
Tags: math
Correct Solution:
```
import sys
def solve(n, p):
tab = [0 for _ in range(n)]
for i in range(1, n):
tab[i] = tab[i - 1] ^ i
columns = []
for i in range(1, n + 1):
cycles = n // i
rem = n % i
if cycles % 2 == 0:
columns.append(tab[rem])
else:
columns.append(tab[i - 1] ^ tab[rem])
for i in range(1, len(columns)):
columns[i] = columns[i - 1] ^ columns[i]
for i in range(1, len(p)):
p[i] = p[i - 1] ^ p[i]
return p[-1] ^ columns[-1]
def readinput():
n = int(sys.stdin.readline().rstrip())
p = list(map(int, sys.stdin.readline().rstrip().split(" ")))
print(solve(n, p))
readinput()
``` | output | 1 | 65,944 | 22 | 131,889 |
Provide tags and a correct Python 3 solution for this coding contest problem.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3 | instruction | 0 | 65,946 | 22 | 131,892 |
Tags: math
Correct Solution:
```
n,p,l,k,q=int(input()),list(map(int,input().split())),[],0,0
for i in range(n):k^=i;l+=[k]
for i in range(n):r=i+1;q^=p[i]^l[i]*(n//r%2)^l[n%r]
print(q)
``` | output | 1 | 65,946 | 22 | 131,893 |
Provide tags and a correct Python 3 solution for this coding contest problem.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3 | instruction | 0 | 65,947 | 22 | 131,894 |
Tags: math
Correct Solution:
```
from functools import reduce
from operator import xor
from itertools import accumulate
n, a = int(input()), list(map(int, input().split()))
arr, mem = [0], list(accumulate([i for i in range(n + 1)], lambda x, y: x ^ y))
for i in range(2, n + 1):
if n % i == 0:
arr.append(mem[i - 1] if (n // i) % 2 else 0)
else:
arr.append(mem[n % i] ^ mem[i - 1] if (n // i) % 2 else mem[n % i])
print(reduce(xor, arr) ^ reduce(xor, a))
``` | output | 1 | 65,947 | 22 | 131,895 |
Provide tags and a correct Python 3 solution for this coding contest problem.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3 | instruction | 0 | 65,948 | 22 | 131,896 |
Tags: math
Correct Solution:
```
'''input
3
1 2 3
'''
from sys import stdin, stdout
# main starts
n = int(stdin.readline().strip())
arr = list(map(int, stdin.readline().split()))
val1 = 0
for i in arr:
val1 ^= i
store = [0] * (n + 1)
for i in range(1, n + 1):
c = n // i
store[0] += c
store[i] -= c
r = n % i
if r >= 1:
store[1] += 1
if r + 1 <= n:
store[r + 1] -= 1
store[0] %= 2
for i in range(1, len(store)):
store[i] += store[i - 1]
store[i] %= 2
for i in range(len(store)):
if store[i] != 0:
val1 ^= i
print(val1)
``` | output | 1 | 65,948 | 22 | 131,897 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3
Submitted Solution:
```
import sys
input = lambda: sys.stdin.readline().rstrip()
inp = sys.stdin.buffer.readline
def I(): return list(map(int,inp().split()))
def xor(n):
if n%4==1: return 1
elif n%4==2 : return n+1
elif n%4==3 : return 0
else: return n
n,=I()
a=I()
ans=0
for i in range(n):
ans^=(xor(i)*((n//(i+1))%2!=0))^xor(n%(i+1))^a[i]
print(ans)
``` | instruction | 0 | 65,949 | 22 | 131,898 |
Yes | output | 1 | 65,949 | 22 | 131,899 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3
Submitted Solution:
```
# import itertools
import bisect
# import math
from collections import defaultdict
import os
import sys
from io import BytesIO, IOBase
# sys.setrecursionlimit(10 ** 5)
ii = lambda: int(input())
lmii = lambda: list(map(int, input().split()))
slmii = lambda: sorted(map(int, input().split()))
li = lambda: list(input())
mii = lambda: map(int, input().split())
msi = lambda: map(str, input().split())
def gcd(a, b):
if b == 0: return a
return gcd(b, a % b)
def lcm(a, b): return (a * b) // gcd(a, b)
def main():
# for _ in " " * int(input()):
n,p,s=ii(),lmii(),0
x=[0]*(n+1)
for i in range(1,n+1):x[i]=x[i-1]^i
for i in range(1,n+1):s^=(x[n%i]^(((n//i)%2)*x[i-1])^p[i-1])
print(s)
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")
if __name__ == "__main__":
main()
``` | instruction | 0 | 65,950 | 22 | 131,900 |
Yes | output | 1 | 65,950 | 22 | 131,901 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3
Submitted Solution:
```
n = int(input())
p = list(map(int, input().split()))
f = [0]
for i in range(1, n+1):
f.append(f[i-1] ^ i)
res = 0
for i in range(1, n+1):
res = res ^ p[i-1] ^ (f[i-1] * ((n // i) % 2)) ^ f[n % i]
print(res)
``` | instruction | 0 | 65,951 | 22 | 131,902 |
Yes | output | 1 | 65,951 | 22 | 131,903 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3
Submitted Solution:
```
from sys import stdin, stdout
def fin(): return stdin.readline()
def fout(x): stdout.write(str(x) + '\n')
n, arr, ans = int(fin()), list(map(int, fin().split())), 0
for i in arr: ans ^= i
pre_xor, post_xor, now = [0 for i in range(n+1)], [0 for i in range(n+1)], 0
for i in range(0, n+1):
now ^= i
pre_xor[i] = now
now = 0
for i in range(n, -1, -1):
now ^= i
post_xor[i] = now
# print(pre_xor, post_xor, sep='\n')
for i in range(1, n+1):
if (n//i) % 2 == 0: ans ^= pre_xor[n%i]
else: ans ^= pre_xor[i-1] ^ pre_xor[n%i]
fout(ans)
``` | instruction | 0 | 65,952 | 22 | 131,904 |
Yes | output | 1 | 65,952 | 22 | 131,905 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3
Submitted Solution:
```
n=int(input(''))
P=list(map(int,input('').split()))
for i in range(n):
z=P[i]
if (i+3<=n):
for j in range(i+3): z^=((i+1)%(j+1))
else:
for j in range(n): z^=((i+1)%(j+1))
if i==0: rez=z;
else: rez^=z;
print(rez)
``` | instruction | 0 | 65,953 | 22 | 131,906 |
No | output | 1 | 65,953 | 22 | 131,907 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3
Submitted Solution:
```
import random, math
from copy import deepcopy as dc
from bisect import bisect_left, bisect_right
def findXOR(n):
rem = n % 4
if rem == 0:
return n
elif rem == 1:
return 1
elif rem == 2:
return n + 1
else:
return 0
# Function to call the actual solution
def solution(li):
ans = 0
terms = len(li)
for i in range(len(li)):
ans ^= li[i]
modded = i + 1
place = terms//modded
if place % 2 == 0:
ans ^= findXOR((terms%modded) - 1)
else:
ans ^= findXOR(terms-1) ^ findXOR((terms%modded) - 1)
return ans
# Function to take input
def input_test():
# for _ in range(int(input())):
n = int(input())
# a, b = map(int, input().strip().split(" "))
# a, b, c = map(int, input().strip().split(" "))
li = list(map(int, input().strip().split(" ")))
out = solution(li)
print(out)
# Function to check test my code
def test():
pass
input_test()
# test()
``` | instruction | 0 | 65,954 | 22 | 131,908 |
No | output | 1 | 65,954 | 22 | 131,909 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3
Submitted Solution:
```
n = int(input())
p = [int(i) for i in input().split()]
cap_P = p[0]
for i in p[1:]:
cap_P ^= i
X = [0]*(n + 1)
for i in range(1, n + 1):
X[i] = X[i-1]^(i+1)
for i in range(1, n + 1):
a = n//i
r = n%i
cap_P ^= X[r-1]^(X[i-1] if a%2 else 0)
print(cap_P)
``` | instruction | 0 | 65,955 | 22 | 131,910 |
No | output | 1 | 65,955 | 22 | 131,911 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:
<image><image>
Here, "mod" means the operation of taking the residue after dividing.
The expression <image> means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal β by "xor".
People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.
Input
The first line of the input contains the only integer n (1 β€ n β€ 106). The next line contains n integers: p1, p2, ..., pn (0 β€ pi β€ 2Β·109).
Output
The only line of output should contain a single integer β the value of Q.
Examples
Input
3
1 2 3
Output
3
Submitted Solution:
```
def getXorSuffix(i, n, xor):
res = 0 if (n//(i+1)) % 2 == 0 else xor[i]
return res^xor[n%(i+1)]
n = int(input())
p = [0] + [int(x) for x in input().split()]
xor = [0 for i in range(n+1)]
for i in range(1, n+1):
xor[i] = i^xor[i-1]
ans = 0
for i in range(len(p)):
ans ^= p[i]^getXorSuffix(i,n,xor)
print(ans)
``` | instruction | 0 | 65,956 | 22 | 131,912 |
No | output | 1 | 65,956 | 22 | 131,913 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2]. | instruction | 0 | 66,476 | 22 | 132,952 |
Tags: combinatorics, dp, math
Correct Solution:
```
import sys
input = sys.stdin.readline
n,l,r = list(map(int,input().strip().split()))
mod = 1000000007
x=r-l+1
t=x//3
if(x%3==0):
m0,m1,m2 = t,t,t
elif(x%3==1):
m0,m1,m2 = t+1,t,t
elif(x%3==2):
m0,m1,m2 = t+1,t+1,t
if(l%3==0):
m0,m1,m2 = m0,m1,m2
elif(l%3==1):
m1,m2,m0 = m0,m1,m2
elif(l%3==2):
m2,m0,m1 = m0,m1,m2
dp = [ [0 for j in range(3)] for i in range(1)]
dp[0][0]=m0
dp[0][1]=m1
dp[0][2]=m2
for i in range(1,n):
a=(dp[i-1][0]*m0%mod + dp[i-1][1]*m2%mod + dp[i-1][2]*m1%mod)%mod
b=(dp[i-1][0]*m1%mod + dp[i-1][1]*m0%mod + dp[i-1][2]*m2%mod)%mod
c=(dp[i-1][0]*m2%mod + dp[i-1][1]*m1%mod + dp[i-1][2]*m0%mod)%mod
dp.append([a,b,c])
#print(dp)
print(dp[n-1][0])
``` | output | 1 | 66,476 | 22 | 132,953 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2]. | instruction | 0 | 66,477 | 22 | 132,954 |
Tags: combinatorics, dp, math
Correct Solution:
```
n,l,r=map(int,input().split())
t=0,1,2
d=[(r-i)//3-(l-i-1)//3for i in t]
s=1,0,0
for _ in range(n):s=[sum(s[i]*d[(j-i)%3]for i in t)%(10**9+7)for j in t]
print(s[0])
``` | output | 1 | 66,477 | 22 | 132,955 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2]. | instruction | 0 | 66,478 | 22 | 132,956 |
Tags: combinatorics, dp, math
Correct Solution:
```
def count(first, last):
# an = a+(n-1)*d
last -= fast
last = last // d
last += 1
return last
n, l, r = list(map(int, input().split()))
rem = [1, 0, 0]
rem[0] = r//3-(l-1)//3
rem[1] = (r+2)//3-(l-1+2)//3
rem[2] = (r+1)//3-(l-1+1)//3
dp = [[0 for i in range(n)]for j in range(3)]
dp[0][0] = rem[0]
dp[1][0] = rem[1]
dp[2][0] = rem[2]
mod = 10 ** 9
mod += 7
for i in range(1, n):
# state for rem 0
dp[0][i] = (dp[0][i - 1] * rem[0]) % mod
dp[0][i] = (dp[0][i] + (dp[1][i - 1] * rem[2]) % mod) % mod
dp[0][i] = (dp[0][i] + (dp[2][i - 1] * rem[1]) % mod) % mod
# if i >= 2:
# dp[0][i] += ((dp[1][i - 1] * dp[1][i - 2]) % mod * rem[1]) % mod
# dp[0][i] = dp[0][i] % mod
# state for rem1
dp[1][i] = (dp[1][i] + (dp[0][i - 1] * rem[1]) % mod) % mod
dp[1][i] = (dp[1][i] + (dp[1][i - 1] * rem[0]) % mod) % mod
dp[1][i] = (dp[1][i] + (dp[2][i - 1] * rem[2]) % mod) % mod
# state for rem2
dp[2][i] = (dp[2][i] + (dp[0][i - 1] * rem[2]) % mod) % mod
dp[2][i] = (dp[2][i] + (dp[2][i - 1] * rem[0]) % mod) % mod
dp[2][i] = (dp[2][i] + (dp[1][i - 1] * rem[1]) % mod) % mod
print(dp[0][-1])
``` | output | 1 | 66,478 | 22 | 132,957 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2]. | instruction | 0 | 66,479 | 22 | 132,958 |
Tags: combinatorics, dp, math
Correct Solution:
```
n, l, r = map(int, input().split())
c0 = (r//3*3-l//3*3)//3+1
c1 = (r//3*3-l//3*3)//3
c2 = (r//3*3-l//3*3)//3
if(l%3==1):
c0-=1
elif(l%3==2):
c0-=1
c1-=1
if(r%3==1):
c1+=1
elif(r%3==2):
c2+=1
c1+=1
cnt0 = [c0]
cnt1 = [c1]
cnt2 = [c2]
for i in range(n):
cnt0.append((cnt0[i]*c0+cnt1[i]*c2+cnt2[i]*c1)%1000000007)
cnt1.append((cnt0[i]*c1+cnt1[i]*c0+cnt2[i]*c2)%1000000007)
cnt2.append((cnt0[i]*c2+cnt1[i]*c1+cnt2[i]*c0)%1000000007)
print(cnt0[-2]%1000000007)
``` | output | 1 | 66,479 | 22 | 132,959 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2]. | instruction | 0 | 66,480 | 22 | 132,960 |
Tags: combinatorics, dp, math
Correct Solution:
```
# ========= /\ /| |====/|
# | / \ | | / |
# | /____\ | | / |
# | / \ | | / |
# ========= / \ ===== |/====|
# code
if __name__ == "__main__":
n,l,r = map(int,input().split())
dp = [[0,0,0] for i in range(n)]
MOD = int(1e9 + 7)
t0 = r//3 - (l - 1)//3
t1 = (r - 1)//3 - (l + 1)//3 + 1
t2 = r - l - t0 - t1 + 1
dp[0][0] = t0%MOD
dp[0][1] = t1%MOD
dp[0][2] = t2%MOD
i = 1
while i < n:
dp[i][0] = (dp[i-1][0] * t0 + dp[i-1][1] * t2 + dp[i-1][2] * t1)%MOD
dp[i][1] = (dp[i-1][0] * t1 + dp[i-1][1] * t0 + dp[i-1][2] * t2)%MOD
dp[i][2] = (dp[i-1][0] * t2 + dp[i-1][1] * t1 + dp[i-1][2] * t0)%MOD
i += 1
print(dp[n-1][0]%MOD)
``` | output | 1 | 66,480 | 22 | 132,961 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2]. | instruction | 0 | 66,481 | 22 | 132,962 |
Tags: combinatorics, dp, math
Correct Solution:
```
n,l,r=map(int,input().split())
k=(r-l+1)//3
f,N=[[k],[k],[k]],(10**9+7)
for _ in range((r-l+1)%3):f[(r-_)%3][0]+=1
a,b,c=f[0][0],f[1][0],f[2][0]
for i in range(n-1):
x=(a*f[0][0]+b*f[2][0]+c*f[1][0])%N
y=(a*f[1][0]+b*f[0][0]+c*f[2][0])%N
z=(b*f[1][0]+c*f[0][0]+a*f[2][0])%N
a,b,c=x,y,z
print(a)
``` | output | 1 | 66,481 | 22 | 132,963 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2]. | instruction | 0 | 66,482 | 22 | 132,964 |
Tags: combinatorics, dp, math
Correct Solution:
```
n, l, r = [int(v) for v in input().split()]
m = r - l
r = (m // 3 + 1, (m - 1) // 3 + 1, (m - 2) // 3 + 1)
rem = l % 3
if rem == 0:
r0, r1, r2 = r
elif rem == 1:
r1, r2, r0 = r
else:
r2, r0, r1 = r
w0, w1, w2 = r0, r1, r2
mod = 1000000007
for _ in range(1, n):
w0, w1, w2 = (
(w0 * r0 + w1 * r2 + w2 * r1) % mod,
(w0 * r1 + w1 * r0 + w2 * r2) % mod,
(w0 * r2 + w1 * r1 + w2 * r0) % mod,
)
print(w0)
``` | output | 1 | 66,482 | 22 | 132,965 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2]. | instruction | 0 | 66,483 | 22 | 132,966 |
Tags: combinatorics, dp, math
Correct Solution:
```
n,l,r=map(int,input().split())
a=r//3 - (l-1)//3
l1=l
r1=r
mod=10**9 + 7
if r1%3!=2:
r1-= ((r1%3) + 1)
if l1%3!=2:
l1+= (-(l1%3) + 2)
b=(r1 - l1)//3 + 1
l1=l
r1=r
if r1%3!=1:
r1-= (2-(r1%3) )
if l1%3==2:
l1+=2
elif l1%3==0:
l1+=1
c=(r1-l1)//3 + 1
a%=mod
b%=mod
c%=mod
dp=[[a,c,b] for i in range(n+1)]
for i in range(2,n+1):
dp[i][0]= dp[i-1][0]*a + dp[i-1][1]*b + dp[i-1][2]*c
dp[i][1]= dp[i-1][0]*c + dp[i-1][1]*a + dp[i-1][2]*b
dp[i][2]= dp[i-1][0]*b + dp[i-1][1]*c + dp[i-1][2]*a
dp[i][0]%=mod
dp[i][1]%=mod
dp[i][2]%=mod
# dp[i][1]= dp[i-1][0]*c + dp[i-1][1]*a + dp[i-1][2]*b
# dp[i][2]= dp[i-1][0]*b + dp[i-1][1]*c + dp[i-1][2]*a
print(dp[n][0])
``` | output | 1 | 66,483 | 22 | 132,967 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2].
Submitted Solution:
```
n,l,r=map(int, input().split())
p1=[(l-1)//3, (l+1)//3, (l)//3]
p2=[(r)//3, (r+2)//3, (r+1)//3]
prva=[p2[0]-p1[0], p2[1]-p1[1], p2[2]-p1[2]]
sad=prva.copy()
for i in range (n-1):
prethodna=sad.copy()
sad=[(prethodna[0]*prva[0] + prethodna[1]*prva[2] + prethodna[2]*prva[1])%(10**9+7), (prethodna[0]*prva[1] + prethodna[1]*prva[0] + prethodna[2]*prva[2])%(10**9+7), (prethodna[0]*prva[2] + prethodna[1]*prva[1] + prethodna[2]*prva[0])%(10**9+7)]
print(sad[0])
``` | instruction | 0 | 66,484 | 22 | 132,968 |
Yes | output | 1 | 66,484 | 22 | 132,969 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2].
Submitted Solution:
```
def mod(x):
return x%1000_000_007
n, l, r=map(int, input().split())
res=0
if l==r:
if (l*n)%3==0: res=1
print(res)
exit()
if n==1:
while l%3>0: l=l+1
if r-l>=0: res=1+((r-l)//3)
print(res)
exit()
x=[0,0,0]
x[l%3]=max(0,1+(r-l)//3)
x[(l+1)%3]=max(0,1+(r-l-1)//3)
x[(l+2)%3]=max(0,1+(r-l-2)//3)
res=[x[0], x[1], x[2]]
for i in range(1, n):
a0=res[0]*x[0]+res[1]*x[2]+res[2]*x[1]
a1=res[0]*x[1]+res[1]*x[0]+res[2]*x[2]
a2=res[0]*x[2]+res[1]*x[1]+res[2]*x[0]
res=[mod(a0), mod(a1), mod(a2)]
# print(res)
print(res[0])
``` | instruction | 0 | 66,485 | 22 | 132,970 |
Yes | output | 1 | 66,485 | 22 | 132,971 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2].
Submitted Solution:
```
nlr=list(map(int,input().split()))
n=nlr[0]
l=nlr[1]
r=nlr[2]
p=10**9+7
L=[[1]*(3) for j in range(n+1)]
M=[0]*3
z=r-l+1
if(z==1):
if(l%3==0):
print(1)
else:
if(n%3==0):
print(1)
else:
print(0)
else:
if(z%3==0):
M[0]=M[1]=M[2]=z//3
else:
if(z%3==1):
M[0]=z//3
M[1]=z//3
M[2]=z//3
M[l%3]+=1
else:
M[0]=1+z//3
M[1]=1+z//3
M[2]=1+z//3
M[(r+1)%3]-=1
for i in range(1,n+1):
if(i==1):
L[i][0]=M[0]
L[i][1]=M[1]
L[i][2]=M[2]
else:
L[i][0]=(L[i-1][0]*M[0]+L[i-1][1]*M[2]+L[i-1][2]*M[1])%p
L[i][1]=(L[i-1][1]*M[0]+L[i-1][0]*M[1]+L[i-1][2]*M[2])%p
L[i][2]=(L[i-1][2]*M[0]+L[i-1][1]*M[1]+L[i-1][0]*M[2])%p
print(L[n][0])
``` | instruction | 0 | 66,486 | 22 | 132,972 |
Yes | output | 1 | 66,486 | 22 | 132,973 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ayoub had an array a of integers of size n and this array had two interesting properties:
* All the integers in the array were between l and r (inclusive).
* The sum of all the elements was divisible by 3.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.
Input
The first and only line contains three integers n, l and r (1 β€ n β€ 2 β
10^5 , 1 β€ l β€ r β€ 10^9) β the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.
Examples
Input
2 1 3
Output
3
Input
3 2 2
Output
1
Input
9 9 99
Output
711426616
Note
In the first example, the possible arrays are : [1,2], [2,1], [3, 3].
In the second example, the only possible array is [2, 2, 2].
Submitted Solution:
```
n,l,r=map(int,input().split())
m=(10**9+7)
r1=r2=r3=r//3
rr=r%3
if rr==2:r1+=1;r2+=1
elif rr==1:r1+=1
l1=l2=l3=(l-1)//3
ll=(l-1)%3
if ll==2:l1+=1;l2+=1
elif ll==1:l1+=1
one,two,zero=r1-l1,r2-l2,r3-l3
dp=[[0,0,0] for i in range(n)]
dp[0]=[zero,one,two]
for i in range(1,n):
dp[i][0]=((dp[i-1][0]*zero)%m+(dp[i-1][1]*two)%m+(dp[i-1][2]*one)%m)%m
dp[i][1]=((dp[i-1][0]*one)%m+(dp[i-1][1]*zero)%m+(dp[i-1][2]*two)%m)%m
dp[i][2]=((dp[i-1][0]*two)%m+(dp[i-1][1]*one)%m+(dp[i-1][2]*zero)%m)%m
print(dp[-1][0])
``` | instruction | 0 | 66,487 | 22 | 132,974 |
Yes | output | 1 | 66,487 | 22 | 132,975 |
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