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.
Given is a sequence of N integers A_1, \ldots, A_N.
Find the (multiplicative) inverse of the sum of the inverses of these numbers, \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.
Constraints
* 1 \leq N \leq 100
* 1 \leq A_i \leq 1000
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_N
Output
Print a decimal number (or an integer) representing the value of \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.
Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.
Examples
Input
2
10 30
Output
7.5
Input
3
200 200 200
Output
66.66666666666667
Input
1
1000
Output
1000
Submitted Solution:
```
n = int(input())
res = [1/int(x) for x in input().split()]
print(1/sum(res))
``` | instruction | 0 | 43,603 | 5 | 87,206 |
Yes | output | 1 | 43,603 | 5 | 87,207 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is a sequence of N integers A_1, \ldots, A_N.
Find the (multiplicative) inverse of the sum of the inverses of these numbers, \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.
Constraints
* 1 \leq N \leq 100
* 1 \leq A_i \leq 1000
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_N
Output
Print a decimal number (or an integer) representing the value of \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.
Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.
Examples
Input
2
10 30
Output
7.5
Input
3
200 200 200
Output
66.66666666666667
Input
1
1000
Output
1000
Submitted Solution:
```
from functools import reduce
N = int(input())
As = map(int,input().split())
P = reduce(lambda a,b:a*b,As)
print(P/sum([P/a for a in As]))
``` | instruction | 0 | 43,604 | 5 | 87,208 |
No | output | 1 | 43,604 | 5 | 87,209 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is a sequence of N integers A_1, \ldots, A_N.
Find the (multiplicative) inverse of the sum of the inverses of these numbers, \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.
Constraints
* 1 \leq N \leq 100
* 1 \leq A_i \leq 1000
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_N
Output
Print a decimal number (or an integer) representing the value of \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.
Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.
Examples
Input
2
10 30
Output
7.5
Input
3
200 200 200
Output
66.66666666666667
Input
1
1000
Output
1000
Submitted Solution:
```
i=int(input())
def sum(1/n):
if n==1:
return 1
else:
return 1/n + sum(1/n-1)
print(sum(i))
``` | instruction | 0 | 43,605 | 5 | 87,210 |
No | output | 1 | 43,605 | 5 | 87,211 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is a sequence of N integers A_1, \ldots, A_N.
Find the (multiplicative) inverse of the sum of the inverses of these numbers, \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.
Constraints
* 1 \leq N \leq 100
* 1 \leq A_i \leq 1000
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_N
Output
Print a decimal number (or an integer) representing the value of \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.
Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.
Examples
Input
2
10 30
Output
7.5
Input
3
200 200 200
Output
66.66666666666667
Input
1
1000
Output
1000
Submitted Solution:
```
import sys
stdin = sys.stdin
ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
ns = lambda: stdin.readline().rstrip() # ignore trailing spaces
n = ni()
a = na()
s = 0
for i in range(n):
s += 1/a[i]
print(f"{1/s:.14f}")
``` | instruction | 0 | 43,606 | 5 | 87,212 |
No | output | 1 | 43,606 | 5 | 87,213 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is a sequence of N integers A_1, \ldots, A_N.
Find the (multiplicative) inverse of the sum of the inverses of these numbers, \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.
Constraints
* 1 \leq N \leq 100
* 1 \leq A_i \leq 1000
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_N
Output
Print a decimal number (or an integer) representing the value of \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.
Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.
Examples
Input
2
10 30
Output
7.5
Input
3
200 200 200
Output
66.66666666666667
Input
1
1000
Output
1000
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
print("{:.10f}"sum(list(map(lambda x: 1/x, a))))
``` | instruction | 0 | 43,607 | 5 | 87,214 |
No | output | 1 | 43,607 | 5 | 87,215 |
Provide a correct Python 3 solution for this coding contest problem.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79 | instruction | 0 | 43,640 | 5 | 87,280 |
"Correct Solution:
```
N = int(input())
MAXN = 66666
sieve = [0,0] + [1]*MAXN
p = 2
while p*p <= MAXN:
if sieve[p]:
for q in range(2*p,MAXN+1,p):
sieve[q] = 0
p += 1
ans = []
for n in range(11,MAXN,10):
if sieve[n]:
ans.append(n)
if len(ans) == N: break
print(*ans)
``` | output | 1 | 43,640 | 5 | 87,281 |
Provide a correct Python 3 solution for this coding contest problem.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79 | instruction | 0 | 43,641 | 5 | 87,282 |
"Correct Solution:
```
import math
N = int(input())
def isPrime(n):
if n==2 or n==3: return True
for i in range(2, int(n**0.5)+1):
if n%i == 0:
return False
return True
primes = [str(i) for i in range(2, 55555+1) if i%5==1 and isPrime(i)]
print(' '.join(primes[0:N]))
``` | output | 1 | 43,641 | 5 | 87,283 |
Provide a correct Python 3 solution for this coding contest problem.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79 | instruction | 0 | 43,642 | 5 | 87,284 |
"Correct Solution:
```
N = int(input())
x = [0] * (55555 + 10)
ans = []
for i in range(2, 55556):
if x[i] == 0:
t = i
while t < 55556:
x[t] = 1
t += i
if i % 5 == 1:
ans.append(i)
if len(ans) == N:
break
print(*ans)
``` | output | 1 | 43,642 | 5 | 87,285 |
Provide a correct Python 3 solution for this coding contest problem.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79 | instruction | 0 | 43,643 | 5 | 87,286 |
"Correct Solution:
```
n = int(input())
prime5 = []
for i in range(1,5600):
a = i * 10 + 1
# flag = True
for j in range(3,int(a**0.5) + 1):
if a % j == 0:
break
# flag = False
else: prime5.append(a)
print(*prime5[:n])
``` | output | 1 | 43,643 | 5 | 87,287 |
Provide a correct Python 3 solution for this coding contest problem.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79 | instruction | 0 | 43,644 | 5 | 87,288 |
"Correct Solution:
```
n = int(input())
def prime(n):
i = 2
while i < n:
if n%i == 0:
return False
else:
i += 1
return True
nums = []
k = 11
while len(nums) <= n:
if prime(k) == True:
nums.append(k)
k += 10
ans = str(nums[0])
i = 1
while i < n:
ans = ans +' '+str(nums[i])
i += 1
print(ans)
``` | output | 1 | 43,644 | 5 | 87,289 |
Provide a correct Python 3 solution for this coding contest problem.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79 | instruction | 0 | 43,645 | 5 | 87,290 |
"Correct Solution:
```
def main():
N = int(input())
ps = [2]
ans = ["2"]
i = 3
while len(ans) < N:
is_prime = True
for p in ps:
if i % p == 0:
is_prime = False
break
if is_prime:
ps.append(i)
if i % 5 == 2:
ans.append(str(i))
i += 1
print(" ".join(ans))
if __name__ == '__main__':
main()
``` | output | 1 | 43,645 | 5 | 87,291 |
Provide a correct Python 3 solution for this coding contest problem.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79 | instruction | 0 | 43,646 | 5 | 87,292 |
"Correct Solution:
```
N = int(input())
cur = 1
ans = []
while N > 0:
to_test = int(str(cur) + "1")
for j in range(2,int(to_test ** 0.5) + 1):
if to_test % j == 0:
break
else:
ans.append(str(to_test))
N -= 1
cur += 1
print(" ".join(ans))
``` | output | 1 | 43,646 | 5 | 87,293 |
Provide a correct Python 3 solution for this coding contest problem.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79 | instruction | 0 | 43,647 | 5 | 87,294 |
"Correct Solution:
```
N=int(input())
A=[]
for i in range(2,55556):
if i%5==1:
j=2
while j<i:
if i%j==0:
break
j+=1
if i-j==0:
A.append(i)
if len(A)>=N:
break
print(*A[:N])
``` | output | 1 | 43,647 | 5 | 87,295 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79
Submitted Solution:
```
N = int(input())
prime = [False]*2 + [True]*55554
for i in range(2, 55556):
if prime[i]:
prime[2*i::i] = [False]*(55555//i-1)
arr = []
for i in range(11, 55556):
if prime[i] and i % 10 == 1:
arr.append(str(i))
print(' '.join(arr[:N]))
``` | instruction | 0 | 43,648 | 5 | 87,296 |
Yes | output | 1 | 43,648 | 5 | 87,297 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79
Submitted Solution:
```
n = int(input())
prime = [1]*55556
prime_num = []
for i in range(2,55556):
if prime[i] and i%5 == 1:
prime_num.append(i)
t = 1
while (t*i <= 55555):
prime[t*i] = 0
t += 1
print(*prime_num[:n])
``` | instruction | 0 | 43,649 | 5 | 87,298 |
Yes | output | 1 | 43,649 | 5 | 87,299 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79
Submitted Solution:
```
a = [0]*55556
N = int(input())
for i in range(2,55556):
for j in range(2*i,55556,i):
a[j] += 1
A = []
for i in range(2,55556):
if a[i]==0 and i%5==1:
A.append(str(i))
print(' '.join(A[:N]))
``` | instruction | 0 | 43,650 | 5 | 87,300 |
Yes | output | 1 | 43,650 | 5 | 87,301 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79
Submitted Solution:
```
n=int(input())
a=[]
for i in range(11,55556):
if i%5==1 and i%2==1:
f=0
for j in range(2,round(i**0.5)+1):
if i%j==0:
f=1
break
if f==0:
a.append(i)
print(*a[:n])
``` | instruction | 0 | 43,651 | 5 | 87,302 |
Yes | output | 1 | 43,651 | 5 | 87,303 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79
Submitted Solution:
```
N=int(input())
print([11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 331, 401, 421, 431, 461, 491, 521, 541, 571, 601, 631, 641, 661, 691, 701, 751, 761, 811, 821, 881, 911, 941, 971, 991, 1021, 1031, 1051, 1061, 1091, 1151, 1171, 1181, 1201, 1231, 1291, 1301, 1321, 1361, 1381][0:N])
``` | instruction | 0 | 43,652 | 5 | 87,304 |
No | output | 1 | 43,652 | 5 | 87,305 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79
Submitted Solution:
```
n = int(input())
d=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863, 17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047, 18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143, 18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301, 18307, 18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461, 18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593, 18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211, 19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793, 19801, 19813, 19819, 19841, 19843, 19853, 19861, 19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973, 19979, 19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051, 20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, 20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, 20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431, 20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551, 20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747, 20749, 20753, 20759, 20771, 20773, 20789, 20807, 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44549, 44563, 44579, 44587, 44617, 44621, 44623, 44633, 44641, 44647, 44651, 44657, 44683, 44687, 44699, 44701, 44711, 44729, 44741, 44753, 44771, 44773, 44777, 44789, 44797, 44809, 44819, 44839, 44843, 44851, 44867, 44879, 44887, 44893, 44909, 44917, 44927, 44939, 44953, 44959, 44963, 44971, 44983, 44987, 45007, 45013, 45053, 45061, 45077, 45083, 45119, 45121, 45127, 45131, 45137, 45139, 45161, 45179, 45181, 45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289, 45293, 45307, 45317, 45319, 45329, 45337, 45341, 45343, 45361, 45377, 45389, 45403, 45413, 45427, 45433, 45439, 45481, 45491, 45497, 45503, 45523, 45533, 45541, 45553, 45557, 45569, 45587, 45589, 45599, 45613, 45631, 45641, 45659, 45667, 45673, 45677, 45691, 45697, 45707, 45737, 45751, 45757, 45763, 45767, 45779, 45817, 45821, 45823, 45827, 45833, 45841, 45853, 45863, 45869, 45887, 45893, 45943, 45949, 45953, 45959, 45971, 45979, 45989, 46021, 46027, 46049, 46051, 46061, 46073, 46091, 46093, 46099, 46103, 46133, 46141, 46147, 46153, 46171, 46181, 46183, 46187, 46199, 46219, 46229, 46237, 46261, 46271, 46273, 46279, 46301, 46307, 46309, 46327, 46337, 46349, 46351, 46381, 46399, 46411, 46439, 46441, 46447, 46451, 46457, 46471, 46477, 46489, 46499, 46507, 46511, 46523, 46549, 46559, 46567, 46573, 46589, 46591, 46601, 46619, 46633, 46639, 46643, 46649, 46663, 46679, 46681, 46687, 46691, 46703, 46723, 46727, 46747, 46751, 46757, 46769, 46771, 46807, 46811, 46817, 46819, 46829, 46831, 46853, 46861, 46867, 46877, 46889, 46901, 46919, 46933, 46957, 46993, 46997, 47017, 47041, 47051, 47057, 47059, 47087, 47093, 47111, 47119, 47123, 47129, 47137, 47143, 47147, 47149, 47161, 47189, 47207, 47221, 47237, 47251, 47269, 47279, 47287, 47293, 47297, 47303, 47309, 47317, 47339, 47351, 47353, 47363, 47381, 47387, 47389, 47407, 47417, 47419, 47431, 47441, 47459, 47491, 47497, 47501, 47507, 47513, 47521, 47527, 47533, 47543, 47563, 47569, 47581, 47591, 47599, 47609, 47623, 47629, 47639, 47653, 47657, 47659, 47681, 47699, 47701, 47711, 47713, 47717, 47737, 47741, 47743, 47777, 47779, 47791, 47797, 47807, 47809, 47819, 47837, 47843, 47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939, 47947, 47951, 47963, 47969, 47977, 47981, 48017, 48023, 48029, 48049, 48073, 48079, 48091, 48109, 48119, 48121, 48131, 48157, 48163, 48179, 48187, 48193, 48197, 48221, 48239, 48247, 48259, 48271, 48281, 48299, 48311, 48313, 48337, 48341, 48353, 48371, 48383, 48397, 48407, 48409, 48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487, 48491, 48497, 48523, 48527, 48533, 48539, 48541, 48563, 48571, 48589, 48593, 48611, 48619, 48623, 48647, 48649, 48661, 48673, 48677, 48679, 48731, 48733, 48751, 48757, 48761, 48767, 48779, 48781, 48787, 48799, 48809, 48817, 48821, 48823, 48847, 48857, 48859, 48869, 48871, 48883, 48889, 48907, 48947, 48953, 48973, 48989, 48991, 49003, 49009, 49019, 49031, 49033, 49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121, 49123, 49139, 49157, 49169, 49171, 49177, 49193, 49199, 49201, 49207, 49211, 49223, 49253, 49261, 49277, 49279, 49297, 49307, 49331, 49333, 49339, 49363, 49367, 49369, 49391, 49393, 49409, 49411, 49417, 49429, 49433, 49451, 49459, 49463, 49477, 49481, 49499, 49523, 49529, 49531, 49537, 49547, 49549, 49559, 49597, 49603, 49613, 49627, 49633, 49639, 49663, 49667, 49669, 49681, 49697, 49711, 49727, 49739, 49741, 49747, 49757, 49783, 49787, 49789, 49801, 49807, 49811, 49823, 49831, 49843, 49853, 49871, 49877, 49891, 49919, 49921, 49927, 49937, 49939, 49943, 49957, 49991, 49993, 49999, 50021, 50023, 50033, 50047, 50051, 50053, 50069, 50077, 50087, 50093, 50101, 50111, 50119, 50123, 50129, 50131, 50147, 50153, 50159, 50177, 50207, 50221, 50227, 50231, 50261, 50263, 50273, 50287, 50291, 50311, 50321, 50329, 50333, 50341, 50359, 50363, 50377, 50383, 50387, 50411, 50417, 50423, 50441, 50459, 50461, 50497, 50503, 50513, 50527, 50539, 50543, 50549, 50551, 50581, 50587, 50591, 50593, 50599, 50627, 50647, 50651, 50671, 50683, 50707, 50723, 50741, 50753, 50767, 50773, 50777, 50789, 50821, 50833, 50839, 50849, 50857, 50867, 50873, 50891, 50893, 50909, 50923, 50929, 50951, 50957, 50969, 50971, 50989, 50993, 51001, 51031, 51043, 51047, 51059, 51061, 51071, 51109, 51131, 51133, 51137, 51151, 51157, 51169, 51193, 51197, 51199, 51203, 51217, 51229, 51239, 51241, 51257, 51263, 51283, 51287, 51307, 51329, 51341, 51343, 51347, 51349, 51361, 51383, 51407, 51413, 51419, 51421, 51427, 51431, 51437, 51439, 51449, 51461, 51473, 51479, 51481, 51487, 51503, 51511, 51517, 51521, 51539, 51551, 51563, 51577, 51581, 51593, 51599, 51607, 51613, 51631, 51637, 51647, 51659, 51673, 51679, 51683, 51691, 51713, 51719, 51721, 51749, 51767, 51769, 51787, 51797, 51803, 51817, 51827, 51829, 51839, 51853, 51859, 51869, 51871, 51893, 51899, 51907, 51913, 51929, 51941, 51949, 51971, 51973, 51977, 51991, 52009, 52021, 52027, 52051, 52057, 52067, 52069, 52081, 52103, 52121, 52127, 52147, 52153, 52163, 52177, 52181, 52183, 52189, 52201, 52223, 52237, 52249, 52253, 52259, 52267, 52289, 52291, 52301, 52313, 52321, 52361, 52363, 52369, 52379, 52387, 52391, 52433, 52453, 52457, 52489, 52501, 52511, 52517, 52529, 52541, 52543, 52553, 52561, 52567, 52571, 52579, 52583, 52609, 52627, 52631, 52639, 52667, 52673, 52691, 52697, 52709, 52711, 52721, 52727, 52733, 52747, 52757, 52769, 52783, 52807, 52813, 52817, 52837, 52859, 52861, 52879, 52883, 52889, 52901, 52903, 52919, 52937, 52951, 52957, 52963, 52967, 52973, 52981, 52999, 53003, 53017, 53047, 53051, 53069, 53077, 53087, 53089, 53093, 53101, 53113, 53117, 53129, 53147, 53149, 53161, 53171, 53173, 53189, 53197, 53201, 53231, 53233, 53239, 53267, 53269, 53279, 53281, 53299, 53309, 53323, 53327, 53353, 53359, 53377, 53381, 53401, 53407, 53411, 53419, 53437, 53441, 53453, 53479, 53503, 53507, 53527, 53549, 53551, 53569, 53591, 53593, 53597, 53609, 53611, 53617, 53623, 53629, 53633, 53639, 53653, 53657, 53681, 53693, 53699, 53717, 53719, 53731, 53759, 53773, 53777, 53783, 53791, 53813, 53819, 53831, 53849, 53857, 53861, 53881, 53887, 53891, 53897, 53899, 53917, 53923, 53927, 53939, 53951, 53959, 53987, 53993, 54001, 54011, 54013, 54037, 54049, 54059, 54083, 54091, 54101, 54121, 54133, 54139, 54151, 54163, 54167, 54181, 54193, 54217, 54251, 54269, 54277, 54287, 54293, 54311, 54319, 54323, 54331, 54347, 54361, 54367, 54371, 54377, 54401, 54403, 54409, 54413, 54419, 54421, 54437, 54443, 54449, 54469, 54493, 54497, 54499, 54503, 54517, 54521, 54539, 54541, 54547, 54559, 54563, 54577, 54581, 54583, 54601, 54617, 54623, 54629, 54631, 54647, 54667, 54673, 54679, 54709, 54713, 54721, 54727, 54751, 54767, 54773, 54779, 54787, 54799, 54829, 54833, 54851, 54869, 54877, 54881, 54907, 54917, 54919, 54941, 54949, 54959, 54973, 54979, 54983, 55001, 55009, 55021, 55049, 55051, 55057, 55061, 55073, 55079, 55103, 55109, 55117, 55127, 55147, 55163, 55171, 55201, 55207, 55213, 55217, 55219, 55229, 55243, 55249, 55259, 55291, 55313, 55331, 55333, 55337, 55339, 55343, 55351, 55373, 55381, 55399, 55411, 55439, 55441, 55457, 55469, 55487, 55501, 55511, 55529, 55541, 55547]
e=d[:5]
i=5
while(len(e)<n):
x=e[-5:]
t=sum(e[-5:])
k = [t+d[i]-e[0],t+d[i]-e[1],t+d[i]-e[2],t+d[i]-e[3],t+d[i]-e[4],]
j=0
for z in k:
if z in d:
j+=1
if j==0:
e.append(d[i])
i+=1
c=[]
for i in range(n):
c.append(str(e[i]))
print(' '.join(c))
``` | instruction | 0 | 43,653 | 5 | 87,306 |
No | output | 1 | 43,653 | 5 | 87,307 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79
Submitted Solution:
```
import math
N = int(input())
pl = [2,3,5,7,11,13]
a = [3,5,7,11]
sums = [26]
for i in range(55555):
if len(a) == N:
break
j = i+13
if not(0 in set([(j % p) for p in pl if p < math.sqrt(j)])):
pl.append(j)
f=0
for x in sums:
if not(0 in set([((x+j) % p) for p in pl if p < math.sqrt(x+j)])):
f=1
break
if f == 0:
a.append(j)
sums = sums + [s - y + j for s in sums for y in a]
if len(a) == N:
break
print(' '.join(map(str,a)))
``` | instruction | 0 | 43,654 | 5 | 87,308 |
No | output | 1 | 43,654 | 5 | 87,309 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:
* a_i (1 \leq i \leq N) is a prime number at most 55 555.
* The values of a_1, a_2, ..., a_N are all different.
* In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.
If there are multiple such sequences, printing any of them is accepted.
Constraints
* N is an integer between 5 and 55 (inclusive).
Input
Input is given from Standard Input in the following format:
N
Output
Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.
Examples
Input
5
Output
3 5 7 11 31
Input
6
Output
2 3 5 7 11 13
Input
8
Output
2 5 7 13 19 37 67 79
Submitted Solution:
```
def is_prime(n):
i = 2
while i * i <=n:
if n % i == 0:
return False
i += 1
return True
def main():
N = int(input())
prime = [2,3,5,7,11]
synth = [sum(prime)]
inf = 55556
for i in range(13,inf,2):
if is_prime(i) == True:
for j in synth:
num = i + j
if is_prime(num) == True:
break
else:
prime.append(num)
if len(prime) == N:
break
print(*prime)
if __name__ == '__main__':
main()
``` | instruction | 0 | 43,655 | 5 | 87,310 |
No | output | 1 | 43,655 | 5 | 87,311 |
Provide a correct Python 3 solution for this coding contest problem.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9 | instruction | 0 | 43,799 | 5 | 87,598 |
"Correct Solution:
```
setA = set()
while True:
try:
a = input()
s = set(map(int, input().split()))
setA = setA.union(s)
except EOFError:
break
for elem in sorted(setA):
print(elem)
``` | output | 1 | 43,799 | 5 | 87,599 |
Provide a correct Python 3 solution for this coding contest problem.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9 | instruction | 0 | 43,800 | 5 | 87,600 |
"Correct Solution:
```
a=int(input())
a_li=list(map(int, input().split()))
b=int(input())
b_li=list(map(int, input().split()))
answer=sorted(set(a_li+b_li))
ans=[print(i) for i in answer]
``` | output | 1 | 43,800 | 5 | 87,601 |
Provide a correct Python 3 solution for this coding contest problem.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9 | instruction | 0 | 43,801 | 5 | 87,602 |
"Correct Solution:
```
n = int(input())
A = set(map(int, input().split()))
m = int(input())
B = set(map(int, input().split()))
for c in sorted(list(A | B)):
print(c)
``` | output | 1 | 43,801 | 5 | 87,603 |
Provide a correct Python 3 solution for this coding contest problem.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9 | instruction | 0 | 43,802 | 5 | 87,604 |
"Correct Solution:
```
n = int(input())
a = list(map(int,input().split()))
m = int(input())
b = list(map(int,input().split()))
c = sorted(set(a)|set(b))
for d in c:print (d)
``` | output | 1 | 43,802 | 5 | 87,605 |
Provide a correct Python 3 solution for this coding contest problem.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9 | instruction | 0 | 43,803 | 5 | 87,606 |
"Correct Solution:
```
if __name__ == '__main__':
input()
A = set(map(int,input().split()))
input()
B = set(map(int,input().split()))
C = sorted(A|B)
for i in C:
print(i)
``` | output | 1 | 43,803 | 5 | 87,607 |
Provide a correct Python 3 solution for this coding contest problem.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9 | instruction | 0 | 43,804 | 5 | 87,608 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
"""
Set Operation - Set Union
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP2_9_A&lang=jp
"""
_ = input()
A = set([int(a) for a in input().split()])
_ = input()
B = set([int(b) for b in input().split()])
print(*sorted(A | B), sep='\n')
``` | output | 1 | 43,804 | 5 | 87,609 |
Provide a correct Python 3 solution for this coding contest problem.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9 | instruction | 0 | 43,805 | 5 | 87,610 |
"Correct Solution:
```
input()
L = [int(x) for x in input().split()]
input()
Q = [int(x) for x in input().split()]
for i in sorted(set(L)|set(Q)):
print(i)
``` | output | 1 | 43,805 | 5 | 87,611 |
Provide a correct Python 3 solution for this coding contest problem.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9 | instruction | 0 | 43,806 | 5 | 87,612 |
"Correct Solution:
```
n=int(input())
A=list(map(int,input().split()))
m=int(input())
B=list(map(int,input().split()))
C=list(set(A)|set(B))
C.sort()
print('\n'.join(map(str,C)))
``` | output | 1 | 43,806 | 5 | 87,613 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9
Submitted Solution:
```
n = int(input())
a = set(map(int, input().split()))
m = int(input())
b = set(map(int, input().split()))
s_union = a.union(b)
print(*sorted(s_union), sep="\n")
``` | instruction | 0 | 43,807 | 5 | 87,614 |
Yes | output | 1 | 43,807 | 5 | 87,615 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9
Submitted Solution:
```
n = int(input())
a = set(map(int,input().split()))
m = int(input())
b = set(map(int,input().split()))
c = a | b
c = list(c)
c.sort()
for i in c:
print(i,sep="\n")
``` | instruction | 0 | 43,808 | 5 | 87,616 |
Yes | output | 1 | 43,808 | 5 | 87,617 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9
Submitted Solution:
```
#組み込み関数頼み
n = int(input())
a = set(map(int, input().split( )))
m = int(input())
b = set(map(int, input().split( )))
sm = a|b
#print(sm)
ans = list(sm)
ans.sort()
#print(*ans)
for i in ans:
print(i)
``` | instruction | 0 | 43,809 | 5 | 87,618 |
Yes | output | 1 | 43,809 | 5 | 87,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the union of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements of $A$ and $B$ are given in ascending order respectively. There are no duplicate elements in each set.
Output
Print elements in the union in ascending order. Print an element in a line.
Example
Input
3
1 5 8
2
5 9
Output
1
5
8
9
Submitted Solution:
```
n = int(input())
alist = list(map(int, input().split()))
m = int(input())
blist = list(map(int, input().split()))
anslist = alist + blist
anslist = list(set(anslist))
anslist.sort()
for ans in anslist:
print(ans)
``` | instruction | 0 | 43,810 | 5 | 87,620 |
Yes | output | 1 | 43,810 | 5 | 87,621 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer n he can represent fraction <image> as a sum of three distinct positive fractions in form <image>.
Help Vladik with that, i.e for a given n find three distinct positive integers x, y and z such that <image>. Because Chloe can't check Vladik's answer if the numbers are large, he asks you to print numbers not exceeding 109.
If there is no such answer, print -1.
Input
The single line contains single integer n (1 ≤ n ≤ 104).
Output
If the answer exists, print 3 distinct numbers x, y and z (1 ≤ x, y, z ≤ 109, x ≠ y, x ≠ z, y ≠ z). Otherwise print -1.
If there are multiple answers, print any of them.
Examples
Input
3
Output
2 7 42
Input
7
Output
7 8 56
Submitted Solution:
```
n=int(input())
if n<=1:
print(-1)
else:
print("%d %d %d"%(n,n*(n+1),n+1))
``` | instruction | 0 | 44,315 | 5 | 88,630 |
Yes | output | 1 | 44,315 | 5 | 88,631 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer n he can represent fraction <image> as a sum of three distinct positive fractions in form <image>.
Help Vladik with that, i.e for a given n find three distinct positive integers x, y and z such that <image>. Because Chloe can't check Vladik's answer if the numbers are large, he asks you to print numbers not exceeding 109.
If there is no such answer, print -1.
Input
The single line contains single integer n (1 ≤ n ≤ 104).
Output
If the answer exists, print 3 distinct numbers x, y and z (1 ≤ x, y, z ≤ 109, x ≠ y, x ≠ z, y ≠ z). Otherwise print -1.
If there are multiple answers, print any of them.
Examples
Input
3
Output
2 7 42
Input
7
Output
7 8 56
Submitted Solution:
```
n = int(input()) ; cond = 0
for i in range(n + 1, 2 * n + 1):
if (2 / n) == (1 / n) + (1 / i) + (1 / (n * i // (i - n))):
print(n, i, n * i // (i - n)) ; cond = 1 ; break
if cond == 0:
print(-1)
``` | instruction | 0 | 44,317 | 5 | 88,634 |
No | output | 1 | 44,317 | 5 | 88,635 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In the School of Magic in Dirtpolis a lot of interesting objects are studied on Computer Science lessons.
Consider, for example, the magic multiset. If you try to add an integer to it that is already presented in the multiset, each element in the multiset duplicates. For example, if you try to add the integer 2 to the multiset \{1, 2, 3, 3\}, you will get \{1, 1, 2, 2, 3, 3, 3, 3\}.
If you try to add an integer that is not presented in the multiset, it is simply added to it. For example, if you try to add the integer 4 to the multiset \{1, 2, 3, 3\}, you will get \{1, 2, 3, 3, 4\}.
Also consider an array of n initially empty magic multisets, enumerated from 1 to n.
You are to answer q queries of the form "add an integer x to all multisets with indices l, l + 1, …, r" and "compute the sum of sizes of multisets with indices l, l + 1, …, r". The answers for the second type queries can be large, so print the answers modulo 998244353.
Input
The first line contains two integers n and q (1 ≤ n, q ≤ 2 ⋅ 10^{5}) — the number of magic multisets in the array and the number of queries, respectively.
The next q lines describe queries, one per line. Each line starts with an integer t (1 ≤ t ≤ 2) — the type of the query. If t equals 1, it is followed by three integers l, r, x (1 ≤ l ≤ r ≤ n, 1 ≤ x ≤ n) meaning that you should add x to all multisets with indices from l to r inclusive. If t equals 2, it is followed by two integers l, r (1 ≤ l ≤ r ≤ n) meaning that you should compute the sum of sizes of all multisets with indices from l to r inclusive.
Output
For each query of the second type print the sum of sizes of multisets on the given segment.
The answers can be large, so print them modulo 998244353.
Examples
Input
4 4
1 1 2 1
1 1 2 2
1 1 4 1
2 1 4
Output
10
Input
3 7
1 1 1 3
1 1 1 3
1 1 1 2
1 1 1 1
2 1 1
1 1 1 2
2 1 1
Output
4
8
Note
In the first example after the first two queries the multisets are equal to [\{1, 2\},\{1, 2\},\{\},\{\}], after the third query they are equal to [\{1, 1, 2, 2\},\{1, 1, 2, 2\},\{1\},\{1\}].
In the second example the first multiset evolves as follows:
\{\} → \{3\} → \{3, 3\} → \{2, 3, 3\} → \{1, 2, 3, 3\} → \{1, 1, 2, 2, 3, 3, 3, 3\}.
Submitted Solution:
```
n, q = [int(i) for i in input().split(' ')]
sets = [[set(), 0] for _ in range(n)]
for _ in range(q):
line = [int(i) for i in input().split(' ')]
# print(sets)
if line[0] == 1:
_, l, r, x = line
for i in range(l - 1, r):
if x in sets[i][0]:
sets[i][1] = (sets[i][1] << 1) % 998244353
else:
sets[i][1] = (sets[i][1] + 1) % 998244353
sets[i][0].add(x)
else:
_, l, r = line
print(sum(map(lambda k: k[1] % 998244353, sets[l - 1: r])))
``` | instruction | 0 | 44,402 | 5 | 88,804 |
No | output | 1 | 44,402 | 5 | 88,805 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In the School of Magic in Dirtpolis a lot of interesting objects are studied on Computer Science lessons.
Consider, for example, the magic multiset. If you try to add an integer to it that is already presented in the multiset, each element in the multiset duplicates. For example, if you try to add the integer 2 to the multiset \{1, 2, 3, 3\}, you will get \{1, 1, 2, 2, 3, 3, 3, 3\}.
If you try to add an integer that is not presented in the multiset, it is simply added to it. For example, if you try to add the integer 4 to the multiset \{1, 2, 3, 3\}, you will get \{1, 2, 3, 3, 4\}.
Also consider an array of n initially empty magic multisets, enumerated from 1 to n.
You are to answer q queries of the form "add an integer x to all multisets with indices l, l + 1, …, r" and "compute the sum of sizes of multisets with indices l, l + 1, …, r". The answers for the second type queries can be large, so print the answers modulo 998244353.
Input
The first line contains two integers n and q (1 ≤ n, q ≤ 2 ⋅ 10^{5}) — the number of magic multisets in the array and the number of queries, respectively.
The next q lines describe queries, one per line. Each line starts with an integer t (1 ≤ t ≤ 2) — the type of the query. If t equals 1, it is followed by three integers l, r, x (1 ≤ l ≤ r ≤ n, 1 ≤ x ≤ n) meaning that you should add x to all multisets with indices from l to r inclusive. If t equals 2, it is followed by two integers l, r (1 ≤ l ≤ r ≤ n) meaning that you should compute the sum of sizes of all multisets with indices from l to r inclusive.
Output
For each query of the second type print the sum of sizes of multisets on the given segment.
The answers can be large, so print them modulo 998244353.
Examples
Input
4 4
1 1 2 1
1 1 2 2
1 1 4 1
2 1 4
Output
10
Input
3 7
1 1 1 3
1 1 1 3
1 1 1 2
1 1 1 1
2 1 1
1 1 1 2
2 1 1
Output
4
8
Note
In the first example after the first two queries the multisets are equal to [\{1, 2\},\{1, 2\},\{\},\{\}], after the third query they are equal to [\{1, 1, 2, 2\},\{1, 1, 2, 2\},\{1\},\{1\}].
In the second example the first multiset evolves as follows:
\{\} → \{3\} → \{3, 3\} → \{2, 3, 3\} → \{1, 2, 3, 3\} → \{1, 1, 2, 2, 3, 3, 3, 3\}.
Submitted Solution:
```
class Multiset():
def __init__(self):
self.elements = list()
self.size = 0
def add(self, x):
if (x in self.elements):
self.size *= 2
else:
self.elements.append(x)
self.size += 1
n, q = list(map(int, input().split()))
a = [Multiset() for i in range(n)]
for i in range(n):
tmp = list(map(int, input().split()))
if (tmp[0] == 1):
for j in range(tmp[1] - 1, tmp[2]):
a[j].add(tmp[3])
elif (tmp[0] == 2):
sum = 0
for j in range(tmp[1] - 1, tmp[2]):
sum += a[j].size
print(sum)
``` | instruction | 0 | 44,403 | 5 | 88,806 |
No | output | 1 | 44,403 | 5 | 88,807 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In the School of Magic in Dirtpolis a lot of interesting objects are studied on Computer Science lessons.
Consider, for example, the magic multiset. If you try to add an integer to it that is already presented in the multiset, each element in the multiset duplicates. For example, if you try to add the integer 2 to the multiset \{1, 2, 3, 3\}, you will get \{1, 1, 2, 2, 3, 3, 3, 3\}.
If you try to add an integer that is not presented in the multiset, it is simply added to it. For example, if you try to add the integer 4 to the multiset \{1, 2, 3, 3\}, you will get \{1, 2, 3, 3, 4\}.
Also consider an array of n initially empty magic multisets, enumerated from 1 to n.
You are to answer q queries of the form "add an integer x to all multisets with indices l, l + 1, …, r" and "compute the sum of sizes of multisets with indices l, l + 1, …, r". The answers for the second type queries can be large, so print the answers modulo 998244353.
Input
The first line contains two integers n and q (1 ≤ n, q ≤ 2 ⋅ 10^{5}) — the number of magic multisets in the array and the number of queries, respectively.
The next q lines describe queries, one per line. Each line starts with an integer t (1 ≤ t ≤ 2) — the type of the query. If t equals 1, it is followed by three integers l, r, x (1 ≤ l ≤ r ≤ n, 1 ≤ x ≤ n) meaning that you should add x to all multisets with indices from l to r inclusive. If t equals 2, it is followed by two integers l, r (1 ≤ l ≤ r ≤ n) meaning that you should compute the sum of sizes of all multisets with indices from l to r inclusive.
Output
For each query of the second type print the sum of sizes of multisets on the given segment.
The answers can be large, so print them modulo 998244353.
Examples
Input
4 4
1 1 2 1
1 1 2 2
1 1 4 1
2 1 4
Output
10
Input
3 7
1 1 1 3
1 1 1 3
1 1 1 2
1 1 1 1
2 1 1
1 1 1 2
2 1 1
Output
4
8
Note
In the first example after the first two queries the multisets are equal to [\{1, 2\},\{1, 2\},\{\},\{\}], after the third query they are equal to [\{1, 1, 2, 2\},\{1, 1, 2, 2\},\{1\},\{1\}].
In the second example the first multiset evolves as follows:
\{\} → \{3\} → \{3, 3\} → \{2, 3, 3\} → \{1, 2, 3, 3\} → \{1, 1, 2, 2, 3, 3, 3, 3\}.
Submitted Solution:
```
n, q = map(int,input().split())
m = 998244353
a = [[set(),0] for i in range(n)]
for i in range(q):
line = list(map(int,input().split()))
if line[0] == 1:
for j in range(line[1]-1,line[2]):
if line[3] in a[j][0]:
a[j][1] *= 2
else:
a[j][0].add(line[3])
a[j][1] += 1
a[j][1] = a[j][1] % m
else:
print(sum(a[j][1] for j in range(n)) % m)
``` | instruction | 0 | 44,404 | 5 | 88,808 |
No | output | 1 | 44,404 | 5 | 88,809 |
Provide a correct Python 3 solution for this coding contest problem.
We have a long seat of width X centimeters. There are many people who wants to sit here. A person sitting on the seat will always occupy an interval of length Y centimeters.
We would like to seat as many people as possible, but they are all very shy, and there must be a gap of length at least Z centimeters between two people, and between the end of the seat and a person.
At most how many people can sit on the seat?
Constraints
* All input values are integers.
* 1 \leq X, Y, Z \leq 10^5
* Y+2Z \leq X
Input
Input is given from Standard Input in the following format:
X Y Z
Output
Print the answer.
Examples
Input
13 3 1
Output
3
Input
12 3 1
Output
2
Input
100000 1 1
Output
49999
Input
64146 123 456
Output
110
Input
64145 123 456
Output
109 | instruction | 0 | 44,518 | 5 | 89,036 |
"Correct Solution:
```
a,b,c=input().split()
a=int(a)
b=int(b)
c=int(c)
print((a-c)//(b+c))
``` | output | 1 | 44,518 | 5 | 89,037 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a long seat of width X centimeters. There are many people who wants to sit here. A person sitting on the seat will always occupy an interval of length Y centimeters.
We would like to seat as many people as possible, but they are all very shy, and there must be a gap of length at least Z centimeters between two people, and between the end of the seat and a person.
At most how many people can sit on the seat?
Constraints
* All input values are integers.
* 1 \leq X, Y, Z \leq 10^5
* Y+2Z \leq X
Input
Input is given from Standard Input in the following format:
X Y Z
Output
Print the answer.
Examples
Input
13 3 1
Output
3
Input
12 3 1
Output
2
Input
100000 1 1
Output
49999
Input
64146 123 456
Output
110
Input
64145 123 456
Output
109
Submitted Solution:
```
x,y,z=map(int,input().split())
print(len(range(z+y,x-z+1,z+y)))
``` | instruction | 0 | 44,520 | 5 | 89,040 |
Yes | output | 1 | 44,520 | 5 | 89,041 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a long seat of width X centimeters. There are many people who wants to sit here. A person sitting on the seat will always occupy an interval of length Y centimeters.
We would like to seat as many people as possible, but they are all very shy, and there must be a gap of length at least Z centimeters between two people, and between the end of the seat and a person.
At most how many people can sit on the seat?
Constraints
* All input values are integers.
* 1 \leq X, Y, Z \leq 10^5
* Y+2Z \leq X
Input
Input is given from Standard Input in the following format:
X Y Z
Output
Print the answer.
Examples
Input
13 3 1
Output
3
Input
12 3 1
Output
2
Input
100000 1 1
Output
49999
Input
64146 123 456
Output
110
Input
64145 123 456
Output
109
Submitted Solution:
```
a, b, c = map(int, input().split())
max = int((a + c) / (b + 2*c))
print(max)
``` | instruction | 0 | 44,524 | 5 | 89,048 |
No | output | 1 | 44,524 | 5 | 89,049 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer n, we denote the integer obtained by reversing the decimal notation of n (without leading zeroes) by rev(n). For example, rev(123) = 321 and rev(4000) = 4.
You are given a positive integer D. How many positive integers N satisfy rev(N) = N + D?
Constraints
* D is an integer.
* 1 ≤ D < 10^9
Input
Input is given from Standard Input in the following format:
D
Output
Print the number of the positive integers N such that rev(N) = N + D.
Examples
Input
63
Output
2
Input
75
Output
0
Input
864197532
Output
1920
Submitted Solution:
```
from collections import deque
D = deque(map(int,input()))
leading_zeros = 0
while D[-1] == 0:
D.pop()
leading_zeros += 1
# (10-x) ways: (0,x)-(9-x,9) -> (-x, x)
# (x) ways: (10-x,0)-(9,x-1) -> (10-x, -10 + x)
def solve(D):
r = 1
while len(D) > 1:
h,t = D.popleft(), D.pop()
c = h + t
if -1 <= c <= 0:
r *= 10-t
D[0] += c*10
elif 9 <= c <= 10:
r *= t
c -= 10
D[0] += c*10
D[-1] += 1
i = -1
while D[i] == 10:
D[i] = 0
D[i-1] += 1
i -= 1
else:
r = 0
D.clear()
if len(D) == 1:
r *= 10 if D[0] == 0 else 0
return r
r = 1
if len(D) >= 2:
h,t = D.popleft(), D.pop()
c = h + t
if not D:
r = t - (leading_zeros == 0) if c == 9 else 0
elif 9 <= c <= 10:
r = t - (leading_zeros == 0)
c -= 10
D[0] += c*10
D[-1] += 1
i = -1
while D[i] == 10:
D[i] = 0
D[i-1] += 1
i -= 1
r *= solve(D)
if leading_zeros > 0:
r *= 9
r = str(r)+'0'*(leading_zeros-1)
print(r)
``` | instruction | 0 | 44,536 | 5 | 89,072 |
No | output | 1 | 44,536 | 5 | 89,073 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a positive integer n, we denote the integer obtained by reversing the decimal notation of n (without leading zeroes) by rev(n). For example, rev(123) = 321 and rev(4000) = 4.
You are given a positive integer D. How many positive integers N satisfy rev(N) = N + D?
Constraints
* D is an integer.
* 1 ≤ D < 10^9
Input
Input is given from Standard Input in the following format:
D
Output
Print the number of the positive integers N such that rev(N) = N + D.
Examples
Input
63
Output
2
Input
75
Output
0
Input
864197532
Output
1920
Submitted Solution:
```
D = int(input())
def table(i, k):
if i == k:
return list(range(9, -1, -1)) + [0]*9
else:
return list(range(10, 0, -1)) + list(range(1, 10))
def nine(i):
return 10**i - 1
def rec(d, i, k):
res = 0
num = table(i, k)
if i == 1:
for j in range(-9, 10):
if 9*j == d:
return num[j]
return 0
if i == 2:
for j in range(-9, 10):
if d == 99*j:
return 10*num[j]
if not -10*nine(i) <= d <= 10*nine(i):
return 0
for j in range(-9, 10):
if d%10 == j*nine(i)%10:
res += num[j] * rec((d-j*nine(i))//10, i-2, k)
return res
l = 0
while D % 10 == 0:
D//= 10
l += 1
if l == 0:
a = 1
else:
a = 9*10**(l-1)
ans = 0
for i in range(1, 13):
if not l:
ans += rec(D, i, i)
else:
ans += rec(D, i, 100)
print(a * ans)
``` | instruction | 0 | 44,537 | 5 | 89,074 |
No | output | 1 | 44,537 | 5 | 89,075 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.
Input
The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).
Output
If it's impossible to find the representation of n as a product of k numbers, print -1.
Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.
Examples
Input
100000 2
Output
2 50000
Input
100000 20
Output
-1
Input
1024 5
Output
2 64 2 2 2
Submitted Solution:
```
def Factor(n):
Ans = []
d = 2
while d * d <= n:
if n % d == 0:
Ans.append(d)
n //= d
else:
d += 1
if n > 1:
Ans.append(n)
return Ans
n ,k = map(int, input().split())
ans1= Factor(n)
if len(ans1) < k:
print('-1')
elif len(ans1) == k:
for elem in ans1:
print(elem, end=' ')
else:
while len(ans1)!=k:
j = int(ans1[0])
ans1.remove(ans1[0])
ans1[0] = j * int(ans1[0])
for elem in ans1:
print(elem, end=' ')
``` | instruction | 0 | 45,071 | 5 | 90,142 |
Yes | output | 1 | 45,071 | 5 | 90,143 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.
Input
The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).
Output
If it's impossible to find the representation of n as a product of k numbers, print -1.
Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.
Examples
Input
100000 2
Output
2 50000
Input
100000 20
Output
-1
Input
1024 5
Output
2 64 2 2 2
Submitted Solution:
```
import math
n , k = map(int,input().split())
l = []
for i in range(2 , n+1):
if n % i == 0 :
while n % i == 0 and len(l) < k - 1:
n //= i
l.append(i)
if n > 1 :
l.append(n)
if k == len(l):
print(*l)
else:
print(-1)
``` | instruction | 0 | 45,072 | 5 | 90,144 |
Yes | output | 1 | 45,072 | 5 | 90,145 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.
Input
The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).
Output
If it's impossible to find the representation of n as a product of k numbers, print -1.
Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.
Examples
Input
100000 2
Output
2 50000
Input
100000 20
Output
-1
Input
1024 5
Output
2 64 2 2 2
Submitted Solution:
```
n, k = map(int, input().split())
arr = []
og = n
i = 2
while i*i <= n:
while n % i == 0:
arr.append(i)
n = n//i
i += 1
if len(arr) >= k-1:
temp = arr[:k-1]
this = 1
for i in temp:
this *= i
if og//this != 1:
print(*arr[:k-1], og//this)
else:
print(-1)
else:
print(-1)
``` | instruction | 0 | 45,073 | 5 | 90,146 |
Yes | output | 1 | 45,073 | 5 | 90,147 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.
Input
The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).
Output
If it's impossible to find the representation of n as a product of k numbers, print -1.
Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.
Examples
Input
100000 2
Output
2 50000
Input
100000 20
Output
-1
Input
1024 5
Output
2 64 2 2 2
Submitted Solution:
```
n, k = map(int, input().split())
i = 2
nn = n
a = []
for i in range(2, n+1):
while nn % i == 0:
if k > 1:
a.append(i)
nn //= i
elif i == nn:
a.append(i)
nn//=i
else:
break
k -= 1
if k == 0:
for i in a:
print(i, end = ' ')
else:
print(-1)
``` | instruction | 0 | 45,074 | 5 | 90,148 |
Yes | output | 1 | 45,074 | 5 | 90,149 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.
Input
The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).
Output
If it's impossible to find the representation of n as a product of k numbers, print -1.
Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.
Examples
Input
100000 2
Output
2 50000
Input
100000 20
Output
-1
Input
1024 5
Output
2 64 2 2 2
Submitted Solution:
```
import math
n, z = map(int, input().split())
S = []
k = 2
q = round(math.sqrt(n))
while k <= q:
if n % k == 0:
S.append(k)
n //= k
q = round(math.sqrt(n))
else:
k += 1
S.append(n)
s = ""
p = 1
if len(S) < z:
print(-1)
else:
if k > 1:
for a in range(z - 2):
s += str(S[a]) + " "
s += str(S[z - 2])
for b in range(z - 1, len(S)):
p *= S[b]
if p > 1:
s += " " + str(p)
print(s)
else:
print(S[0])
``` | instruction | 0 | 45,076 | 5 | 90,152 |
No | output | 1 | 45,076 | 5 | 90,153 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.
Input
The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).
Output
If it's impossible to find the representation of n as a product of k numbers, print -1.
Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.
Examples
Input
100000 2
Output
2 50000
Input
100000 20
Output
-1
Input
1024 5
Output
2 64 2 2 2
Submitted Solution:
```
m,n=map(int,input().split())
t=2
count=0
x=m
l=[]
while t<=m-1 and m>0:
#print(m,t," ")
if m%t==0:
count+=1
#print(m,t)
m//=t
l.append(t)
else:
t+=1
#print(m,t)
if m>1:
count+=1
l.append(m)
print(l)
if count>=n:
ln=l[:n]
if count!=n:
i,temp=n,1
while count!=n and i<len(l):
temp*=l[i]
i+=1
count-=1
ln[-1]=temp
for i in ln:
print(i,end=" ")
else:
print(-1)
``` | instruction | 0 | 45,077 | 5 | 90,154 |
No | output | 1 | 45,077 | 5 | 90,155 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.
Input
The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).
Output
If it's impossible to find the representation of n as a product of k numbers, print -1.
Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.
Examples
Input
100000 2
Output
2 50000
Input
100000 20
Output
-1
Input
1024 5
Output
2 64 2 2 2
Submitted Solution:
```
n, k = map(int, input().split(" "))
i = 2
table = []
while i * i <= n:
while n % i == 0:
n /= i
table.append(i)
i += 1
if n > 1:
table.append(n)
if len(table) >= k:
ans = []
for j in range(k-1):
ans.append(table[j])
tmp = 1
for j in range(k-1, len(table)):
tmp *= table[j]
ans.append(tmp)
print(" ".join(map(str,ans)))
else:
print(-1)
``` | instruction | 0 | 45,078 | 5 | 90,156 |
No | output | 1 | 45,078 | 5 | 90,157 |
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