Problem:
Score : 400 points

Problem Statement

Give a pair of integers (A, B) such that A^5-B^5 = X.
It is guaranteed that there exists such a pair for the given integer X.

Constraints

1 \leq X \leq 10^9

X is an integer.

There exists a pair of integers (A, B) satisfying the condition in Problem Statement.

Input

Input is given from Standard Input in the following format:

X

Output

Print A and B, with space in between.
If there are multiple pairs of integers (A, B) satisfying the condition, you may print any of them.

A B

Sample Input 1

33

Sample Output 1

2 -1

For A=2 and B=-1, A^5-B^5 = 33.

Sample Input 2

1

Sample Output 2

0 -1

Solution in C (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <math.h>

int main(void)
{
  long long a,b,x;

  scanf("%lld", &x);

  /*a>=0 b=all*/

  long long i, i_max, j, tmp;
  /*b<0 search*/
  if(pow(x, 5.0) - 1 == 0) i = pow(x, 5.0);
  else i = (long long)pow(x, 5.0)+1;
  i_max = i;
  for ( ; i > 0; i--) {
    b = -i;
    tmp = x - i*i*i*i*i;
    for (j = 0; j < i_max; j++) {
      if (tmp == j*j*j*j*j) { a = j; goto END; }
    }
  }

  /*b>=0 search*/
  for (i = i_max; ; i++) {
    b = pow(x-i*i*i*i*i, 5.0);
    if (b*b*b*b*b + a*a*a*a*a == x) {
      a = i;
	break;
    }
  }

 END:
  printf("%lld %lld\n", a, b);

  return 0;
}