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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);

		Long X = sc.nextLong();
		Long a = (long) 1;

		while(true){
			if(X%a==0){
				Long ans = calc(X,a);
				if(ans!=0){
					System.out.println((ans+a) + " " + ans);
					return;
				}
			}
			a++;
		}
	}

	public static Long calc(Long target, Long a){
      
      	Long chk = target - (long) Math.pow(a,5);
		Long b = (long) 1;

		while(true){
            if(chk%a==0){
              Long A = (long) Math.pow(b,5);
              Long B = (long) Math.pow(a+b,5);
              boolean bl = false;
              if(B-A>target){
                  bl = true;
              }
              if(B-A==target){
                  return b;
              }

              B = (long) Math.pow(a-b,5);
              if(bl&&(B+A>target)){
                  return (long) 0;
              }
              if(B+A==target){
                  return -b;
              }
            }
			b++;
		}
	}
}