Problem:
Score : 300 points

Problem Statement

There are N integers a_1, a_2, ..., a_N not less than 1.
The values of a_1, a_2, ..., a_N are not known, but it is known that a_1 \times a_2 \times ... \times a_N = P.

Find the maximum possible greatest common divisor of a_1, a_2, ..., a_N.

Constraints

1 \leq N \leq 10^{12}

1 \leq P \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N P

Output

Print the answer.

Sample Input 1

3 24

Sample Output 1

2

The greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.

Sample Input 2

5 1

Sample Output 2

1

As a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.

Sample Input 3

1 111

Sample Output 3

111

Sample Input 4

4 972439611840

Sample Output 4

206

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

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

int main(void){
	long N,P,ans=1;
	scanf("%ld %ld",&N,&P);
	
	if(N==1){
		printf("%ld",P);
		return 0;
	}
	
	int div=0;
	while(P%2==0){
		P/=2;
		div++;
		if(div>=N) {
			ans*=2;
			div-=N;
		}
	}
	
	for(int i=3;P>1&&i<=sqrt(P);i+=2){
		div=0;
		while(P%i==0){
			P/=i;
			div++;
			if(div>=N) {
				ans*=i;
				div-=N;
			}
		}
		
	}
	
	printf("%ld",ans);
	
	return 0;
}