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: Wrong Answer)

#include<stdio.h>

long ruijo(long a,long b){
	int i;
	long r=1;
	for(i=0;i<b;i++)r=r*a;
	return r;
}

int main(){
	long n,p,ans=1;scanf("%ld%ld",&n,&p);
	long i;
	if(n==1){
		printf("%ld\n",p);
		return 0;
	}
	if(n>=37){
		puts("1");
		return 0;
	}
	for(i=2;ruijo(i,n)<=p;i++){
		if(p%ruijo(i,n)==0){
			ans=ans*i;
			p=p/(ruijo(i,n));
		}
	}
	printf("%ld\n",ans);
	return 0;
}