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>
#include<math.h>

long long int N, P, F, ans, l, i, j, k;

int main(void){
	scanf("%lld%lld", &N, &P);
	if(N==1){printf("%lld\n", P);return 0;}
	if(P==1){printf("1\n");return 0;}
	ans=1;
	j=0;while(P%2==0){P/=2;j++;}if(j/N!=0){for(k=0; k<j/N; k++){ans*=2;}}
	j=0;while(P%3==0){P/=3;j++;}if(j/N!=0){for(k=0; k<j/N; k++){ans*=3;}}
	j=0;while(P%5==0){P/=5;j++;}if(j/N!=0){for(k=0; k<j/N; k++){ans*=5;}}
	for(i=5, l=sqrt(P); i<l; i+=6){
		j=0;while(P%i==0){P/=i;j++;}if(j/N!=0){for(k=0; k<j/N; k++){ans*=i;}}
		j=0;while(P%(i+2)==0){P/=(i+2);j++;}if(j/N!=0){for(k=0; k<j/N; k++){ans*=(i+2);}}
	}
	printf("%lld\n", ans);
	return 0;
}