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>

int main() {
    long long N,P,i=2,j,k,c=1,memo[80000]={2,3},e=0;
    int a;

    scanf("%lld %lld",&N,&P);
    
    if(N==1) {
        i=P+1;
        c=P;
    }

    for(;i<=P;i++) {
        a=0;

        for(j=1;memo[j]*memo[j]<=i;j++) {
            if(i%memo[j]==0) {
                a=1;
                i++;
                break;
            }
        }

        if(a==1) continue;

        k=1;
        j=1;
        while(j<=N) {
            k*=i;
            j++;
            if(k>P) {
                a=1;
                break;
            }
        }

        if(a==1) break;

        memo[e]=i;
        e++;

        while(P%k==0) {
            c*=i;
            P/=k;
        }
        while(P%i==0) P/=i;

        if(i!=2) i++;
    }

    printf("%lld\n",c);
    return 0;
}