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 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
int main(void){
    double i,n,p,ans=0;
    scanf("%lf %lf",&n,&p);
    if(n==1)ans=p;
    else if(n>=40 || n>=p)ans=1;
    else if(n==2){
        for(i=1; i<=1000000; i++){
            if(fmod(p,pow(i,2))==0)ans=i;
        }
    }
    else if(n==3){
        for(i=1; i<=10000; i++){
            if(fmod(p,pow(i,3))==0)ans=i;
        }
    }
    else for(i=1; i<=1000; i++){
        if(fmod(p,pow(i,n))==0)ans=i;
    }
    printf("%.0lf",ans);
    return 0;
}