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<stdlib.h>
 
#define NEW(p,n){p=malloc((n)*sizeof(p[0]));if(p==NULL){printf("not enough memory\n");exit(1);};}
//pの型の変数n個の要素分のメモリを確保し、そのアドレスをpに代入するマクロ
 
#define INFTY 999999
 
//素数判定する関数(素数1,not0)
int prime_judge(unsigned long n){
    int ans=1;
    int i=2;
    while(i<n){
        if(n%i==0){
            ans=0;
            break;
        }
        else{
            i++;
        }
    }
 
    return ans;
}
 
int main(void){
    unsigned long N;
    unsigned long P;
 
    scanf("%ld",&N);
    scanf("%ld",&P);
 
    unsigned long testp=P;
 
    unsigned long ans=1;
    for(unsigned long i=2;i<=P;i++){
        if(prime_judge(i)==1){
            int count=0;
            while(testp%i==0){
                count++;
                testp=testp/i;
            }
            if(count>=N){
                ans=ans*i;
            }
        }
        if(testp==1){
            break;
        }
        if(prime_judge(testp)==1&&N!=1){
            break;
        }
    }
 
    printf("%ld\n",ans);
 
    return 0;
    
}