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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main(int argc, char *argv)
{
    long long n, p;

    long long maxCommon; 
    long long maxN;
    long long i;
    long long num;

    scanf("%lld %lld", &n, &p);

    maxCommon = 1;
    maxN = pow(p, 1/((double)n));

    // i = 2のとき
    while (1) {
        num = pow(maxCommon * 2, n);

        if (p % num == 0) {
            maxCommon *= 2;
        } else {
            break;
        }
    }

    i = 3;
    while(i <= maxN) {
        num = pow(maxCommon * i, n);
        if (num > p) {break;}

        if (p % num == 0) {
            maxCommon *= i;
        } else {
            i += 2;
        }
    }

    printf("%lld\n", maxCommon);
     

    return 0;
}