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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function main(input) {
    const args = input.split('\n');
    const Num = args[0].split(' ');

    const N = parseInt(Num[0]);
    const P = parseInt(Num[1]);

    if (N === 1) {
        console.log(P)
        return 0;
    }

    var PrimeFactors = [];

    var prime = 7;
    var step = 4;

    const getPrimeFactors = n => {
        if (n < 2) return [];
        if (n === 2 || n === 3 || n === 5) return [n];
        if (n % 2 === 0) return [2, ...getPrimeFactors(n / 2)];
        if (n % 3 === 0) return [3, ...getPrimeFactors(n / 3)];
        if (n % 5 === 0) return [5, ...getPrimeFactors(n / 5)];
        const limit = Math.sqrt(n);
        while (prime <= limit) {
            if (n % prime === 0) return [prime, ...getPrimeFactors(n / prime)];
            prime += step;
            step = 6 - step;
        }
        return [n];
    };

    PF = getPrimeFactors(P);

    var counts = {};

    for (var i = 0; i < PF.length; i++) {
        var key = PF[i];
        counts[key] = (counts[key]) ? counts[key] + 1 : 1;
    }

    

    var ans = 1;

    var key = Object.keys(counts);

    for(var i = 0; i < key.length; i++) {
        if(parseInt(counts[key[i]]) >= N) {
            ans = ans * parseInt(key[i]);
        }
    }

    console.log(ans);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));