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 12.16.1) (judge verdict: Wrong Answer)

const factorization = (n) => {
    let primes= []
    for(let i=2; i*i<=n; i++) {
        let exponent = 0
        while(n%i===0) {
            n /= i
            exponent++
        }
        if(exponent) {
            primes.push({p:i, e:exponent})
        }
    }
    
    if(n!==1) {
        primes.push({p:n, e:1})
    }
    return primes
}

const main = (arg) => {
    const [N,P] = arg.split(" ").map(Number)
    const f = factorization(P)
    
    let gcd = BigInt(1);
    for(let i=0; i<f.length; i++){
        let tmp = parseInt(f[i].e/N)
        console.log(tmp)
        gcd *= BigInt(f[i].p**tmp)
    }
    console.log(gcd)
    
}

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