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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn prime_factorization(n: usize) -> Vec<(usize, usize)> {
    let mut p = vec![];
    if n < 2 {
        return p;
    }
    let mut n = n; // shadowing
    for i in 2.. {
        if i * i > n {
            break;
        }
        let mut c = 0;
        while n % i == 0 {
            c += 1;
            n /= i;
        }
        if c > 0 {
            p.push((i, c));
        }
    }
    if n != 1 {
        p.push((n, 1));
    }
    p
}

fn main() {
    input! {
        n: usize,
        p: usize,
    };
    let mut x = 1_usize;
    for (p_i, q_i) in prime_factorization(p) {
        x *= p_i.pow((q_i / n) as u32);
    }
    let ans = x;
    println!("{}", ans);
}