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)

#[allow(unused_imports)]
use itertools::Itertools;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn main() {
    input! {
        n: u64,
        mut p: u64,
    }
    let mut f = std::collections::BTreeMap::new();
    for i in 2.. {
        if i * i > p {
            if p != 1 {
                f.insert(p, 1);
            }
            break;
        }
        let mut c = 0;
        while p % i == 0 {
            p /= i;
            c += 1;
        }
        if c != 0 {
            f.insert(i, c);
        }
    }
    // println!("{:?}", f);
    let mut res = 1;
    for (p, c) in f {
        res *= p.pow((c / n) as u32);
    }
    println!("{}", res);
}