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)

fn factor(mut n: u128) -> Vec<(u128, u128)> {
    let mut ret = vec![];
    for i in 2.. {
        if i * i > n {
            break;
        }
        let mut cnt = 0;
        while n % i == 0 {
            cnt += 1;
            n /= i;
        }
        if cnt != 0 {
            ret.push((i, cnt));
        }
    }
    if n != 1 {
        ret.push((n, 1));
    }
    ret
}

fn main() {
    proconio::input! {
        n: u128,
        p: u128,
    }
    let factors = factor(p);
    let gcd_candidates = factors
        .iter()
        .filter(|(_factor, num)| *num >= n)
        .collect::<Vec<_>>();
    let ans = gcd_candidates.iter().fold(1u128, |sum, (factor, num)| {
        sum * factor.pow((num / n) as u32)
    });
    println!("{}", ans);
}