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 main() {
    input! {
        n: usize,
        p: usize,
    }

    let sqrt = (p as f64).sqrt().ceil() as usize;

    let mut ans = 1;
    let mut rem = p;
    for i in 2..=sqrt {
        let mut count = 0;
        while rem > 0 {
            if rem % i != 0 {
                break;
            } 
            rem /= i;
            count += 1;
        }
        if count >= n {
            ans *= i.pow((count / n) as u32);
        }
    }

    if n == 1 {
        ans = p;
    }

    println!("{}", ans);
}