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 (1.15.1) (judge verdict: Accepted)

use std::collections::HashMap;

use std::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

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

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: u64 = iterator.next().unwrap().parse().unwrap();
    let p: u64 = iterator.next().unwrap().parse().unwrap();

    if n == 1 {
        return p.to_string()
    }

    let mut counts: HashMap<u64, u64> = HashMap::new();

    let mut i = 2;
    while i * i <= p {
        if !is_prime(i) {
            i += 1;
            continue;
        }
        let mut x = p;
        while x % i == 0 {
            x /= i;
            *counts.entry(i).or_insert(0) += 1;
        }
        i += 1;
    }

    let mut g: u64 = 1;
    for (k, v) in counts {
        g *= k.pow((v / n) as u32);
    }
    return g.to_string();
}

fn is_prime(n: u64) -> bool {
    let mut i: u64 = 2;
    while i * i <= n {
        if n % i == 0 {
            return false;
        }
        i += 1;
    }
    return true;
}