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: Wrong Answer)

use std::io;
use std::collections::HashMap;


fn main() {
    let (n, p) = {
        let i = read::<u64>();
        (i[0], i[1])
    };

    let mut hm = HashMap::new();
    let mut x = p;
    while let Some(f) = divide(x) {
        x /= f;
        *hm.entry(f).or_insert(0) += 1;
    }
    *hm.entry(x).or_insert(0) += 1;

    let mut ans = 1;

    for (k, v) in hm.iter() {
        if v >= &n {
            ans *= k * (v / n);
        }
    }

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


fn divide(n: u64) -> Option<u64> {
    for i in 2..(n as f64).sqrt().ceil() as u64 + 2 {
        if n % i == 0 {
            return Some(i);
        }
    } 
    return None;
}

#[allow(dead_code)]
fn read<T>() -> Vec<T>
where T:
    std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.split_whitespace()
        .map(|s| s.trim().parse().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_one<T>() -> T
where T:
    std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().parse().unwrap()
}