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: Runtime Error)

use std::io::Read;

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: u32 = itr.next().unwrap().parse().unwrap();
    let mut p: u64 = itr.next().unwrap().parse().unwrap();

    if n == 1 {
        println!("{}", p);
        return;
    }
    let mut ans: u64 = 1;
    let mut i: u64 = 2;
    while i * i <= p {
        let mut cnt: u32 = 0;
        while p % i == 0 {
            cnt += 1;
            p /= i;
        }
        ans *= i.pow(cnt / n);
        i += 1;
    }
    println!("{}", ans);
}