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 std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("faild to read char") as char)
        .take_while(|c| !c.is_whitespace())
        .collect();
    token
        .parse()
        .ok()
        .expect("faild to parse token")
}

fn main(){
    let n: u64 = read();
    let p: u64 = read();
    let mut m = p;
    let mut ret = 1;

    for i in 2..p {
        if p < i * i {
            break;
        }
        let mut tmp = 0;
        while m % i == 0 {
            tmp += 1;
            m /= i;
        }
        ret *= pow(i, tmp / n);
    }
    if m > 1 {
        ret *= pow(m, 1 / n);
    }
    println!("{}", ret);
}

fn pow(a: u64, b: u64) -> u64 {
    if b == 0 {
        return 1;
    } else if b == 1 {
        return a;
    }

    let prev = pow(a, b / 2);
    if b % 2 == 0 {
        prev * prev
    } else {
        prev * prev * a
    }
}