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::io;
use std::cmp;
use std::collections::HashMap;
fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let N: i64 = iter.next().unwrap().parse().unwrap();
    let P: i64 = iter.next().unwrap().parse().unwrap();
    let mut max: i64 = 1;
    for (divisor, count2) in &primeFactor(P) {
//        println!("{} {}", *divisor,*count2);
        let mut count: i64 = *count2;
                while count >= N {
                    max *= *divisor;
                    count -= N;
                }
    }
    println!("{}", max);
}
fn primeFactor(n0: i64) -> HashMap<i64,i64> {
    let mut n: i64 = n0;
    let mut res: HashMap<i64,i64> = HashMap::new();
    let mut i: i64 = 2;
    while i*i<=n {
        while n % i == 0 {
            let count = match res.get(&i) {
                Some(&c) => c,
                None => 0
            };
            res.insert(i, 1+count);
            n/=i;
        }
        i+=1;
    }
    if n!=1 {
            let count = match res.get(&n) {
                Some(&c) => c,
                None => 0
            };
            res.insert(n, 1+count);
//            match res.get(&n) {
//                Some(count) => res.insert(n, 1+count),
//                None => res.insert(n, 1)
//            }
//            let count: i64 = * res.get(&n).unwrap();
//        res.insert(n, 1+count);
    }
    return res;
}