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)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
#![macro_use]

use std::cmp::*;
use std::collections::*;
use std::io::*;
use std::mem::*;
use std::num::*;
use std::slice::*;

fn main() {
    let mut io = IO::new(stdin(), stdout(), stderr());
    // ===================================== //
    let (n, p): (i64, i64) = (io.read(), io.read());
    let pf = prime_factor(p as i64);

    let mut ans = 1;
    for (key, value) in &pf {
        if *value >= n {
            let kakeru = *value / n;
            let mut mm = kakeru;
            let mut b = *key;
            while mm > 0 {
                if mm & 1 == 1 {
                    ans *= b;
                }
                b = b * b;
                mm >>= 1;
            }
        }
    }
    println!("{}", ans);
}

pub fn prime_factor(mut n: i64) -> HashMap<i64, i64> {
    let mut res: HashMap<i64, i64> = HashMap::new();
    let mut i = 2;
    while i * i <= n {
        while n % i == 0 {
            let v = match res.get(&i) {
                Some(v) => *v + 1,
                None => 1,
            };
            res.insert(i, v);
            n /= i;
        }
        i += 1;
    }
    if n != 1 {
        res.insert(n, 1);
    }
    res
}
// IO
struct IO<R: Read, W: Write, E: Write> {
    Read: R,
    Write: BufWriter<W>,
    Error: BufWriter<E>,
}
impl<R: Read, W: Write, E: Write> IO<R, W, E> {
    fn new(r: R, w: W, e: E) -> IO<R, W, E> {
        IO {
            Read: r,
            Write: BufWriter::new(w),
            Error: BufWriter::new(e),
        }
    }
    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
    {
        let next: String = self
            .Read
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect();
        next.parse().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
    fn readn<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect::<Vec<_>>()
    }
    fn readmat<T: std::str::FromStr>(&mut self, n: usize, m: usize) -> Vec<Vec<T>> {
        (0..n).map(|_| self.readn(m)).collect()
    }
    fn write<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
    }
    fn writeln<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
        self.Write.write(b"\n");
    }
    fn debug<S: std::fmt::Debug>(&mut self, val: S) {
        writeln!(self.Error, "(debug) {:?}", &val);
    }
}