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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
)

func main() {
	N, P := ReadInt(), ReadInt()
	factors := Factorization(P)
	ans := 1
	for i := 0; i < len(factors); i++ {
		factor, cnt := factors[i][0], factors[i][1]
		ans *= Pow(factor, cnt/N)
	}
	fmt.Println(ans)
}

func Pow(a, b int) int {
	x := 1
	for b > 0 {
		if b&1 == 1 {
			x *= a
		}
		a *= a
		b >>= 1
	}
	return x
}

func Factorization(n int) [][]int {
	res := [][]int{}
	for i := 2; i*i <= n; i++ {
		if n%i != 0 {
			continue
		}
		cnt := 0
		for n%i == 0 {
			n /= i
			cnt++
		}
		res = append(res, []int{i, cnt})
	}
	if n != 1 {
		res = append(res, []int{n, 1})
	}
	return res
}

var reader = bufio.NewReader(os.Stdin)

func Scan(a ...interface{}) {
	if _, err := fmt.Fscan(reader, a...); err != nil {
		panic(err)
	}
}
func ReadInt() (i int)       { Scan(&i); return }
func ReadString() (s string) { Scan(&s); return }
func ReadInts(n int) []int {
	v := make([]int, n)
	for i := 0; i < n; i++ {
		Scan(&v[i])
	}
	return v
}