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 (1.6) (judge verdict: Accepted)

package main

import "fmt"

func prmFac(x int) map[int]int {
	pfm := make(map[int]int)
	for i := 2; i*i <= x; i++ {
		for x%i == 0 {
			x /= i
			pfm[i]++
		}
	}
	if x > 1 {
		pfm[x]++
	}
	return pfm
}

func main() {
	var n, p int
	fmt.Scan(&n, &p)

	ans := 1
	for pn, cnt := range prmFac(p) {
		for i := 0; i < cnt; i++ {
			x := 1
			for j := 0; j < n; j++ {
				x *= pn
				if x > p {
					break
				} else if j == n-1 && p%x == 0 {
					ans *= pn
					p /= x
				}
			}
		}
	}
	fmt.Println(ans)
}