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: Wrong Answer)

package main

import (
	"fmt"
	"math"
)

var memo map[int][]int

func main() {
	memo = make(map[int][]int)

	var n int
	fmt.Scan(&n)
	var p int
	fmt.Scan(&p)

	mp := make(map[int]int)
	for _, a := range fact(p, 2) {
		mp[a] = mp[a] + 1
	}

	direct := 1
	for k, v := range mp {
		if v >= n {
			direct = direct * k
		}
	}
	fmt.Println(direct)

}

func fact(n int, start int) []int {
	_, exist := memo[n]
	if exist {
		return memo[n]
	}

	ret := make([]int, 0)
	flag := false
	for i := start; i <= int(math.Floor(float64(n)/2)); i++ {
		if (n % i) == 0 {
			ret = append(ret, i)
			ret = append(ret, fact(n/i, i)...)
			flag = true
			break
		}
	}
	if !flag {
		ret = append(ret, n)
	}
	return ret
}

/*
func isPrime(n int) bool {
	for i := 2; i <= int(math.Floor(float64(n)/2)); i++ {
		if n%i == 0 {
			return false
		}
	}
	return n > 1
}
*/