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"
	"math"
)

func main() {
	var n int
	var p int

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

	if n == 1 {
		fmt.Println(p)
		return
	}

	result := p
	end := int(math.Pow(float64(p), float64(1.0)/float64(n)))
	for i := 1; i <= end; i++ {
		pow := int(math.Floor((math.Pow(float64(i), float64(n)))))
		if (p % pow) == 0 {
			result = i
		}
	}
	fmt.Println(result)
}