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"
	"os"
	"strconv"
	"strings"
	"bufio"
)

var (
	sc = bufio.NewScanner(os.Stdin)
	buf = make([]byte, 1000)
)

func scanText() string{
	sc.Scan()
	return sc.Text()
}

func scanTextArray(n int) []string {
	out := make([]string, n)
	for i, v := range(strings.Split(scanText(), "")) {
		out[i] = v
	}
	return out
}

func scanInt() int {
	out, e := strconv.Atoi(scanText())
	if e != nil {
        panic(e)
    }
	return out
}

func scanIntArray(n int) []int {
	out := make([]int, n)
	for i, v := range(strings.Split(scanText(), " ")) {
		num, e := strconv.Atoi(v)
		if e != nil {
			panic(e)
		}
		out[i] = num
	}
	return out
}
func pow(x, n int) int{
	ans := 1
	for i:=0; i<n; i++ {
		ans *= x
	}
	return ans
}
//  template end

func main() {
	sc.Buffer(buf, 10000)
	np := scanIntArray(2)
	N, P := np[0], np[1]
	x := 2
	ans := 1
	if N == 1 {
		ans = P
	} else if P == 1 {
		ans = 1
	} else {
		for {
			x_pow := pow(x, N)
			// fmt.Println(x, N, x_pow, P)
			if P < x_pow {
				break
			} else {
				if P % x_pow == 0 {
					ans *= x
					P /= x_pow
				}
			}
			x++
		}
	}
	fmt.Println(ans)
}