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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.math.BigInteger

fun main(args: Array<String>) {
    val (n, p) = readLine()!!.split(" ").map { it.toLong() }
    println(solve(n, p))
}

fun solve(n: Long, p: Long): Long {
    if (n >= 60) return 1
    if (n == 1L) return p
    var max = 1L
    var x = 1L
    while (true) {
        if (BigInteger.valueOf(x).pow(n.toInt()) > BigInteger.valueOf(p)) {
            break
        }
        val xp = BigInteger.valueOf(x).pow(n.toInt()).toLong()
        if (p % xp == 0L) {
            max = x
        }
        x++
    }
    return max
}