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 (1.3.71) (judge verdict: Accepted)

// https://atcoder.jp/contests/caddi2018/tasks/caddi2018_a

fun main() {
    caddi2018a()
}

fun caddi2018a() {
    val (n, p) = readLine()!!.split(" ").map { it.toLong() }
    if (n == 1L) {
        println(p)
        return
    }
    if (p == 1L) {
        println(1)
        return
    }
    // 素因数分解
    val primes = mutableMapOf<Long, Int>()
    var t = p
    var i = 2L
    while (i * i <= t) {
        var count = 0
        while (t % i == 0L) {
            t /= i
            count++
        }
        primes[i] = count
        i++
    }
    if (t != 1L) primes[t] = 1
    var gcd = 1L
    for ((prime, count) in primes.filterValues { it >= n }) {
        val factor = count / n
        repeat(factor.toInt()) {
            gcd *= prime
        }
    }
    println(gcd)
}