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: Wrong Answer)

fun main(args: Array<String>) {
    caddi2018c()
}

fun caddi2018c() {
    val (n, p) = readLine()!!.split(" ").map { it.toLong() }

    val primes = primeFactorization(p)

    val answer = primes.map { Math.max(1, it.key * (it.value / n)) }.fold(1L) { acc, l -> acc * l }

    println(answer)
}

//素因数分解
private fun primeFactorization(n: Long): Map<Long, Long> {
    val factors = mutableMapOf<Long, Long>()
    var temp = n
    var i = 2L
    while (i * i <= temp) {
        while (temp % i == 0L) {
            factors[i] = (factors[i] ?: 0) + 1
            temp /= i
        }
        i++
    }
    // 素数が残った場合、それも含めるように(1は素数でないので含めない)
    if (temp > 1) factors[temp] = 1
    return factors
}