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)

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

    var current = p
    var factors = mutableMapOf<Long, Long>()
    divisors.forEach {
        while (current != 1L && current % it == 0L) {
            current /= it
            factors[it] = (factors[it] ?: 0L) + 1L
        }
    }
    factors[current] = 1L

    var ans = 1L
    factors.forEach {
        if (it.value >= n) {
            ans *= Math.pow(it.key.toDouble(), (it.value / n).toDouble()).toLong()
        }
    }

    println(ans)
}

fun prime(from : Long, to : Long = from) : List<Long> {
    return (from..to).filter { i ->
        val max = Math.sqrt(i.toDouble()).toLong()
        (2..max).all { j ->  i % j != 0L }
    }
}

fun decom(value : Long) : List<Long>{
    if (value == 1L) return listOf(1)
    val max = Math.sqrt(value.toDouble()).toLong()
    return prime(2, max).filter { value % it == 0L }
}