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>) {
    var (n, p) = readLine()!!.split(' ').map(String::toLong)
    val factors = calcFactors(p)
    var filterd = factors.filter { it.value >= n }

    if (filterd.isEmpty()) {
        println(1)
    } else {
        var total = 1L
        while (filterd.isNotEmpty()) {
            filterd.forEach { total *= it.key }
            n *= 2
            filterd = filterd.filter { it.value >= n }
        }
        println(total)
    }
}

fun calcFactors(n: Long): Map<Long, Long> {//素因数分解
    val factors = mutableMapOf<Long, Long>()
    var tmp = n
    var i = 2L
    while (i * i <= tmp) {
        while (tmp % i == 0L) {
            factors[i] = factors.getOrElse(i) { 0L } + 1L
            tmp /= i
        }
        i++
    }
    if (tmp > 1L) factors[tmp] = 1L
    return factors
}