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 Scala (2.11.7) (judge verdict: Accepted)

import annotation.tailrec
import collection.mutable.{ ListBuffer, HashMap }
import scala.io.StdIn

object Main extends App {

  @tailrec
  def primeFactRec(acc:ListBuffer[Long], num:Long, root:Long):List[Long] = {

    if(root * root > num) (acc += num).toList
    else {
      if(num % root == 0L) primeFactRec((acc += root), num/root, root)
      else primeFactRec(acc, num, root+1L)
    }
  }

  def callPrimeFactRec(n:Long):List[Long] = {

    val ret = ListBuffer.empty[Long]
    primeFactRec(ret, n, 2L)
  }

  val Array(n, p) = StdIn.readLine.split(" ").map(_.toLong)

  val div = callPrimeFactRec(p)
  val ans = {
    val map = HashMap.empty[Long,Long]
    div.foreach(p => {
      if(!map.contains(p)) map += (p -> 1L)
      else map += (p -> (map(p) + 1L))
    })

    map.map(e => math.pow(e._1, e._2/n))
      .filter(_ != 0).product.toLong
  }

  println(ans)
}