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 JavaScript (node.js v5.12) (judge verdict: Accepted)

inp = require('fs').readFileSync('/dev/stdin', 'utf8').trim().split('\n')
l = inp.shift().split(' ')
N = l.shift() * 1
P = l.shift() * 1

// 素因数分解
_primFactors = function(n) {
  var arr = []
  if (n == 1) {
      return [{n:1, r:1}]
  }
  s = n

  var i = 2
  r = 0
  if (n % i === 0) {
    do {
      r++
      n /= i
    } while(n%i===0)
    arr.push({n: i, r: r})
  }
  
  for (i = 3; i*i <= s; i+=2) {
    r = 0
    if (n % i === 0) {
       do {
           r++
           n /= i
       } while(n%i===0)
       arr.push({n: i, r: r})
    }
  }
  if (n > 1) {
      arr.push({n: n, r: 1})
  }
  return arr
}

arr = _primFactors(P)
ans = 1
for (i=0; i<arr.length;i++) {
    a = arr[i]
    r = a.r
    while (r>=N) {
        ans *= a.n
        r -= N
    }
}
console.log(ans)