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 Ruby (2.3.3) (judge verdict: Accepted)

# frozen_string_literal: true

$factors = {}

def factrize(n)
  (2..Math.sqrt(n)).each do |d|
    ex = 0
    while n % d == 0
      ex += 1
      $factors.store(d, ex)
      n /= d
    end
  end
  $factors.store(n, 1) if n != 1
end

n, p = gets.split.map(&:to_i)
ans = 1
factrize(p)
list = $factors.to_a
list.each do |factor|
  (1..factor[1] / n).each do |_i|
    ans *= factor[0]
  end
end

puts ans