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: Wrong Answer)

#!/usr/bin/env ruby

(n, p) = gets.chomp.split(/ /).map(&:to_i)
array = []
if (n == 1)
  puts p
  exit
end
if (p == 1)
  puts 1
  exit
end

q = p
i = 2
while (i * i <= q)
  if(q % i == 0)
    array << i 
    q /= i
  end
  i += 1
end

array2 = []
array.each do |k|
  m = 0
  while (p % k == 0)
    p /= k
    m += 1
  end
  array2 << [k, m]
end

r = 1
array2.each do |a|
  if (a[1] / n > 0)
    r = r * a[0] * (a[1] / n)
  end
end
puts r