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.split(/ /).map(&:to_i)

if (n == 1)
  puts 1
  exit
end
array = []

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

j = 0
c = 1
ans = 1
#p array
array.each do |i|
  if (j == i)
    c += 1
    if (c == n)
      ans *= i
      c = 1
    end
  else
    c = 1
  end
  j = i
end

puts ans