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)

a = gets.chomp.split.map{|aa|aa.to_i}
require 'prime'
b = a[1].prime_division
anan = Array.new(b.size).map{Array.new}
ans = []
for bb in 0...b.size
  b[bb][1].times do
    anan[bb].push(b[bb][0])
  end
end
for bb in 0...anan.size
  if (anan[bb].size / a[0]) >= 1
    ans.push(anan[bb][0])
  end
end
if ans.size == 0
  puts "1"
else
  if a[0] = 1
    puts a[1]
  else
  aaaa = 1
  unless a[1] == 1
  puts ans.map{|aaa|aaaa = aaaa*aaa}.pop
  else
    puts "1"
  end
end
end