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: Time Limit Exceeded)

require 'prime'

n, p = gets.split.map(&:to_i)
h = Hash.new(0)
g = Prime::EratosthenesGenerator.new
d = g.next
while d < p / 2
  q = p
  while q % d == 0
    h[d] += 1
    q /= d
  end
  d = g.next
end
if h == {} || p == 1
  puts 1
elsif n == 1
  puts p
else
  ans = 1
  h.sort_by{|k, v| -v}.each do |k, v|
    ans *= k if v >= n
  end
  puts ans
end