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)

n,m = gets.chomp.split(" ").map(&:to_i)
require 'prime'
pr = [1]
if n == 1
  puts m
  exit
end
Prime.each(10**7) do |prime|
  pr.push(prime)
end
pr2 = Array.new(pr.length, 0)
for i in 1..pr.length - 1
  while m % pr[i] == 0
    m /= pr[i]
    pr2[i] += 1
  end
  if m == 1
    break
  end
end
if m != 1
  pr2.push(1)
end
ans = 1
for i in 1..pr2.length - 1
  if pr2[i] >= n
    ans *= (pr[i]**(pr2[i]/n))
  end
end
puts ans