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)

array = gets.split.map(&:to_i)

def factorization (m)
ary = []
  s = Math.sqrt(m.to_f).to_i
for i in(2..s)
  r = 0
  while m%i==0
      m=m/i
      r +=1
    end
    unless r ==0
    ary.push([i,r])
  end
end
if (m>s)
  ary.push([m,1])
end
return ary
end

n= array[0]
p = array[1]

factor_s =factorization(p)
ans = 1
factor_s.each{|fs|
  while fs[1]>=n
    ans *=fs[0]
    fs[1] -=n
  end}
p ans