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)

n,p=gets.chomp.split(' ').map(&:to_i)
a=p**(1.0/n)
a=a.floor
a.times do |i|
  i=a-i
  if p%i==0
     check=true
     if n==2
       puts i 
       break
    end
     x=p/i
     (n-1).times do 
       if x%i != 0 && x%(i+1) != 0
         check=false
         break
       elsif x%i !=0 && x%(i+1) == 0
         i=i+1
         x=x/i
       else
         x=x/i
       end
     end
     if check
      puts i
     break
     end
  end
end