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)

n,num=gets.chomp.split(" ").map(&:to_i)
if num == 1
 puts 1
 exit
elsif n == 1
 puts num
 exit
end
 
np = num
ln = np / 2
n_c = 0
c = 1
i = 2
ft = false
while (i <= ln && i <= np) do
  ni = i ** n
  if np % ni == 0
    c = c * i
    np = np / ni
  else
    i += 2
    i -= 1if i == 4
  end
end
 
puts c