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 Lua (5.3.2) (judge verdict: Time Limit Exceeded)

N, P = io.read("*n","*n")
io.read()

i = 3
a = 1

while P % (2^N) == 0 and P ~= 0 do
  P = P // (2^N)
  a = a * 2
end

while i^N <= P do
  while P % (i^N) == 0 and P ~= 0 do
    P = P // (i^N)
    a = a * i
  end
  
  i = i + 2
end

print(a)