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 Julia (0.5.0) (judge verdict: Time Limit Exceeded)

parseInt(x) = parse(Int, x)

function main()
	n,p=map(parseInt,split(readline()))
	d = Dict{Int,Int}()
	x = p
	i = 2
	while x > 1 || i <= sqrt(x)
		if x%i == 0
			if haskey(d,i)
				d[i] += 1
			else
				d[i] = 1
			end
			x = div(x, i)
		else
			i += 1
		end
	end
	k = 1
	for key in keys(d)
		z = div(d[key],n)
		k *= key^z
	end
	print(k)
end

main()