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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
implicit None
	integer(8)::n,p,q,i
	
	read *,n,p
	
	if(n >= 40)then
		print 101,1
		stop
		else if(n ==1)then
			print 101,p
			stop
	endif 
	
	q = int(real(p)**(1.0/real(n))+0.00001)
	
	do i =  q,2,-1
		if(mod(p,i**n) == 0)then
			print 101,i
			stop
		endif
	enddo
	
	print 101,1
101 format(i0)
end program main