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 (GNU Fortran 9.2.1) (judge verdict: Accepted)

program CADDiB2018C
    implicit none
    integer(8)::N,P,Ps,i,i_cnt,ans=1
    read*,N,P
    Ps=int(sqrt(real(P)))+1
    do i=2,Ps
        if(mod(P,i)==0)then
            i_cnt=0
            do
                if(mod(P,i)/=0)exit
                P=P/i
                i_cnt=i_cnt+1
            end do
            ans=ans*(i**(i_cnt/N))
        end if
    end do
    ans=ans*(P**(1/N))
    print'(i0)',ans
end program CADDiB2018C