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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
    n,p,s:int64;
    f:array[0..1000010] of longint;
    i,j,t:longint;
begin
    read(n,p);
    if n=1 then
    begin
        writeln(p);
        halt;
    end;
    if p=1 then 
    begin
        writeln(1);
        halt;
    end;
    fillchar(f,sizeof(f),0);
    i:=1;
    t:=trunc(sqrt(p))+1;
    while (p<>1) and (i<=t) do
    begin
        inc(i);
        while p mod i=0 do
        begin
            p:=p div i;
            inc(f[i]);
        end;
    end;
    s:=1;
    for i:=2 to t do
        if f[i]>=n then
            for j:=1 to f[i] div n do s:=s*i;
    writeln(s);
end.