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
	i,ans,n,p,c:int64;
	j:Longint;
begin
	read(n,p);
	if n=1 then begin
		writeln(p);
		exit;
	end;
	i:=2;
	ans:=1;
	while i*i<=p do begin
		c:=0;
		while p mod i=0 do begin
			p:=p div i;
			inc(c);
		end;
		for j:=1 to c div n do ans:=ans*i;
		inc(i);
	end;
	writeln(ans);
end.