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 OCaml (4.02.3) (judge verdict: Accepted)

let rec fix f x = f (fix f) x
let factors n = (* O(sqrt n) *)
  let m,r = ref n,ref [] in
  for i=2 to (2+int_of_float (sqrt @@ float_of_int n)) do
    if !m mod i = 0 then (
      let k = ref 0 in
      while !m mod i = 0 do
        k := !k + 1; m := !m / i;
      done;
      r := (i,!k) :: !r
    )
  done;
  if !m>1 then (!m,1)::!r else !r
let pow n k =
  let rec f a n = function
  | 0 -> a | 1 -> n*a | k when k mod 2 = 0 -> f a (n*n) (k/2) | k -> f (a*n) (n*n) (k/2)
  in f 1 n k
let n,p = Scanf.scanf " %d %d" @@ fun u v -> u,v
let () = print_int (factors p |> List.fold_left (fun u (m,k) ->
  u * (if k>=n then pow m (k/n) else 1)) 1)