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 (n, p) = Scanf.scanf "%d %d\n" @@ fun n p -> (n, p)

let prime_fact n =
  let rec f arr i n =
    if n <= 1 then arr
    else if n < i * i then n :: arr
    else if n mod i = 0 then f (i :: arr) i (n / i)
    else f arr (i + 1) n
  in
  match f [] 2 n with
    | [] -> []
    | p :: ps ->
        let (acc, p, n) = List.fold_left (fun (acc, p, n) q ->
          if p = q
          then (acc, p, n + 1)
          else ((p, n) :: acc, q, 1)) ([], p, 1) ps in
        (p, n) :: acc

let rec pow n = function
  | 0 -> 1
  | i -> n * pow n (i - 1)

let () = 
  prime_fact p
    |> List.map (fun (i, j) -> pow i (j / n))
    |> List.fold_left ( * ) 1
    |> print_int