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)

(* O(√p) *)
let n, p = Scanf.scanf " %d %d" @@ fun a b -> a, b
let factorize_primes n =
  let rec f acc c d m =
    if d > m || d * d > n then
      List.rev @@ if c > 0 then (d, c) :: acc else if m > 1 then (m, 1) :: acc else acc
    else
      if m mod d = 0 then f acc (c + 1) d @@ m / d
      else f (if c > 0 then (d, c) :: acc else acc) 0 (d + 1) m in
  f [] 0 2 n
let rec pow b n = if n <= 0 then 1 else b * pow b (n - 1)
let ps = factorize_primes p
let _ = List.fold_left (fun acc (b, c) -> acc * pow b (c / n)) 1 ps |> Printf.printf "%d\n"