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 (4.10.0) (judge verdict: Accepted)

let (n, p) = Scanf.sscanf (read_line ()) "%d %d" @@ fun n p -> (n, p)

let rec prime_fact acc i n =
  if n = 0 then acc
  else if n < i * i then n :: acc
  else if n mod i = 0 then prime_fact (i :: acc) i (n / i)
  else prime_fact acc (i + 1) n

let prime_fact n =
  List.fold_left (fun acc i ->
    match acc with
      | [] -> [(i, 1)]
      | (v, cnt) :: xs -> if v = i then (v, cnt + 1) :: xs else (i, 1) :: (v, cnt) :: xs
  ) [] @@ prime_fact [] 2 n

let ps = prime_fact p

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


let () = 
  let ans = List.fold_left (fun ans (v, cnt) ->
    ans * (pow v (cnt / n))
  ) 1 ps in
  Printf.printf "%d\n" ans