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(√n) *)
let lowest_prime_factor n =
  let m = int_of_float (floor (sqrt (float_of_int n))) in
  let rec loop i =
    if i > m then
      n
    else
      if n mod i = 0 then i else loop (i + 1)
  in
    loop 2

(* O(√n * log(n)) *)
let factorize_primes n =
  if n <= 1 then
    []
  else
    let rec loop sofar (p, count) m =
      if m = 1 then
        List.tl (List.rev ((p, count) :: sofar))
      else
        let prime = lowest_prime_factor m in
        if p = prime then
          loop sofar (p, count + 1) (m / p)
        else
          loop ((p, count) :: sofar) (prime, 1) (m / prime)
    in
      loop [] (1, 0) n

let solve n p =
  if p = 1 then
    1
  else
    List.fold_left
      (fun sofar (p, count) ->
        let factor = int_of_float (float_of_int p ** float_of_int (count / n)) in
        sofar * factor)
      1
      (factorize_primes p)

let _ = Scanf.scanf "%d %d" (fun n p -> solve n p |> string_of_int |> print_endline)