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: Time Limit Exceeded)

(* log(n) *)
let rec is_divisible n m c =
  if c = 0 then
    true
  else
    if n mod m = 0 then
      is_divisible (n / m) m (c - 1)
    else
      false

(* O(√p * log(p)) *)
let solve n p =
  if n = 1 then
    p
  else (* n >= 2 *)
    let m = int_of_float (floor (sqrt (float_of_int p))) in
    let rec loop g =
      if is_divisible p g n then
        g
      else
        loop (g - 1)
    in
      loop m (* n >= 2 では g <= m (∵ 指数関数の単調増加性より) *)

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