For given integers m and n, compute mn (mod 1,000,000,007). Here, A (mod M) is the remainder when A is divided by M.

Constraints

* 1 ≤ m ≤ 100
* 1 ≤ n ≤ 109

Input


m n


Two integers m and n are given in a line.

Output

Print mn (mod 1,000,000,007) in a line.

Examples

Input

2 3


Output

8


Input

5 8


Output

390625
let z = 1000000007

let rec pow (x, n) =
  if n = 0 then 1
  else if n mod 2 = 0 then pow (x * x, n / 2)
  else pow (x * x, n / 2) * x mod z

let () =
  Scanf.scanf "%d %d\n" (fun m n -> (m, n))
  |> pow |> Printf.printf "%d\n"