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 power m n =
  let rec doit m n acc =
    if n = 0 then acc
    else if n mod 2 = 0 then doit (m * m) (n / 2) acc
    else doit m (n - 1) (acc * m) in
  doit m n 1

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