Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.

Snuke can perform the following two actions:

* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.

* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.




Find the minimum time that Snuke needs to have slimes in all N colors.

Constraints

* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9

Input

The input is given from Standard Input in the following format:


N x
a_1 a_2 ... a_N


Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
let rec tabulate n f = 
  let rec loop acc m =
    if m < n then loop (f m :: acc) (m + 1)
    else List.rev acc in
  loop [] 0

let () =
  let n, x = Scanf.scanf "%d %d\n" (fun n x -> n, x) in
  let as_ = Array.init n (fun _ -> Scanf.scanf "%d " (fun a -> a)) in
  tabulate n (fun i ->
    tabulate n (fun j -> as_.(j) + x * min ((n + i - j) mod n) ((n + j - i) mod n))
    |> List.fold_left min max_int)
  |> List.fold_left ( + ) 0
  |> Printf.printf "%d\n"
