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 for_fold a b f v = if a >= b then v else for_fold (a+1) b f (f v a)
let _ = Scanf.scanf "%d %d" @@ fun n x ->
  let a = Array.init n (fun _ -> Scanf.scanf " %d" ((+) 0)) in
  for_fold 0 n (fun s i ->
    let s' = Array.fold_left (+) 0 a in
    for i = n downto 1 do
      a.(i mod n) <- min a.(i mod n) a.((i-1) mod n)
    done;
    min s (s' + i*x)) 10101010101010
  |> Printf.printf "%d\n"