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
import qualified Data.ByteString.Char8 as BS
import Data.Maybe
import Data.List

main :: IO ()
main = do
  [n, x] <- map read . words <$> getLine
  a <- map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine
  let
    solve [] (_, i) = (0, i)
    solve (y:ys) (s, i) =
      let
        (next, j) = if s + x * (i+1) < y then (s, i+1) else (y, i)
      in (\x1 (x2, y2) -> (x1 + x2, y2)) next $ solve ys (next, j)
    ans = flip map [1..n] $ \i -> let
        (l, r) = splitAt i a
        (v, j) = solve (r++l) (10^9+1, 0)
      in v + x * j
  print $ minimum ans
