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 Control.Applicative ((<$>), (<*>))
import Control.Monad
import Data.List

main :: IO ()
main = do
  solve <$> getl (wrds toInt) <*> getl (wrds toInt) >>= print

solve :: [Int] -> [Int] -> Int
solve [n, x] as = h . g . transpose . f n $ [[(0,i)| i <- as]]
  where
    f m ys
      | m == 1 = ys
      | otherwise = let zs = (tail.head) ys ++ [(head.head) ys] in f (m-1)  (map (\(i,j) -> (i+1,j)) zs : ys)
    g ys = map (minimumBy (\(i,j) (k,l) -> (i*x+j) `compare` (k*x+l))) ys
    h ys = (sum . map snd) ys + (maximum . map fst) ys * x
    
toInt :: String -> Int
toInt = read

wrds :: (String -> a) -> String -> [a]
wrds f = map f . words

getl :: (String -> a) -> IO a
getl f = f <$> getLine
