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 Data.List( sortBy, subsequences, foldl')
import Data.Function( on)
import Data.Array.IArray( Array, listArray, (!))
import qualified Data.Array.IArray as A
import Data.IntSet( lookupGE, IntSet, map, elems, delete
		    , fromList, null)
import qualified Data.IntSet as S
import Data.Map( Map, (!), map, empty, insert)
import qualified Data.Map as M
import Control.Applicative( (<$>))
main = do
    [n,x] <- return . (read <$>) . words =<< getLine
    as <- return . (read <$>) . words =<< getLine
    let cost = listArray (1,n) as::Array Int Int
	iniSet = fromList [1..n]

	magic::IntSet -> IntSet
	magic = S.map shift
	  where
	    shift k = if k==1 then n else k-1
	minFrom:: IntSet -> Integer
	minFrom =
	    let minMem::Map IntSet Integer
		minMem = foldl' (\m s->insert s (zenka s) m)
				    M.empty powSet
		powSet = S.fromList <$> subsequences [1..n] 
		zenka::IntSet->Integer
		zenka toEllim
		  | S.null toEllim  = 0
		  | otherwise =
		      let bruteforce = do
			    (c,st) <- zip ((fromIntegral x*) <$> [0..]) $
					take n$iterate magic toEllim
			    e <- elems st
			    return $ c + fromIntegral ((A.!) cost e)
					+ minFrom (delete e st)
		      in minimum bruteforce
	    in (M.!) minMem
    print $ minFrom iniSet