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
{-# LANGUAGE MultiParamTypeClasses,FlexibleContexts,FlexibleInstances,TypeSynonymInstances,BangPatterns,RankNTypes,TupleSections #-}
import Control.Monad
import Control.Monad.ST
import Control.Applicative
import Control.Arrow
import Debug.Trace
import Text.Printf

import Data.List
import Data.Int
import Data.Bits
import Data.Maybe
import Data.Monoid
import Data.Array.Unboxed
import Data.Array.ST
import Data.Array.Base
import Data.Function(on)
import Data.Tuple(swap)
import qualified Data.Map as M
import qualified Data.Set as S
import qualified Data.ByteString.Char8 as B

main :: IO ()
main = do
    (n, x) <- readIntPair
    as <- readInts
    let ans = minimum [ d * x + calc d | d <- [0..n-1]]
        calc d = sum [ minimum $ take (d+1) cs  | cs <- take n $tails $ cycle (reverse as) ]
    print ans


-- IO
readInt :: B.ByteString -> Int
readInt = fromJust . fmap fst . B.readInt
readInts :: IO [Int]
readInts = map readInt . B.words <$> B.getLine
readIntPair :: IO (Int,Int)
readIntPair = l2p . map readInt . take 2 . B.words <$> B.getLine
readAllInts :: IO [[Int]]
readAllInts = map (map readInt . B.words) . B.lines <$> B.getContents
readLns :: Read a => IO [a]
readLns = map read . words <$> getLine

-- Utilities
l2p :: [a] -> (a,a)
l2p (a:b:_) = (a,b)
l2p _ = error "l2p: the input list is too short"
p2l :: (a,a) -> [a]
p2l (a,b) = [a,b]
itof :: Int -> Double
itof = fromIntegral
inf :: Int
inf = maxBound `div` 2

-- Monad
stepM_ :: Monad m => a -> (a -> Bool) -> (a -> a) -> (a -> m ()) -> m ()
stepM_ i0 judge incr step = sub i0 where 
    sub i | judge i = step i >> sub (incr i) 
          | otherwise = return ()
rep_ :: Monad m => Int -> (Int -> m ()) -> m ()
rep_ n = stepM_ 0 (<n) (+1)
thru :: Monad m => (v -> m ()) -> v -> m v
thru m v = m v >> return v
memoize :: (Monad m) => (k -> m (Maybe v)) -> (k -> v -> m ()) -> k -> m v -> m v
memoize getter setter key action = do
    mv <- getter key
    case mv of
        Just v -> return v
        Nothing -> action >>= thru (setter key)

-- Array
newUArray :: (MArray (STUArray s) e (ST s),Ix i) => 
             (i,i) -> e -> ST s (STUArray s i e)
newUArray = newArray
newBArray :: (Ix i) => (i,i) -> e -> ST s (STArray s i e)
newBArray = newArray
defaultArray :: (IArray a e,Ix i) => e -> (i,i) -> [(i,e)] -> a i e
defaultArray = accumArray $ curry snd
fromEdges :: Ix i => (i,i) -> [(i,e)] -> Array i [e]
fromEdges = accumArray (flip (:)) []
