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 Data.List
import Data.Maybe
import Data.Array

main = do
  [n,x] <- map read . words <$> getLine :: IO [Int]
  as <- listArray (0,n-1) . map read . words <$> getLine :: IO (Array Int Int)

  let m = array ((0,0),(n-1,n-1)) $
        [((i,0),as!i) | i <- [0..n-1]] ++
        [((i,k), min (m!(i,k-1)) (as!((i-k+n)`mod`n))) | k <- [1..n-1], i <- [0..n-1]]

  --print $ m
        
  print $ minimum [sum [m!(i,k) | i <- [0..n-1]] + k*x | k <- [0..n-1]]
  
