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
-- Try AtCoder
-- author: Leonardone @ NEETSDKASU

main = print . solve . map read . words =<< getContents

solve (n:x:a) = ans where
    sm = sum a
    mn = minimum a
    (h, t) = span (mn <) a
    xs = t ++ h
    (r, s, c) = foldl (\(r, s, c) k -> if k > mn then (r, s + 1, c) else (maximum [r, s], 0, c + k)) (0, 0, 0) xs
    m = maximum [r, s]
    xx =  m * mn + x * m + c
    ans = minimum [sm, xx]
