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 math

N,x= list(map(int,input().split(" ")))
As = list(map(int,input().split(" ")))

ans = 0
inds = []
for i in range(N): # to
    temp = 10 ** 20 #これは指標
    tempfrom = 0 # これは毎回足す
    tempind = 0 #これは格納しておいて一度に使う

    for j in range(N): # fromを一通り試す j番目の要素から
        # jからiへ向かう
        # i - j
        diff =  i - j
        if  diff < 0:
            diff %= N

        if temp >= diff * x + As[j]: # 元の生産コスト + toまでのコスト
            mindiff = diff
            temp = diff * x + As[j] #総コスト
            tempstart = As[j] #元の生産コスト
    ans += tempstart
    inds.append(mindiff)
ans += max(inds) * x
print(ans)