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

minlist = {}
m = (N, 1000000001)
for i in range(N):
    if a[i] <= x:
        minlist[i] = (a[i],0)
    if m[1] > a[i]:
        m = (i, a[i])
if len(minlist) == 0:
    minlist[m[0]] = (m[1],0)

i = 0
while len(minlist) < N:
    if i not in minlist:
        if i == 0:
            if N-1 in minlist:
                if minlist[N-1][0] + (minlist[N-1][1]+1)*x < a[i]:
                    minlist[i] = (minlist[N-1][0], minlist[N-1][1]+1)
                else:
                    minlist[i] = (a[i],0)
        else:
            if i-1 in minlist:
                if minlist[i-1][0] + (minlist[i-1][1]+1)*x < a[i]:
                    minlist[i] = (minlist[i-1][0], minlist[i-1][1]+1)
                else:
                    minlist[i] = (a[i],0)
    if i == N-1:
        i = 0
    else:
        i += 1
ans = 0
for i in range(N):
    ans += minlist[i][0]
print(ans + max(minlist.values(),key=lambda x:x[1])[1]*x)
