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()) # 横に2個
A = list(map(int, input().split()))


ans = 0
curll = []
for i, a in enumerate(A):
    k = a
    ind = i
    curl = False
    count = 0
    cost = a
    minc = 0
    while k > 0 or count < N:
        count += 1
        if ind == N-1:
            ind = 0
        else:
            ind += 1
        if k > A[ind] + x:
            cost0 = A[ind] + x*count
            if cost0 < cost:
                cost = cost0
                minc = count
            curl = True
        k -= x
    if not curl:
        ans += a
    else:
        ans += cost - x*minc
        curll.append(minc)

if curll:
    ans += max(curll)*x

print(ans)