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()))

# 最短時間で色iにするとき、捕まえるときの色と魔法を唱える回数
time = [float('inf')] * n
color = [float('inf')] * n
magic = [0] * n

# 色jで捕まえて、色iになるまで

for i in range(n):
    for j in range(n):
        # 色 n-1 -> 0 の変化をまたぐとき
        if i < j:
            if a[j] + (n - j + i) * x < time[i]:
                time[i] = a[j] + (n - j + i) * x
                color[i] = j
                magic[i] = n - j + i
        else:
            if a[j] + (i - j) * x < time[i]:
                time[i] = a[j] + (i - j) * x
                color[i] = j
                magic[i] = i - j

ans = max(magic) * x
for i in range(n):
    ans += time[i] - magic[i] * x

print(ans)