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()))

amin = 10**10
for i in range(N):
    if a[i] <= amin:
        start_list = [i]
        amin = a[i]
    elif a[i] == amin:
        start_list.append(i)

ans_min = float('inf')
for start in start_list:
    cnt = 0
    tmp = 0
    use = 0
    ans = 0
    for _i in range(N):
        i = (_i + start) % N
        if a[i] < amin + x:
            tmp = a[i]
            use = cnt
            ans += tmp
        else:
            if use > 0:
                use -= 1
                ans += tmp
            else:
                cnt += 1
                ans += amin + x
    ans_min = min(ans, ans_min)

print(ans_min)
