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
def solve():
    n, x = map(int, input().split())
    al = [int(i) for i in input().split()]
    minnum = min(al)
    minidx = al.index(minnum)
    al = al[minidx:] + al[:minidx]

    cnt = 0
    cntlist = [0 for i in range(n)]
    anlist = []
    anlist.append(minnum)
    mincost = minnum
    for i in range(1, n):
        cost = min(mincost + x, al[i])
        if cost == al[i]:
            mincost = al[i]
            cnt = 0
            cntlist[i] = cnt
            anlist.append(al[i])
        else:
            mincost = cost
            cnt += 1
            cntlist[i] = cnt

    ans = 0
    anidx = -1
    cnt = 0
    for i in range(n):
        if cntlist[i] == 0:
            if anidx >= 0:
                ans += anlist[anidx] * cnt
                cnt = 0
                anidx += 1
            else:
                anidx = 0
                cnt = 0
        cnt += 1
    else:
        ans += anlist[anidx] * cnt
        ans += max(cntlist) * x

    print(ans)

if __name__=="__main__":
    solve()