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**9+1
ind = -1
for i in range(N):
    if A[i]<amin:
        ind = i
        amin = A[i]
B = [0 for _ in range(N)]
cnt = 0
for i in range(N):
    if A[i]<=amin+x:
        B[i] = 1
        cnt += A[i]
while True:
    if B[ind]==0:
        B[ind] = 1
        cnt += amin
    else:
        flg = 0
        for i in range(ind-1,ind-N,-1):
            i = i%N
            if B[i]==0:
                j = i
                flg = 1
                break
        if flg==0:break
        if amin+((ind-j)%N)*x<A[j]:
            C = [0 for _ in range(N)]
            for i in range(N):
                C[(i+ind-j)%N] = B[i]
            B = C[:]
            cnt += ((ind-j)%N)*x
        else:
            B[j] = 1
            cnt += A[j]
print(cnt)