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()))
dp=[a[i] for i in range(n)]
sp_cnt=[0 for i in range(n)]
for i in range(1,n):
    if a[n-i]+i*x<dp[0]:
        dp[0]=a[n-i]+i*x
        sp_cnt[0]=i

for i in range(1,n):
    for j in range(i):
        if a[i-j]+j*x<dp[0]:
            dp[i]=a[i-j]+j*x
            sp_cnt[i]=max(sp_cnt[i],j)
            
all_sp_cnt=sum(sp_cnt)
max_sp_cnt=max(sp_cnt)

ans=sum(dp)-(all_sp_cnt-max_sp_cnt)*x
print(ans)