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 = [ int(v) for v in input().split() ]
color_list = [ int(v) for v in input().split() ]

dp_list = [ 10**10 for i in range(n) ]
ans_list = [ None for i in range(n) ]
for i in range(n):
    new_dp_list = [ 10**10 for i in range(n) ]
    c = color_list[i]
    for j in range(n):
        a = (i+j)%n
        if c + x*j < dp_list[a]:
            new_dp_list[a] = c + x*j
            ans_list[a] = (c,j)
        elif c+ x*j == dp_list[a] and ans_list[a] is not None:
            if j > ans_list[a][1]:
                ans_list[a] = (c,j)
            new_dp_list[a] = dp_list[a]
        else:
            new_dp_list[a] = dp_list[a]
    dp_list = new_dp_list

y, z = zip(*ans_list)
print(sum(y)+x*max(z))
