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()))

def v_1(value):
    v = value + 1
    return v if v < n else 0

visited = [0 for x in range(n)]
result = 0
origin = a[:]
while sum(visited) != n:
    minv = [(i, x1, x2) for i, (x1, x2) in enumerate(zip(a, origin[1:] + [origin[0]])) if x1 < x2 or visited[i]]
    s1 = sum(v[2] for v in minv if not visited[v_1(v[0])])
    s2 = sum(v[1] for v in minv if not visited[v[0]]) + x
    if s1 > s2:
        result += s2
        for v in minv:
            visited[v[0]] = 0
            a[v_1(v[0])] = v[1]
        for v in minv:
            visited[v_1(v[0])] = 1
    else:
        # print("s1", s1, minv, [v for v in minv if not visited[v_1(v[0])]])
        result += s1
        for v in minv:
            visited[v_1(v[0])] = 1
    # print(visited)
    # print("r", result)
# print(" --- ")
print(result)
