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 min_k_shift(k, a, N, x, range_min):
    cost = k*x
    for j in range(N):
        cost += range_min[(j-k)%N][j] #min(a[(j-sj)%N] for sj in range(k))
    return cost

N, x = [int(s) for s in raw_input().split()]

a = [int(s) for s in raw_input().split()]

range_min = [[0]*N for st in range(N)]
for st in range(N):
    range_min[st][st] = a[st]

for k in range(1,N):
    for st in range(N):
        range_min[st][(st+k)%N] = min(range_min[st][(st+k-1)%N],a[(st+k)%N])

print(min(min_k_shift(k,a,N,x,range_min) for k in range(N)))