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()))

ans = float("inf")
get_dis = lambda bi,i:  (i - bi ) if bi < i else  i+N-bi
for loop in range(0, N+1):
  mxcnt = loop
  NC=[ (i, A[i]) for i in range(N) ]
  for i in range(2*N+1):
    i %= N
    bi = i-1 if i >= 1 else N-1

    # print("get_dis: ", "bi: ", bi, "NCbi0: ", NC[bi][0], "i: ", i,  "dis: ", get_dis(NC[bi][0], i )) 
    if NC[bi][1] < NC[i][1] and get_dis(NC[bi][0],i) <= mxcnt :
        NC[i] = NC[bi]
  tmp = (mxcnt)*X + sum(list(zip(*NC))[1])

  # if tmp < ans:
  #     print("loop!: ", loop, tmp)
  # print(loop, NC)
  ans = min(tmp, ans)
print(ans)
exit(0)
