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")
bik = A[:]

get_idx_back = lambda idx,b: idx-b if idx>=b else idx+N-b

for loop in range(0, N+1):
  if loop == 0:
      bik = A[:]
  else: 
      for i in range(N):
          bik[i] = min(bik[i], A[ get_idx_back(i, loop) ])

  tmp = (loop)*X + sum(bik)

  ans = min(tmp, ans)
print(ans)
exit(0)
