Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

2 10
1 100

Sample Output 1

12

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Cast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.

Catch a slime in color 1. This takes 1 second.

Sample Input 2

3 10
100 1 100

Sample Output 2

23

Snuke can act as follows:

Catch a slime in color 2. This takes 1 second.

Cast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Cast the soell. The color of each slime changes: 3 → 1, 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Sample Input 3

4 10
1 2 3 4

Sample Output 3

10

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Catch a slime in color 2. This takes 2 seconds.

Catch a slime in color 3. This takes 3 seconds.

Catch a slime in color 4. This takes 4 seconds.

Solution in PyPy3 (2.4.0) (judge verdict: Wrong Answer)

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)