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)

loop, magic_cost = map(int, input().split(" "))
cost = [n for n in map(int, input().split(" "))]
answer = float("inf")
for i in range(loop):
    min_catch_cost = cost[i]
    last_catch_index = i
    sum_cost = min_catch_cost
    max_magic_time = 0
    total_magic_time = 0
    temp_magic_time = 0
    for j in range(i + 1, i + loop):
        if cost[j % loop] >= magic_cost + min_catch_cost:
            sum_cost += min_catch_cost
            total_magic_time += 1
            temp_magic_time += 1
        else:
            min_catch_cost = cost[j % loop]
            last_catch_index = j
            sum_cost += cost[j % loop]
            temp_magic_time = 0
        max_magic_time = max(temp_magic_time, max_magic_time)
#         print(i, j, min_catch_cost, last_catch_index, sum_cost)
    answer = min(answer, sum_cost + (magic_cost * (max_magic_time)))
print(answer)