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 LuaJIT (2.0.4) (judge verdict: Accepted)

local n, x = io.read("*n", "*n")
local a = {}
for i = 1, n do
  a[i] = io.read("*n")
end
local inf = 1000000000
local cost = {}
for i = 1, n * n do
  cost[i] = 0
end
local mmi = math.min
for i = 1, n do
  for j = 0, n - 1 do
    local it = i + j
    if n < it then it = it - n end
    cost[j * n + it] = i
  end
end
for i = 1, n do
  for j = 0, n - 2 do
    local idx = j * n + i
    local pre_i = cost[idx]
    local pre_len = i - pre_i
    if pre_len < 0 then pre_len = pre_len + n end
    local pre_cost = a[pre_i]
    local next_idx = idx + n
    local next_cost = a[cost[next_idx]]
    if pre_cost < next_cost then
      cost[next_idx] = pre_i
    end
  end
end
local ret = 2000 * 1000000000
for j = 0, n - 1 do
  local sum = j * x
  for i = 1, n do
    sum = sum + a[cost[i + j * n]]
  end
  ret = mmi(ret, sum)
end
print(ret)