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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n, x = gets.split(" ").map(&:to_i)
a = gets.split(" ").map(&:to_i)

a_twice = a + a

arr_total_times = []
n.times do |i|
    # i回魔法を唱えるときの最短時間を調べる
    # 魔法の分の時間
    total_time = x * i
    min_time_of_j = 0
    min_time_of_j_index = -1
    n.times do |j|
        if j <= min_time_of_j_index and min_time_of_j_index <= j + i \
                and min_time_of_j < a_twice[j + i]
            total_time = min_time_of_j
        else
            min_time_of_j = a_twice[j]
            min_time_of_j_index = j
            j.upto(j + i) do |k|
                if min_time_of_j > a_twice[k]
                    min_time_of_j = a_twice[k]
                end
            end
        end
        total_time = total_time + min_time_of_j
    end
    arr_total_times.push(total_time)
end
puts arr_total_times.min