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 = 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
            if min_time_of_j < a_twice[j + 1]
                total_time = min_time_of_j
            else
                total_time = a_twice[j + 1]
            end

        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
