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), A) = $stdin.read.lines.map(&:chomp).map{|l| l.split(" ").map(&:to_i)}

NN = A.length

b=[]
s=[]
ak = 0
NN.times do |k|
  b[k] = []
  NN.times do |i|
    b[k][i] = if k.zero?
                A[i]
              else
                [b[k-1][i], A[i-k]].min
              end
    s[k] ||= 0
    s[k] += b[k][i]
  end
  ak = k if s[k] < s[ak]
end

puts ak * X + s[ak]
