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

m = 0
e = []
a = []
NN.times do |i|
  NN.times do |j|
    d = (i - j) % NN
    e[i] ||= []
    e[i][j] = A[j] + d * N
    a[i] = [j,d] if a[i].nil? || e[i][j] < e[i][a[i].first]
  end
end

ans = 0
a.each do |j,d|
  ans += A[j]
  m = d if m < d
end
ans += m * X
puts ans
