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)

Node = Struct.new(:v, :dist) do
  def value
    A[v] + X * dist + 0.0001 * dist
  end
end

D = Array.new(N)

A.each_with_index do |a, v|
  D[v] = Node.new(v, 0)
end

(N - 1).times do
  N.times do |i|
    u = (i + 1) % N

    node = D[i]
    cand = Node.new(node.v, node.dist + 1)

    if D[u].value > cand.value
      D[u] = cand
    end
  end
end

ans = 0
max_dist = 0

D.each do |node|
  max_dist = node.dist if max_dist < node.dist
  ans += A[node.v]
end

puts ans + max_dist * X
