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.chomp.split(" ").map(&:to_i)
a = gets.chomp.split(" ").map(&:to_i)
maxj = 0
ans = 0
for i in 0..n-1
  min = a[i]
  cap = i
  for j in 1..n-1
    if x*j >= a[i]
      break
    end
    k = i-j
    if k < 0
      k += n
    end
    temp = a[k]+x*j
    if temp < min
      min = temp
      cap = k
      if maxj < j
        maxj = j
      end
    end
  end
end
for i in 0..n-1
  mina = a[i]
  for j in 1..maxj
    k = i-j
    if k < 0
      k += n
    end
    if mina > a[k]
      mina = a[k]
    end
  end
  ans += mina
end
puts ans+x*maxj