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
program colorful_slimes
  implicit none
  integer :: n, i, j, k
  integer(8) :: x, a(4000)
  a = 0_8
  read(*,*) n, x
  read(*,*) a(1:n)
  a(n+1:2*n) = a(1:n)
  do k = 1, 3
    do i = n+1, 2*n
      do j = i-n-1, i-1
        a(i) = min(a(i),a(j)+int(i-j,8)*x)
      end do
      a(i-n) = a(i)
    end do
  end do
  write(*,'(i0)') sum(a(1:n))
  stop
end program colorful_slimes