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
parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
	n,x = readline() |> split |> parseMap
	a = readline() |> split |> parseMap
	d = zeros(Int,n,n)
	t = Int[i for i in 1:n]
	for i in 1:n
		d[i,i] = a[i]
		l = 1
		for j in i+1:n
			if a[i]+l*x<a[j]
				d[i,j] = a[i]+l*x
				l = 1
			else
				l += 1
				d[i,j] = a[j]
			end
		end
		for j in 1:i-1
			if a[i]+l*x<a[j]
				d[i,j] = a[i]+l*x
				l = 1
			else
				l += 1
				d[i,j] = a[j]
			end
		end
	end
	m = 0
	for i in 1:n
		m += minimum(d[:,i])
	end
	println(m)
end

main()