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{|a|a.to_i}
A = gets.chomp.split(" ").map{|a|a.to_i}
Amin = Array.new(N){Array.new(N)}
for j in 0..(N-1)
	Amin[0][j] = A[j]
end
for i in 1..(N-1)
	for j in 0..(N-1)
		Amin[i][j] = [Amin[i-1][j], A[(j-i+N)%N]].min
	end
end
min = A.inject(0){|sum,a| sum+a}
for i in 1..(N-1)
	tmp = Amin[i].inject(0){|sum,a| sum+a} + i*x
	min = tmp if min > tmp
end
puts min
