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
s = gets.split.map &:to_i
max = s.inject :+

min = s.min
size = s.size

indexes = []
now = 0
count = 10
until (i=s[now..-1].index(min)) == nil
    now += i
    indexes << now
    now+=1
end

if indexes.size == 1
    r = (size-1)*x + size*min
    p r < max ? r : max
else
    first = indexes[0]
    indexes.map!{|e| e-first}
    s = s[first..-1]+s[0...first] if first != 0
    indexes << s.size
    tmp = indexes.each_cons(2).map{|a,b| b-a-1}.to_a
    r = tmp.max*x+(tmp.inject :+)*min+1
    p r < max ? r : max
end
