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
#!/usr/bin/env crystal
n,x=gets.not_nil!.split.map(&.to_i64)
a=gets.not_nil!.split.map(&.to_i64)
(n*3).times{|i|
	a[(i+1)%n]=[a[i%n]+x,a[(i+1)%n]].min
}
p a

p a.map{|z|
	b=[] of Int64
	interval=[] of Int64
	a.size.times{|i|
		if a[i]<=z
			b<<a[i]
			interval<<i.to_i64
		end
	}
	interval<<interval[0]+n
	interval2=[] of Int64
	interval.each_cons(2){|e|
		interval2<<e[1]-e[0]
	}
	r=x*(interval2.max-1)
	b.size.times{|i|r+=b[i]*interval2[i]}
	r
}.min