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)

arr = gets.split.map(&:to_i)
ans = 0
saisyou = arr.min

arr2 = Array.new(n).map{Array.new(n,0)}

i=0

n.times{
    
   j=0
   min = arr[i]
   n.times{
       
       arr2[i][j] = min
       
       min = [arr[(i-j-1)%n],min].min
       
       
       
       
       
       
      j+=1 
   }
    
    
    
    i+=1
}


arr2 = arr2.transpose


k = 0
min = 10**20
n.times{
    
  min = [arr2[k].inject(:+)+k*x,min].min 
    
 
    
    
  k+=1  
}

p min


