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 = map(int,input().split( ))

a = list(map(int, input().split( )))

#a_ch = []
a_chmx = [0]*n
a_num = [0]*n
for i in range(n):
    mn_a = a[i]
    ind = i
    for j in range(n):
        #print(mn_a, x*((i-j+n)%n) + a[j])
        if mn_a > x*((i-j+n)%n) + a[j]:
            mn_a = a[j] + ((i-j+n)%n)*x
            ind = j#この項はここ
            if (i-j+n)%n>a_chmx[j]:
                a_chmx[j] = (i-j+n)%n
 
    #print(ind,i)
    a_num[ind] += 1
#print(a)
#print(a_chmx)
#print(a_num)
ans = 0
for i in range(n):
    ans += a[i]*a_num[i]
ans += sum(a_chmx)*x
print(ans)