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) = (input()).split()
N = int(N)
x = int(x)
astr = input()
a = [int(aa) for aa in astr.split()]

#TLE!

res = 0
magic = 0

i = 0
while i < N:
    sumi = 10 ** 18
    counti = 2000
    geti = 0
    tmpsum = 0
    tmpcount = 0
    j = 0
    while j < N:
        if(i < j):
            tmpcount = N - j + i
        else:
            tmpcount = i - j
        tmpsum = a[j] + tmpcount * x
        if tmpsum < sumi:
            counti = tmpcount
            geti = j
        j += 1
    res += a[geti]
    magic = max(counti, magic)
    
    i += 1

res += magic * x

print(res)

