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
colors,magic = (int(n) for n in input().split(' '))
times = [int(n) for n in input().split(' ')]
ans = [0 for n in range(colors)]
sumit = 0
magicnt = {}
maxmagic = {}
for m in range(colors):
    tempans = float("inf")
    tempmag = 0
    for n in range(colors):
        if magic > times[m]:
            break
        elif n == m:
            continue
            #tempans = min(tempans,times[n])
        else:
            if tempans > times[n] + magic * ((m - n) % colors):
                tempmag = n
                tempans = times[n] + magic * ((m - n) % colors)
    if times[m] < tempans:
        sumit += times[m]
    else:
        magicnt[tempmag] = magicnt.get(tempmag,0) + 1
        maxmagic[tempmag] = max(tempans,maxmagic.get(tempmag,0))

for ind,value in magicnt.items():
    sumit += (times[ind]) * (value - 1)
for value in maxmagic.keys():
    sumit += maxmagic[value]

print(sumit)
