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
from sys import stdin
from sys import stdout

N,x = stdin.readline().split()
costs = map(int, stdin.readline().split())
avgx = float(x)/float(N)

startId = costs.index(min(costs))
realcosts = [0]* len(costs)
magiccount = [0]* len(costs)

realcosts[startId] = costs[startId]
magiccount[startId] = 0 
i = startId+1
while i!=startId:
        j = (i+int(N)-1)%int(N)
        if costs[i] < realcosts[j] + avgx*(magiccount[j]+1):
                realcosts[i] = costs[i]
                magiccount[i] = 0 
        else:
                realcosts[i] = realcosts[j]                                                                                                                          
                magiccount[i] = magiccount[j]+1
        i = (i +1)%int(N)

print sum(realcosts) + int(x) * max(magiccount)