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 copy import deepcopy as dc
#n,x=map(int,input().split())
x=int(input()) #
a=list(map(int,input().split()))
n=len(a) #
a=[[i,i,0] for i in a]
b=[]

m=0
while(b!=a):
    b=dc(a)
    for _ in range(2):
        for i in range(n):
            j=i-1
            if j==-1:
                j=n-1
            if a[i][1]!=a[j][1]:
                if a[i][0]>=a[j][1]+x or (a[i][0]>=a[j][1] and a[j][2]<m):
                    a[i][0]=a[j][1]+x
                    a[i][1]=a[j][1]
                    a[i][2]=a[j][2]+1
    for i in a:
        m=max(i[2],m)
        
s=0
s+=m*x
for i in a:
    s+=i[1]
print(s)