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()))

mcost = [ (i, A[i]) for i in range(N)] # A[:]

from collections import defaultdict
cnt = defaultdict(int)
cstlst = [[] for _ in range(N)]

for i in range(1,N):
    if mcost[i-1][1] + 10 < mcost[i][1]:
        mcost[i] = (mcost[i-1][0], mcost[i-1][1]+10)

if mcost[N-1][1] + 10 < mcost[0][1]:
    mcost[0] = ( mcost[N-1][0], mcost[N-1][1]+10)

for i in range(1,N):
    if mcost[i-1][1] + 10 < mcost[i][1]:
        mcost[i] = (mcost[i-1][0], mcost[i-1][1]+10)

# lst = []
inf = float("inf")
maxlist = [0] * (N+1)
for idx,cst in mcost:
    cnt[idx] += 1
    # cstlst[idx].append(cst)
    # lst.append( (idx,cst) )
    if maxlist[idx] < cst:
        maxlist[idx] = cst

# lst = sorted(lst, lambda x: (idx, -cst) )
# from bisect import bisect_left as bll

ans = 0

# print(maxlist)
# exit(0)
for k in cnt.keys():
    if cnt[k] == 1:
        ans += A[k]
    else:
        ans += (cnt[k]-1)*A[k] + maxlist[k]

print(ans)

# print( list(zip(*mcost))[0] )
# print( list(zip(*mcost))[1] )
