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)] 

from collections import defaultdict
cnt = defaultdict(int)

for i in range(1,2*N):
    
    bef = (i-1)%N if i >= 1 else N-1
    i %= N
    if mcost[bef][1] + X <= mcost[i][1]:
        mcost[i] = (mcost[bef][0], mcost[bef][1]+X)

mxcnt=0
mxidx=0
for idx,cst in mcost:
    cnt[idx] += 1
    if cnt[idx]>mxcnt:
      mxcnt=cnt[idx] 
      mxidx=idx
if mxcnt == 1:
  print(sum(A)) 
  exit(0)
#print("mxidx: ",mxidx,"mxcnt: ", mxcnt)        


NC=A[:]
for i in range(2*N+1):
  if i >=N: i%=N
  if i != mxidx:
    pcnt=1
    pi=i+1
    v=A[i]
    while pcnt<=mxcnt:
      if pi>=N: pi=pi%N
      if v>=NC[pi]: break
      if pi == mxidx: break
      else:        
        NC[pi]=v
        pcnt+=1
        pi+=1
  if i==mxidx:
    pi=(i+1)%N 
    ccnt=mxcnt-1
    while ccnt:
      NC[pi]=A[i]
      pi=(pi+1)%N
      ccnt-=1

#print("NC:")
#print(NC)
      
ans = (mxcnt-1)*(X) + sum(NC)
print(ans)

