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 itertools import accumulate

N,x=map(int,input().split())

A=[int(x) for x in input().split()]

m=A.index(min(A))
A=A[m:]+A[:m]
dp=[[int(x) for x in A] for i in range(2)]

#dp[i]:k回魔法を唱えた時にA[i]を手に入れる最小の時間。
#dp=Aで初期化。その後、１〜Nまでのdp[i]はmin(dp[i-1],A[i])で順に更新されていく。
#更新前後のdpを保持するため蟻本P60に記載のある「配列の再利用」を行う。
#各回におけるsum(dp)+k*xを算出して最小値が答え。

#ans初期値は魔法を唱えず、全てを入手した数字（sum(A))
ans=sum(A)
for k in range(1,N):
  cnt=dp[0][0]
  for i in range(1,N):
    dp[(k+1)&1][i]=min(dp[k&1][i-1],A[i])
    cnt+=dp[(k+1)&1][i]
  ans=min(ans,cnt+k*x)
  
print(ans)
