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()))
# スライムの色は0-initialで考える
# スライムiを捕まえてスライムjに変化させるために必要な時間をc[i][j]とする
c=[[-1 for j in range(N)] for i in range(N)]
# スライムjを捕まえてスライムiに変化させるために必要な時間をdとする
d=[[-1 for j in range(N)] for i in range(N)]

for i in range(N):
    for j in range(N):
        d[(i+j)%N][i]=c[i][(i+j)%N]=a[i]+x*j
'''
for ci in c:
    print(ci)
print()
for di in d:
    print(di)
print()
'''
# スライムiを最も早く得るために必要なスライムj=s[i]と魔法を唱える回数k[i]=(j-i)%Nを計算する
s=[d[i].index(min(d[i])) for i in range(N)]
k=[(s[i]-i)%N for i in range(N)]
'''
print(s)
print(k)
'''
# 魔法を唱える回数の最大値(=魔法を唱える回数の合計)*xに，各スライムを捕まえるのに必要な時間Σa[s[i]]を合計する
ans=max(k)*x+sum([a[s[i]] for i in range(N)])

print(ans)