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
"""

入れる場所とそこから波及する場所の最大距離が魔法使用回数

魔法使用回数を決め打ちしてdp？

魔法をp回使うとすると、左p箇所のうち最小の場所から入れるのが最適になる
heapを使うか～

2000 * 2000 * log(2000)
間に合うかなぁ～

4*10**7かぁ
"""

import heapq

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

a = list(map(int,input().split()))

ans = float("inf")

for p in range(N):

    now = x * p

    q = []

    for i in range(-1*p , 0):
        heapq.heappush(q,[a[i] , i])

    for i in range(N):

        heapq.heappush(q , [a[i] , i])

        while q[0][1] < i - p:
            heapq.heappop(q)

        now += q[0][0]

    ans = min(ans , now)

print (ans)
