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
loop, magic_cost = map(int, input().split(" "))
cost = [n for n in map(int, input().split(" "))]
answer = float("inf")
for i in range(loop):
    min_catch_cost = cost[i]
    last_catch_index = i
    sum_cost = min_catch_cost
    max_magic_time = 0
    total_magic_time = 0
    temp_magic_time = 0
    for j in range(i + 1, i + loop):
        if cost[j % loop] >= magic_cost + min_catch_cost:
            sum_cost += min_catch_cost
            total_magic_time += 1
            temp_magic_time += 1
        else:
            min_catch_cost = cost[j % loop]
            last_catch_index = j
            sum_cost += cost[j % loop]
            temp_magic_time = 0
        max_magic_time = max(temp_magic_time, max_magic_time)
#         print(i, j, min_catch_cost, last_catch_index, sum_cost)
    answer = min(answer, sum_cost + (magic_cost * (max_magic_time)))
print(answer)