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()))

ans = [[0, 0] for _ in range(n)]
min_ind = a.index(min(a))
ans[min_ind] = [min(a), 0]

for i in range(min_ind + 1, n):
	if a[i] > ans[i-1][0] + x * (ans[i-1][1] + 1):
		ans[i] = [ans[i-1][0], ans[i-1][1] + 1]
	else:
		ans[i] = [a[i], 0]

if a[0] > ans[-1][0] + x * (ans[-1][1] + 1):
	ans[0] = [ans[-1][0], ans[-1][1] + 1]
else:
	ans[0] = [a[0], 0]


for i in range(1, min_ind):
	if a[i] > ans[i-1][0] + x * (ans[i-1][1] + 1):
		ans[i] = [ans[i-1][0], ans[i-1][1] + 1]
	else:
		ans[i] = [a[i], 0]

#print(ans)

print(sum([ans[i][0] for i in range(n)]) + max([ans[i][1] for i in range(n)]) * x)