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
if __name__ == "__main__":
	N, x = input().split(" ")
	N = int(N)
	x = int(x)
	a = []
	for e in input().split(" "):
		a.append(int(e))

	min_cost = []
	for i in range(N):
		min_cost.append([0] * N)

	min_total_cost = -1
	for k in range(N):
		temp_sum = 0
		if k==0:
			for i in range(N):
				min_cost[k][i] = a[i]
				temp_sum += min_cost[k][i]
		else:
			for i in range(N):
				idx = (i-k) % N
				min_cost[k][i] = min(min_cost[k-1][i], a[idx])
				temp_sum += min_cost[k][i]

		if min_total_cost == -1:
			min_total_cost = (k * x) + temp_sum
		else:
			temp = (k * x) + temp_sum
			if temp < min_total_cost:
				min_total_cost = temp

	print (min_total_cost)