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
def solve(n, x, a):
	costs = []
	cost_min = 0
	for k in range(n):
		if k == 0:
			costs = a.copy()
		else:
			for i in range(n):
				costs[i] = min(costs[i], a[(i-k)%n])
		cost_k = sum(costs) + k*x
		if k == 0:
			cost_min = cost_k
		else:
			cost_min = min(cost_min, cost_k)

n, x = [int(i) for i in input().split()]
a = [int(i) for i in input().split()]
print(solve(n,x,a))


