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
import sys


fin = sys.stdin.readline
N, x = [int(elem) for elem in fin().split()]
a_list = [int(elem) for elem in fin().split()]

min_cost_for = a_list.copy()
this_is_from = list(range(N))

max_num_magics = 0
for i, a in enumerate(a_list): 
    for j, other_a in enumerate(a_list):
        if i == j: continue
        num_magics = i - j if j < i else (N - j + i)
        cost = other_a + num_magics * x
        if cost < min_cost_for[i]:
            min_cost_for[i] = cost
            max_num_magics = max(num_magics, max_num_magics)
            this_is_from[i] = j


total_cost = sum(a_list[origin] for origin in this_is_from) + x * max_num_magics
print(total_cost)
