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
num, change_duration = tuple([ int(x) for x in raw_input().split() ])
get_durations = tuple([ int(x) for x in raw_input().split() ])

def solve(num, change_duration, get_durations):
    change_num = 0
    min_duration = min(get_durations)
    min_index = get_durations.index(min_duration)
    get_times = [0] * num
    change_nums = [0] * num
    for count in xrange(num):
        if count == 0:
            get_times[min_index] = min_duration
            continue
        index = min_index + count
        if index >= num:
            index -= num
        gd = get_durations[index]
        prev_gd = get_times[index-1]
        if prev_gd + change_duration <= gd:
            change_nums[index] = change_nums[index-1]+1
            get_times[index] = prev_gd
        else:
            get_times[index] = gd
    max_change_num = max(change_nums)
    all_change_time = max_change_num * change_duration
    all_get_time = sum(get_times)
    temp_change_num = max_change_num
    while True:
        temp_change_num += 1
        for count in xrange(num):
            if count == 0:
                get_times[min_index] = min_duration
                continue
            index = min_index + count
            if index >= num:
                index -= num
            gd = get_times[index]
            temp_index = index - temp_change_num
            if abs(temp_index) > num:
                temp_index += num
            candidates = get_durations[temp_index:index+1]
            if len(candidates) > 0:
                get_times[index] = min(candidates)
        temp_all_get_time = sum(get_times)
        if all_get_time < temp_all_get_time + change_duration:
            break
        else:
            all_get_time = temp_all_get_time
            all_change_time += change_duration
    return all_get_time + all_change_time

print solve(num, change_duration, get_durations)
