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

def get_read_func(fileobject):
    if fileobject == None :
        return raw_input
    else:
        return fileobject.readline

def main():
    if len(sys.argv) > 1:
        f = open(sys.argv[1])
    else:
        f = None
    read_func = get_read_func(f);
    input_raw = read_func().strip().split()
    [N, x] = [int(input_raw[0]), int(input_raw[1])]
    A = []
    input_raw = read_func().strip().split()
    for i in range(N):
        A.append(int(input_raw[i]))

    max_shift_num = 0
    sum_Aj = 0
    for i in range(N):
        min_time = A[i]
        min_Aj = A[i]
        min_time_shift_num = 0
        for j in range(N):
            if i == j:
                continue;
            if i - j < 0:
                shift_num = N + (i - j)
            else:
                shift_num = i - j
            time = shift_num * x + A[j]
            if time < min_time:
                min_time = time
                min_Aj = A[j]
                min_time_shift_num = shift_num
        sum_Aj += min_Aj
        if  min_time_shift_num > max_shift_num:
            max_shift_num = min_time_shift_num
    print sum_Aj + max_shift_num * x


if __name__ == '__main__':
    main()
