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 numpy as np
N, x = map(int, raw_input().split())
a = np.array(map(int, raw_input().split()))

if max(a) <= x:
    print sum(a)
else:
    flg = a <= x
    t = sum(a[flg])
    flg = np.roll(flg, 1)
    t += x
    
    while (flg == False).sum() > 0:
        ndx = np.where(flg == False)[0]
        i = np.argmin(a[ndx])
        if a[i] <= x:
            t += a[i]
            flg[i] = True
        else:
            t += x
            flg = np.roll(flg, 1)

    print t
