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 java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        long x = in.nextLong();
        long[] a = new long[n];
        long[] min = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = min[i] = in.nextLong();
        }
        long ans = Arrays.stream(min).sum();
        for(int k = 1; k < n; k++) {
            long[] tmp = new long[n];
            for (int i = n; i < n*2; i++) {
                tmp[i%n] = Math.min(min[i%n], a[(i-k)%n]);
            }
            ans = Math.min(ans, Arrays.stream(tmp).sum() + (long)k * x);
            min = Arrays.copyOf(tmp, tmp.length);
        }
        System.out.println(ans);
    }
}   