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 void main(Scanner sc) {
        int n = sc.nextInt();
        long x = sc.nextInt();
        long a[] = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }

        long b[] = new long[n];
        Arrays.fill(b, Long.MAX_VALUE);

        long ans = n * 1000000000L;
        for (int magic = 0; magic < n; magic++) {
            for (int i = 0; i < n; i++) {
                b[i] = Math.min(b[i], a[(i + n - magic) % n]);
            }
            ans = Math.min(ans, magic * x + Arrays.stream(b).sum());
        }

        System.out.println(ans);
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        new Main().main(sc);
        sc.close();
    }
}
