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.Scanner;

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

    private static void solve(Scanner in) {
        int N = in.nextInt();
        int x = in.nextInt();
        int[] a = new int[N];
        for (int i = 0; i < N; i++) {
            a[i] = in.nextInt();
        }
        // b[k(magic)][i]
        long[][] b = new long[N][N];
        long ans = 0;

        // no magic
        for (int i = 0; i < N; i++) {
            b[0][i] = a[i];
            ans += b[0][i];
        }

        for (int k = 1; k < N; k++) {
            long sumb = 0;
            for (int i = 0; i < N; i++) {
                b[k][i] = Math.min(b[k - 1][i == 0 ? N - 1 : i - 1], a[i]);
                sumb += b[k][i];
            }
            ans = Math.min(ans, (long) k * x + sumb);
        }
        System.out.println(ans);
    }
}