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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.stream.LongStream;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BColorfulSlimes solver = new BColorfulSlimes();
        solver.solve(1, in, out);
        out.close();
    }

    static class BColorfulSlimes {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt(), x = in.nextInt();
            long[] a = LongStream.range(0, n).map(z -> in.nextInt()).toArray();
            long pick = 0, magic = 0;
            for (int i = 0; i < n; i++) {
                long minCost = Long.MAX_VALUE;
                int minOffset = 0;
                for (int offset = 0; offset < n; offset++) {
                    long cost = a[(i + n - offset) % n] + offset * x;
                    if (cost < minCost) {
                        minOffset = offset;
                        minCost = cost;
                    }
                }
                magic = Math.max(magic, minOffset);
                pick += a[(i + n - minOffset) % n];
            }
            out.println(pick + magic * x);
        }

    }
}

