A sequence a0, a1, ..., at - 1 is called increasing if ai - 1 < ai for each i: 0 < i < t.

You are given a sequence b0, b1, ..., bn - 1 and a positive integer d. In each move you may choose one element of the given sequence and add d to it. What is the least number of moves required to make the given sequence increasing?

Input

The first line of the input contains two integer numbers n and d (2 ≤ n ≤ 2000, 1 ≤ d ≤ 106). The second line contains space separated sequence b0, b1, ..., bn - 1 (1 ≤ bi ≤ 106).

Output

Output the minimal number of moves needed to make the sequence increasing.

Examples

Input

4 2
1 3 3 2


Output

3
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author captainTurtle
 */
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);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int d = in.nextInt();
            int dizi[] = new int[n];
            int check;
            int sayac = 0;
            for (int i = 0; i < n; i++) {
                dizi[i] = in.nextInt();
            }
            for (int i = 1; i < n; i++) {
                if (dizi[i] > dizi[i - 1]) {
                    continue;
                } else if (dizi[i] == dizi[i - 1]) {
                    dizi[i] += d;
                    sayac += 1;
                } else {
                    check = (int) Math.ceil((dizi[i - 1] - dizi[i]) / (d / 1.0));
                    dizi[i] += d * check;
                    if (dizi[i] == dizi[i - 1]) {
                        check += 1;
                        dizi[i] += d;
                    }
                    sayac += check;
                }
            }
            System.out.print(sayac);
        }

    }
}

