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.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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) {
            while (testNumber-- != 0) {
                int n = in.nextInt();
                int d = in.nextInt();
                int[] arr = new int[n];
                for (int i = 0; i < n; i++) {
                    arr[i] = in.nextInt();
                }

                int count = 0;
                for (int i = 1; i < arr.length; i++) {
                    if (arr[i - 1] >= arr[i]) {
                        int temp = ((arr[i - 1] - arr[i]) / d) + 1;
                        count += temp;
                        arr[i] += (d * temp);

                    }
                }
                out.println(count);

            }

        }

    }
}

