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.InputStreamReader;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Created by IntelliJ IDEA.
 * User: ��������
 * Date: 26.04.2010
 * Time: 20:06:51
 * To change this template use File | Settings | File Templates.
 */
public class Solution implements Runnable {
    Scanner in;
    PrintWriter out;

    void solveA() {
        int n = in.nextInt();
        long d = in.nextLong();
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextLong();
        }
        long s = 0;
        for (int i = 1; i < n; i++) {
            if (a[i] <= a[i - 1]) {
                long k = (a[i - 1] - a[i]) / d + 1;
                s += k;
                a[i] += k * d;
            }
        }
        out.print(s);
    }

    public void run() {
        try {
          in = new  Scanner(new InputStreamReader(System.in));
          out = new PrintWriter(System.out);
          solveA();
        } catch (Exception e) {
            e.printStackTrace();
        } finally {
            out.close();
        }

    }
    public static void main(String[] args) {
        (new Thread(new Solution())).start();
    }

}
