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.*;

/**
 * Created by James on 1/29/2015.
 */

public class Driver {
    public static void main(String [] args) throws IOException {
        BufferedReader scanner = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        String [] pieces = scanner.readLine().split("\\s+");

        int N = Integer.parseInt(pieces[0]), D = Integer.parseInt(pieces[1]), count = 0, prev;

        pieces = scanner.readLine().split("\\s+");
        prev = Integer.parseInt(pieces[0]);

        for (int i = 1; i < N; ++i) {
            int cur = Integer.parseInt(pieces[i]);

            if (cur <= prev) {
                int diff = (int)Math.ceil((prev + 1 - cur) / (double)D);
                diff = Math.max(diff, 1);
                count += diff;
                cur += diff * D;
            }

            prev = cur;
        }

        out.println(count);
        out.close();
    }
} 