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.util.Scanner;

/**
 * User: Sasha
 * Date: 24.02.11
 * Time: 21:37
 */
public class Main {
    private static Scanner sc = new Scanner(System.in);

    public static void main(String args[]) {
        int n, d, a, prev = -1, result = 0;

        n = sc.nextInt();
        d = sc.nextInt();

        for (int i = 0; i < n; ++i) {
            a = sc.nextInt();

            int k = 0;
            if (a <= prev) {
                k = (prev - a) / d + 1;
            }
            result += k;
            prev = a + k * d;
        }

        System.out.println(result);
    }
}
