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;

public class Prob11A
{

    public static void main(String[] args)
    {

        Scanner scan = new Scanner(System.in);

        int n = scan.nextInt(), d = scan.nextInt();

        int prev = 0, current, steps = 0;

        for(int i = 0; i < n; i++)
        {
            current = scan.nextInt();


            if(current <= prev){
                int local_steps = (prev - current) / d + 1;
                current += d * local_steps;
                steps += local_steps;
            }

            prev = current;


        }

        System.out.println(steps);


    }

}