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;

/**
 * Created by Jordan on 3/31/2015.
 */
public class Testy
{
    public static void main(String[] args)
    {
        int[] numArray;
        //Scanner scan = new Scanner("input.txt");
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int d = scan.nextInt();
        double diff = 0;
        int count = 0;

        numArray = new int[n];

        for(int i = 0; i < n; ++i)
        {
            numArray[i] = scan.nextInt();
        }

        for(int i = 1; i < n; ++i)
        {
            while(numArray[i] <= numArray[i-1])
            {
                diff = numArray[i-1] - numArray[i];
                if(diff == 0)
                {
                    count += 1;
                    numArray[i] += d;
                }
                else
                {
                    count += (int) Math.ceil(diff / d);
                    numArray[i] += d * (int) Math.ceil(diff / d);
                }
            }
        }

        System.out.println(count);
    }
}
