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.FileNotFoundException;
import java.util.ArrayList;
import java.util.Scanner;

/**
 * Created with IntelliJ IDEA.
 * User: arcadia
 * Date: 11/6/13
 * Time: 11:55 PM
 * To change this template use File | Settings | File Templates.
 */
public class Sequences
{
    public static void main(String[] args) throws FileNotFoundException
    {
        long[] numbers;
        long lambda;
        int n, d;
        int counter = 0;

        try(Scanner in = new Scanner(System.in);)
        {
            n = in.nextInt();
            d = in.nextInt();

            numbers = new long[n];

            for (int i = 0; i < n; i++)
            {
                numbers[i]=in.nextLong();
            }
        }

        for (int i = 1; i < numbers.length; i++)
        {
            if(numbers[i] <= numbers[i-1])
            {
                lambda = (numbers[i-1]-numbers[i])/ d;
                numbers[i]+=d*lambda;
                while(numbers[i] <= numbers[i-1])
                {
                    lambda++;
                    numbers[i]+=d;
                }
                counter += lambda;
            }
        }

        System.out.print(counter);
    }

    public static long roundUp(long num, long divisor) {
        return (num + divisor - 1) / divisor;
    }
}
