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.*;

public class IncreasingSequence {
    public static void main(String [] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        int d = input.nextInt();

        int [] arr = new int [n];
        for(int i = 0; i < n; i++)
            arr [i] = input.nextInt();

        int counter = 0;
        for(int i = 0; i < n - 1; i++){
            if(arr [i] == arr [i + 1]){
                counter ++;
                arr [i + 1] += d;
            }
            else if(arr [i] > arr [i + 1]){
                int diff = arr [i] - arr [i + 1];

                if(diff < d){
                    counter ++;
                    arr [i + 1] += d;
                }
                else if(diff == d){
                    counter += 2;
                    arr [i + 1] += (d * 2);
                }
                else{
                    counter += ((diff / d) + 1);
                    arr [i + 1] += (((diff / d) + 1) * d);
                }
            }
        }

        System.out.println(counter);
    }
}