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 Main {

    public static void main(String[] args) {
	Scanner in = new Scanner(System.in);
	int n = in.nextInt();
	int[] l = new int[10000];
	int k=0;
			int d= in.nextInt();
		for (int i=0;i<n;i++){
			l[i]=in.nextInt();}
		for (int i=0;i<n;i++){
			if (l[i+1]<=l[i]&&l[i+1]!=0) {int r=(int)(Math.ceil((double)(l[i]-l[i+1]+1)/(double) d));	k+=r==0?1:r;l[i+1]+=r==0?d:d*r;}


		}
		System.out.println(k);
    }
}
