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 d=in.nextInt();
		int [] l= new int[n];
		int j=0;
		for(int i=0;i<n;i++){
			l[i]=in.nextInt();
			}
		for(int i=0;i<n-1;i++){
			if(l[i]>=l[i+1]){
				int x=(int)(Math.ceil((double)(l[i]-l[i+1]+1)/(double)d));
				x= x==0? 1:x;
		l[i+1]+=d*x; j+=x;}
		}
System.out.println(j);

		}
	     }
