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 anotherMain {

	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		String s=sc.nextLine();
		String ar[]=s.split(" ");
         int nums=Integer.parseInt(ar[0]);
         int d=Integer.parseInt(ar[1]);
        String sr=sc.nextLine();
        String array[]=sr.split(" ");
        int couner=0;
        for (int i = 0; i < array.length-1; i++) {
	int	frist=	Integer.parseInt(array[i]);
		int second=	Integer.parseInt(array[i+1]);
		int factor=0;
			if(second<=frist){
				int off=frist-second;
				if(off==0){
					couner+=1;
					array[i+1]=(second+d)+"";
				}else{
					 factor=(off/d)+1;
					couner+=factor;
					array[i+1]=second+(factor*d)+"";
				}
				
			}
			
		}
        System.out.println(couner);

	}

}
