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 increasingnumber {
    public static void main(String args[]){
        Scanner input  =new Scanner(System.in);
        String baris1=input.nextLine();
        String []data=baris1.split(" ");
    
        String baris2=input.nextLine();
        String angka[]=baris2.split(" ");
        int number[]=new int[angka.length];
        int moves=0;
        
        
        for(int i=0;i<number.length;i++){
        number[i]=Integer.parseInt(angka[i]);
            if (i==0){
            continue;
            }
            else if(number[i-1]>=number[i]){
                moves+=((number[i-1]-number[i])/Integer.parseInt(data[1]))+1;
                number[i]+=(((number[i-1]-number[i])/Integer.parseInt(data[1]))*Integer.parseInt(data[1]))+Integer.parseInt(data[1]);
                }
        }
            System.out.println(moves);
    
    
    }
    
}
