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 codeforce {
    public static void main(String[]args){
        Scanner sc= new Scanner(System.in);
        int n=sc.nextInt();
        int d=sc.nextInt();
        int [] mas= new int [n];
        for(int i=0;i<n;i++){
            mas[i]=sc.nextInt();
        }
        int c=0;
        for(int i=1;i<n;i++){
            if(mas[i]<=mas[i-1]){
                c+=(mas[i-1]-mas[i])/d+1;
                mas[i]+=((mas[i-1]-mas[i])/d+1)*d;
            }
        }
        System.out.println(c);
    }
}
