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;
import static java.lang.Math.*;
public class Main{
    public static void main(String[]args){
        Scanner x = new Scanner (System.in);
                int y = x.nextInt();
                double z = x.nextDouble();
                int [] w = new int [y];
                for(int i=0;i<y;i++){
                    int a = x.nextInt();
                    w[i]=a;
                } double k=0,m=0;
                for(int i=1;i<y;i++){
                    int j=i-1;
                    if(w[j]>=w[i]){w[j]+=1;double r =w[j]-w[i];k=ceil(r/z);w[i]+=(int)(k*z);m+=k;}
                }int u = (int)m;
                System.out.println(u);
    }
}