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 Main
{
	public static void main(String[] args) {
	    Scanner sc=new Scanner(System.in);
	    int n=sc.nextInt(),d=sc.nextInt(),ans=0;
	    int a[]=new int[n];
	    for(int i=0;i<n;i++)a[i]=sc.nextInt();
	    for(int i=0;i<n-1;i++){
	        if(a[i]<a[i+1])continue;
	        else{
	            int cur=((a[i]-a[i+1])/d);
	            a[i+1]+=cur*d;
	            ans+=cur;
	            if(a[i+1]<=a[i]){
	                ans++;
	                a[i+1]+=d;
	            }
	        }
	    }
	    System.out.println(ans);
	}
}
