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.io.*;
import static java.lang.Math.*;
import java.util.*;
public class CF {
    String solve(int n, long d ,String[] s){
        long cnt=0;
        long[] b=new long[n];
        b[0]   += Long.parseLong(s[0]);
       for(int i=0 ; i<b.length-1 ; i++){
            b[i+1] += Long.parseLong(s[i+1]);
            if( b[i]>b[i+1] ) {
                long c=(long)(b[i]-b[i+1])/d;
                if( (b[i]-b[i+1])%d>0 ) c+=1L;
                if( b[i]==b[i+1]+d*c ) c++;
                b[i+1]+= d*c;
                cnt+=c;}
            else if( b[i]==b[i+1] ) {cnt++; b[i+1]+=d;}
        }
        return cnt+"";
    }
    public void run(String[] args) {
	try{
	    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    String str = br.readLine();
            int n = Integer.parseInt(str.split(" ")[0]);
            long d = Long.parseLong(str.split(" ")[1]);
            String line = br.readLine();
	    System.out.println( solve(n,d,line.split(" ")) );

	}catch(Exception e){ e.printStackTrace(); }
    }
    public static void main(String[] args){
	Locale.setDefault(Locale.US);
	(new CF()).run(args);
    }
}