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 java.util.*;

public class A11{
	public static void main(String args[])throws IOException{
		Scanner sc=new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		PrintWriter pw=new PrintWriter(System.out);
		int n=sc.nextInt();
		int d=sc.nextInt();
		long arr[]=new long[n];
		arr[0]=sc.nextLong();
		int count=0;
		for(int i=1;i<n;i++){
			arr[i]=sc.nextLong();
			if(arr[i]<=arr[i-1]){
				long div=(long)Math.ceil(1.0*(1+arr[i-1]-arr[i])/d);
				arr[i]+=(1L*d*div);
				count+=div;
			}
		}
		pw.println(count);
		pw.close();
	}
}