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;
public class Main {
	public static void main(String[] args)	{
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt(),d=scan.nextInt();
		int a[]=new int[n+1];
		for (int i=1;i<=n;i++)
			a[i]=scan.nextInt();
		int ans=0;
		for (int i=2;i<=n;i++)	{
			if	(a[i]<=a[i-1])	{
				ans+=(a[i-1]-a[i])/d+1;
				a[i]+=((a[i-1]-a[i])/d+1)*d;
			}
		}
		System.out.print(ans);
	}
}