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.*;
import java.math.*;

public class Main{
    public static void main(String [] args)
    {
        Scanner scan=new Scanner(System.in);
        int n=scan.nextInt();
        int d=scan.nextInt();
        int a[]=new int[n];
        for(int i=0;i<n;i++)
        {
            a[i]=scan.nextInt();
        }
        
        int ans=0;
        for(int i=1;i<n;i++)
        {
            if(a[i]<=a[i-1])
            {
                int c =(int)(Math.ceil((a[i-1]-a[i]+1)/(d*1.0)));
                ans +=c;
                a[i] += d*c;
            }
        }
        System.out.println(ans);
    }
}