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 posledov
{
    public static void main(String[] args) 
    {
        Scanner in = new Scanner(System.in);
        int size = in.nextInt();
        int d = in.nextInt();
        int hod = 0;
        int dat[] = new int[size];
        for (int i = 0; i < dat.length; i++)
        {
            dat[i] = in.nextInt();
        }
        for (int i = 1; i < dat.length; i++)
        {
            int vrem2 = 0;
            if(dat[i] <= dat[i-1])
            {
                int vrem = Math.abs(dat[i] - dat[i-1]);
                
            
                    hod+=(vrem/d)+1;
                    vrem2 = (vrem/d)+1;
                
                dat[i] += d*vrem2;
            }
            
        }
        System.out.println(hod);
    }

}
