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  javaapplication2 {

    
    public static void main(String[] args) {
       Scanner in = new Scanner(System.in);
       int a = in.nextInt();
       int b = in.nextInt();
       int counter = 0;
       int arr[] = new int[a];
        for (int i = 0; i < a; i++) {
            arr[i] = in.nextInt();
            if(i > 0)
            {
            if(arr[i] <= arr[i-1])
            {
                int x = arr[i-1] - arr[i];
                if(x < b)
                {
                    arr[i]+=b;
                    counter++;
                }
                else
                {
                    counter+= (x/b)+1;
                    arr[i]+= ((x/b)+1)*b;
                }
               
            }
            }
        }
        System.out.println(counter);
    }
    
}