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) {
	// write your code here
        Scanner scanner = new Scanner(System.in);
        int [] sequence = new int[2005];
        int n = scanner.nextInt();
        int d = scanner.nextInt();
        for (int i = 0; i < n; i++)
            sequence[i] = scanner.nextInt();

        int index = 1;
        int count = 0;
        while (index < n){
            if (sequence[index] <= sequence[index - 1]){
                int difference = sequence[index - 1] - sequence[index];
                count += difference / d + 1;
                sequence[index] += (difference / d + 1) * d;
            }
            index++;


        }
        System.out.println(count);



    }

}


		 		 	   		       		 	 	