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 Test{
        public static void main(String[] args) {
            Scanner input = new Scanner(System.in);
            int n = input.nextInt();
            int d = input.nextInt();
            int b0 = input.nextInt();
            int moves = 0;
            for (int i = 1; i < n; i++) {
                int b_next = input.nextInt();
                if (b_next <= b0){
                    int moves_t = (int) Math.ceil((double)(b0-b_next)/d);
                    moves += moves_t;
                    b_next += moves_t*d;
                    if (b_next == b0){
                        moves += 1;
                        b_next += d;
                    }
                } else if (b_next == b0){
                    moves += 1;
                    b_next += d;
                }
                b0 = b_next;
            }
            System.out.println(moves);
        }
    }