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 {
    static Scanner scanner = new Scanner(System.in);

    public static void main(String[] args) {
        int n = scanner.nextInt();
        int d = scanner.nextInt();
        int counter = 0;

        int a = scanner.nextInt();
        for (int i = 1; i < n; i++) {
            int b = scanner.nextInt();
            if (a >= b) {
                int x = ((a - b) / d) + 1;
                counter += x;
                b +=  (x * d);
            }
            a = b;
        }
        System.out.println(counter);
    }
}