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) {
        Scanner scanIn = new Scanner(System.in);

        int n = scanIn.nextInt();
        int d = scanIn.nextInt();
        int[] sequence = new int[n];
        int count = 0;

        for (int i = 0; i < n; i++) {
            sequence[i] = scanIn.nextInt();
        }

        for (int i = 1; i < n; i++) {
            if (sequence[i-1] >= sequence[i])
            {
                int dif = (sequence[i-1]+1) - sequence[i];
                int x = (int)Math.ceil(((double)dif)/d);
                sequence[i] += x*d;
                count += x;
            }
        }

        System.out.println(count);
    }
}
