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 in = new Scanner(System.in);

    public static void main(String[] args) {
        new Main.problem().run();

    }

    static class problem {

        void run() {
            int n = in.nextInt();
            int d = in.nextInt();
            int[] arr = new int[n];
            arr[0] = in.nextInt();
            int ans = 0;
            for (int i = 1; i <= n - 1; i++) {
                int temp = 0;
                arr[i] = in.nextInt();
                if (arr[i-1] >= arr[i]) {
                    temp = (((arr[i - 1] - arr[i]) / d)+1);
                }
                arr[i]+=temp*d;
                ans += temp;
            }
            System.out.println(ans);
        }
    }
}
