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
//http://codeforces.com/problemset/problem/11/A
import java.util.Scanner;

public class GrowingSequence {
    static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        int n = sc.nextInt(), d = Integer.parseInt(sc.nextLine().trim()), counter = 0;
        int[] elements = new int[n];
        for (int i = 0; i < n; i++){
            elements[i] = sc.nextInt();
            if (i > 0){
                if (elements[i] < elements[i-1]){
                    double temp = Math.ceil(((double) elements[i-1] - (double) elements[i])/d);
                    elements[i] += d*temp;
                    counter+=temp;
                }
                if (elements[i] == elements[i-1]) {
                    elements[i] += d;
                    counter++;
                }
            }
        }
        System.out.println(counter);
    }
}