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 Codeforces {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int a = in.nextInt();
        int result = 0;
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            int k = in.nextInt();
            arr[i] = k;
        }
        for (int i = 1; i < arr.length; i++) {
            if (arr[i] <= arr[i - 1]) {
                    result+=((arr[i-1]-arr[i])/a)+1;
                    arr[i]+=(((arr[i-1]-arr[i])/a)+1)*a;
            }
        }
        System.out.println(result);
    }

}