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 sc = new Scanner(System.in);
        int n = sc.nextInt(), k = sc.nextInt();
        int pre = sc.nextInt(), count = 0;

        for (int i = 1 ; i < n ; i ++) {
            int temp = sc.nextInt();
            if(pre < temp) {
                pre = temp;
                continue;
            }
            int times =(int) Math.ceil((pre - temp + 1)/(k*1.0));
            count += times;
            pre = temp + times * k;
        }
        System.out.println(count);
    }
}