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 read = new Scanner(System.in);
        int n = read.nextInt();
        int d = read.nextInt();
        int last = read.nextInt();
        int step = 0;
        for(int i = 1; i < n; i ++) {
            int a = read.nextInt();
            if(a <= last) {
                step += (last - a + 1) / d;
                a += ((last - a + 1) / d) * d;
                if(a <= last) {
                    ++ step;
                    a += d;
                }
            }
            last = a;
        }
        System.out.println(step);
    }
}