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.*;

public class a {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int d = in.nextInt();
		int tot = 0;
		int prev = in.nextInt();
		for(int i=1; i<n; i++) {
			int crnt = in.nextInt();
			if(crnt == prev) {
				crnt += d;
				tot++;
				prev = crnt;
				continue;
			}
			int t = prev-crnt+1;
			int x = (int)Math.max(0,Math.ceil(t/(double)d));
			tot += x;
			crnt += x*d;
			prev = crnt;
		}
		System.out.println(tot);
	}
}
