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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Sequence {
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] temp = in.readLine().split(" ");
		int x = Integer.parseInt(temp[0]);
		int y = Integer.parseInt(temp[1]);
		String[] temp2 = in.readLine().split(" ");
		int tt = Integer.parseInt(temp2[0]);
		int c = 0;
		for(int i = 1;i<x;i++){
			int pp = Integer.parseInt(temp2[i]);
			if(pp <= tt){
				int h = tt - pp;
				int hh = (h)/y +1;
				pp += (hh)*y;
				c+=hh;
			}

			tt = pp;
		}
		System.out.println(c);
	}
}
