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
//package acm.w1;
import java.util.*;
public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		@SuppressWarnings("resource")
		Scanner in = new Scanner (System.in);
		long n = in.nextLong();
		long d = in.nextLong();
		long last = -1;
		long ans = 0;long x;
		for (int i = 0;i < n;++i){
			x = in.nextLong();
			if (x <= last){
				long t = (last - x)/d;
				x += t*d;
				while (x <= last) {
					++t;
					x += d;
				}
				ans += t;
			}
			last = x;
		}
		System.out.println(ans);
	}

}

					 	 			  		  	  	  				 	 	