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.*;
import java.util.*;
 

public class Main {
	
	public static void main(String[] args) throws java.lang.Exception {
		//BufferedReader kek = new BufferedReader(new InputStreamReader(System.in));
		Scanner skek = new Scanner(System.in);
		PrintWriter outkek = new PrintWriter(System.out);
		
		int N = skek.nextInt(), D = skek.nextInt();
		int valToBeat = 0;
		int count = 0;
		
		for(int i = 0; i < N; i++){
			int current = skek.nextInt();
			
			if(current <= valToBeat){
				int cnt = (valToBeat - current) / D + 1;
				count += cnt;
				current += cnt * D;
			}
			
			valToBeat = current;
		}

		outkek.println(count);
		skek.close();
		outkek.close();
	}	
	
}
