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 IncreasingSequenceDriver 
{

	public static Scanner scanner = new Scanner(System.in);
	
	public static void main(String[] args)
	{
		int sequenceSize = scanner.nextInt();
		int d = scanner.nextInt();
		
		int[] sequence = new int[sequenceSize];
		
		for(int s = 0; s<sequenceSize; s++)
		{
			sequence[s]=scanner.nextInt();
		}
		
		int count = 0;
		for(int i = 1; i<sequenceSize; i++)
		{
			
			if(sequence[i] == sequence[i-1])
			{
				sequence[i] += d;
				count++;
			}
			
			if(sequence[i] < sequence[i-1])
			{
				int newInt = sequence[i-1] - sequence[i];
				int moves = (newInt/d) + 1;
				sequence[i] += moves * d;
				count += moves;
			}
				
		}//end i loop

		System.out.println(count);
	}//end main
	
}//end class driver
