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 IncreasingSequence
{
	public Scanner in = new Scanner(System.in);
	public PrintStream out = System.out;

	public int n;
	public long[] B;
	public long d;
	
	public void main()
	{
		n = in.nextInt();
		d = in.nextLong();
		
		B = new long[n];
		
		int i;
		long k, res = 0;
		for(i=0;i<n;++i) B[i] = in.nextLong();
		
		for(i=1;i<n;++i)
		{
			if(B[i-1] >= B[i])
			{
				k = (B[i-1]-B[i])/d;
				B[i] += k*d;
				res += k;
				
				while(B[i] <= B[i-1])
				{
					++res;
					B[i] += d;
				}
			}
		}
		
		out.println(res);
	}//end public void main()

	public static void main(String[] args)
	{
		(new IncreasingSequence()).main();
	}
}