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 Main
{
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);

		int n = in.nextInt();
		int d = in.nextInt();
		int b[] = new int[n];
		int a[] = new int[n];
		int ans = 0;
		for (int i = 0; i < n; i++) 
		{
			b[i] = in.nextInt();
			if (i > 0 && b[i] - b[i-1] <= 0)
			{
				int temp = (b[i-1] - b[i] + d) / d;
				b[i] += temp * d;
				ans += temp;
			}
		}
		System.out.println(ans);
		in.close();
	}
}
