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.Scanner;
public class A11 {
	public static void main(String[] args)
	{
		Scanner scan = new Scanner(System.in);
		int n = Integer.parseInt(scan.next());
		int d = Integer.parseInt(scan.next());
		int[] b = new int[n];
		for(int i=0; i<n; i++)
			b[i] = Integer.parseInt(scan.next());
		int moves = 0;
		for(int i=1; i<n; i++)
		{
			if(b[i] <= b[i-1])
			{
				int k = (b[i-1]-b[i])/d;
				k++;
				moves+=k;
				b[i]+=k*d;
			}
		}
		System.out.println(moves);
	}
	
}
