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 Slotuin {
	public static void main(String[] args) {
		Scanner x = new Scanner(System.in);
		int n = x.nextInt();
		long d = x.nextLong();
		long A0 = x.nextLong();
		long A = 0;
		long c = 0;
		for(int i = 1;i < n;i++)
		{
			A = x.nextLong();
			if(A0 >= A)
			{
				long z = (A0 - A)/d + 1;
				c = c + z;
				A0 = A + z * d;
			}
			else
			{
				A0 = A;
			}
		}
		System.out.print(c);
		x.close();
	}
 
}