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 IncreasingSequence {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n=scan.nextInt();
		int d=scan.nextInt();
		int b0=0,c=0;;
		while(n-->0)
		{
			int b=scan.nextInt();
			if(b<=b0)
			{
				int x=(b0-b)/d+1;
				c+=x;
				b0=b+x*d;
			}
			else
			{
				b0=b;
			}
		}
		System.out.println(c);
	}
	

}
