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 Increasing {
	public static void main(String[] args){
		Scanner reader=new Scanner(System.in);
		int n,d;
		n=reader.nextInt();
		d=reader.nextInt();
		int[]num=new int[n];
		for(int i=0;i<n;i++){
			num[i]=reader.nextInt();
		}
		int x,ans=0;
		for(int i=1;i<n;i++){
			if(num[i-1]>=num[i]){
			x=(num[i-1]-num[i])/d+1;
			num[i]+=x*d;
			ans+=x;
				
				
			}
				}
		

	System.out.println(ans);
		
	}
	
	

}