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 A {

	public static void main(String[] args){
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		int d=in.nextInt();
		int count=0;
		int[] var=new int[n];
		for(int i=0;i<n;i++){
			var[i]=in.nextInt();
		}
		in.close();
		for(int i=1;i<n;i++){
			if(var[i]<=var[i-1]){
				if(var[i]==var[i-1]){
					var[i]+=d;
					count++;
				}
				else{
					int t=((var[i-1]-var[i])/d)+1;
					var[i]+=t*d;
					count=count+t;
				}
			}
		}
		System.out.println(count);
	}
	
}
