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 sc=new Scanner(System.in);
        int n=sc.nextInt();
        int d=sc.nextInt();

        int res=0;
        int prev=sc.nextInt();
        for(int i=1; i < n; i++)
        {
            int next=sc.nextInt();
            if(next<=prev){
                res+=(prev-next)/d+1;
                prev=next+((prev-next)/d + 1)*d;
            }
            else
                prev=next;
            
        }
        System.out.println(res);
    }
}