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 Solution {

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