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 Class1 {
    public static void main(String[] args) {
     Scanner reader = new Scanner(System.in);
     
        int n=reader.nextInt();
        int d=reader.nextInt();
        int[]seq=new int[n];
        for(int i=0;i<n;i++)
        {
            seq[i]=reader.nextInt();
            }
        int step=0;
        for(int j=0 ;j <n-1 ;j++)
         {
            if(seq[j]>=seq[j+1])
            {
                int sub=seq[j]-seq[j+1];
                int times=sub/d;
                step+=times;
                    seq[j+1]+=times*d;
                if(seq[j]>=seq[j+1]){
                        step++;
                        seq[j+1]+=d;    
                    }
                                    
                     
                }
           
                       
         }
        
                                
         
         System.out.println(step);
                             
                             
                             
                             }
    }
