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.io.*;
import java.util.*;
public class HelloWorld{

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