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.*;
import java.lang.*;
import java.util.Arrays;



public class geek {
static class comp{
    int a,b;
    public comp(){}
    public comp(int a,int b){
        this.a=a;
        this.b=b;
    }
}

    public static void main(String[] args) {
        try {
            Scanner s = new Scanner(System.in);

            StringBuffer sb=new StringBuffer();
           int n=s.nextInt();
          int d=s.nextInt();
          int a[]=new int[n];
          for(int i=0;i<n;i++){
              a[i]=s.nextInt();
          }
          int ans=0;
          for(int i=0;i<n-1;i++){
              if(a[i+1]<=a[i]){
                  int tp=a[i]-a[i+1];
                 int x=((tp)/d)+1;
                 a[i+1]=a[i+1]+x*d;
                 ans+=x;
              }
          }
          sb.append(ans+"\n");


            System.out.println(sb);
        } catch (Exception e) {
            System.out.println(e.getMessage());
        }
    }
}