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.*;

public class A
{
   public static void main(String[] args)
   {
      new A(new Scanner(System.in));
   }

   public A(Scanner in)
   {
      int n = in.nextInt();
      long d = in.nextInt();

      long[] b = new long[n];
      for (int i=0; i<n; i++)
         b[i] = in.nextInt();

      int res = 0;
      for (int j=1; j<n; j++)
      {
         if (b[j-1] >= b[j])
         {
            long diff = b[j-1]-b[j];
            long u = (diff+d)/d;
            b[j] += u*d;
            res+=u;
         }
      }

      System.out.println(res);
   }
}
