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
//package projects;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class CF11A
{
  public static void main(String[] args) throws IOException
  {
    BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));
    String[] lineItems = sc.readLine().split(" ");
    int n = Integer.parseInt(lineItems[0]);
    int d = Integer.parseInt(lineItems[1]);
    long total = 0;
    lineItems = sc.readLine().split(" ");
    long a = -1;
    
    for (int i = 0; i < n; i++)
    {
      long b = Long.parseLong(lineItems[i]);
      if (a + 1 > b)
      {
        long t = (long) Math.ceil((double) (a + 1 - b) / d);
        total += t;
        a = b + t * d;
      }
      else
      {
        a = b;
      }
    }
    
    System.out.println(total);
  }
}
