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 seq
{
  public static void main(String[] args)
  {
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt(),d=sc.nextInt();
    int[] list=new int[n];
    for(int i=0;i<n;i++)
    {
      list[i]=sc.nextInt();
    }
int move=0;
for(int i=0;i<list.length-1;i++)
{
    if (list[i+1]<=list[i]) {
        int steps = (int)((list[i]-list[i+1])/d) + 1;
        list[i+1] += steps*d;
        move += steps;
    }
}
    System.out.println(move);
  }
  //so hard much wow
}