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 Codeforces {
    static Scanner sr = new Scanner(System.in);
    public static void main(String[] args) throws java.lang.Exception {
          int n=sr.nextInt();
          int d=sr.nextInt();
          int a[]=new int[n];
          for(int i=0;i<n;i++)
              a[i]=sr.nextInt();
          int c=0;
          for(int i=0;i<n-1;i++)
          {
              if(a[i]==a[i+1])
              {
                  ++c;
                  a[i+1]+=d;
              }
              else if(a[i]>a[i+1])
              {
                  int x=(int)Math.ceil((a[i]-a[i+1]+1.0)/d);
                  c=c+x;
                  a[i+1]=a[i+1]+d*x;
              }
          }
        System.out.println(c);

    }
}

