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;

/**
 *
 * @author Программирование
 */
public class JavaApplication3 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int d = in.nextInt();
        int c = 0;
      //  int[] mas = new int[n+1];
        int last = in.nextInt();
        for(int i=1; i<n; i++){
            int curr = in.nextInt();
            if(curr<=last){
                int tmp = (last+d-curr)/d;
                c+=tmp;
                last=curr+(tmp*d);
            }else{
                last=curr;
            }
        }
   /*     for(int i=0; i<n-1; ++i){
                while(mas[i] >= mas[i+1]){
                    mas[i+1] = mas[i+1] + d;
                    c++;
                }
        }*/
        System.out.println(c);

    }
}
