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.io.FileInputStream;
import java.io.FileNotFoundException;
import java.util.Scanner;


public class IncreasingSequence {
    
    public IncreasingSequence(){
        Scanner sc = new Scanner(System.in);    
        
        int moves = 0;
        int temp = 0;
        int mod=0;
        
        int n = sc.nextInt();
        int d = sc.nextInt();
        
        double b_i;
        double b_i_plus_plus;
        
        b_i_plus_plus = sc.nextInt();
        
        while(sc.hasNext()){
            temp = 0;
            b_i = b_i_plus_plus;
            b_i_plus_plus = sc.nextInt();
            
            if(b_i >= b_i_plus_plus){
                temp = (int) Math.ceil(((b_i - b_i_plus_plus)/(double)d));
                mod = (int) Math.ceil(((b_i - b_i_plus_plus)%(double)d));
                temp = (mod==0)?++temp:temp;
                b_i_plus_plus += temp*d;
            }
            moves += temp;
        }
        System.out.println(moves);
    }
    
    /**
     * @param args
     */
    public static void main(String[] args) {

//      try {
//          System.setIn(new FileInputStream("IncreasingSequence_input.in"));
            IncreasingSequence increasingSequence = new IncreasingSequence();
//      } catch (FileNotFoundException e) {
//          e.printStackTrace();
//      }
    }


}
