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.*;
import java.util.*;

public class Task {
    public static void main(String[] args) throws FileNotFoundException {
        Scanner in = new Scanner(System.in);
        
        int n = in.nextInt();
        int d = in.nextInt();
        
        int count = 0;
        
        int[] a = new int[n];
        
        for(int i=0;i<n;i++){
            a[i] = in.nextInt();
        }
        
        for(int i=0;i<n-1;i++){
            if(a[i]>=a[i+1]){
                int s =(Math.abs((a[i+1]-a[i]))/d)+1;
                count += s;
                a[i+1] += s*d;
            }
        }
        
        System.out.println(count);
        
    }

}

