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.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;


public class P11A {
    public static void S1() throws IOException{
        Scanner scanner = new Scanner(
            //new File("in.txt")
            System.in
            );
        int n = scanner.nextInt();
        int d = scanner.nextInt();
        int ans = 0;
        int x=0, y, k;
        for (int i=0; i<n; i++){
            y = scanner.nextInt();
            if (x>=y){
                k = (x-y)/d;
                y += k*d;
                while (y<=x){
                    y+=d;
                    k++;
                }
                ans += k;
            }
            x = y;
        }
        System.out.println(ans);
    }
    public static void S2() throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(
            //new FileInputStream("in.txt")
            System.in
            ));
        String []s = br.readLine().split(" ");
        int n = Integer.parseInt(s[0]);
        int d = Integer.parseInt(s[1]);
        int ans = 0;
        int x=0, y, k;
        
        s = br.readLine().split(" ");
        for (int i=0; i<n; i++){
            y = Integer.parseInt(s[i]);
            if (x>=y){
                k = (x-y)/d;
                y += k*d;
                while (y<=x){
                    y+=d;
                    k++;
                }
                ans += k;
            }
            x = y;
        }
        System.out.println(ans);
        //FileOutputStream fout = new FileOutputStream("in.txt");
    }
    public static void main(String args[]) throws Exception{
        S2();
    }
}
