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;
import java.lang.Math;

public class main{
    public static void main(String []args){
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int b = s.nextInt();
        int arr[] = new int[n];
        for(int i = 0;i<n;i++){
            arr[i] = s.nextInt();
        }
        int inc = 0;
        for (int i = 1;i<n;i++){
            if(arr[i]<=arr[i-1]){
                int p = (int)Math.ceil((arr[i-1]-arr[i])/(double)b);
                arr[i] += p*b;
                if(arr[i]==arr[i-1]){
                    inc++;
                    arr[i] += b;
                }
                inc += p;
            }
        }
        System.out.println(inc);
    }
}
   