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;

public class PowerConsumptionCalculation {
    final static int MAX = 2000;
    public static void main(String[] args) {
        int n=0;int d=0;
        int[] arr = new int[MAX];
        int count = 0;
        Scanner scanner = new Scanner(System.in);
        n = scanner.nextInt();
        d = scanner.nextInt();
        for (int i = 0; i < n; i++) {
            arr[i] = scanner.nextInt();
        }

        for (int i = 0; i < n-1; i++) {
            if (arr[i]>=arr[i+1]){
                count += (arr[i]-arr[i+1])/d +1;
                arr[i+1]+= ((arr[i]-arr[i+1])/d +1)*d;
            }
        }
        System.out.println(count);

    }
}

 			 	 				 	  	  	 	  		   	