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 Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int d = sc.nextInt();
		int arr[] = new int[n];
		int count = 0;
		for(int i = 0;i<n;i++){
			arr[i] = sc.nextInt();
		}
		sc.close();
		for(int i =1;i<n;i++){
			if(arr[i]<=arr[i-1]){
				int diff = arr[i-1]-arr[i]+1;
				int toAdd= (int)Math.ceil((double)diff/d);
				count+=toAdd;
				arr[i]+=toAdd*d;
			}
		}
		System.out.println(count);

	}

}
