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 cf11A {
	public static void main(String[] args) throws Exception {
		
		//BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int d = sc.nextInt();
		
		int[] arr = new int[n];
		for(int i=0;i<n;i++)	arr[i] = sc.nextInt();
		
		int mov = 0;
		for(int i=1;i<n;i++)
		{
			if(arr[i] <= arr[i-1])
			{
				mov += (arr[i-1]-arr[i])/d + 1;
				arr[i] += ((arr[i-1]-arr[i])/d + 1)*d;
			}
		}
		System.out.println(mov);
	}
}
