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 IncreasingSequence {
	Scanner stream ;
	public IncreasingSequence(){
		stream = new Scanner (System.in);
		int n = stream.nextInt ();
		int d = stream.nextInt() ;
		int [] arr = new int [n];
		for (int i = 0 ; i <n ; i++){
			arr[i] = stream.nextInt () ;
		}
		sequance (arr , d);
	}
	public void sequance (int[] arr , int d){
		int count = 0 ;
		int num ;
		for (int i = 1 ; i < arr.length ; i++){
			if (arr[i] < arr[i-1]){
				num = arr[i-1] - arr[i] ;
				count += num/d + 1 ;
				arr[i] += (num/d + 1)*d ;
			}else if (arr[i] == arr [i-1]){
				arr[i] += d ;
				count ++ ;
			}
		}
		System.out.println(count);
	}
	public static void main (String [] args){
		new IncreasingSequence ();
	}
}