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.*;

public class Main {

	public static void main(String[] args) {
		Scanner kb = new Scanner(System.in);
		int n = kb.nextInt();
		int d = kb.nextInt();
		int a[] = new int[n];
		for(int i=0;i<n;i++){
			a[i]=kb.nextInt();
		}
		int temp = a[0];
		int count = 0;
		for(int i=1;i<n;i++){
			if(a[i]<=temp){
				
				int diff = temp-a[i];
				int num = -1;
				if(diff==0)
					num=1;
				else
					num = (int)Math.ceil((double)diff/(double)d);
				a[i]+=(d*num);
				if(a[i]==temp){
					a[i]+=d;
					count++;
				}
				count+=num;
			}
			temp=a[i];
		}
		System.out.println(count);


	}

}
