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 A {

	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int x=sc.nextInt(), d=sc.nextInt(), cnt=0;
		int[] res=new int[x];
		for(int i=0; i<x; ++i) res[i]=sc.nextInt();
		for(int i=1; i<x; ++i)
		{
			if(res[i]<=res[i-1])
			{
				cnt+=(res[i-1]-res[i]+d)/d;
				res[i]+=(res[i-1]-res[i]+d)/d*d;
			}
		}
		System.out.println(cnt);
		sc.close();
	}

}
