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 n=sc.nextInt(),d=sc.nextInt();
		int[] a=new int[n];
		for(int i=0;i<n;i++)
			a[i]=sc.nextInt();
		int res=0;
		for(int i=1;i<n;i++){
			if(a[i]<=a[i-1]){
				int count=(a[i-1]-a[i])/d+1;
				res+=count;
				a[i]+=count*d;
			}
		}
		System.out.println(res);
	}
}
