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 IncreasingSequence {

	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int a=sc.nextInt();
		int b=sc.nextInt();
		int count=0,ans=0;
		int f=sc.nextInt();
		for(int i=1;i<a;i++) {
			int s=sc.nextInt();
			if(s>f) {
				f=s;
				continue;
			}
			else if(s==f) {
				count++;
				f=s+b;
				continue;
			}
			else {
				ans=((f-s)/b)+1;
				count+=ans;
				f=s+(ans*b);
			}
			//System.out.println(f+"f");
			//System.out.println(count+"count");
		}
		System.out.println(count);
	}

}
