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 Main {

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

}
