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 A11 {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int i;
		int k=0,k1=0;
		int n=scan.nextInt();
		int d=scan.nextInt();
		scan.nextLine();
		int []a=new int[n];
		for(i=0;i<n;i++)
		a[i]=scan.nextInt();
		for(i=1;i<n;i++)
		{	
					if (a[i]<=a[i-1]) 
						{
						k=(a[i-1]-a[i])/d+1;
						a[i]+=d*k;
						k1+=k;		
						}
		}
		System.out.println(k1);
	}
}
