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 Main{
	public static void main(String [] args){
 		Scanner s=new Scanner (System.in);
		int  n=s.nextInt(),d=s.nextInt();
		long [] a=new long [2005];
		for(int i=1;i<=n;i++)  a[i]=s.nextLong();
		long  ans=0;
		for(int i=2;i<=n;i++){
			if(a[i]>a[i-1]) continue ;
			ans+=(a[i-1]-a[i])/d+1;
			a[i]=a[i]+(a[i-1]-a[i])/d*d+d;
		}
		System.out.println(ans);
		s.close();
	}
}
