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 RoundN111 {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int d = in.nextInt();
		int[] a = new int[n];
		for(int i=0;i<n;i++)a[i]=in.nextInt();
		int ans=0;
		for(int i=0;i<n-1;i++){
			int dif=a[i]-a[i+1];
			if(dif>=0){
				ans+=(dif/d)+1;
				a[i+1]=a[i+1]+((dif/d)+1)*d;
			}
		}


		System.out.println(ans);
	}
}