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 CF11A {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
	   
		int n=scan.nextInt(); double d=scan.nextInt();
		double[] b=new double[n]; int c=0;int k=0;
		for(int i=0;i<n;i++) b[i]=scan.nextInt(); scan.close();
		for(int i=0;i<n-1;i++) { if(b[i+1]<=b[i]) {k=(int) Math.ceil((b[i]-b[i+1]+1)/(d));b[i+1]+=k*d;c+=k;}}
		System.out.println(c);
		}
}