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 IncreasingSequence {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int d = in.nextInt();
		int count = 0;
		int lastnum = in.nextInt();
		for (int i = 1; i < n; i++) {
			int temp = in.nextInt();
			if (temp <= lastnum) {
				int dif = ((lastnum - temp) / d) + 1;
				count += dif;
				temp += dif * d;
			}
			lastnum = temp;
		}
		in.close();
		System.out.println(count);
	}
}
