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 sc = new Scanner(System.in);
		int n = sc.nextInt();
		int d = sc.nextInt();
		long max = -1;
		long ans = 0;
		for (int i = 0; i < n; i++) {
			long cur = sc.nextInt();
			if (max + 1 > cur) {
				long t = (long) Math.ceil((double) (max + 1 - cur) / d);
				ans += t;
				max = cur + t * d;
			} else {
				max = cur;
			}
		}
		System.out.println(ans);
		sc.close();
	}
}