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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class A {

	public static void main(String[] args) {
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(
				System.in)));
		int n = sc.nextInt();
		long d = sc.nextInt();
		long last = sc.nextInt();
		long cnt = 0;
		for (int i = 1; i < n; i++) {
			long next = sc.nextInt();
			if (next > last)
				last = next;
			else {
				long diff = last - next;
				long k = 1 + diff / d;
				cnt += k;
				last = next + k * d;
			}
		}
		System.out.println(cnt);
	}

}
