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.IOException;
import java.io.InputStreamReader;

public class Round11ProblemA {

	public static void main(String[] args) {
		BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
		try {
			int[] param = parseIntegers(input.readLine());
			int n = param[0];
			int d = param[1];
			int[] b = parseIntegers(input.readLine());
			int total = 0;
			for (int i = 0; i < n - 1; i++) {
				if (b[i] >= b[i+1]) {
					int count = (b[i] - b[i+1]) / d + 1;
					total += count;
					b[i+1] += d * count;
				}
			}
			System.out.println(total);
		} catch (Exception e) {
			e.printStackTrace();
		} finally {
			try {
				input.close();
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
	}

	public static int[] parseIntegers(String line) {
		String[] strings = line.split("\\s");
		int[] numbers = new int[strings.length];
		for (int i = 0; i < strings.length; i++) {
			numbers[i] = Integer.parseInt(strings[i]);
		}
		return numbers;
	}
}
