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.*;
import java.util.*;

public class CF11A {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		int d = Integer.parseInt(st.nextToken());
		st = new StringTokenizer(br.readLine());
		int a = Integer.parseInt(st.nextToken());
		int cnt = 0;
		for (int i = 1; i < n; i++) {
			int b = Integer.parseInt(st.nextToken());
			if (a >= b) {
				int c = (a + 1 - b) / d + ((a + 1 - b) % d == 0 ? 0 : 1);
				cnt += c;
				a = b + c * d;
			} else
				a = b;
		}
		System.out.println(cnt);
	}
}
