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.*;
import java.io.*;
import java.util.stream.*;
 
public class Solution {
	public static void main(String[] args) throws Exception {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int d = scan.nextInt();
		int prev = 0;
		int curr = 0;
		int minStep = 0;
		for(int i = 0; i < n; i++) {
			curr = scan.nextInt();
			if(i > 0) {
				if(prev == curr) {
					curr += d;
					minStep++;
				} else
				if(prev > curr) {
					int diff = prev - curr;
					curr += d*(diff/d) + d;
					minStep += (diff/d) + 1;
				}
			}
			prev = curr;
		}
		
		System.out.println(minStep);
	}	
}