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
//package round11;



import java.io.BufferedOutputStream;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.io.StringReader;
import java.util.Arrays;
import java.util.Scanner;

public class A {
	private Scanner in;
	private PrintWriter out;
	
	public void solve()
	{
		int n = ni();
		int d = ni();
		int[] b = new int[n];
		for(int i = 0;i < n;i++){
			b[i] = ni();
		}
		
		int ct = 0;
		for(int i = 1;i < n;i++){
			if(b[i-1] >= b[i]){
				int c = (b[i-1] - b[i]) / d + 1;
				b[i] += c * d;
				ct += c;
			}
		}
		out.println(ct);
	}
	
	public void run() throws Exception
	{
//		in = new Scanner(new StringReader("4 2 1 3 3 2"));
		in = new Scanner(System.in);
		System.setOut(new PrintStream(new BufferedOutputStream(System.out)));
		out = new PrintWriter(System.out);
		
//		int n = in.nextInt();
		int n = 1;
		for(int i = 1;i <= n;i++){
			long t = System.currentTimeMillis();
			solve();
			out.flush();
//			System.err.printf("%04d/%04d %7d%n", i, n, System.currentTimeMillis() - t);
		}
	}
	
	
	public static void main(String[] args) throws Exception
	{
		new A().run();
	}
	
	private int ni() { return Integer.parseInt(in.next()); }
	private static void tr(Object... o) { System.out.println(o.length == 1 ? o[0] : Arrays.toString(o)); }
	private void tra(int[] a) {System.out.println(Arrays.toString(a));}
	private void tra(int[][] a)
	{
		for(int[] e : a){
			System.out.println(Arrays.toString(e));
		}
	}
	
}
