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.Scanner;
import java.util.Set;
import java.util.TreeSet;

public class Solution11A {
	public static void main(String... g) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		long d = s.nextInt();
		long[] a = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = s.nextLong();
		}
		int r = 0;
		for (int i = 1; i < a.length; i++) {
			if (a[i] <= a[i - 1]) {
				long diff = a[i-1] - a[i];
				long c = 0;
				if (diff == 0) {
					c = 1; 
				} else {
					c = (long)Math.ceil((a[i - 1] - a[i] + d) / d);
				}
				a[i] += c * d;
				r += c;
			}
		}
		System.out.println(r);
	}
	
}
