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.Arrays;
import java.util.Scanner;

public class x11A {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int times=0;
		int plus = sc.nextInt();
		int[] numbers = new int[n];
		for(int a=0;a<n;a++){
			numbers[a] = sc.nextInt();
			}
		for(int a=1;a<n;a++){
			if(numbers[a-1]>=numbers[a]){
				int x = (numbers[a-1]-numbers[a])/plus;
				numbers[a]+=(plus*(x+1));
				times+=(x+1);
			}
		}
		System.out.println(times);
	}
}
