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;

public class Main {
    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        long n = in.nextLong();
        long d = in.nextLong();
        long[] a = new long[2005];
        int ans = 0;
        for(int i=0;i<n;i++){
            a[i] = in.nextLong();
            if(i==0)
                continue;
            if(a[i] <= a[i-1]){
                long tmp = (a[i-1] - a[i])/d + 1;
                a[i] += tmp * d;
                ans+=tmp;
            }
        }
        System.out.println(ans);
    }
}


								 		       	  	  							