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 static java.util.Arrays.*;
import java.util.*;
import java.io.*;
public class a {

    public static void main(String[] args) throws Exception {
        // Scanner sc = new Scanner(System.in);
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(in.readLine());
        int  n = Integer.parseInt(st.nextToken());
        int d = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(in.readLine());
        int[] nums = new int[n];
        int cnt=0;
        for(int i=0; i<n; ++i) {
            nums[i] = Integer.parseInt(st.nextToken());
            if(i!=0) {
                int mid = nums[i-1]-nums[i];
                if(mid>=0) {
                    if(mid<d) {
                        cnt++;
                        nums[i]+=d;
                    } else {
                        cnt+= mid/d+1;
                        nums[i]+= mid/d*d+d;
                    }
                }
            }
        }
        
        System.out.println(cnt);
    }
}