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.io.*;
import java.util.*;

public class IncreasingSequence {
    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        int d = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(f.readLine());
        int prev = Integer.parseInt(st.nextToken());
        int sum = 0;
        for (int i = 1; i < n; i++)
        {
            int b = Integer.parseInt(st.nextToken());
            int add = Math.max(0,(prev-b+d)/d);
            sum += add;
            prev = b + d*add;
        }
        System.out.println(sum);
    }   
}