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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Scanner;
public class Main {
    
    public static void main(String[] args) throws IOException {
        Scanner in=new Scanner(new InputStreamReader(System.in));
        PrintWriter out=new PrintWriter(System.out);
        int n=in.nextInt();
        int d=in.nextInt();
        long[] num=new long[n];
        for (int i=0; i<n; i++)
        {
            num[i]=in.nextInt();
        }
        long count=0;
        for (int i=1; i<n; i++)
        {
            if (num[i]<=num[i-1])
            {
                long k=(num[i-1]-num[i])/d+1;
                num[i]+=d*k;
                count+=k;
            }
        }
        out.print(count);
        out.close();
    }

}
