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 Prob011A
{
    public static void main( String[] Args )
    {
        Scanner scan = new Scanner( System.in );
        int numbers = scan.nextInt();
        int d = scan.nextInt();
        int prev = 0;
        int numMoves =0;

        for ( int x = 0; x < numbers; x++ )
        {
            int temp = scan.nextInt();
            if (prev >= temp)
            {
                int moves = (prev - temp)/d + 1;
                temp += moves * d;
                numMoves += moves;
            }
            prev = temp;
        }

        System.out.println(numMoves);
    }
}
