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
/**
 * Created by Spenser on 3/17/2015.
 */
import java.util.*;

public class RapidProblemSolving {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int sequenceSize = scan.nextInt();
        int numAdd = scan.nextInt();
        Vector<Integer> Sequence = new Vector<Integer>();
        for(int x = 0; x < sequenceSize; x++){
            Sequence.add(scan.nextInt());
        }
        int numMoves = 0;
        int prevElem = Sequence.get(0);
        for(int x = 1; x < sequenceSize; x++){
            if(prevElem >= Sequence.get(x)) {
                int temp = (prevElem + numAdd) - Sequence.get(x);
                int tempMoves = temp/numAdd;
                numMoves += tempMoves;
                prevElem = Sequence.get(x)+(numAdd*tempMoves);
            }else {
                prevElem = Sequence.get(x);
            }
        }
        System.out.println(numMoves);
    }
}

