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;

/**
 * Created by wencan on 2015/5/30.
 */
public class IncreasingSequence {
    public static void main(String[] args) {
        IncreasingSequence m = new IncreasingSequence();
        m.resolve();
    }

    private void resolve() {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int d = scanner.nextInt();

        long a = scanner.nextInt();
        long b;
        long count = 0;
        long temp;
        for (int i = 0; i < n-1; i++) {
            b = scanner.nextInt();
            if (a >= b) {
                temp = (a - b) / d + 1;
                count+= temp;
                a = b + temp*d;
            } else a = b;
        }

        System.out.println(count);

        scanner.close();
    }
}
