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 Main {

    Scanner cin;

    public static void main(String[] args) throws Exception {
        Main mn = new Main();
        mn.cin = new Scanner(System.in);
        mn.solve();
    }

    private void solve() {
        int n = cin.nextInt();
        int d = cin.nextInt();
        long prev = Integer.MIN_VALUE;
        long steps = 0;
        for (int i = 0; i < n; i++) {
            long b = cin.nextLong();
            if (b <= prev) {
                long multiple = Math.max((prev - b + d) / d, 1);
                steps += multiple;
                prev = b + multiple * d;
            } else {
                prev = b;
            }
        }
        System.out.println(steps);
    }

}
