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.*;

public class A11 {
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int d = in.nextInt();
        int b[] = new int[n];
        for (int i = 0; i < n; i++) {
            b[i] = in.nextInt();
        }
        int moves = 0;
        for (int i = 1; i < n; i++) {
            if (b[i - 1] == b[i]) {
                ++moves;
                b[i] += d;
            } else if (b[i - 1] > b[i]) {
                int diff = b[i - 1] - b[i];
                ++diff;
                int quot = diff / d;
                int rem = diff % d;
                moves += quot;
                b[i] += (d * quot);
                if (rem > 0) {
                    ++moves;
                    b[i] += d;
                }
                    
            }
        }
        System.out.println(moves);
    }
}
