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 Solution {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);

        int n = s.nextInt();
        int d = s.nextInt();
        int[] A = new int[n];

        int res = 0;

        for (int i = 0; i < n; i++)
            A[i] = s.nextInt();

        for (int i = 1; i < n; i++) {
            int diff = A[i - 1] - A[i];

            if (diff >= 0) {
                res += diff / d + 1;
                A[i] += d * (diff / d + 1);
            }
        }

        System.out.println(res);

        s.close();
    }
}