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 IncreasingSequence {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt(), d = in.nextInt();
        int[] nums = new int[n];
        int move = 0;
        for (int i = 0; i < n; i++) {
            nums[i] = in.nextInt();
            if (i > 0 && nums[i] <= nums[i-1]) {
                int tmp = (nums[i-1] - nums[i])/d+1;
                move += tmp;
                nums[i] += d*tmp;
            }
        }
        System.out.println(move);
    }
}
