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.io.PrintWriter;
import java.util.Scanner;

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

        int n = in.nextInt();

        int d = in.nextInt();

        long[] arr = new long[n];

        int ans = 0;

        arr[0] = in.nextLong();

        for (int i = 1; i < arr.length; i++) {
            arr[i] = in.nextLong();
            if (arr[i] <= arr[i - 1]) {
                long diff = arr[i - 1] - arr[i];
                long count = 0;
                if (diff % d == 0) {
                    count = diff / d + 1;
                    arr[i] += count * d;
                } else {
                    count = (long) Math.ceil((double) diff / d);
                    arr[i] += count * d;
                }
                ans += count;
            }
        }

        out.print(ans);

        out.close();
    }
}
