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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class CodeForces {
    public static void main(String[] args) {
        FastReader reader = new FastReader();

        int n = reader.nextInt();
        double d = reader.nextInt();

        long previous = reader.nextInt();
        int moves = 0;

        for (int i = 0; i < n - 1; i++) {
            int next = reader.nextInt();

            if (next <= previous) {
                int movesToAdd = (int) Math.ceil((previous - next + 1) / d);
                moves += movesToAdd;
                next += movesToAdd * d;
            }

            previous = next;
        }

        System.out.println(moves);
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return "";
        }
    }
}
