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.*;
import java.io.*;

public class P11A {

  private static void solve() {
    int n = nextInt();
    int d = nextInt();

    int last = nextInt();
    long ans = 0;
    for (int i = 1; i < n; i++) {
      int cur = nextInt();

      if (cur < last) {
        int diff = last - cur;
        int count = diff / d + 1;
        cur += d * count;
        ans += count;
      } else if (cur == last) {
        cur += d;
        ans++;
      }
      last = cur;
    }

    System.out.println(ans);
  }

  private static void run() {
    br = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out);

    solve();

    out.close();
  }

  private static StringTokenizer st;
  private static BufferedReader br;
  private static PrintWriter out;

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

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

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

  public static void main(String[] args) {
    run();
  }
}