Problem: While Grisha was celebrating New Year with Ded Moroz, Misha gifted Sasha a small rectangular pond of size n × m, divided into cells of size 1 × 1, inhabited by tiny evil fishes (no more than one fish per cell, otherwise they'll strife!).

The gift bundle also includes a square scoop of size r × r, designed for fishing. If the lower-left corner of the scoop-net is located at cell (x, y), all fishes inside the square (x, y)...(x + r - 1, y + r - 1) get caught. Note that the scoop-net should lie completely inside the pond when used.

Unfortunately, Sasha is not that skilled in fishing and hence throws the scoop randomly. In order to not frustrate Sasha, Misha decided to release k fishes into the empty pond in such a way that the expected value of the number of caught fishes is as high as possible. Help Misha! In other words, put k fishes in the pond into distinct cells in such a way that when the scoop-net is placed into a random position among (n - r + 1)·(m - r + 1) possible positions, the average number of caught fishes is as high as possible.

Input

The only line contains four integers n, m, r, k (1 ≤ n, m ≤ 105, 1 ≤ r ≤ min(n, m), 1 ≤ k ≤ min(n·m, 105)).

Output

Print a single number — the maximum possible expected number of caught fishes.

You answer is considered correct, is its absolute or relative error does not exceed 10 - 9. Namely, let your answer be a, and the jury's answer be b. Your answer is considered correct, if <image>.

Examples

Input

3 3 2 3


Output

2.0000000000


Input

12 17 9 40


Output

32.8333333333

Note

In the first example you can put the fishes in cells (2, 1), (2, 2), (2, 3). In this case, for any of four possible positions of the scoop-net (highlighted with light green), the number of fishes inside is equal to two, and so is the expected value.

<image>

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Set;
import java.util.StringTokenizer;

/*
 public class _912D {

 }

 */
public class _912D {
  public void solve() throws FileNotFoundException {
    InputStream inputStream = System.in;

    InputHelper in = new InputHelper(inputStream);

    // actual solution
    long n = in.readInteger();
    long m = in.readInteger();

    long r = in.readInteger();

    long k = in.readInteger();

    double den = (n - r + 1) * (m - r + 1);

    // 1..
    long midn = (n + 1) / 2;
    long midm = (m + 1) / 2;

    long maxval = move(midn, midm, n, m, r);

    PriorityQueue<ele> pq =
        new PriorityQueue<_912D.ele>((e1, e2) -> (int) Math.signum(e2.val - e1.val));

    Set<Long> vis = new HashSet<Long>();

    pq.add(new ele(midn, midm, maxval));

    vis.add(comb(midn, midm, n, m));

    double ans = 0;

    while (!pq.isEmpty() && k > 0) {
      ele ce = pq.poll();

      ans += ce.val;

      k--;

      long ci = ce.i;
      long cj = ce.j;

      if (ci > 1 && !vis.contains(comb(ci - 1, cj, n, m))) {
        pq.add(new ele(ci - 1, cj, move(ci - 1, cj, n, m, r)));
        vis.add(comb(ci - 1, cj, n, m));
      }

      if (cj > 1 && !vis.contains(comb(ci, cj - 1, n, m))) {
        pq.add(new ele(ci, cj - 1, move(ci, cj - 1, n, m, r)));
        vis.add(comb(ci, cj - 1, n, m));
      }

      if (ci < n && !vis.contains(comb(ci + 1, cj, n, m))) {
        pq.add(new ele(ci + 1, cj, move(ci + 1, cj, n, m, r)));
        vis.add(comb(ci + 1, cj, n, m));
      }

      if (cj < m && !vis.contains(comb(ci, cj + 1, n, m))) {
        pq.add(new ele(ci, cj + 1, move(ci, cj + 1, n, m, r)));
        vis.add(comb(ci, cj + 1, n, m));
      }
    }

    System.out.println(ans / den);
    // end here
  }

  long comb(long i, long j, long n, long m) {
    return (i - 1) * m + j;
  }

  class ele {
    long i;
    long j;
    long val;

    /**
     * @param i
     * @param j
     * @param val
     */
    public ele(long i, long j, long val) {
      super();
      this.i = i;
      this.j = j;
      this.val = val;
    }
  }

  long[] cnt(int i, int j, int n, int m, int r) {
    long maxn = Math.min(r, i);
    long maxm = Math.min(j, r);

    long minn = Math.max(r - (n - i + 1), 1);
    long minm = Math.max(r - (m - j + 1), 1);

    long an = -1;
    int cr = -1;
    int cc = -1;

    if (n >= 2 * r) {
      an = n - 2 * (r - 1);
      cr = r - 1;
    } else {
      an = n - 2 * (n - r);
      cr = (n - r);
    }

    long am = -1;

    if (m >= 2 * r) {
      am = m - 2 * (r - 1);
      cc = r - 1;
    } else {
      am = m - 2 * (m - r);
      cc = m - r;
    }

    return new long[] { an * am, cr, cc };
  }

  long move(long i, long j, long n, long m, long r) {

    if (i > n || i <= 0 || j > m || j <= 0)
      return -1;

    long maxn = Math.min(r, i);
    long maxm = Math.min(j, r);

    long minn = Math.max(r - (n - i), 1);
    long minm = Math.max(r - (m - j), 1);

    if (maxn < minn || maxm < minm)
      return 0;

    return (maxn - minn + 1) * (maxm - minm + 1);
  }

  public static void main(String[] args) throws FileNotFoundException {
    (new _912D()).solve();
  }

  class InputHelper {
    StringTokenizer tokenizer = null;
    private BufferedReader bufferedReader;

    public InputHelper(InputStream inputStream) {
      InputStreamReader inputStreamReader = new InputStreamReader(inputStream);
      bufferedReader = new BufferedReader(inputStreamReader, 16384);
    }

    public String read() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          String line = bufferedReader.readLine();
          if (line == null) {
            return null;
          }
          tokenizer = new StringTokenizer(line);
        } catch (IOException e) {
          e.printStackTrace();
        }
      }

      return tokenizer.nextToken();
    }

    public Integer readInteger() {
      return Integer.parseInt(read());
    }

    public Long readLong() {
      return Long.parseLong(read());
    }
  }
}