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.util.*;
import java.io.*;

public class CFA {
  BufferedReader br;
  PrintWriter out;
  StringTokenizer st;
  boolean eof;
  private static final long MOD = 1000L * 1000L * 1000L + 7;
  private static final int[] dx = {0, -1, 0, 1};
  private static final int[] dy = {1, 0, -1, 0};
  private static final String yes = "Yes";
  private static final String no = "No";

  void solve() {
//    int T = nextInt();
    int T = 1;
    for (int i = 0; i < T; i++) {
      helper();
    }
  }

  int n;
  int m;
  int r;
  TreeSet<Pair> pq;
  Set<Long> visited;
  void helper() {
    n = nextInt();
    m = nextInt();
    r = nextInt();
    int k = nextInt();
    long dem = 1L * (n - r + 1) * (m - r + 1);
    long res = 0;

    int middleX = (n - 1) / 2;
    int middleY = (m - 1) / 2;

    pq = new TreeSet<>();
    visited = new HashSet<>();
    for (int i = -2; i <= 2; i++) {
      for (int j = -2; j <= 2; j++) {
        add(middleX + i, middleY + j);
      }
    }

    for (int i = 0; i < k; i++) {
      Pair cur = pq.pollFirst();
      visited.add(cur.first * MOD + cur.second);
      res += findCnt(cur.first, cur.second);

      for (int j = 0; j < dx.length; j++) {
        add(cur.first + dx[j], cur.second + dy[j]);
      }
    }

    outln(1.0 * res / dem);
  }

  void add(int x, int y) {
    if (x >= 0 && x < n && y >= 0 && y < m) {
      long newPair = x * MOD + y;
      if (!visited.contains(newPair)) {
        pq.add(new Pair(x, y));
      }
    }
  }

  class Pair implements Comparable<Pair> {
    int first;
    int second;

    public Pair(int first, int second) {
      this.first = first;
      this.second = second;
    }

    public String toString() {
      return "(" + first + ", " + second + ")";
    }

    @Override
    public int compareTo(Pair o) {
      long c1 = findCnt(first, second);
      long c2 = findCnt(o.first, o.second);
      if (c1 != c2) {
        return Long.compare(c2, c1);
      }
      if (first != o.first) {
        return Integer.compare(first, o.first);
      }
      return Integer.compare(second, o.second);
    }
  }

  long findCnt(int x, int y) {
    int xs = Math.max(0, x - (r - 1));
    int ys = Math.max(0, y - (r - 1));
    int xb = Math.min(x, n - r);
    int yb = Math.min(y, m - r);
    return 1L * (xb - xs + 1) * (yb - ys + 1);
  }

  void shuffle(int[] a) {
    int n = a.length;
    for(int i = 0; i < n; i++) {
      int r = i + (int) (Math.random() * (n - i));
      int tmp = a[i];
      a[i] = a[r];
      a[r] = tmp;
    }
  }

  int gcd(int a, int b) {
    while(a != 0 && b != 0) {
      int c = b;
      b = a % b;
      a = c;
    }
    return a + b;
  }
  private void outln(Object o) {
    out.println(o);
  }
  private void out(Object o) {
    out.print(o);
  }
  private void formatPrint(double val) {
    outln(String.format("%.9f%n", val));
  }
  public CFA() {
    br = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out);
    solve();
    out.close();
  }
  public static void main(String[] args) {
    new CFA();
  }

  public long[] nextLongArr(int n) {
    long[] res = new long[n];
    for(int i = 0; i < n; i++)
      res[i] = nextLong();
    return res;
  }
  public int[] nextIntArr(int n) {
    int[] res = new int[n];
    for(int i = 0; i < n; i++)
      res[i] = nextInt();
    return res;
  }
  public String nextToken() {
    while (st == null || !st.hasMoreTokens()) {
      try {
        st = new StringTokenizer(br.readLine());
      } catch (Exception e) {
        eof = true;
        return null;
      }
    }
    return st.nextToken();
  }
  public String nextString() {
    try {
      return br.readLine();
    } catch (IOException e) {
      eof = true;
      return null;
    }
  }
  public int nextInt() {
    return Integer.parseInt(nextToken());
  }
  public long nextLong() {
    return Long.parseLong(nextToken());
  }
  public double nextDouble() {
    return Double.parseDouble(nextToken());
  }
}