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

import static java.lang.Math.abs;
import static java.lang.Math.copySign;
import static java.lang.Math.max;
import static sun.nio.ch.IOStatus.check;

public class D {

    public static class Cell implements Comparable<Cell> {

        int i;
        int j;

        long score = 0;

        @Override
        public int compareTo(Cell o) {
            return -Long.compare(score, o.score);
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Cell cell = (Cell) o;

            if (i != cell.i) return false;
            return j == cell.j;

        }

        @Override
        public int hashCode() {
            int result = i;
            result = 31 * result + j;
            return result;
        }
    }

    public static void main(String[] args) {

        PrintWriter out = new PrintWriter(System.out);
        MyScanner in = new MyScanner();

        int sizeI = in.nextInt();
        int sizeJ = in.nextInt();
        int r = in.nextInt();
        int k = in.nextInt();


//        int[][] cnt = new int[sizeI][sizeJ];
//        for (int i = 0; i < sizeI; ++i) {
//            for (int j = 0; j < sizeJ; ++j) {
//                if (i + r <= sizeI && j + r <= sizeJ) {
//                    for (int i1 = i; i1 < i + r; ++i1) {
//                        for (int j1 = j; j1 < j + r; ++j1) {
//                            cnt[i1][j1]++;
//                        }
//                    }
//                }
//            }
//        }
//
//        PriorityQueue<Long> rQueue = new PriorityQueue<>();
//        for (int i = 0; i < sizeI; ++i) {
//            for (int j = 0; j < sizeJ; ++j) {
//                rQueue.add((long)cnt[i][j]);
//            }
//        }
//
//        while(rQueue.size()>k){
//            rQueue.poll();
//        }

        PriorityQueue<Long> resQueue = new PriorityQueue<>();


        Set<Cell> visited = new HashSet<>();
        PriorityQueue<Cell> queue = new PriorityQueue<>();

        Cell start = new Cell();
        start.i = sizeI / 2;
        start.j = sizeJ / 2;
        start.score = getScore(sizeI, sizeJ, r, start);
        queue.add(start);

        visited.add(start);

        int[][] directions = new int[][]{{-1, 0}, {1, 0}, {0, 1}, {0, -1}};
        while (queue.size() > 0 && resQueue.size() <  k + 10 && visited.size() <= 1L*sizeI * sizeJ) {
            Cell cell = queue.poll();
            resQueue.add(cell.score);
            for (int direction = 0; direction < 4; ++direction) {
                int ni = cell.i + directions[direction][0];
                int nj = cell.j + directions[direction][1];
                if(ni<0||nj<0||ni==sizeI||nj==sizeJ){
                    continue;
                }
                Cell c = new Cell();
                c.i = ni;
                c.j = nj;
                c.score = getScore(sizeI, sizeJ, r, c);
//                out.println(c.i +" "+c.j+" "+c.score);
                if(!visited.contains(c)){
                    queue.add(c);
                    visited.add(c);
                }
            }
        }

        while (resQueue.size() > k) {
            resQueue.poll();
        }

        long sum = 0;
        while (resQueue.size() > 0) {
//            out.println(resQueue.peek());
            sum += resQueue.poll();
//            out.println(sum);
        }

        out.println(1.0 * sum / (sizeI - r + 1) / (sizeJ - r + 1));


        out.close();
    }

    private static long getScore(int sizeI, int sizeJ, int r, Cell cell) {
        int i0 = Math.max(0, cell.i + 1 - r);
        int i1 = Math.min(sizeI, cell.i + r);

        int j0 = Math.max(0, cell.j + 1 - r);
        int j1 = Math.min(sizeJ, cell.j + r);
        return 1L * (i1 - i0 - r + 1) * (j1 - j0 - r + 1);
    }


    // -----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    // --------------------------------------------------------


}