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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.io.BufferedWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Deque;
import java.util.Map;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.LinkedList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author cacophonix
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        long n;
        long m;
        long r;
        long k;
        OutputWriter outt;

        long fun2(long n, long r) {
            if (r > n) return 0;
            return n - r + 1;
        }

        double fun(long rr, long cc) {
            rr++;
            cc++;
            long ver = n - r + 1;
            ver -= fun2(rr - 1, r);
            ver -= fun2(n - rr, r);
            long hori = m - r + 1;
            hori -= fun2(cc - 1, r);
            hori -= fun2(m - cc, r);
            //outt.printLine(rr,cc,ver,hori);
            double t = ver * hori;
            t /= (n - r + 1) * (m - r + 1);

            return t;
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            outt = out;
            n = in.readLong();
            m = in.readLong();
            r = in.readLong();
            k = in.readLong();
            Deque<IntIntPair> queue = new LinkedList<>();

            PriorityQueue<Pair<Double, IntIntPair>> pq = new PriorityQueue<>();

            Map<IntIntPair, Boolean> visit = new HashMap<>();

            pq.add(Pair.makePair(-fun(n / 2, m / 2), IntIntPair.makePair((int) n / 2, (int) m / 2)));
            visit.put(IntIntPair.makePair((int) n / 2, (int) m / 2), true);

//        if(n%2==1&&m%2==1){
//            queue.add(IntIntPair.makePair((int)n/2,(int)m/2));
//            visit.put(IntIntPair.makePair((int)n/2,(int)m/2),true);
//        }
//        else if(n%2==1||m%2==1){
//            if(n%2==0){
//                queue.add(IntIntPair.makePair((int)n/2-1,(int)m/2));
//                visit.put(IntIntPair.makePair((int)n/2-1,(int)m/2),true);
//                queue.add(IntIntPair.makePair((int)n/2,(int)m/2));
//                visit.put(IntIntPair.makePair((int)n/2,(int)m/2),true);
//            }
//            else{
//                queue.add(IntIntPair.makePair((int)n/2,(int)m/2-1));
//                visit.put(IntIntPair.makePair((int)n/2,(int)m/2-1),true);
//                queue.add(IntIntPair.makePair((int)n/2,(int)m/2));
//                visit.put(IntIntPair.makePair((int)n/2,(int)m/2),true);
//            }
//        }
//        else{
//            queue.add(IntIntPair.makePair((int)n/2,(int)m/2));
//            visit.put(IntIntPair.makePair((int)n/2,(int)m/2),true);
//            queue.add(IntIntPair.makePair((int)n/2-1,(int)m/2));
//            visit.put(IntIntPair.makePair((int)n/2-1,(int)m/2),true);
//            queue.add(IntIntPair.makePair((int)n/2,(int)m/2-1));
//            visit.put(IntIntPair.makePair((int)n/2,(int)m/2-1),true);
//            queue.add(IntIntPair.makePair((int)n/2-1,(int)m/2-1));
//            visit.put(IntIntPair.makePair((int)n/2-1,(int)m/2-1),true);
//        }

            double ans = 0;

            int[] rr = {0, 0, -1, -1, -1, 1, 1, 1};
            int[] cc = {-1, 1, -1, 0, 1, -1, 0, 1};

            for (int i = 0; i < k; i++) {
                Pair<Double, IntIntPair> p = pq.poll();
                ans += -p.first;
                for (int j = 0; j < 8; j++) {
                    int nr = p.second.first + rr[j];
                    int nc = p.second.second + cc[j];
                    if (nr < 0 || nr == n) continue;
                    if (nc < 0 || nc == m) continue;
                    if (!visit.containsKey(IntIntPair.makePair(nr, nc))) {
                        pq.add(Pair.makePair(-fun(nr, nc), IntIntPair.makePair(nr, nc)));
                        visit.put(IntIntPair.makePair(nr, nc), true);
                    }
                }
            }

            out.print(ans);

        }

    }

    static class Pair<U, V> implements Comparable<Pair<U, V>> {
        public final U first;
        public final V second;

        public static <U, V> Pair<U, V> makePair(U first, V second) {
            return new Pair<U, V>(first, second);
        }

        private Pair(U first, V second) {
            this.first = first;
            this.second = second;
        }


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

            Pair pair = (Pair) o;

            return !(first != null ? !first.equals(pair.first) : pair.first != null) &&
                    !(second != null ? !second.equals(pair.second) : pair.second != null);
        }


        public int hashCode() {
            int result = first != null ? first.hashCode() : 0;
            result = 31 * result + (second != null ? second.hashCode() : 0);
            return result;
        }


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

        @SuppressWarnings({"unchecked"})
        public int compareTo(Pair<U, V> o) {
            int value = ((Comparable<U>) first).compareTo(o.first);
            if (value != 0) {
                return value;
            }
            return ((Comparable<V>) second).compareTo(o.second);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class IntIntPair implements Comparable<IntIntPair> {
        public final int first;
        public final int second;

        public static IntIntPair makePair(int first, int second) {
            return new IntIntPair(first, second);
        }

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


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

            IntIntPair pair = (IntIntPair) o;

            return first == pair.first && second == pair.second;
        }


        public int hashCode() {
            int result = first;
            result = 31 * result + second;
            return result;
        }


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

        @SuppressWarnings({"unchecked"})
        public int compareTo(IntIntPair o) {
            int value = Integer.compare(first, o.first);
            if (value != 0) {
                return value;
            }
            return Integer.compare(second, o.second);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void close() {
            writer.close();
        }

    }
}