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:
//package contests.c912;

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

public class C912D implements Runnable {

    private void solve() throws Exception {
        int n = i(), m = i(), r = i(), k = i();
        ArrayList<Set<Integer>> visited = new ArrayList<>(n);
        for (int i = 0; i < n; i++) visited.add(i, new HashSet<>());

        int[] nCounts = calcCounts(n, r);
        int[] mCounts = calcCounts(m, r);

        PriorityQueue<Cell> q = new PriorityQueue<>(Comparator.comparing(Cell::getCount).reversed());

        for (int i = (n - 1) / 2; i <= (n - 1) / 2 + 1 && i < n; i++)
            for (int j = (m - 1) / 2; j <= (m - 1) / 2 + 1 && j < m; j++) {
                var cell = new Cell(i, j, nCounts[i] * mCounts[j]);
                q.add(cell);
                visited.get(i).add(j);
            }

        long catched = 0L;
        for (int l = 0; l < k; l++) {
            var cell = q.poll();
            if (cell == null) break;

            catched += cell.count;


            for (int i = cell.i - 1; i <= cell.i + 1; i++) {
                for (int j = cell.j - 1; j <= cell.j + 1; j++) {
                    if (!(i == cell.i && j == cell.j) && i >= 0 && j >= 0 && i < n && j < m && !visited.get(i).contains(j)) {
                        Cell cell2 = new Cell(i, j, nCounts[i] * mCounts[j]);
                        q.add(cell2);
                        visited.get(i).add(j);
                    }
                }
            }
        }

        long total = (n - r + 1L) * (m - r + 1L);

        w(1.0 * catched / total);
    }

    static class Cell {
        int i, j;
        int count;

        public Cell(int i, int j, int count) {
            this.i = i;
            this.j = j;
            this.count = count;
        }

        public int getCount() {
            return count;
        }

        @Override
        public String toString() {
            return "Cell{" +
                    "i=" + i +
                    ", j=" + j +
                    ", count=" + count +
                    '}';
        }
    }

    private int[] calcCounts(int n, int r) {
        int[] counts = new int[n];
        for (int i = 0; i < n; i++) {
            counts[i] = min(i + 1, n - i, n - r + 1, r);
        }
        return counts;
    }

    public void run() {
        try {
            solve();
        } catch (Exception e) {
            throw new RuntimeException(e);
        } finally {
            out.close();
        }
    }

    public static void main(String[] args) throws Exception {
        new C912D().run();
    }

    //@formatter:off
    InputStream inputStream;
    FastWriter out;

    private C912D() {
        this(System.in, System.out);
    }

    public C912D(InputStream inputStream, OutputStream outputStream){
        this.inputStream = inputStream;
        this.out = new FastWriter(outputStream);
    }

    private final byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = inputStream.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    private char c() { return (char) skip(); }
    private char[] ca(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    private char[][] caa(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) map[i] = ca(m);
        return map;
    }

    private int i() { return (int) l(); }
    private int[] ia(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = i();
        return a;
    }
    private int[][] iaa(int n, int m) {
        int[][] map = new int[n][];
        for (int i = 0; i < n; i++) map[i] = ia(m);
        return map;
    }
    private int[][] iaaT(int n, int m) {
        int[][] map = new int[m][];
        for (int i = 0; i < m; i++) map[i] = new int[n];
        for (int i = 0; i < n; i++) {
            int[] t = ia(m);
            for (int j = 0; j < m; j++) map[j][i] = t[j];
        }
        return map;
    }

    private long l() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    private long[] la(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = l();
        return a;
    }

    private double d() { return Double.parseDouble(s()); }

    private String s() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    //@formatter:on

    public static class FastWriter {
        private static final int BUF_SIZE = 1 << 13;
        private final byte[] buf = new byte[BUF_SIZE];
        private final OutputStream out;
        private int ptr = 0;
        private boolean isFirst = true;

        public FastWriter(OutputStream os) {
            this.out = os;
        }

        private FastWriter write(byte b) {
            buf[ptr++] = b;
            if (ptr == BUF_SIZE)
                innerflush();
            return this;
        }

        private FastWriter write(char c) {
            return write((byte) c);
        }

        private FastWriter write(char[] s) {
            for (char c : s) {
                buf[ptr++] = (byte) c;
                if (ptr == BUF_SIZE) innerflush();
            }
            return this;
        }

        private FastWriter write(String s) {
            s.chars().forEach(c -> {
                buf[ptr++] = (byte) c;
                if (ptr == BUF_SIZE) innerflush();
            });
            return this;
        }

        public static int countDigits(int l) {
            if (l >= 1000000000) return 10;
            if (l >= 100000000) return 9;
            if (l >= 10000000) return 8;
            if (l >= 1000000) return 7;
            if (l >= 100000) return 6;
            if (l >= 10000) return 5;
            if (l >= 1000) return 4;
            if (l >= 100) return 3;
            if (l >= 10) return 2;
            return 1;
        }

        private FastWriter write(int x) {
            if (x == Integer.MIN_VALUE) {
                return write((long) x);
            }
            if (ptr + 12 >= BUF_SIZE) innerflush();
            if (x < 0) {
                write((byte) '-');
                x = -x;
            }
            int d = countDigits(x);
            for (int i = ptr + d - 1; i >= ptr; i--) {
                buf[i] = (byte) ('0' + x % 10);
                x /= 10;
            }
            ptr += d;
            return this;
        }

        public static int countDigits(long l) {
            if (l >= 1000000000000000000L) return 19;
            if (l >= 100000000000000000L) return 18;
            if (l >= 10000000000000000L) return 17;
            if (l >= 1000000000000000L) return 16;
            if (l >= 100000000000000L) return 15;
            if (l >= 10000000000000L) return 14;
            if (l >= 1000000000000L) return 13;
            if (l >= 100000000000L) return 12;
            if (l >= 10000000000L) return 11;
            if (l >= 1000000000L) return 10;
            if (l >= 100000000L) return 9;
            if (l >= 10000000L) return 8;
            if (l >= 1000000L) return 7;
            if (l >= 100000L) return 6;
            if (l >= 10000L) return 5;
            if (l >= 1000L) return 4;
            if (l >= 100L) return 3;
            if (l >= 10L) return 2;
            return 1;
        }

        private FastWriter write(long x) {
            if (x == Long.MIN_VALUE) {
                return write("" + x);
            }
            if (ptr + 21 >= BUF_SIZE) innerflush();
            if (x < 0) {
                write((byte) '-');
                x = -x;
            }
            int d = countDigits(x);
            for (int i = ptr + d - 1; i >= ptr; i--) {
                buf[i] = (byte) ('0' + x % 10);
                x /= 10;
            }
            ptr += d;
            return this;
        }

        private FastWriter write(double x, int precision) {
            if (x < 0) {
                write('-');
                x = -x;
            }
            x += Math.pow(10, -precision) / 2;
            //		if(x < 0){ x = 0; }
            write((long) x).write(".");
            x -= (long) x;
            for (int i = 0; i < precision; i++) {
                x *= 10;
                write((char) ('0' + (int) x));
                x -= (int) x;
            }
            return this;
        }

        public FastWriter writeDelimeter() {
            if (isFirst) {
                isFirst = false;
            } else {
                write(' ');
            }
            return this;
        }

        public FastWriter writeNewline() {
            write('\n');
            isFirst = true;
            return this;
        }

        private void innerflush() {
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
            } catch (IOException e) {
                throw new RuntimeException("innerflush");
            }
        }

        public void flush() {
            innerflush();
            try {
                out.flush();
            } catch (IOException e) {
                throw new RuntimeException("flush");
            }
        }

        public void close() {
            writeNewline();
            flush();
        }
    }

    //@formatter:off
    private void w(int x) { out.writeDelimeter().write(x); }
    private void w(long x) { out.writeDelimeter().write(x); }
    private void w(double x) { out.writeDelimeter().write(x, 16); }
    private void lnw(int x) { out.writeNewline().write(x); }
    private void lnw(long x) { out.writeNewline().write(x); }

    private static int log(int a) {
        if (a <= 0) throw new RuntimeException("log(a): a <= 0");
        return Integer.SIZE - 1 - Integer.numberOfLeadingZeros(a);
    }
    private static int log(long a) {
        if(a <= 0) throw new RuntimeException("log(a): a <= 0");
        return Long.SIZE - 1 - Long.numberOfLeadingZeros(a);
    }
    private static int max(int a, int b) {return Math.max(a, b);}
    private static long max(long a, long b) {return Math.max(a, b);}
    private static int min(int a, int b) {return Math.min(a, b);}
    private static int min(int a, int b, int c) {return min(a, min(b, c));}
    private static int min(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    private static long min(long a, long b) {return Math.min(a, b);}
    private static long min(long a, long b, long c) {return min(a, min(b, c));}
    private static long min(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    private static int pow(int a, int b) {if (a == 0) return 0; int r = 1; while (b > 0) {if ((b & 1) > 0) r *= a; a *= a; b >>= 1;} return r;}
    private static long pow(long a, int b) {if (a == 0) return 0; long r = 1; while (b > 0) {if ((b & 1) > 0) r *= a; a *= a; b >>= 1;} return r;}
    //@formatter:on
}