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.*;
import java.math.BigDecimal;
import java.math.MathContext;
import java.util.*;
import java.util.function.Function;

import static java.math.BigDecimal.ROUND_HALF_UP;

public class Solution {
    static MyScanner sc;
    private static PrintWriter out;
    static long M2 = 1_000_000_000L + 7;

    public static void main(String[] s) throws Exception {
        StringBuilder stringBuilder = new StringBuilder();
//        stringBuilder.append("100000 1000000000 10001 100000 ");
//        for (int i = 1; i < 100000; i++) {
//            stringBuilder.append(" 10000 100000 ");
//        }
        if (stringBuilder.length() == 0) {
            sc = new MyScanner(System.in);
        } else {
            sc = new MyScanner(new BufferedReader(new StringReader(stringBuilder.toString())));
        }


        out = new PrintWriter(new OutputStreamWriter(System.out));
        initData();
        solve();
        out.flush();
    }


    private static void initData() {

    }

    static HashSet<Integer>[] vis;
    static int n;
    static int m;
    static TreeSet<int[]> data;

    private static void solve() throws IOException {
        n = sc.nextInt();
        m = sc.nextInt();
        vis = new HashSet[n];
        int r = sc.nextInt();
        int k = sc.nextInt();


        Function<int[], Long> kk = new Function<int[], Long>() {
            @Override
            public Long apply(int[] ints) {
                long h1 = Math.min(ints[0] + 1, n - ints[0]);
                long h2 = Math.min(r, n - r + 1);

                long w1 = Math.min(ints[1] + 1, m - ints[1]);
                long w2 = Math.min(r, m - r + 1);


                return Math.min(h2, h1) * Math.min(w1, w2);
            }
        };

        kk.apply(new int[]{n / 2, m / 2});

        data = new TreeSet<>((f1, f2) -> {
            long s1 = kk.apply(f1);
            long s2 = kk.apply(f2);
            if (s1 != s2) return Long.compare(s1, s2);
            if (f1[0] == f2[0]) return f1[1] - f2[1];
            return f1[0] - f2[0];
        });
        long total = 1L * (n - r + 1) * (m - r + 1);
        long ans = 0;
        data.add(new int[]{n / 2, m / 2});
        dadd(n / 2, m / 2);

        while (k > 0) {
            int[] ll = data.pollLast();
            ans += kk.apply(ll);
            dadd(ll[0] - 1, ll[1]);
            dadd(ll[0] + 1, ll[1]);
            dadd(ll[0], ll[1] - 1);
            dadd(ll[0], ll[1] + 1);
            k--;
//            out.println("ADD " + ll[0] + " " + ll[1]);
        }

//
//        for (int i = 0; i < n; i++) {
//            for (int j = 0; j < m; j++) {
//                if (inn[i][j]) {
//                    out.print("+");
//                } else {
//                    out.print("_");
//                }
//                out.print(kk.apply(new int[]{i, j}) + " ");
//            }
//            out.println();
//        }


        out.println(ans * 1.0 / total);
    }

    private static void dadd(int i, int i1) {
        if (i < 0 || i1 < 0 || i >= n || i1 >= m) return;
        if (dcont(i, i1)) return;
        dda(i, i1);
        data.add(new int[]{i, i1});
    }

    private static void dda(int i, int i1) {
        if (vis[i] == null) vis[i] = new HashSet<>();
        vis[i].add(i1);
    }

    private static boolean dcont(int i, int i1) {
        return vis[i] != null && vis[i].contains(i1);
    }


    private static final class DU {
        int[] par;
        int[] ct;

        private DU(int n) {
            par = new int[n];
            ct = new int[n];
            for (int i = 0; i < n; i++) {
                par[i] = i;
            }
        }

        private void union(int l1, int l2) {
            int r1 = r(l1);
            int r2 = r(l2);
            if (ct[r1] > ct[r2]) {
                par[r2] = r1;
                ct[r1] += ct[r2] + 1;
            } else {
                par[r1] = r2;
                ct[r2] += ct[r1] + 1;
            }
        }

        private int r(int l2) {
            int from = l2;
            while (l2 != par[l2]) {
                l2 = par[l2];
            }
            while (from != l2) {
                int s = par[from];
                par[from] = l2;
                from = s;
            }
            return l2;
        }
    }


    private static void solveT() throws IOException {
        int t = sc.nextInt();
        while (t-- > 0) {
            solve();
        }
    }

    private static long gcd(long l, long l1) {
        if (l > l1) return gcd(l1, l);
        if (l == 0) return l1;
        return gcd(l1 % l, l);
    }

    private static long pow(long a, long b, long m) {
        if (b == 0) return 1;
        if (b == 1) return a;
        long pp = pow(a, b / 2, m);
        pp *= pp;
        pp %= m;
        return (pp * (b % 2 == 0 ? 1 : a)) % m;
    }


    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        MyScanner(BufferedReader br) {
            this.br = br;
        }

        public MyScanner(InputStream in) {
            this(new BufferedReader(new InputStreamReader(in)));
        }

        void findToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
        }

        String next() {
            findToken();
            return st.nextToken();
        }

        Integer[] nab(int n) {
            Integer[] k = new Integer[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.fi();
            }
            return k;
        }

        int[] na(int n) {
            int[] k = new int[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.fi();
            }
            return k;
        }

        long[] nl(int n) {
            long[] k = new long[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.nextLong();
            }
            return k;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int fi() {
            String t = next();
            int cur = 0;
            boolean n = t.charAt(0) == '-';
            for (int a = n ? 1 : 0; a < t.length(); a++) {
                cur = cur * 10 + t.charAt(a) - '0';
            }
            return n ? -cur : cur;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }


}