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:

// Problem : D. Fishes
// Contest : Codeforces - Codeforces Round #456 (Div. 2)
// URL : https://codeforces.com/contest/912/problem/D
// Memory Limit : 256 MB
// Time Limit : 1000 ms
// Powered by CP Editor (https://github.com/cpeditor/cpeditor)

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

public class a implements Runnable{
	
    public static void main(String[] args) {
        new Thread(null, new a(), "process", 1<<26).start();
    }
	public void run() {
		FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		//PrintWriter out = new PrintWriter("file.out");
		Task solver = new Task();
		//int t = scan.nextInt();
		int t = 1;
		for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
		out.close();
	}

	static class Task {
		static final int inf = Integer.MAX_VALUE;
		int n; int m; int k;
		public void solve(int testNumber, FastReader sc, PrintWriter pw) {
			//CHECK FOR QUICKSORT TLE
			//***********************//
			//CHECK FOR INT OVERFLOW
			//***********************//
			n = sc.nextInt();
			m = sc.nextInt();
			k = sc.nextInt();
			int r = sc.nextInt();
			double ev = 0;
			PriorityQueue<Long> pq = new PriorityQueue<>(500000, new comp(n, m));
			int qpt = 0;
			int qpop = 0;
			HashSet<Long> vis = new HashSet<Long>();
			pq.add(100004l * (n / 2) + m / 2);
			vis.add(100004l * (n / 2) + m / 2);
			if(n % 2 == 0 && m % 2 == 0){
				pq.add(100004l * (n / 2 - 1) + m / 2);
				pq.add(100004l * (n / 2) + m / 2 - 1);
				pq.add(100004l * (n / 2 - 1) + m / 2 - 1);
				vis.add(100004l * (n / 2 - 1) + m / 2);
				vis.add(100004l * (n / 2) + m / 2 - 1);
				vis.add(100004l * (n / 2 - 1) + m / 2 - 1);
			}
			else if(n % 2 == 0){
				pq.add(100004l * (n / 2 - 1) + m / 2);
				vis.add(100004l * (n / 2 - 1) + m / 2);
				
			}
			else if(m % 2 == 0) {
				pq.add(100004l * (n / 2 - 1) + m / 2);
				vis.add(100004l * (n / 2 - 1) + m / 2);
			}
			while(qpop < r){
				long coord = pq.poll();
				qpop++;
				long x = coord / 100004;
				long y = coord % 100004;
				//pw.println(x + " " + y + " " + (Math.min(n - k, x) - Math.max(0, x - k + 1) + 1) *
				//	(Math.min(m - k, y) - Math.max(0, y - k) + 1));
				ev += 1l * (Math.min(n - k, x) - Math.max(0, x - k + 1) + 1l) *
					(Math.min(m - k, y) - Math.max(0, y - k + 1) + 1l);
				if(x < n - 1 && !vis.contains(100004l * (x + 1) + y)){
					pq.add(100004l * (x + 1) + y);
					vis.add(100004l * (x + 1) + y);
				}
				if(x > 0 && !vis.contains(100004l * (x - 1) + y)){
					pq.add(100004l * (x - 1) + y);
					vis.add(100004l * (x - 1) + y);
				}
				if(y < m - 1 && !vis.contains(100004l * x + y + 1)){
					pq.add(100004l * x + y + 1);
					vis.add(100004l * x + y + 1);
				}
				if(y > 0 && !vis.contains(100004l * x + y - 1)){
					pq.add(100004l * x + y - 1);
					vis.add(100004l * x + y - 1);
				}
			}
			ev /= 1l * (n - k + 1) * (m - k + 1);
			pw.println(ev);
		}
		long f(long x, long y){
			return (Math.min(n - k, x) - Math.max(0, x - k + 1) + 1) * (Math.min(m - k, y) - Math.max(0, y - k + 1) + 1);
		}
		class comp implements Comparator<Long>{
			int a, b;
			comp(int a, int b){
				this.a=a;
				this.b=b;
			}
			@Override
			public int compare(Long a, Long b){
				long ax = a / 100004;
				long ay = a % 100004;
				long bx = b / 100004;
				long by = b % 100004;
				return f(bx, by) == f(ax, ay) ? 1 : (Long.compare(f(bx, by), f(ax, ay)));
			}
			
		}
	}
	static long binpow(long a, long b, long m) {
		a %= m;
		long res = 1;
		while (b > 0) {
			if ((b & 1) == 1)
				res = res * a % m;
			a = a * a % m;
			b >>= 1;
		}
		return res;
	}
	static void sort(int[] x){
		shuffle(x);
		Arrays.sort(x);
	}
	static void sort(long[] x){
		shuffle(x);
		Arrays.sort(x);
	}
	static class tup implements Comparable<tup>{
		int a, b;
		tup(int a,int b){
			this.a=a;
			this.b=b;
		}
		@Override
		public int compareTo(tup o){
			return Integer.compare(o.b,b);
		}
	}
	static void shuffle(int[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			int temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}

	static void shuffle(long[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			long temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public FastReader(String s) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(new File(s)));
		}

		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;
		}
	}

}