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.util.*;
import java.util.logging.Level;
import java.awt.Point;

import java.io.*;

public class tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static final double EPS = 1e-9;
	static long mod = 1000000007;
	static int inf = (int) 1e9 + 2;
	static long[] fac;
	static int[] si;
	static ArrayList<Integer> primes;
	static ArrayList<qu>[] ad;
	static ArrayList<qu>[] d;
	static edge[] ed;
	static int[] ch;
	static int[] occ;
	static long[][] adjMatrix;
	static Queue<Integer>[] can;
	static String s;
	static int[][] memo;
	static int n, m, r, k;
	static int[] o;
	static boolean[] t;
	static HashMap<Integer, Integer> pri;
	static TreeMap<qu, Integer> map;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		n = sc.nextInt();
		m = sc.nextInt();
		r = sc.nextInt();
		k = sc.nextInt();
		PriorityQueue<seg> pq = new PriorityQueue<>();
		pq.add(new seg(n / 2, m / 2, cal(n / 2, m / 2)));
		double ans = 0;
		TreeSet<pair> ts = new TreeSet<>();
		ts.add(new pair(n/2, m/2));
		int []xx= {1,-1,0,0};
		int []yy= {0,0,1,-1};
		while (k-- > 0) {
			//System.out.println(pq);
			seg cur = pq.poll();
			ans += cur.v;
            for(int i=0;i<4;i++) {
            	int x=cur.a+xx[i];
            	int y=cur.b+yy[i];
         //   	System.out.println(ts.contains(new pair(x, y))+" "+valid(x, y));
            	if(ts.contains(new pair(x, y)))
            		continue;
            	if(!valid(x, y))
            		continue;
              	ts.add(new pair(x, y));
              	pq.add(new seg(x, y, cal(x, y)));
            }
		}
		System.out.println(ans / (double) ((n - r + 1) *1l* (m - r + 1)));
		out.flush();
	}

	static boolean valid(int i, int j) {
		return i >= 0 && i < n && j >= 0 && j < m;
	}

	static long cal(int i, int j) {
		return (Math.min(i, n - r) - Math.max(0, i - r + 1) + 1) * 1l
				* (Math.min(j, m - r) - Math.max(0, j - r + 1) + 1);
	}

	static class qu implements Comparable<qu> {
		int a;
		int b;
		int w;
		int i;

		qu(int aa, int bb, int cc, int id) {
			a = aa;
			b = bb;
			w = cc;
			i = id;
		}

		public String toString() {
			return a + " " + b + " " + w + " " + i;
		}

		public int compareTo(qu o) {
			if (a == o.a)
				if (b == o.b)
					return i - o.i;
				else
					return b - o.b;
			return a - o.a;
		}
	}

	static class seg implements Comparable<seg> {
		int a;
		int b;
		long v;

		seg(int s, int e, long vv) {
			a = s;
			b = e;
			v = vv;
		}

		public String toString() {
			return a + " " + b + " " + v;
		}

		public int compareTo(seg o) {
			// if(a==o.a)
			return Long.compare(o.v, v);
			// return
		}
	}

	static class pair implements Comparable<pair> {
		int to;
		int number;

		pair(int t, int n) {
			number = n;
			to = t;
		}

		public String toString() {
			return to + " " + number;
		}

		@Override
		public int compareTo(pair o) {
			if (to == o.to)
				return number - o.number;
			return to - o.to;
		}

	}

	static long modPow(long a, long e)

	{
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1)
				res = (res * a) % mod;
			a = (a * a) % mod;
			e >>= 1;
		}
		return res;
	}

	static long inver(long x) {
		long a = x;
		long e = (mod - 2);
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1) {
				res = ((1l * res * a) % mod);
			}
			a = ((1l * a * a) % mod);
			e >>= 1;
		}
		return res % mod;
	}

	static class edge implements Comparable<edge> {
		int from;
		int to;
		int number;

		edge(int f, int t, int n) {
			from = f;
			to = t;
			number = n;
		}

		public String toString() {
			return from + " " + to + " " + number;
		}

		public int compareTo(edge f) {
			return f.number - number;
		}
	}

	static void seive(int N) {
		si = new int[N];
		primes = new ArrayList<>();
		si[1] = 1;
		for (int i = 2; i < N; i++) {
			if (si[i] == 0) {
				si[i] = i;
				primes.add(i);
			}
			for (int j = 0; j < primes.size() && primes.get(j) <= si[i] && (i * primes.get(j)) < N; j++)
				si[primes.get(j) * i] = primes.get(j);
		}
	}

	static long fac(int n) {
		if (n == 0)
			return fac[n] = 1;
		if (n == 1)
			return fac[n] = 1;
		long ans = 1;
		for (int i = 1; i <= n; i++)
			fac[i] = ans = (i % mod * ans % mod) % mod;
		return ans % mod;
	}

	static long gcd(long a, long b) {

		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static class unionfind {
		int[] p;
		int[] size;
		int[] max;
		int num;

		unionfind(int n) {
			p = new int[n];
			size = new int[n];
			max = new int[n];
			for (int i = 0; i < n; i++) {
				p[i] = i;
				max[i] = i;
			}
			Arrays.fill(size, 1);
			num = n;
		}

		int findSet(int v) {
			if (v == p[v])
				return v;

			max[v] = Math.max(max[v], max[p[v]]);

			p[v] = findSet(p[v]);

			max[v] = Math.max(max[v], max[p[v]]);

			return p[v];
		}

		boolean sameSet(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			return false;
		}

		int max() {
			int max = 0;
			for (int i = 0; i < size.length; i++)
				if (size[i] > max)
					max = size[i];
			return max;
		}

		boolean combine(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			// System.out.println(num+" ppp");
			num--;
			if (size[a] > size[b]) {
				p[b] = a;
				max[a] = Math.max(max[a], max[b]);
				size[a] += size[b];

			} else {
				p[a] = b;
				max[b] = Math.max(max[a], max[b]);
				size[b] += size[a];
			}
			return false;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}