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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;


import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Random;
import java.util.TreeSet;


public final class CF_456_D{

	static boolean verb=true;
	static void log(Object X){if (verb) System.err.println(X);}
	static void log(Object[] X){if (verb) {for (Object U:X) System.err.print(U+" ");System.err.println("");}}
	static void log(int[] X){if (verb) {for (int U:X) System.err.print(U+" ");System.err.println("");}}
	static void log(int[] X,int L){if (verb) {for (int i=0;i<L;i++) System.err.print(X[i]+" ");System.err.println("");}}
	static void log(long[] X){if (verb) {for (long U:X) System.err.print(U+" ");System.err.println("");}}

	static void logWln(Object X){if (verb) System.err.print(X);}
	static void info(Object o){	System.out.println(o);}
	static void output(Object o){outputWln(""+o+"\n");	}
	static void outputWln(Object o){try {out.write(""+ o);} catch (Exception e) {}}


	static long mod=1000000007;



	// Global vars
	static BufferedWriter out;
	static InputReader reader;


	static long getNum(long mid,ArrayList<Long> lx,ArrayList<Long> ly){

		long num=0;
		for (long v:lx){
			long y=mid/v;
			if (y*v<mid)
				y++;
			int id=Collections.binarySearch(ly,y);
			if (id<0)
				id=-id-1;
			if (id<0)
				id=0;
			if (id<ly.size()){
				num+=(ly.size()-id);
			}
		}
		return num;
	}
	
	
	
	static long getNum(long mid,ArrayList<Composite> lx,ArrayList<Composite> ly,ArrayList<Long> numx,ArrayList<Long> numy){

		long num=0;
		for (Composite X:lx){
			long v=X.v;
			long y=mid/v;
			if (y*v<mid)
				y++;
			int id=Collections.binarySearch(ly,new Composite(y,0));
			if (id<0)
				id=-id-1;
			if (id<0)
				id=0;
			if (id<ly.size()){
				num+=numy.get(ly.size()-1);
				if (id>0)
					num-=numy.get(id-1);
			}
		}
		return num;
	}
	
	static class Composite implements Comparable<Composite> {
		
		long v;
		long num;
		
		public int compareTo(Composite X){
			if (v<X.v)
				return -1;
			if (v>X.v)
				return 1;
			if (num<X.num)
				return -1;
			if (num>X.num)
				return 1;
			return 0;
		}
		
		public Composite(long v, long num) {
			this.v = v;
			this.num = num;
		}
		
		
		
		
		
	}

	static void solveKO(int n,int m,int r,int k){
		log("==============");
		log(n+" "+m+" "+r+" "+k);
		long bx=0;
		long by=0;
		ArrayList<Long> lx=new ArrayList<Long>();
		ArrayList<Long> ly=new ArrayList<Long>();

		for (int i=0;i<n;i++){
			int minx=Math.max(i-r+1, 0);
			int maxx=Math.min(i, n-r);
			long dx=maxx-minx+1;
			lx.add(dx);

		}

		for (int j=0;j<m;j++){
			int miny=Math.max(j-r+1, 0);
			int maxy=Math.min(j, m-r);
			long dy=maxy-miny+1;
			ly.add(dy);
		}

		Collections.sort(lx);
		Collections.sort(ly);
		int idx=lx.size()-1;
		int idy=ly.size()-1;
		long res=0;


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


		long lo=0;
		long hi=tot;
		long mid=(lo+hi)/2;
		log("lo:"+lo+" hi:"+hi);

		long gn=getNum(lo,lx,ly);

		if (gn>2*k) {	
			loop:while (lo+1<hi){
				mid=(lo+hi)/2;
				log("lo:"+lo+" hi:"+hi);
				// now count how many have bigger than mid
				long num=getNum(mid,lx,ly);
				
				if (num>=k && num<=2*k){
					lo=mid;
					log("stopping with num:"+num);
					break loop;
				}
				
				if (num>2*k)
					lo=mid;
				if (num<k)
					hi=mid;
			}
		}
		log("step 2");
		log("target:"+lo);
		ArrayList<Long> lst=new ArrayList<Long>();
		loop:for (int j=lx.size()-1;j>=0;j--){
			long v=lx.get(j);
			long y=lo/v;
			if (y*v<lo)
				y++;
			int id=Collections.binarySearch(ly,y);
			if (id<0)
				id=-id-1;
			log("v:"+v+" y:"+y+" id:"+id+" "+ly.size());
			if (id>=ly.size())
				break loop;
			if (id>=0)
				for (int i=id;i<ly.size();i++){
					lst.add(-ly.get(i)*v);
				}
		}
		log("step 3 //"+lst.size());
		Collections.sort(lst);
		log(lst.size()+" "+k);
		for (int i=0;i<k;i++)
			res+=-lst.get(i);

		double bob=res;
		bob/=tot;
		output(bob);

	}
	
	static void solve(int n,int m,int r,int k){
		//log("==============");
		//log(n+" "+m+" "+r+" "+k);
		long bx=0;
		long by=0;


		int[] vx=new int[n+1];
		for (int i=0;i<n;i++){
			int minx=Math.max(i-r+1, 0);
			int maxx=Math.min(i, n-r);
			int dx=maxx-minx+1;
			vx[dx]++;

		}

		int[] vy=new int[m+1];
		
		for (int j=0;j<m;j++){
			int miny=Math.max(j-r+1, 0);
			int maxy=Math.min(j, m-r);
			int dy=maxy-miny+1;
			vy[dy]++;
		}

		ArrayList<Composite> lx=new ArrayList<Composite>();
		ArrayList<Composite> ly=new ArrayList<Composite>();
		for (int i=0;i<n+1;i++){
			if (vx[i]>0){
				lx.add(new Composite(i,vx[i]));
			}
		}
		
		for (int i=0;i<m+1;i++){
			if (vy[i]>0){
				ly.add(new Composite(i,vy[i]));
			}
		}
		
		ArrayList<Long> numx=new ArrayList<Long>();
		ArrayList<Long> numy=new ArrayList<Long>();
		
		long nm;
		nm=0;
		for (Composite x:lx){
			nm+=x.num;
			numx.add(nm);
		}
		nm=0;
		for (Composite y:ly){
			nm+=y.num;
			numy.add(nm);
		}
		
		
		int idx=lx.size()-1;
		int idy=ly.size()-1;
		long res=0;


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

		long lo=0;
		long hi=tot;
		long mid=(lo+hi)/2;
		//log("lo:"+lo+" hi:"+hi);

		long gn=getNum(lo,lx,ly,numx,numy);

		if (gn>2*k) {	
			loop:while (lo+1<hi){
				mid=(lo+hi)/2;
				////log("lo:"+lo+" hi:"+hi);
				// now count how many have bigger than mid
				long num=getNum(mid,lx,ly,numx,numy);
				
				if (num>=k && num<=2*k){
					lo=mid;
					//log("stopping with num:"+num);
					break loop;
				}
				
				if (num>2*k)
					lo=mid;
				if (num<k)
					hi=mid;
			}
		}
		//log("step 2");
		//log("target:"+lo);
		ArrayList<Long> lst=new ArrayList<Long>();
		HashMap<Long,Long> hm=new HashMap<Long,Long>();
	
		loop:for (int j=lx.size()-1;j>=0;j--){
			Composite X=lx.get(j);
			long v=X.v;
			long y=lo/v;
			if (y*v<lo)
				y++;
			int id=Collections.binarySearch(ly,new Composite(y,0));
			if (id<0)
				id=-id-1;
			////log("v:"+v+" y:"+y+" id:"+id+" "+ly.size());
			if (id>=ly.size())
				break loop;
			if (id>=0)
				for (int i=id;i<ly.size();i++){
					Composite Y=ly.get(i);
					long mul=Y.v*X.v;
					Long Z=hm.get(mul);
					if (Z==null) {
						lst.add(mul);
						Z=0L;
					}
					hm.put(mul,Z+X.num*Y.num);
				}
		}
		
		//log("step 3 //"+lst.size());
		Collections.sort(lst);
		long cur=0;
		for (int i=lst.size()-1;i>=0 && cur<k;i--){
			long v=lst.get(i);
			long num=Math.min(hm.get(v),k-cur);
			cur+=num;
			res+=num*v;
		}
	

		double bob=res;
		bob/=tot;
		output(bob);

	}
	


	static void test(){

		int NMAX=10;
		int MMAX=10;
		for (int n=1;n<NMAX;n++)
			for (int m=1;m<MMAX;m++)
				for (int r=1;r<=Math.min(n, m);r++)
					for (int k=1;k<=n*m;k++){
						solve(n,m,r,k);
					}
		log("done");
	}

	static void process() throws Exception {


		out = new BufferedWriter(new OutputStreamWriter(System.out));
		reader=new InputReader(System.in);

		//test();

		int n=reader.readInt();
		int m=reader.readInt();
		int r=reader.readInt();
		int k=reader.readInt();



		solve(n,m,r,k);

		// point at i,j
		// net at x,y

		// x<=0
		// x<=i
		// i<=x+r-1
		// x+r-1<=n-1
		// which means x belongs to [Math.max(i-r+1,0),Math.min(i,n-r)]


		// which means x belongs to [Math.


		try {
			out.close();
		}
		catch (Exception EX){}


	}


	public static void main(String[] args) throws Exception {
		process();

	}

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

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

		private int read() throws IOException {
			if (curChar >= numChars) {
				curChar = 0;
				numChars = stream.read(buf);
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}


		public final String readString() throws IOException {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res=new StringBuilder();
			do {
				res.append((char)c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public final int readInt() throws IOException {
			int c = read();
			boolean neg=false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d=(char)c;
			//log("d:"+d);
			if (d=='-') {
				neg=true;
				c = read();
			}
			int res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			//log("res:"+res);
			if (neg)
				return -res;
			return res;

		}

		public final long readLong() throws IOException {
			int c = read();
			boolean neg=false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d=(char)c;
			//log("d:"+d);
			if (d=='-') {
				neg=true;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			//log("res:"+res);
			if (neg)
				return -res;
			return res;

		}




		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	}


}
/*

11 10
0 0 0 1 0 0 0 1 0 1 1
9 7
7 4
10 8
8 6
4 3
5 3
6 3
3 2
2 1
1 0


12 12
0 0 0 1 0 0 0 1 0 1 1 0
9 7
7 4
10 8
8 6
4 3
5 3
6 3
3 2
2 1
1 0
11 7
10 11

 */