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.io.*;
 
public class ProblemG
{
 
    static int mod = (int) (1e9+7);
    static InputReader in;
    static PrintWriter out;
    static long n;
    static long m;
    static long r;
    static long k;
    
    static long get(long x, long y){
        return (Math.min(n - r + 1, x) - Math.max(1, x - r + 1) + 1) * ( Math.min(m - r + 1, y) - Math.max(1, y - r + 1) + 1);
    }
    
    static void solve()
    {
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);            
        
        n = in.nextInt();
        m = in.nextInt();
        r = in.nextInt();
        k = in.nextInt();
        
        double count = 0;
        HashSet<Long> set = new HashSet<>();
        PriorityQueue<Pair> pq = new PriorityQueue<>(
                (x1,x2) -> -Long.compare(get(x1.x,x1.y),get(x2.x,x2.y)));
        
        long x = (n + 1) / 2;
        long y = (m + 1) / 2;
        pq.add(new Pair(x, y));
        long tmp = (x << 32) | y;
        set.add(tmp);
            
        int[][] next = new int[][]{
            {1 , -1},
            {1 , 0},
            {1 , 1},
            {-1 , -1},
            {-1 , 0},
            {-1 , 1},
            {0 , -1},
            {0 , 1},
        };
        
        while(k-- > 0){
            x = pq.peek().x;
            y = pq.peek().y;
            pq.poll();
            count += get(x, y);
            for(int i = 0; i < 8; i++){
                long nx = x + next[i][0];
                long ny = y + next[i][1];
                tmp = (nx << 32) | ny;
                if(nx > 0 && ny > 0 && nx <= n && ny <= m && !set.contains(tmp)){
                    pq.add(new Pair(nx, ny));
                    set.add(tmp);
                }
            }
        }
        
        count /= (n - r + 1.0);
        count /= (m - r + 1.0);
        
        out.println(count);
        out.close();
    }
    
    public static void main(String[] args)
    {
        new Thread(null ,new Runnable(){
            public void run(){
                try{
                    solve();
                } catch(Exception e){
                    e.printStackTrace();
                }
            }
        },"1",1<<26).start();
        
    }
 
    static class Pair implements Comparable<Pair>
    {
 
        long x,y;
 
        Pair (long x,long y)
        {
                this.x = x;
                this.y = y;
        }
        public int compareTo(Pair o)
        {
            return Long.compare(this.x,o.x);
                //return 0;
        }
 
        public boolean equals(Object o)
        {
            if (o instanceof Pair)
            {
                Pair p = (Pair)o;
                return p.x == x && p.y==y;
            }
            return false;
        }
 
        @Override
        public String toString()
        {
            return x + " "+ y ;
        }
 
        /*public int hashCode()
        {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }*/
 
    } 
 
    static long add(long a,long b){
        long x=(a+b);
        while(x>=mod) x-=mod;
        return x;
    }
 
    static long sub(long a,long b){
        long x=(a-b);
        while(x<0) x+=mod;
        return x;
    }
    
    static long mul(long a,long b){
        long x=(a*b);
        while(x>=mod) x-=mod;
        return x;
    }
    
    static String rev(String s){
        StringBuilder sb=new StringBuilder(s);
        sb.reverse();
        return sb.toString();
    }
    
    static long gcd(long x,long y)
    {
        x = Math.abs(x);
        y = Math.abs(y);
        if(y==0)
                return x;
        else
                return gcd(y,x%y);
    }
 
    static int gcd(int x,int y)
    {
        x = Math.abs(x);
        y = Math.abs(y);
        if(y==0)
                return x;
        else 
                return gcd(y,x%y);
    }
 
    static long pow(long n,long p,long m)
    {
         long  result = 1;
          if(p==0){
            return 1;
          }
          
        while(p!=0)
        {
            if(p%2==1)
                result *= n;
            if(result >= m)
               result %= m;
            p >>=1;
            n*=n;
            if(n >= m)
                n%=m;
        }
        
        return result;
    }
 
    static long pow(long n,long p)
    {
        long  result = 1;
          if(p==0)
            return 1;
 
        while(p!=0)
        {
            if(p%2==1)
                result *= n;	    
            p >>=1;
            n*=n;	    
        }
        return result;
    }
 
    static void debug(Object... o)
    {
            System.out.println(Arrays.deepToString(o));
    }
 
    static class InputReader
    {
 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream)
        {
                this.stream = stream;
        }
 
        public int snext()
        {
                if (snumChars == -1)
                        throw new InputMismatchException();
                if (curChar >= snumChars)
                {
                        curChar = 0;
                        try
                        {
                                snumChars = stream.read(buf);
                        } catch (IOException e)
                        {
                                throw new InputMismatchException();
                        }
                        if (snumChars <= 0)
                                return -1;
                }
                return buf[curChar++];
        }
 
        public int nextInt()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-')
                {
                        sgn = -1;
                        c = snext();
                }
                int res = 0;
                do
                {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }
 
        public long nextLong()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-')
                {
                        sgn = -1;
                        c = snext();
                }
                long res = 0;
                do
                {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }
 
        public int[] nextIntArray(int n)
        {
                int a[] = new int[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextInt();
                }
                return a;
        }
 
        public long[] nextLongArray(int n)
        {
                long a[] = new long[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextLong();
                }
                return a;
        }
 
        public String readString()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                StringBuilder res = new StringBuilder();
                do
                {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
        }
 
        public String nextLine()
        {
                int c = snext();
                while (isSpaceChar(c))
                        c = snext();
                StringBuilder res = new StringBuilder();
                do
                {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isEndOfLine(c));
                return res.toString();
        }
 
        public boolean isSpaceChar(int c)
        {
                if (filter != null)
                        return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c)
        {
                return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
                public boolean isSpaceChar(int ch);
        }
 
    }
}