Problem: On vacations n pupils decided to go on excursion and gather all together. They need to overcome the path with the length l meters. Each of the pupils will go with the speed equal to v1. To get to the excursion quickly, it was decided to rent a bus, which has seats for k people (it means that it can't fit more than k people at the same time) and the speed equal to v2. In order to avoid seasick, each of the pupils want to get into the bus no more than once.

Determine the minimum time required for all n pupils to reach the place of excursion. Consider that the embarkation and disembarkation of passengers, as well as the reversal of the bus, take place immediately and this time can be neglected. 

Input

The first line of the input contains five positive integers n, l, v1, v2 and k (1 ≤ n ≤ 10 000, 1 ≤ l ≤ 109, 1 ≤ v1 < v2 ≤ 109, 1 ≤ k ≤ n) — the number of pupils, the distance from meeting to the place of excursion, the speed of each pupil, the speed of bus and the number of seats in the bus. 

Output

Print the real number — the minimum time in which all pupils can reach the place of excursion. Your answer will be considered correct if its absolute or relative error won't exceed 10 - 6.

Examples

Input

5 10 1 2 5


Output

5.0000000000


Input

3 6 1 2 1


Output

4.7142857143

Note

In the first sample we should immediately put all five pupils to the bus. The speed of the bus equals 2 and the distance is equal to 10, so the pupils will reach the place of excursion in time 10 / 2 = 5.

Solution (in JAVA):

Solution:
//>>>BaZ<<<//
import java.util.*;
import java.io.*;
import static java.lang.Math.*;
public class Student
{  
    static int dx[] = {-1,1,0,0};
    static int dy[] = {0,0,1,-1};
    static long MOD = 1000000007;
    static int INF = Integer.MAX_VALUE/10;
    static PrintWriter pw;
    static Reader scan;
    //static MyFileReader scan;
    //static MyFileReader1 ss;
    static int ni() throws IOException{return scan.nextInt();}
    static long nl() throws IOException{return scan.nextLong();}
    static double nd() throws IOException{return scan.nextDouble();}
    static void pl() throws IOException{pw.println();}
    static void pl(Object o) throws IOException{pw.println(o);}
    static void p(Object o) throws IOException {pw.print(o+" ");}
    static void psb(StringBuilder sb) throws IOException {pw.print(sb);}
    public static void main(String[] args){
        new Thread(null,null,"BaZ",99999999)
        {
            public void run()
            {
                try
                {
                    solve();
                }
                catch(Exception e)
                {  
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }
    static void solve() throws IOException
    {  
        Calendar CAL1 = Calendar.getInstance();
        CAL1.setTime(new Date());
        scan = new Reader();
        //scan = new MyFileReader();
        //ss = new MyFileReader1();
        pw = new PrintWriter(System.out,true);
        //pw = new PrintWriter(new File("C://Users/Aman deep/Desktop/output.txt"));  
        StringBuilder sb = new StringBuilder();
        int n = ni();
        double l = ni();
        double v1 = ni();
        double v2 = ni();
        int k = ni();
        double x;
        if(n%k==0)
            x = n/k;
        else x = n/k+1;
        x--;
        //pl("x : "+x);
        double udhar = l*(1/v1-1/v2);
        double idhar = 2*x*(v2-v1)/(v1+v2);
        idhar+=v2/v1;
        idhar-=1;
        double t = udhar/idhar;
        double mytime = t+(l-v2*t)/v1;
        pl(mytime);
        Calendar CAL2 = Calendar.getInstance();
        CAL2.setTime(new Date());
        double Execution_Time = (double)(CAL2.getTimeInMillis()-CAL1.getTimeInMillis())/1000.000;
        //System.out.println("Execution time : "+Execution_Time+" seconds");
        pw.flush();
        pw.close();
    }
    static class Reader {
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException {
        byte[] buf = new byte[64];
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n') break;
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg) return -ret;
        return ret;
    }

    public long nextLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg) return -ret;
        return ret;
    }

    public double nextDouble() throws IOException {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
        if (neg) return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1) buffer[0] = -1;
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead) fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException {
        if (din == null) return;
        din.close();
    }
}
     static class MyFileReader                                          //File input template
    {
        StringTokenizer st;
        BufferedReader br;
        MyFileReader() throws IOException
        {
            br = new BufferedReader(new FileReader("C://Users/Aman deep/Desktop/input.txt"));
        }
        String nextLine() throws IOException
        {
            return br.readLine();
        }
        String next() throws IOException
        {
            if(st==null || !st.hasMoreTokens())
                st = new StringTokenizer(nextLine());
            return st.nextToken();
        }
        int nextInt() throws IOException
        {
            return Integer.parseInt(next());
        }
        long nextLong() throws IOException
        {
            return Long.parseLong(next());
        }
        double nextDouble() throws IOException
        {
            return Double.parseDouble(next());
        }
    }
     static class MyFileReader1                                          //File input template
    {
        StringTokenizer st;
        BufferedReader br;
        MyFileReader1() throws IOException
        {
            br = new BufferedReader(new FileReader("C://Users/Aman deep/Desktop/output.txt"));
        }
        String nextLine() throws IOException
        {
            return br.readLine();
        }
        String next() throws IOException
        {
            if(st==null || !st.hasMoreTokens())
                st = new StringTokenizer(nextLine());
            return st.nextToken();
        }
        int nextInt() throws IOException
        {
            return Integer.parseInt(next());
        }
        long nextLong() throws IOException
        {
            return Long.parseLong(next());
        }
        double nextDouble() throws IOException
        {
            return Double.parseDouble(next());
        }
    }
}