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:
//package baobab;
import java.io.*;
import java.util.*;

public class E {

    public static void main(String[] args) {
        EIO io = new EIO();
        try {
            Esolver solver = new Esolver(io);
            solver.solve();
        } finally {
            io.close();
        }
    }

}

class Esolver {
    EIO io;
    int pupilsAtStart;
    long originalDist;
    long walkSpeed;
    long busSpeed;
    int k;
    double bestTime;

    public Esolver(EIO io) {
        this.io = io;
    }

    public void solve() {
        pupilsAtStart = io.nextInt();
        originalDist = io.nextInt();
        walkSpeed = io.nextInt();
        busSpeed = io.nextInt();
        k = io.nextInt();
        bestTime = originalDist*1.0/walkSpeed;

        double min = 0;
        double max = originalDist;
        for (int i=1; i<100; i++) {
            double guess = (min+max)/2;
            boolean ok = f(guess);
            if (ok) {
                min = guess;
            } else {
                max = guess;
            }
        }

        io.println(bestTime);
    }


    boolean f(double firstShipDist) {
        double timeSpent = 0;
        double distA = originalDist;
        double distB = firstShipDist;
        int pupils = pupilsAtStart;

        // first shipment
        pupils -= k;
        double timeToDest = (distA - distB) / busSpeed;
        distA -= walkSpeed * timeToDest;
        timeSpent += timeToDest;

        while (pupils > 0) {
            // go back to get more pupils
            double timeToPupils = (distA - distB) / (busSpeed + walkSpeed);
            distA -= walkSpeed * timeToPupils;
            distB -= walkSpeed * timeToPupils;
            distB = Math.max(distB, 0);
            timeSpent += timeToPupils;

            // next shipment
            pupils -= k;
            timeToDest = (distA - distB) / (busSpeed - walkSpeed);
            if (timeToDest * walkSpeed > distB) {
                // if front walkers reach destination while bus is on the way
                // or they have reached it earlier, distB == 0
                // we dont want the bus to travel beyond final point
                timeToDest = distA / busSpeed;
                distB = 0;
            } else {
                distB -= walkSpeed * timeToDest;
            }
            distA -= walkSpeed * timeToDest;
            timeSpent += timeToDest;
        }

        timeSpent += (distB / walkSpeed); // the front walker group must walk to goal
        bestTime = Math.min(bestTime, timeSpent);
        return (distB == 0);
    }

    private static class Pair implements Comparable<Pair> {
        int id;
        long val;

        public Pair(long val, int id) {
            this.val = val;
            this.id = id;
        }

        @Override
        public int compareTo(Pair o) {
            if (this.val < o.val) return -1;
            if (this.val > o.val) return 1;
            return this.id - o.id;
        }
    }

}

class EIO extends PrintWriter {
    private InputStreamReader r;
    private static final int BUFSIZE = 1 << 15;
    private char[] buf;
    private int bufc;
    private int bufi;
    private StringBuilder sb;

    public EIO() {
        super(new BufferedOutputStream(System.out));
        r = new InputStreamReader(System.in);

        buf = new char[BUFSIZE];
        bufc = 0;
        bufi = 0;
        sb = new StringBuilder();
    }

    private void fillBuf() throws IOException {
        bufi = 0;
        bufc = 0;
        while(bufc == 0) {
            bufc = r.read(buf, 0, BUFSIZE);
            if(bufc == -1) {
                bufc = 0;
                return;
            }
        }
    }

    private boolean pumpBuf() throws IOException {
        if(bufi == bufc) {
            fillBuf();
        }
        return bufc != 0;
    }

    private boolean isDelimiter(char c) {
        return c == ' ' || c == '\t' || c == '\n' || c == '\r' || c == '\f';
    }

    private void eatDelimiters() throws IOException {
        while(true) {
            if(bufi == bufc) {
                fillBuf();
                if(bufc == 0) throw new RuntimeException("IO: Out of input.");
            }

            if(!isDelimiter(buf[bufi])) break;
            ++bufi;
        }
    }

    public String next() {
        try {
            sb.setLength(0);

            eatDelimiters();
            int start = bufi;

            while(true) {
                if(bufi == bufc) {
                    sb.append(buf, start, bufi - start);
                    fillBuf();
                    start = 0;
                    if(bufc == 0) break;
                }

                if(isDelimiter(buf[bufi])) break;
                ++bufi;
            }

            sb.append(buf, start, bufi - start);

            return sb.toString();
        } catch(IOException e) {
            throw new RuntimeException("IO.next: Caught IOException.");
        }
    }

    public int nextInt() {
        try {
            int ret = 0;

            eatDelimiters();

            boolean positive = true;
            if(buf[bufi] == '-') {
                ++bufi;
                if(!pumpBuf()) throw new RuntimeException("IO.nextInt: Invalid int.");
                positive = false;
            }

            boolean first = true;
            while(true) {
                if(!pumpBuf()) break;
                if(isDelimiter(buf[bufi])) {
                    if(first) throw new RuntimeException("IO.nextInt: Invalid int.");
                    break;
                }
                first = false;

                if(buf[bufi] >= '0' && buf[bufi] <= '9') {
                    if(ret < -214748364) throw new RuntimeException("IO.nextInt: Invalid int.");
                    ret *= 10;
                    ret -= (int)(buf[bufi] - '0');
                    if(ret > 0) throw new RuntimeException("IO.nextInt: Invalid int.");
                } else {
                    throw new RuntimeException("IO.nextInt: Invalid int.");
                }

                ++bufi;
            }

            if(positive) {
                if(ret == -2147483648) throw new RuntimeException("IO.nextInt: Invalid int.");
                ret = -ret;
            }

            return ret;
        } catch(IOException e) {
            throw new RuntimeException("IO.nextInt: Caught IOException.");
        }
    }

    public long nextLong() {
        try {
            long ret = 0;

            eatDelimiters();

            boolean positive = true;
            if(buf[bufi] == '-') {
                ++bufi;
                if(!pumpBuf()) throw new RuntimeException("IO.nextLong: Invalid long.");
                positive = false;
            }

            boolean first = true;
            while(true) {
                if(!pumpBuf()) break;
                if(isDelimiter(buf[bufi])) {
                    if(first) throw new RuntimeException("IO.nextLong: Invalid long.");
                    break;
                }
                first = false;

                if(buf[bufi] >= '0' && buf[bufi] <= '9') {
                    if(ret < -922337203685477580L) throw new RuntimeException("IO.nextLong: Invalid long.");
                    ret *= 10;
                    ret -= (long)(buf[bufi] - '0');
                    if(ret > 0) throw new RuntimeException("IO.nextLong: Invalid long.");
                } else {
                    throw new RuntimeException("IO.nextLong: Invalid long.");
                }

                ++bufi;
            }

            if(positive) {
                if(ret == -9223372036854775808L) throw new RuntimeException("IO.nextLong: Invalid long.");
                ret = -ret;
            }

            return ret;
        } catch(IOException e) {
            throw new RuntimeException("IO.nextLong: Caught IOException.");
        }
    }

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

}