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:
/**
 * Created by Bakytzhan_Manaspayev on 8/17/2016.
 */

import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintStream;
import java.util.StringTokenizer;

public class TimeBusStudentProblem {

    static Scanner in;
    static Output out;
    static Statistic printer = new Statistic();
    static boolean isFile = false;


    static void solve() throws Exception {
        double studentCount = in.nextDouble();
        double totalDistance = in.nextDouble();
        double walkingSpeed = in.nextDouble();
        double busSpeed = in.nextDouble();
        double busCapacity = in.nextDouble();

        int groupCount = (int) Math.ceil(studentCount / busCapacity);

        double low = 0;
        double high = totalDistance / walkingSpeed;

        while ((high - low) > 5e-7) {
            double mid = (high + low) / 2;
            double timePassed = 0;

            for (int i = 0; i < groupCount; i++) {
                //TODO: удоствоериться что timepassed не обойдет mid;
                //TODO: распечатать mid,x,позиция куда прибыл автобус, скок пешом идти
                double x = (totalDistance - walkingSpeed * mid) / (busSpeed - walkingSpeed);
                timePassed += x;
                if (i + 1 < groupCount) {
                    double y = x * (busSpeed - walkingSpeed) / (walkingSpeed + busSpeed);
                    timePassed += y;
                }
            }

            if (timePassed > mid) {
                low = mid;
            } else {
                high = mid;
            }

        }
        out.println(high);

    }


    static Exception exception = null;

    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, () -> {
            try {
                initReaderWriter();
                solve();
                out.close();
            } catch (Exception ex) {
                exception = ex;
            }
        }, "", 1 << 26);
        thread.start();
        thread.join();

        if (exception != null) {
            throw exception;
        }
    }

    static void initReaderWriter() throws Exception {
        if (isFile) {
            in = new Scanner("input.txt");
            out = new Output(new File("output.txt"));
        } else {
            in = new Scanner();
            out = new Output(System.out);
        }
    }

    static class Scanner {

        StringTokenizer st = null;
        BufferedReader bf;

        Scanner() {
            bf = new BufferedReader(new InputStreamReader(System.in));
        }

        Scanner(String fileName) throws FileNotFoundException {
            bf = new BufferedReader(new FileReader(fileName));
        }

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

        char readByte() throws IOException {
            return (char) bf.read();
        }

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

        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 Output extends PrintStream {

        Output(OutputStream out) {
            super(new BufferedOutputStream(out));
        }

        Output(File file) throws FileNotFoundException {
            super(new BufferedOutputStream(new FileOutputStream(file)));
        }
    }

    static class Statistic {
        void printMemory() {
            Runtime runtime = Runtime.getRuntime();

            long allocatedMemory = runtime.totalMemory();
            long freeMemory = runtime.freeMemory();

            long div = 1L * 1024 * 1024;
            System.out.println("used memory[mgb]: " + (allocatedMemory - freeMemory) / div);
        }

        void printCurrentTime() {
            out.flush();
            System.out.println("Time: " + (System.currentTimeMillis() - appCurrentTime));
            System.out.println("Time Nano: " + (System.nanoTime() - appCurrentTimeNano));
        }

        long appCurrentTime = System.currentTimeMillis();
        long appCurrentTimeNano = System.nanoTime();
    }

}