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:
import java.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().run(in, out);
        out.close();
    }

    public static long mod = 17352642619633L;


    int N, L, V1, V2, K;
    double busspeed;
    double personspeed;

    public static double eps = 1e-11;
    void run(FastScanner in, PrintWriter out) {

        N = in.nextInt(); // num people
        L = in.nextInt(); // length
        personspeed = in.nextInt(); // speed of people
        busspeed = in.nextInt(); // speed of bus, V2 > V1
        K = in.nextInt(); // size of bus

        // binary search
        double lo = 0;
        double hi = L/personspeed;

        // while (hi-lo > eps) {
        //     double m = (hi+lo)/2;
        for (int rep = 0; rep <= 80; rep++) {
            double m = (hi+lo)/2;
            if (can(m)) {
                hi = m;
            } else {
                lo = m+eps;
            }
        }
        // System.out.println(can(4.0));

        out.println(lo);
    }

    boolean can(double t) {


        double buspos = 0;
        double personpos = 0;
        double time = 0;

        // bring them as far as possible
        // and they can walk on their own
        for (int tripnum = 0; tripnum*K < N; tripnum++) {

            // when will bus meet the people
            // bus should be in front of the people
            // personpos + t*personspeed = buspos - t*busspeed
            // t*(personspeed + busspeed) = buspos - personspeed
            // t = (buspos - personpos) / (personspeed + busspeed)

            double meetdelta = (buspos - personpos) / (personspeed + busspeed);
            double meetpos = buspos - meetdelta * busspeed;

            // how far do i have to go such that they will be able to walk on their own
            // within t time
            // meetpos + t1*busspeed + t2*personspeed = L
            // (t1 + t2) = remaining time [our budget]
            // meetpos + t1 * busspeed + (t-t1)*personspeed = L
            // t1*busspeed + t*personspeed - t1*personspeed = L-meetpos
            // t1(busspeed - personspeed) = L-meetpos - t*personspeed
            // t1 = (L-meetpos -t*personspeed)/(busspeed-personspeed)
            // t1 = bustravel time, t2 = person travel time

            if (t-time-meetdelta < 0) return false;
            double busTravelTime = (L-meetpos-(t-time-meetdelta)*personspeed) / (busspeed - personspeed);

            // System.out.println(t + " " +meetdelta + " " + meetpos + " "+ busTravelTime);
            // System.out.println(meetpos + " " + personpos + " " + buspos);
            // System.out.println(Math.abs(meetdelta-eps) > 0);
            // System.out.println();

            // System.out.println(time);
            // if (meetdelta < 0 || busTravelTime < 0) return false;
            // if (Math.abs(meetdelta-eps) > 0 && meetdelta < 0) return false;
            // if (Math.abs(busTravelTime-eps) > 0 && busTravelTime < 0) return false;

            buspos = meetpos + busTravelTime * busspeed;
            personpos = meetpos + busTravelTime * personspeed;
            time += meetdelta + busTravelTime;
            if (time > t) return false;
        }

        return true;
    }




    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}