Problem: A car moves from point A to point B at speed v meters per second. The action takes place on the X-axis. At the distance d meters from A there are traffic lights. Starting from time 0, for the first g seconds the green light is on, then for the following r seconds the red light is on, then again the green light is on for the g seconds, and so on.

The car can be instantly accelerated from 0 to v and vice versa, can instantly slow down from the v to 0. Consider that it passes the traffic lights at the green light instantly. If the car approaches the traffic lights at the moment when the red light has just turned on, it doesn't have time to pass it. But if it approaches the traffic lights at the moment when the green light has just turned on, it can move. The car leaves point A at the time 0.

What is the minimum time for the car to get from point A to point B without breaking the traffic rules?

Input

The first line contains integers l, d, v, g, r (1 ≤ l, d, v, g, r ≤ 1000, d < l) — the distance between A and B (in meters), the distance from A to the traffic lights, car's speed, the duration of green light and the duration of red light.

Output

Output a single number — the minimum time that the car needs to get from point A to point B. Your output must have relative or absolute error less than 10 - 6.

Examples

Input

2 1 3 4 5


Output

0.66666667


Input

5 4 3 1 1


Output

2.33333333

Solution (in JAVA):

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


public class Forces{

	public static PrintWriter cout;

	public static int[] dp;
	public static void main(String ...arg) throws IOException
	{
		//Read cin = new Read();
		InputReader cin = new InputReader(System.in);
		//Scan cin =new Scan();
		cout = new PrintWriter(new BufferedOutputStream(System.out));
		int l = cin.nextInt();
		int d = cin.nextInt();
		int v = cin.nextInt();
		int g = cin.nextInt();
		int r = cin.nextInt();

		boolean b;
		double time = (double)d/v;
		double mod = Math.floor(time)%(g+r) + (time-Math.floor(time));
		//cout.print(mod + "\n");
		if(mod < g)
			b = true;
		else
			b = false;

		if(b)
			cout.print((double)l/v);
		else
			cout.print(time + (g+r-mod) + (double)(l-d)/v);
		cout.close();
 	}


 	static class InputReader {
        final InputStream is;
        final byte[] buf = new byte[1024];
        int pos;
        int size;
 
        public InputReader(InputStream is) {
            this.is = is;
        }
 
        public int nextInt() {
            int c = read();
            while (isWhitespace(c))
                c = read();
            int sign = 1;
            if (c == '-') {
                sign = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = read();
            } while (!isWhitespace(c));
            return res * sign;
        }
 
        int read() {
            if (size == -1)
                throw new InputMismatchException();
            if (pos >= size) {
                pos = 0;
                try {
                    size = is.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (size <= 0)
                    return -1;
            }
            return buf[pos++] & 255;
        }
 
        static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
    }




static class Scan {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
            throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
            return true;
            return false;
        }
    }

}

class Read
{
    private BufferedReader br;
    private StringTokenizer st;

    public Read()
    { br = new BufferedReader(new InputStreamReader(System.in)); }

    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()); }

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

    String nextLine()
    {
        String str = "";
        try {str = br.readLine();}
        catch(IOException e)
            {e.printStackTrace();}
        return str;
    }
}