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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.ObjectInputStream.GetField;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;


	public class Q1 {
		
		static long MOD = 1000000007;
		static boolean b[], b1[];
		static ArrayList<Integer>[] amp, pa;
		static ArrayList<Graph>[] amp1;
		static int left[],s[],right[],sum[],dist[],cnt[],arr[],start[],color[],parent[],prime[],size[];
		static long ans = 0,k;
		static int p = 0;
		static FasterScanner sc = new FasterScanner(System.in);
		static Queue<Pair> queue = new LinkedList<>();
		static PriorityQueue<Integer> pq;
		static BufferedWriter log;
		static HashSet<Integer>[] hs;
		static HashMap<String,Integer> hm;
		static HashMap<Pair,Integer> hmp;
		static Stack<Integer> st;
		static Pair prr[];
		static long parent1[],parent2[],size1[],size2[],arr1[];
		public static void main(String[] args) throws Exception {
	    	new Thread(null, new Runnable() {
				public void run() {
					try {
						soln();
					} catch (Exception e) {
						System.out.println(e);
					}
				}
			}, "1", 1 << 26).start();
		}
		public static void soln() throws IOException {
			//FasterScanner in = new FasterScanner(new FileInputStream("C:\\Users\\Admin\\Desktop\\QCL.txt"));
			//PrintWriter out = new PrintWriter("C:\\Users\\Admin\\Desktop\\A1.txt");
			Scanner sc = new Scanner(System.in);
			log = new BufferedWriter(new OutputStreamWriter(System.out));
			double n = sc.nextDouble(), l = sc.nextDouble(), v1 = sc.nextDouble(), v2 = sc.nextDouble(), k = sc.nextDouble();
			int c = (int) Math.ceil(n/k)-1;
			if(c==0) System.out.println(l/v2);
			else{
			double dist = (l*(v1+v2))/((v1+v2+2*v1*c));
			double t1 = dist/v2;
			double t2 = (l-dist)/v1;
			double ans = t1+t2;
			//System.out.println((4.7142857143*(v1*v2)-v2*l)/(v1-v2));
			System.out.printf("%.9f",ans);
			}
			//System.out.println(Math.min(ans,L/v1));
			
			log.close();
			//out.close();
		}
		static void dfs(int x){
			b[x] = true;
			for(Graph g:amp1[x]){
				if(!b[g.vertex]){
					int min = g.weight, max = min;
					ans+=2*min;
					for(Graph g1:amp1[g.vertex]){
						ans+=Math.max(max, prr[g1.vertex].v);
						ans+=Math.min(min, prr[g1.vertex].u);
					}
				}
			}
		}
		public static void buildWeightedGraph(int n){
			for(int i =0 ;i< n; i++){
				int x = sc.nextInt(), y = sc.nextInt(), w = sc.nextInt();
				amp1[--x].add(new Graph(--y,w));
				amp1[y].add(new Graph(x,w));
			}
		}
		
		public static void seive(int n){
			b = new boolean[(n+1)];
			Arrays.fill(b, true);
			b[1] = false;
			for(int i = 2;i*i<=n;i++){
				if(b[i]){
					for(int p = 2*i;p<=n;p+=i){
						b[p] = false;
						prime[p] = i;
					}
				}
			}
			for(int i = 2;i<=n;i++){
				if(b[i]) prime[i] = i;
			}
		}
		long sum1 = 0;
		public static long recur1(long n){
			if(n==0) return 0;
			if(n==1) return 1;
			return 1+2*recur1(n/2);
		}
		
		static class Graph{
			int vertex;
			int weight;
			Graph(int v, int w){
				vertex = v;
				weight = w;
			}
		}
		static class Pair implements Comparable<Pair> {
			int u;
			int v;
			public Pair(int u, int v) {
				this.u = u;
				this.v = v;
			}
			
			public int hashCode() {
				int hu = (int) (u ^ (u >>> 32));
				int hv = (int) (v ^ (v >>> 32));
				return 31*hu + hv;
			}
	 
			public boolean equals(Object o) {
				Pair other = (Pair) o;
				return ((u == other.u && v == other.v));
			}
	 
			public int compareTo(Pair other) {
				return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(v, other.v));
				//return Long.compare(w, other.w);
			}
			
			public String toString() {
				return "[u=" + u + ", v=" + v + "]";
			}
		}
		
		public static void buildGraph(int n){
			for(int i =0;i<n;i++){
				int x = sc.nextInt()-1, y = sc.nextInt()-1;
				amp[x].add(y);
			}
		}
		
		
		public static int getParent(long x){
			while(parent[(int) x]!=x){
				parent[ (int) x] = parent[(int) parent[ (int) x]];
				x = parent[ (int) x];
			}
			return (int) x;
		}
		static long min(long a, long b, long c){
			if(a<b && a<c) return a;
			if(b<c) return b;
			return c;
		}
		/*
		
		static class Pair3{
			int x, y ,z;
			Pair3(int x, int y, int z){
				this.x = x;
				this.y = y;
				this.z = z;
			}
		}*/
		static int sum(int n){
			String str = Integer.toString(n);
			int cnt = 0;
			for(int i = 0; i< str.length();i++){
				cnt+=(str.charAt(i)-'0');
			}
			return cnt;
		}
		 static void KMPSearch(String pat, String txt)
		    {
		        int M = pat.length();
		        int N = txt.length();
		 
		        // create lps[] that will hold the longest
		        // prefix suffix values for pattern
		        int lps[] = new int[M];
		        int j = 0;  // index for pat[]
		 
		        // Preprocess the pattern (calculate lps[]
		        // array)
		        computeLPSArray(pat,M,lps);
		 
		        int i = 0;  // index for txt[]
		        while (i < N)
		        {
		            if (pat.charAt(j) == txt.charAt(i))
		            {
		                j++;
		                i++;
		            }
		            if (j == M)
		            {
		               // parent.add((i-j));
		                j = lps[j-1];
		            }
		 
		            // mismatch after j matches
		            else if (i < N && pat.charAt(j) != txt.charAt(i))
		            {
		                // Do not match lps[0..lps[j-1]] characters,
		                // they will match anyway
		                if (j != 0)
		                    j = lps[j-1];
		                else
		                    i = i+1;
		            }
		        }
		    }
		 static void computeLPSArray(String pat, int M, int lps[])
		    {
		        // length of the previous longest prefix suffix
		        int len = 0;
		        int i = 1;
		        lps[0] = 0;  // lps[0] is always 0
		 
		        // the loop calculates lps[i] for i = 1 to M-1
		        while (i < M)
		        {
		            if (pat.charAt(i) == pat.charAt(len))
		            {
		                len++;
		                lps[i] = len;
		                i++;
		            }
		            else  // (pat[i] != pat[len])
		            {
		                // This is tricky. Consider the example.
		                // AAACAAAA and i = 7. The idea is similar 
		                // to search step.
		                if (len != 0)
		                {
		                    len = lps[len-1];
		 
		                    // Also, note that we do not increment
		                    // i here
		                }
		                else  // if (len == 0)
		                {
		                    lps[i] = len;
		                    i++;
		                }
		            }
		        }
		    }
		private static void permutation(String prefix, String str) {
		    int n = str.length();
		    if (n == 0); //hs.add(prefix);
		    else {
		        for (int i = 0; i < n; i++)
		            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
		    }
		}
		public static char give(char c1,char c2){
			if(c1!='a' && c2!='a') return 'a';
			if(c1!='b' && c2!='b') return 'b';
			return 'c';
		}
		
		public static void buildTree(int n){
			int arr[] = sc.nextIntArray(n);
			for(int i = 0;i<n;i++){
				int x = arr[i]-1;
				amp[i+1].add(x);
				amp[x].add(i+1);
			}
		}
		
		static class SegmentTree {
			long st[];
			//long lazy[];

			SegmentTree(int n) {
				int size = 4 * n;
				st = new long[size];
				//lazy = new long[size];
				//build(0, n - 1, 1);
			}
			
			/*long[] build(int ss, int se, int si) {
				if (ss == se) {
					st[si][0] = 1;
					st[si][1] = 1;
					st[si][2] = 1;
					return st[si];
				}
				int mid = (ss + se) / 2;
				long a1[] = build(ss, mid, si * 2), a2[] = build(mid + 1, se,
						si * 2 + 1);
				long ans[] = new long[3];
				if (arr[mid] < arr[mid + 1]) {
					ans[1] = Math.max(a2[1], Math.max(a1[1], a1[2] + a2[0]));
					if (a1[1] == (mid - ss + 1))
						ans[0] = ans[1];
					else
						ans[0] = a1[0];
					if (a2[2] == (se - mid))
						ans[2] = ans[1];
					else
						ans[2] = a2[2];
				} else {
					ans[1] = Math.max(a1[1], a2[1]);
					ans[0] = a1[0];
					ans[2] = a2[2];
				}
				st[si] = ans;
				return st[si];
			}*/

			void update(int si, int ss, int se, int idx, int val) {
				if (ss == se) {
					//arr[idx] += val;
					st[si]=val;
				} 
				else {
					int mid = (ss + se) / 2;
					if(ss <= idx && idx <= mid)
			        {
			             update(2*si, ss, mid, idx, val);
			        }
			        else
			        { update(2*si+1, mid+1, se, idx, val);
			        }
					st[si] = st[2*si]+st[2*si+1];
				}
			}
			long get(int qs, int qe, int ss, int se, int si){
				if(qs>se || qe<ss) return 0;
				if (qs <= ss && qe >= se) {
					return st[si];
				}
				int mid = (ss+se)/2;
				return get(qs, qe, ss, mid, si * 2)+get(qs, qe, mid + 1, se, si * 2 + 1);
			}
			/*void updateRange(int node, int start, int end, int l, int r, int val)
			{
			    if(lazy[node] != 0)
			    { 
			        // This node needs to be updated
			        st[node] += (end - start + 1) * lazy[node];    // Update it
			        if(start != end)
			        {
			            lazy[node*2] += lazy[node];                  // Mark child as lazy
			            lazy[node*2+1] += lazy[node];                // Mark child as lazy
			        }
			        lazy[node] = 0;                                  // Reset it
			    }
			    if(start > end || start > r || end < l)              // Current segment is not within range [l, r]
			        return;
			    if(start >= l && end <= r)
			    {
			        // Segment is fully within range
			        st[node] += (end - start + 1) * val;
			        if(start != end)
			        {
			            // Not leaf node
			            lazy[node*2] += val;
			            lazy[node*2+1] += val;
			        }
			        return;
			    }
			    int mid = (start + end) / 2;
			    updateRange(node*2, start, mid, l, r, val);        // Updating left child
			    updateRange(node*2 + 1, mid + 1, end, l, r, val);   // Updating right child
			    st[node] = st[node*2] + st[node*2+1];        // Updating root with max value 
			}

			int queryRange(int node, int start, int end, int l, int r)
			{
			    if(start > end || start > r || end < l)
			        return 0;         // Out of range
			    if(lazy[node] != 0)
			    {
			        // This node needs to be updated
			        st[node] += (end - start + 1) * lazy[node];            // Update it
			        if(start != end)
			        {
			            lazy[node*2] += lazy[node];         // Mark child as lazy
			            lazy[node*2+1] += lazy[node];    // Mark child as lazy
			        }
			        lazy[node] = 0;                 // Reset it
			    }
			    if(start >= l && end <= r)             // Current segment is totally within range [l, r]
			        return (int) st[node];
			    int mid = (start + end) / 2;
			    int p1 = queryRange(node*2, start, mid, l, r);         // Query left child
			    int p2 = queryRange(node*2 + 1, mid + 1, end, l, r); // Query right child
			    return (p1 + p2);
			}*/
			void print() {
				for (int i = 0; i < st.length; i++) {
					System.out.print(st[i]+" ");
				}
				System.out.println();
			}
		}
		static int convert(int x){
			int cnt = 0;
			String str = Integer.toBinaryString(x);
			//System.out.println(str);
			for(int i = 0;i<str.length();i++){
				if(str.charAt(i)=='1'){
					cnt++;
				}
			}
			int ans = (int) Math.pow(3, 6-cnt);
			return ans;
		}
		static class Node2{
			Node2 left = null;
			Node2 right = null;
			Node2 parent = null;
			int data;
		}
		static class BinarySearchTree{
			Node2 root = null;
			int height = 0;
			int max = 0;
			int cnt = 1;
			ArrayList<Integer> parent = new ArrayList<>();
			HashMap<Integer, Integer> hm = new HashMap<>();
			public void insert(int x){
				Node2 n = new Node2();
				n.data = x;
				if(root==null){
					root = n;
				}
				else{
					Node2 temp = root,temp2 = null;
					while(temp!=null){
						temp2 = temp;
						if(x>temp.data) temp = temp.right;
						else temp = temp.left;
					}
					if(x>temp2.data) temp2.right = n;
					else temp2.left = n;
					n.parent = temp2;
					parent.add(temp2.data);
				}
			}
			public Node2 getSomething(int x, int y, Node2 n){
				if(n.data==x || n.data==y) return n;
				else if(n.data>x && n.data<y) return n;
				else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
				else return getSomething(x,y,n.left);
			}
			public Node2 search(int x,Node2 n){
				if(x==n.data){
					max = Math.max(max, n.data);
					return n;
				}
				if(x>n.data){
					max = Math.max(max, n.data);
					return search(x,n.right);
				}
				else{
					max = Math.max(max, n.data);
					return search(x,n.left);
				}
			}
			public int getHeight(Node2 n){
				if(n==null) return 0;
				height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
				return height;
			}
		}
		static long findDiff(long[] arr, long[] brr, int m){
			int i = 0, j = 0;
			long fa = 1000000000000L;
			while(i<m && j<m){
				long x = arr[i]-brr[j];
				if(x>=0){
					if(x<fa) fa = x;
					j++;
				}
				else{
					if((-x)<fa) fa = -x;
					i++;
				}
			}
			return fa;
		}
		public static long max(long x, long y, long z){
			if(x>=y && x>=z) return x;
			if(y>=x && y>=z) return y;
			return z;
		}
		
		static long modInverse(long a, long mOD2){
		            return  power(a, mOD2-2, mOD2);
		}
		static long power(long x, long y, long m)
		{
		    if (y == 0)
		        return 1;
		    long p = power(x, y/2, m) % m;
		    p = (p * p) % m;
		 
		    return (y%2 == 0)? p : (x * p) % m;
		}
		static long power2(long x,BigInteger y,long m){
			long ans = 1;
			BigInteger two = new BigInteger("2");
			while(y.compareTo(BigInteger.ZERO)>0){
				if(y.getLowestSetBit()==y.bitCount()){
					x = (x*x)%MOD;
					y = y.divide(two);
				}
				else{
					ans = (ans*x)%MOD;
					y = y.subtract(BigInteger.ONE);
				}
			}
			return ans;
		}
		static BigInteger power2(BigInteger x, BigInteger y, BigInteger m){
			BigInteger ans = new BigInteger("1");
			BigInteger one  = new BigInteger("1");
			BigInteger two  = new BigInteger("2");
			BigInteger zero  = new BigInteger("0");
			while(y.compareTo(zero)>0){
				//System.out.println(y);
				if(y.mod(two).equals(one)){
					ans = ans.multiply(x).mod(m);
					y = y.subtract(one);
				}
				else{
					x = x.multiply(x).mod(m);
					y = y.divide(two);
				}
			}
			return ans;
		}
		static BigInteger power(BigInteger x, BigInteger y, BigInteger m)
		{
		    if (y.equals(0))
		        return (new BigInteger("1"));
		    BigInteger p = power(x, y.divide(new BigInteger("2")), m).mod(m);
		    p = (p.multiply(p)).mod(m);
		 
		    return (y.mod(new BigInteger("2")).equals(0))? p : (p.multiply(x)).mod(m);
		}
		static long d,x,y;
		public static void extendedEuclidian(long a, long b){
			if(b == 0) {
		        d = a;
		        x = 1;
		        y = 0;
		    }
		    else {
		        extendedEuclidian(b, a%b);
		        int temp = (int) x;
		        x = y;
		        y = temp - (a/b)*y;
		    }
		}
		
		public static long gcd(long n, long m){
			if(m!=0) return gcd(m,n%m);
			else return n;
		}
		
		static BufferedReader reader;
	    static StringTokenizer tokenizer;
	    static PrintWriter writer;
	
	
	   
	    static class FasterScanner {

			private final InputStream stream;
			private final byte[] buf = new byte[8192];
			private int curChar, snumChars;
			private SpaceCharFilter filter;

			public FasterScanner(InputStream stream) {
				this.stream = stream;
			}

			public int snext() {
				if (snumChars == -1)
					throw new InputMismatchException();
				if (curChar >= snumChars) {
					curChar = 0;
					try {
						snumChars = stream.read(buf);
					} catch (IOException e) {
						throw new InputMismatchException();
					}
					if (snumChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}

			public int nextInt() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = snext();
				}
				int res = 0;
				do {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}

			public long nextLong() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = snext();
				}
				long res = 0;
				do {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}

			public int[] nextIntArray(int n) {
				int a[] = new int[n];
				for (int i = 0; i < n; i++) {
					a[i] = nextInt();
				}
				return a;
			}

			public long[] nextLongArray(int n) {
				long a[] = new long[n];
				for (int i = 0; i < n; i++) {
					a[i] = nextInt();
				}
				return a;
			}
	                
			public String readString() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = snext();
				} while (!isSpaceChar(c));
				return res.toString();
			}

			public String nextLine() {
				int c = snext();
				while (isSpaceChar(c))
					c = snext();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = snext();
				} while (!isEndOfLine(c));
				return res.toString();
			}

			public boolean isSpaceChar(int c) {
				if (filter != null)
					return filter.isSpaceChar(c);
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}

			private boolean isEndOfLine(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}

			public interface SpaceCharFilter {
				public boolean isSpaceChar(int ch);
			}
		}
	}