Problem: Julia is going to cook a chicken in the kitchen of her dormitory. To save energy, the stove in the kitchen automatically turns off after k minutes after turning on.

During cooking, Julia goes to the kitchen every d minutes and turns on the stove if it is turned off. While the cooker is turned off, it stays warm. The stove switches on and off instantly.

It is known that the chicken needs t minutes to be cooked on the stove, if it is turned on, and 2t minutes, if it is turned off. You need to find out, how much time will Julia have to cook the chicken, if it is considered that the chicken is cooked evenly, with constant speed when the stove is turned on and at a constant speed when it is turned off.

Input

The single line contains three integers k, d and t (1 ≤ k, d, t ≤ 1018).

Output

Print a single number, the total time of cooking in minutes. The relative or absolute error must not exceed 10 - 9.

Namely, let's assume that your answer is x and the answer of the jury is y. The checker program will consider your answer correct if <image>.

Examples

Input

3 2 6


Output

6.5


Input

4 2 20


Output

20.0

Note

In the first example, the chicken will be cooked for 3 minutes on the turned on stove, after this it will be cooked for <image>. Then the chicken will be cooked for one minute on a turned off stove, it will be cooked for <image>. Thus, after four minutes the chicken will be cooked for <image>. Before the fifth minute Julia will turn on the stove and after 2.5 minutes the chicken will be ready <image>.

In the second example, when the stove is turned off, Julia will immediately turn it on, so the stove will always be turned on and the chicken will be cooked in 20 minutes.

Solution (in JAVA):

Solution:
		     
		import java.io.*;
		        		    import java.math.*;
		        		    import java.util.*;
	import java.util.regex.Pattern;
	
	import javafx.scene.shape.Line;
		    	     
		        		    public class Main{
		        		  	private static InputStream stream;
		        		    	private static byte[] buf = new byte[1024];
		        		    	private static int curChar;
		        		    	private static int numChars;
		        		    	private static SpaceCharFilter filter;
		        		    	private static PrintWriter pw;
		        		    	private static long count = 0,mod=(long)1e9+7;
		        		    //	private static TreeSet<Integer> ts=new TreeSet[200000];
		public final static int INF = (int) 1E9;
		
		public static void main(String args[]) {
	    	
			InputReader(System.in);
			pw = new PrintWriter(System.out); 
		    new Thread(null ,new Runnable(){
		       public void run(){
		           try{
		        		
		               test();
	
		               pw.close();
		           } catch(Exception e){
		               e.printStackTrace();
		           }
		       }
		   },"1",1<<26).start();
		   	   }
		    static StringBuilder sb;
		    public static void test() throws IOException{
		    	 sb=new StringBuilder();
		    	
		    	 int t=1;
		    	 
		    	 while(t-->0){
		    		
		    		solve();
		    		//pw.println();
		    		//sb.append("\n");
		    	}
		    	//pw.println(sb);
		    }
		    
		    public static long pow(long n, long p,long mod) {
				if(p==0)
					return 1;
				if(p==1)
					return n%mod;
				if(p%2==0){
					long temp=pow(n, p/2,mod);
				return (temp*temp)%mod;
				}else{
					 	long temp=pow(n,p/2,mod);
					 	temp=(temp*temp)%mod;
					 	return(temp*n)%mod;
					 	
				}
			}
		    public static long pow(long n, long p) {
				if(p==0)
					return 1;
				if(p==1)
					return n;
				if(p%2==0){
					long temp=pow(n, p/2);
				return (temp*temp);
				}else{
					 	long temp=pow(n,p/2);
					 	temp=(temp*temp);
					 	return(temp*n);
					 	
				}
			}
		    public static void Merge(long a[],int p,int r){
		        if(p<r){
		            int q = (p+r)/2;
		            Merge(a,p,q);
		            Merge(a,q+1,r);
		            Merge_Array(a,p,q,r);
		        }
		    }
		    public static void Merge_Array(long a[],int p,int q,int r){
		       long b[] = new long[q-p+1];
		        long c[] = new long[r-q];
		        for(int i=0;i<b.length;i++)
		            b[i] = a[p+i];
		        for(int i=0;i<c.length;i++)
		            c[i] = a[q+i+1];
		        int i = 0,j = 0;
		        for(int k=p;k<=r;k++){
		            if(i==b.length){
		                a[k] = c[j];
		                j++;
		            }
		            else if(j==c.length){
		                a[k] = b[i];
		                i++;
		            }
		            else if(b[i]<c[j]){
		                a[k] = b[i];
		                i++;
		            }
		            else{
		                a[k] = c[j];
		                j++;
		            }
		        }
		    }
		    
		  
			public static long gcd(long x, long y) {
				if (x == 0)
					return y;
				else
					return gcd( y % x,x);
			}	
			
			public static boolean isPrime(int n) {
				if (n <= 1)
					return false;
				if (n <= 3)
					return true;
		 
				if (n % 2 == 0 || n % 3 == 0)
					return false;
		 
				for (int i = 5; i * i <= n; i = i + 6)
					if (n % i == 0 || n % (i + 2) == 0)
						return false;
		 
				return true;
			}
			
		        static LinkedList<Integer> adj[],adj2[];
		        static boolean Visited[];
		        static HashSet<Integer> exc;
		        static long oddsum[]=new long[1000001];
		        static long co=0;
		        static int indeg[],outdeg[];
  		      
		    
		    	private static void buildgraph(int n){
		    		adj=new LinkedList[n+1];
		    		adj2=new LinkedList[n+1];
		    		Visited=new boolean[n+1];
		    		levl=new int[n+1];
		    		indeg=new int[n+1];
		    		outdeg=new int[n+1];
		    		for(int i=0;i<=n;i++){
		    			adj[i]=new LinkedList<Integer>();
		    			adj2[i]=new LinkedList<Integer>();
		    		}
		
		
		    	}
		      
		       
		        static int[] levl;
		        static int[] eat;
		        static int n,m;
		        static int price[];
		        //ind frog crab
		    
		        
		        static long d,x,y;
				static long modInverse(long A, long M)
				{
				extendedEuclid(A,M);
				return (x%M+M)%M;    //x may be negative
				}
				static void extendedEuclid(long A, long B) {
				if(B == 0) {
				d = A;
				x = 1;
				y = 0;
				}
				else {
				extendedEuclid(B, A%B);
				long temp = x;
				x = y;
				y = temp - (A/B)*y;
				}
				}
		        static double distance(int x1,int y1,int x2,int y2){
		        	return Math.sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));
		        }
		        static double area(int x1, int y1, int x2, int y2, int x3, int y3)
		        {
		           return Math.abs((x1*(y2-y3) + x2*(y3-y1)+ x3*(y1-y2))/2.0);
		        }
		        static boolean isInside(int x1, int y1, int x2, int y2, int x3, int y3, int x, int y)
		        {   
		           double A = area (x1, y1, x2, y2, x3, y3);
		         
		           double A1 = area (x, y, x2, y2, x3, y3);
		         
		           double A2 = area (x1, y1, x, y, x3, y3);
		         
		           double A3 = area (x1, y1, x2, y2, x, y);
		           
		          return (A == A1 + A2 + A3);
		        }
		      
				static int col[];
		    public static boolean isVowel(char c){
		    	if(c=='a' || c=='e'||c=='i' || c=='o' || c=='u')
		    		return true;
		    	return false;
		    }
		static long arr[], lazy[],ans[];
		static int c[],nodes[];
		static int dp[][];
		static long a[][];
		
		private static boolean isPrim(long n,int p){
			for (long i = 2; i * i <= n; i++) {
		        if (n % i == 0 && i <= p) return false;
		    }
		    return true;
		}
		//price - starting index of string with given hash
		//rating-count of number of time of a hash
		static ArrayList<String> all_perm;
		public static void solve() throws IOException{
			double k = nextLong();
			double d = nextLong();
			double t = nextLong();
			double ans = 0;
			double aans = 0;
			double temp = 0;
			
			if (k >= d) {
			    long first_multiple = 0;
			    if (k % d == 0) first_multiple = (long) k;
			    else first_multiple = (long) (((long) (k / d) + 1) * d);
			    temp = (k + (first_multiple - k) / 2);
			    ans = (long) (t / temp);
			    t = t - (ans * temp);
			    aans = ((ans * k) + (ans * (first_multiple - k)));
			    if (t > k) {
			        t -= k;
			        aans += k;
			        aans += (2 * t);
			    } else {
			        aans += (t);
			    }
			} else {
			    temp = k + ((d - k) / 2);
			    ans = ((long) (t / temp));
			    t = t - (ans * temp);
			    aans = (ans * k) + (ans * (d - k));
			    if (t > k) {
			        t -= k;
			        aans += k;
			        aans += (2 * t);
			    } else {
			        aans += (t);
			    }
			}
			pw.println(aans);
		}
		
				private static boolean check(int x,int y,int n,int m){
			if(x>=0 && x<n && y>=0 && y<m)
				return true;
			return false;
		}
				
				
				
				private static void dfs(int curr,int par){
			Visited[curr]=true;
			for(int i:adj[curr]){
				if(!Visited[i]){
					dfs(i,curr);
				}
			}
			dp[curr][nodes[curr]]++;
			for(int i=0;i<26;i++){
				dp[par][i]+=dp[curr][i];
			}
		}
	
		
		
		    private static boolean Check(int x,int y,int n){
				if(x>=0 && x<n && y>=0 && y<n)
					return true;
				return false;
			}
		    
		    public static String reverseString(String s) {
				StringBuilder sb = new StringBuilder(s);
				sb.reverse();
				return (sb.toString());
			}
		    
		  /*  
		   private static void BFS(int sou){
		    	Queue<Integer> q=new LinkedList<Integer>();
		    	q.add(sou);
		    	Visited[sou]=true;
		    	levl[sou]=0;
		    	while(!q.isEmpty()){
		    		int top=q.poll();
		    		
		    		for(int i:adj[top]){
		    			//pw.println(i+" "+top);
					if(!Visited[i])
					{
						
						q.add(i);
						levl[i]=levl[top]+1;
					}
					
					Visited[i]=true;
					
					}
				}
			}*/
			
		
		
		
		    		      
		    		   /* private static void kahn(int n){
		    		    	
		    		    	PriorityQueue<Integer> q=new PriorityQueue<Integer>();
		    				for(int i=1;i<=n;i++){
		    					if(indeg[i]==0){
		    						q.add(i);
		    					}
		    				}
		    				while(!q.isEmpty()){
		    					int top=q.poll();
		    					st.push(top);
		    					for(Node i:adj[top]){
		    						indeg[i.to]--;
		    						if(indeg[i.to]==0){
		    							q.add(i.to);
		    						}
		    					}
		    				}
		    		    }
		    		        
		    		        static int state=1;
		    		        static long no_exc=0,no_vert=0;
		    		      static Stack<Integer> st;
		    		      static HashSet<Integer> inset;
		    		     /*   private static void topo(int curr){
		    		        	
		    		        	Visited[curr]=true;
		    		        	inset.add(curr);
		    		        	for(int x:adj[curr]){
		    		        		if(adj[x].contains(curr) || inset.contains(x)){
		    		        			state=0;
		    		        			return;
		    		        		}
		    		        		if(state==0)
		    		        			return;
		    		        		
		    		        	}
		    		        	st.push(curr);
		    		        	
		    		        	inset.remove(curr);
		    		        }*/
		    		        static HashSet<Integer> hs;
		    		       
		    		     
		    		     	static boolean prime[];
							static int spf[];
							public static void sieve(int n){
								prime=new boolean[n+1];
								spf=new int[n+1];
								
								Arrays.fill(spf, 1);
								Arrays.fill(prime, true);
							prime[1]=false;
								spf[2]=2;
								
							for(int i=4;i<=n;i+=2){
								spf[i]=2;
							}
							for(int i=3;i<=n;i+=2){
								if(prime[i]){
									spf[i]=i;
									for(int j=2*i;j<=n;j+=i){
										
										prime[j]=false;
									if(spf[j]==1){
										spf[j]=i;
									}
									}
								}
							}
							
								
							}
		    		     	
		    		    	// To Get Input
		// Some Buffer Methods
		 
		    		     	public static void sort(long a[]){
		    		     		Merge(a, 0, a.length-1);
		    		     	}
		    		    	public static void InputReader(InputStream stream1) {
		    		    		stream = stream1;
		    		    	}
		 
		    		    	private static boolean isWhitespace(int c) {
		    		    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		    		    	}
		 
		    		    	private static boolean isEndOfLine(int c) {
		    		    		return c == '\n' || c == '\r' || c == -1;
		    		    	}
		 
		    		    	private static int read() {
		    		    		if (numChars == -1)
		    		    			throw new InputMismatchException();
		    		    		if (curChar >= numChars) {
		    		    			curChar = 0;
		    		    			try {
		    		    				numChars = stream.read(buf);
		    		    			} catch (IOException e) {
		    		    				throw new InputMismatchException();
		    		    			}
		    		    			if (numChars <= 0)
		    		    				return -1;
		    		    		}
		    		    		return buf[curChar++];
		    		    	}
		 
		    		    	private static int nextInt() {
		    		    		int c = read();
		    		    		while (isSpaceChar(c))
		    		    			c = read();
		    		    		int sgn = 1;
		    		    		if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
		    		    			c = read();
		    		    		} while (!isSpaceChar(c));
		    		    		return res * sgn;
		    		    	}
		 
		    		    	private static long nextLong() {
		    		    		int c = read();
		    		    		while (isSpaceChar(c))
		    		    			c = read();
		    		    		int sgn = 1;
		    		    		if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
		    		    			c = read();
		    		    		} while (!isSpaceChar(c));
		    		    		return res * sgn;
		    		    	}
		 
		    		    	private static String nextToken() {
		    		    		int c = read();
		    		    		while (isSpaceChar(c))
		    		    			c = read();
		    		    		StringBuilder res = new StringBuilder();
		    		    		do {
		    		    			res.appendCodePoint(c);
		    		    			c = read();
		    		    		} while (!isSpaceChar(c));
		    		    		return res.toString();
		    		    	}
		 
		    		    	private static String nextLine() {
		    		    		int c = read();
		    		    		while (isSpaceChar(c))
		    		    			c = read();
		    		    		StringBuilder res = new StringBuilder();
		    		    		do {
		    		    			res.appendCodePoint(c);
		    		    			c = read();
		    		    		} while (!isEndOfLine(c));
		    		    		return res.toString();
		    		    	}
		 
		    		    	private static int[] nextIntArray(int n) {
		    		    		int[] arr = new int[n];
		    		    		for (int i = 0; i < n; i++) {
		    		    			arr[i] = nextInt();
		    		    		}
		    		    		return arr;
		    		    	}
		 
		    		    	private static long[][] next2dArray(int n, int m) {
		    		    		long[][] arr = new long[n][m];
		    		    		for (int i = 0; i < n; i++) {
		    		    			for (int j = 0; j < m; j++) {
		    		    				arr[i][j] = nextLong();
		    		    			}
		    		    		}
		    		    		return arr;
		    		    	}
		    		    	private static char[][] nextCharArray(int n,int m){
		    		    		char [][]c=new char[n][m];
		    		    		for(int i=0;i<n;i++){
		    		    			String s=nextLine();
		    		    			for(int j=0;j<s.length();j++){
		    		    				c[i][j]=s.charAt(j);
		    		    			}
		    		    		}
		    		    		return c;
		    		    	}
		 
		    		    	private static long[] nextLongArray(int n) {
		    		    		long[] arr = new long[n];
		    		    		for (int i = 0; i < n; i++) {
		    		    			arr[i] = nextLong();
		    		    		}
		    		    		return arr;
		    		    	}
		 
		    		    	private static void pArray(int[] arr) {
		    		    		for (int i = 0; i < arr.length; i++) {
		    		    			pw.print(arr[i] + " ");
		    		    		}
		    		    		pw.println();
		    		    		return;
		    		    	}
		 
		    		    	private static void pArray(long[] arr) {
		    		    		for (int i = 0; i < arr.length; i++) {
		    		    			pw.print(arr[i] + " ");
		    		    		}
		    		    		pw.println();
		    		    		return;
		    		    	}
		 
		    		    	private static void pArray(boolean[] arr) {
		    		    		for (int i = 0; i < arr.length; i++) {
		    		    			pw.print(arr[i] + " ");
		    		    		}
		    		    		pw.println();
		    		    		return;
		    		    	}
		 
		    		    	private static boolean isSpaceChar(int c) {
		    		    		if (filter != null)
		    		    			return filter.isSpaceChar(c);
		    		    		return isWhitespace(c);
		    		    	}
		 
		    		    	private interface SpaceCharFilter {
		    		    		public boolean isSpaceChar(int ch);
		    		    	}
		    		    	
		
		}
		    		    
		    		        class Node{
		    		    	int to;
		    		    	long dist;
		    		    	Node(int to,long dist){
		    		    		this.to=to;
		    		    		this.dist=dist;
		    		    	}
		    		    	
		    		    }
		    		        class Qu{
		    		    		long a0,a1,a2,a3;
		    		    		public Qu(long a0,long a1,long a2,long a3) {
		    		    			this.a0=a0;
		    		    			this.a1=a1;
		    		    			this.a2=a2;
		    		    			this.a3=a3;
		    		    		}
		    		    }
		    		
		class Dsu{
		private int rank[], parent[] ,n;
		long str[],si[],larg[];
		long max=0;
		int cnt=0;
		private static int[] parent1;
		Dsu(int size){
			this.n=size+1;
			rank=new int[n];
			cnt=n-1;
			//parent=new int[n];
		    		    		    		parent=new int[n];
		    		    		    		str=new long[n];
		    		    		    		si=new long[n];
		    		    		
		    		    		    		larg=new long[n];
		    		    		    		makeSet();
		    		    		
		    		    		    	}
		    		    		    	
		    		    		    	void makeSet(){
		    		    		    		for(int i=0;i<n;i++){
		    		    		    			parent[i]=i;
		    		    		    			si[i]=1;
		    		    		    		}
		    		    		    	}
		    		    		    	
		    		    		    	int find(int x){
		    		    		    		if(parent[x]!=x){
		    		    		    			
		    		    		    			parent[x]=find(parent[x]);
		    		    		    		}
		    		    		    		return parent[x];
		    		    		    	}
		    		    		    	
		    		    		    	void join(int ind,long val){
		    		    		    		if(str[ind]==0){
		    		    		    			str[ind]=val;
		    		    		    			larg[ind]=val;
		    		    		    			max=Math.max(max, str[ind]);
		    		    		    		}
		    		    		    		int prev_ind=(ind-1);
		    		    		    		int next_ind=(ind+1);
		    		    		    		if(prev_ind>0 && larg[prev_ind]!=0){
		    		    		    			union(prev_ind,ind);
		    		    		    		}
		    		    		    		if(next_ind<n && larg[next_ind]!=0){
		    		    		    			union(next_ind,ind);
		    		    		    		}
		    		    		    		
		    		    		    	}
		    		    		    
		    		    		    	
		    		    		    	boolean union(int x,int y){
		    		    		    		int xRoot=find(x);
		    		    		    		int yRoot=find(y);
		    		    		    
		    		    		    	
		    		    		    		if(xRoot==yRoot)
		    		    		    			return false;
		    		    		    		if(rank[xRoot]<rank[yRoot]){
		    		    		    		parent[xRoot]=yRoot;
		    		    		    		
		    		    		    		larg[yRoot]=Math.max(larg[xRoot], larg[yRoot]);
		    		    		    		
		    		    		    		si[yRoot]+=si[xRoot];
		    		    		    		str[yRoot]=larg[yRoot]*si[yRoot];
		    		    		    			max=Math.max(str[yRoot], max);
		    		    		    		}else if(rank[yRoot]<rank[xRoot]){
		    		    		    			parent[yRoot]=xRoot;
		     
		    		    		    			larg[xRoot]=Math.max(larg[xRoot], larg[yRoot]);
		        		    		    		
		        		    		    		si[xRoot]+=si[yRoot];
		        		    		    		str[xRoot]=larg[xRoot]*si[xRoot];
		    			    		    		max=Math.max(str[xRoot], max);
		    		    		    		}else{
		    		    		    			parent[yRoot]=xRoot;
		    		    		    			rank[xRoot]++;
		     
		    		    		    			larg[xRoot]=Math.max(larg[xRoot], larg[yRoot]);
		        		    		    		
		        		    		    		si[xRoot]+=si[yRoot];
		        		    		    		str[xRoot]=larg[xRoot]*si[xRoot];
		    			    		    		max=Math.max(str[xRoot], max);
		    		    		    		
		    		    		    		}
		    		    		    		cnt--;
		    		    		    		return true;
		    		    		    	}
		    	
		    		    		     
		    		    		    }
	class Pair1 implements Comparable<Pair1>{
			long price,rating;
			Pair1(long a,long b){
				this.price=a;
				this.rating=b;
			}
			@Override
			public int compareTo(Pair1 arg0) {
				
					return (int)(price-arg0.price);
				
			}
		
		
		}