Problem:
Score : 200 points

Problem Statement

Takahashi has many red balls and blue balls. Now, he will place them in a row.

Initially, there is no ball placed.

Takahashi, who is very patient, will do the following operation 10^{100} times:

Place A blue balls at the end of the row of balls already placed. Then, place B red balls at the end of the row.

How many blue balls will be there among the first N balls in the row of balls made this way?

Constraints

1 \leq N \leq 10^{18}

A, B \geq 0

0 < A + B \leq 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

Print the number of blue balls that will be there among the first N balls in the row of balls.

Sample Input 1

8 3 4

Sample Output 1

4

Let b denote a blue ball, and r denote a red ball. The first eight balls in the row will be bbbrrrrb, among which there are four blue balls.

Sample Input 2

8 0 4

Sample Output 2

0

He placed only red balls from the beginning.

Sample Input 3

6 2 4

Sample Output 3

2

Among bbrrrr, there are two blue balls.

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

/*********************************************
* 20.05.08 AtCoder Beginner Contest 158. A, B, C
* 
*
*********************************************/
/*********************************************
::test input::
*********************************************/

namespace TempName{
    using System;
    using System.Linq;
    using System.Collections.Generic;
    using System.Reflection;
    using static System.Console;
    using static IOmacro.CsharpInput; 
    using static IOmacro.CppInput;
    

    public class CRun{
        public readonly char problem_num = 'B';
        
        public void solve_1() {
            //A. Station and Bus
            
            string input = _string;
            
            string ans = "No";
            for (int i = 1; i < input.Length; i++) {
                if (input[i] != input[i-1]) {
                    ans = "Yes";
                    break;
                }
            }
            WriteLine(ans);
        }
        public void solve_2() {
            //B. Count Balls
            
            int N = cin, A = cin, B = cin;
            
            int x = N / (A + B);
            int y = N % (A + B);
            
            int ans = 0;
            ans += x * A;
            ans += (y > A ? A : y);
            WriteLine(ans);
        }
        public void solve_3() {
            
        }
    }
    
    class Program { 
        static void Main() { 
            var run = new CRun();
            if (run.problem_num == 'A') run.solve_1(); 
            if (run.problem_num == 'B') run.solve_2(); 
            if (run.problem_num == 'C') run.solve_3();
        } 
    }
}

namespace IOmacro {
    //20.05.08. 수정
    
    using System; 
    using System.Linq; 
    using System.IO;
    using System.Collections.Generic;
    
    public class CsharpInput {
        public static StreamWriter _writer = new StreamWriter(Console.OpenStandardOutput());
        public const char separator = ' ';
        public static string _string{get{return Console.ReadLine();}}
        public static string[] _stringa{get{return (Console.ReadLine().Split(separator));}}
        public static int _int{get{return int.Parse(Console.ReadLine());}}
        public static int[] _inta{get{return Console.ReadLine().Split(separator).Select(int.Parse).ToArray();}}
        public static long _long{get{return long.Parse(Console.ReadLine());}}
        public static long[] _longa{get{return Console.ReadLine().Split(separator).Select(long.Parse).ToArray();}}    
        public static double _double{get{return double.Parse(Console.ReadLine());}}
        public static double[] _doublea{get{return Console.ReadLine().Split(separator).Select(double.Parse).ToArray();}}    
    }
    
    public class CConst {
        public static readonly int MINI = int.MaxValue;
        public static readonly long INF = Int64.MaxValue;
    }
    
    public class CppInput {
        public static CppInput cin => new CppInput();
        public const char separator = ' ';
        private static readonly Queue<string> _input = new Queue<string>();
        private CppInput(){}
        public static implicit operator string(CppInput _) {
            if (_input.Count == 0) Console.ReadLine().Split(separator).foreachExtension(x => _input.Enqueue(x));
            return _input.Dequeue();
        }
        public static implicit operator int(CppInput _){
            if (_input.Count == 0) Console.ReadLine().Split(separator).foreachExtension(x => _input.Enqueue(x));
            return int.Parse(_input.Dequeue());
        }
        public static implicit operator long(CppInput _){
            if (_input.Count == 0) Console.ReadLine().Split(separator).foreachExtension(x => _input.Enqueue(x));
            return long.Parse(_input.Dequeue());
        }
        public static implicit operator double(CppInput _){
            if (_input.Count == 0) Console.ReadLine().Split(separator).foreachExtension(x => _input.Enqueue(x));
            return double.Parse(_input.Dequeue());
        }
    }
    
    public static class EnumerableExtension {
        public delegate void Function<in T>(T val);
        public static void foreachExtension<T>(this IEnumerable<T> enumerable, Function<T> function) {
            foreach (var x in enumerable) function(x);
        }
    }
}