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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>                                                                                  
#include<string.h>
#include<stdlib.h>

int main(void){
    int A;
    int AS; 
    int B;
    int BS; 
    int N;
    int flag=1;
    int sum=0;
//    char *heap;

    scanf("%d",&N);
    scanf("%d",&A);
    scanf("%d",&B);
    AS = A;
    BS = B;
 //   heap = (char *)malloc(N*sizeof(char));

    for(int i=0;i<N;i++){
        if(flag==1){
            //heap[i]='b';
            if(AS == 0){ 
                flag =0; 
            }else{
            A--;
            sum++;
            if(A == 0){ 
                A = AS; 
                flag=0;
            }   
            }   
        }else if(flag==0){
            //heap[i]='r';
            if(BS == 0){ 
                flag = 1;
            }else{
            B--;
            if(B == 0){ 
                B =BS;
                flag =1; 
            }   
            }   
        }   

    }   
    printf("%d\n",sum);
   // printf("%s",heap);

  //  free(heap); 

    return 0;
}