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: Time Limit Exceeded)

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

#ifdef TEST
struct test {
    int ans;
} td[] = {
    {},
};
#endif

void
solver(long long n, long long a, long long b)
{
    long long all = 0;

    while(1) {
        if(n >= a) {
            all += a;
            n -= a;
        } else {
            all += n;
            n = 0;
        }
        n -= b;
        if(n <= 0)
            break;
    }
    printf("%lld\n", all);
}

int
main(int argc, char *argv[])
{
    long long N, A, B;
#ifdef TEST
    int tt;
    for(tt = 0; tt < sizeof(td) / sizeof(struct test); tt++) {
        solver();
        printf("%d\n", td[tt].ans);
    }
#endif
    scanf("%lld%lld%lld", &N, &A, &B);
    solver(N, A, B);
    return 0;
}