﻿ ABC158 B - Count Balls - Atcoder

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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.

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.

8 0 4

### Sample Output 2

0

He placed only red balls from the beginning.

6 2 4

### Sample Output 3

2

Among bbrrrr, there are two blue balls.