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 Rust (1.42.0) (judge verdict: Time Limit Exceeded)

use whiteread::parse_line;

fn main() {
    let (n, a, b): (i64, i64, i64) = parse_line().unwrap();
    let mut i: i64 = 0;
    let mut ac: i64 = 0;
    while i < n {
        let mut ak: i64 = 0;
        while ak < a {
            ak = ak + 1;
            ac = ac + 1;
            i = i + 1;
            if i == n {
                break;
            }
        }
        if i == n {
            break;
        }
        let mut bk: i64 = 0;
        while bk < b {
            bk = bk + 1;
            i = i + 1;
            if i == n {
                break;
            }
        }
    }
    println!("{}", ac);
}