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 (1.15.1) (judge verdict: Wrong Answer)

use std::io;
use std::cmp::min;

fn main() {
	let mut buf = String::new();
	io::stdin().read_line(&mut buf).expect("can't read");
	let mut iter = buf.split_whitespace();
	
	let n:u64 = match iter.next().unwrap().parse() {
		Ok(num) => num,
		_ => panic!("error"),
	};
	let a:u64 = match iter.next().unwrap().parse() {
		Ok(num) => num,
		_ => panic!("error"),
	};
	let b:u64 = match iter.next().unwrap().parse() {
		Ok(num) => num,
		_ => panic!("error"),
	};
	let mut ans = n;
	for i in 0..(((a as f64).log2()) as u64 + 1) {
		ans = ans/((a+b)*(a+b));
	}
	let rem = n%(a+b);
	ans += min(rem, a);
	println!("{}", ans);
}