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 OCaml (4.02.3) (judge verdict: Accepted)

(*
ocamlfind ocamlopt -package batteries -linkpkg main.ml -o a.out
*)
open Batteries

let n, a, b = Scanf.sscanf (read_line ()) "%d %d %d" (
        fun n a b -> 
                n, a, b
)


let ablue = 
        let amari = n mod (a + b) in
                if amari < a then
                        amari
                else
                        a

let () =
        (
                let div = n / (a + b) in
                let sblue = a * div in
                        sblue + ablue
        ) |> Printf.printf "%d\n"