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 Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

(defun calc (n a b &optional (current 0) (result 0))
  (if (<= n current)
      result
      (let ((tmp (+ a current)))
        (if (<= n tmp)
            (calc n a b tmp (+ result (- a (- tmp n))))
            (calc n a b (+ tmp b) (+ result a))))))

(let ((N (read))
      (A (read))
      (B (read)))
  (princ (if (= A 0)
             0
             (calc N A B))))