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 Python (3.4.3) (judge verdict: Runtime Error)

n, a, b = map(int, input().split())
if a == 0 or n == 0:
  print(0)
else:
  v = 10 ** 100
  s = ""
  str_length = 0
  count = 0
  b_str = "b" * a
  r_str = "r" * b
  for i in range(v):
    s = b_str
    if b > 0:
      s += r_str
    
    str_length = (i + 1) * (a + b)
    if str_length >= n:
      target_length = n - (a+b) * i
      res = s[:target_length]
      count += res.count("b")
      print(count)
      break

    count += s.count("b")