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: Accepted)

n, a, b = map(int, input().split())

if a + b == 0:
    b = 1

x = n // (a + b) * a
# print(x)
y = n % (a + b)
# print(y)

# 余った(色の塊の途中で区切られた)ボールが赤なのか青なのか考える
if y <= a:
    ans = x + y
else:
    ans = x + a

# 11 3 2だとして
# 3 2 3 2 1 y1(青1)
# 12 3 2だとして
# 3 2 3 2 2 y2(青2)
# 13 3 2だとして
# 3 2 3 2 3  y3(青3)
# これらの場合はあまりをそのまま足す

# 14 3 2 だと
# 3 2 3 2 3 1 y4(青3赤1)
# この場合余りを全てたすと赤がまざってしまう

# 15 3 2 だと
# 3 2 3 2 3 2 y0(割り切れるのでそのまま答えが出る)

# つまり青(a)の範囲は0~3なので 
# aがyと同じかそれ以下なら足して
# 違うなら(3+1の状態)a(青3つ)だけ足す


print(ans)