B - Count Balls
B - Count Balls
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:
Output
Print the number of blue balls that will be there among the first $N$ balls in the row of balls.
8 3 4
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.
8 0 4
0
He placed only red balls from the beginning.
6 2 4
2
Among bbrrrr, there are two blue balls.