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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>

using namespace std;
using ll = long long;
#define rep(i,n) for (int i = 0; i < (int)n; i++)

const int inf = 1'000'000'000;

#include<bits/stdc++.h>

using namespace std;
using ll = long long;
#define rep(i,n) for (int i = 0; i < (int)n; i++)

int main(){
  ll n,a,b;
  cin >> n >> a >> b;
  ll c = a+b;
  ll ans = a * (n/c);
  // 青の途中で切れた場合と赤のボールにまで行った場合
  ans += min(n%c, a);
  cout << ans << endl;
}