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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define INF INT_MAX
#define ll  long long
#define ull unsigned long long
#define rep(i,n) for(ll i=0; i<n; ++i)
#define FOR(i, s, e) for(ll i=s; i<e; ++i)
#define MOD 1000000007
using namespace std;
template<class T> inline bool chmin(T& a, T b) { if(a>b) {a=b; return true;} return false;}
template<class T> inline bool chmax(T& a, T b) { if(a<b) {a=b; return true;} return false;}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll N, A, B; cin >> N >> A >> B;
  cout << N/(A+B)*A + min(N%(A+B),A) << endl;
}