Problem:
Score : 400 points

Problem Statement

Snuke has one biscuit and zero Japanese yen (the currency) in his pocket.
He will perform the following operations exactly K times in total, in the order he likes:

Hit his pocket, which magically increases the number of biscuits by one.

Exchange A biscuits to 1 yen.

Exchange 1 yen to B biscuits.

Find the maximum possible number of biscuits in Snuke's pocket after K operations.

Constraints

1 \leq K,A,B \leq 10^9

K,A and B are integers.

Input

Input is given from Standard Input in the following format:

K A B

Output

Print the maximum possible number of biscuits in Snuke's pocket after K operations.

Sample Input 1

4 2 6

Sample Output 1

7

The number of biscuits in Snuke's pocket after K operations is maximized as follows:

Hit his pocket. Now he has 2 biscuits and 0 yen.

Exchange 2 biscuits to 1 yen. his pocket. Now he has 0 biscuits and 1 yen.

Hit his pocket. Now he has 1 biscuits and 1 yen.

Exchange 1 yen to 6 biscuits. his pocket. Now he has 7 biscuits and 0 yen.

Sample Input 2

7 3 4

Sample Output 2

8

Sample Input 3

314159265 35897932 384626433

Sample Output 3

48518828981938099

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define REP(i, a, n) for (int i = (a); i < (int)(n); ++i)
#define REPC(i, a, n) for (int i = (a); i <= (int)(n); ++i)
#define ALL(t) t.begin(), t.end()
#define RALL(t) t.rbegin(), t.rend()
#define MATINIT(type, row, col, init) \
  vector<vector<type>>(row, vector<type>(col, init));
#define Yes(cond) cout << (cond ? "Yes" : "No") << endl;
#define YES(cond) cout << (cond ? "YES" : "NO") << endl;
using namespace std;
using LL = long long;
using ULL = unsigned long long;
template <class T>
using VEC = std::vector<T>;
template <class T>
using MAT = std::vector<std::vector<T>>;
void DUMP() { cerr << endl; }
template <class Head, class... Tail>
void DUMP(Head &&head, Tail &&... tail) {
  cerr << head << ", ";
  DUMP(std::move(tail)...);
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &vec) {
  os << "{";
  for (auto v : vec) os << v << ",";
  os << "}";
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, map<T1, T2> &m) {
  os << "{";
  for (auto p : m) os << p << ",";
  os << "}";
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  os << "[" << p.first << " " << p.second << "]";
  return os;
}

int main() {
  ULL K, A, B;
  cin >> K >> A >> B;
  ULL first = A - 1;
  ULL remain = K - first;
  ULL ans = 0;
  if (B - A <= 2) {
    ans = K + 1;

  } else {
    if (remain % 2 == 0) {
      ULL num = remain / 2;
      ans = (num - 1) * (B - A) + B;
    } else {
      ULL num = remain / 2;
      ans = (num - 1) * (B - A) + B+1;
    }
  }
  // DUMP(first, remain);
  cout << ans << endl;

  return 0;
}