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: Accepted)

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i,n) for( ll i = 0;i < (ll) n;++i)

int main(){
  ll k,a,b;
  cin >> k >> a >> b;
  ll bis = 1;
  ll m = 0;
  rep(i,k){
    if( i == k-1 ){
      if( m != 0 ){
        m--;
        bis += b;
      }else{
        bis++;
      }
      break;
    }
    if( a <= b ){
      if( bis < a && m == 0 ){
        bis++;
        //cout << 'a' << endl;
      }else if( m != 0 ){
        m--;
        bis += b;
        //cout << 'b' << endl;
      }else if( bis >= a && m == 0 ){
        bis -= a;
        m++;
        //cout << 'c' << endl;
      }else{
        bis++;
        //cout << 'd' << endl;
      }
    }else{
      bis++;
    }
  }
  cout << max(bis,k+1) << endl;
  return 0;
}