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;

#define REP(i, n) for(ll i = 0;i < n;i++)
#define REP1(i, n) for(ll i = 1;i < n;i++)
#define REPR(i, n) for(ll i = n-1;i >= 0;i--)
#define FOR(i, m, n) for(ll i = m;i < n;i++)

#define VSORT(v) sort(v.begin(), v.end())
#define VRSORT(v) sort(v.rbegin(), v.rend())

#define ll long long
#define ALL(a)  (a).begin(),(a).end()

#define pb(a) push_back(a)

ll k,a,b;


int main(){
  ll ans=0;
  cin >> k>>a>>b;
  if (b-a>2){
    ll t=b-a;//2回で増やせるビスケット数
    ll x=k-a+1;
    if (x<=0){
      ans=k+1;
      cout<<ans<<endl;
      return 0;
    }
    
    ans=a+(x/2)*t;
    if (x%2==1)ans++;
    
      cout<<ans<<endl;
      return 0;

  }else{
    ans=k+1;
    cout<<ans<<endl;
    return 0;
  }
return 0;

}