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>
#define all(a) (a).begin(), (a).end()
#define REP(i, n) for(int (i)=0; (i)<(n); (i)++)
#define RREP(i, n) for(int (i)=(n)-1; (i)>=0; (i)--)
#define ios() cin.tie(0), ios::sync_with_stdio(false)
typedef long long ll;
typedef unsigned long long ull;
ll const MOD = 1e9+7;
ll const INF = 1e18;
using namespace std;

int main(){
    ll k, a, b;
    cin >> k >> a >> b;

    if(b - a < 2){
        cout << k + 1 << endl;
        return 0;
    }

    ll ans = 1;
    ans += min(a-1, k);
    if(k < a - 1){
        cout << ans << endl;
        return 0;
    }

    k -= a - 1;

    ans += (b - a) * (k / 2);
    ans += k % 2;

    cout << ans << endl;

    return 0;
}