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>
#include <iostream>
#include <complex>
#include <sstream>
#include <string>
#include <algorithm>
#include <deque>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <vector>
#include <set>
#include <limits>
#include <cstdio>
#include <cctype>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <ctime>
#include <climits>
#include <iomanip>

#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, j, k) for(int i = (int)(j); i < (int)(k); ++i)
#define ROF(i, j, k) for(int i = (int)(j); i >= (int)(k); --i)
#define FORLL(i, n, m) for(long long i = n; i < (long long)(m); i++)
#define SORT(v, n) sort(v, v+n)
#define REVERSE(v) reverse((v).begin(), (v).end())

using namespace std;
using ll = long long;
const ll MOD=1000000007LL;
typedef pair<int, int> P;

ll ADD(ll x, ll y) { return (x+y) % MOD; }
ll SUB(ll x, ll y) { return (x-y+MOD) % MOD; }
ll MUL(ll x, ll y) { return x*y % MOD; }
ll POW(ll x, ll e) { ll v=1; for(; e; x=MUL(x,x), e>>=1) if (e&1) v = MUL(v,x); return v; }
ll DIV(ll x, ll y) { /*assert(y%MOD!=0);*/ return MUL(x, POW(y, MOD-2)); }

template<class T> bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}return 0;}
template<class T> bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}return 0;}

const ll MAXN = 1e9;

int
main(void){  
  ios_base::sync_with_stdio(false);
  cin.tie(0);

  ll K, A, B;
  cin >> K >> A >> B;

  if(B-A <= 1 || K < A){cout << K+1 << endl; return 0;}

  //k回目
  ll ans = A, num = K-(A-1);

  if(num%2 == 0) cout << ans + (B-A)*(num/2) << endl;
  else cout << ans + (B-A)*((num-1)/2)+1 << endl;
  
  
  return 0;
}