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 <algorithm>
#include <cstdio>
#include <iostream>
#include <cfloat>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <queue>
#include <sstream>
#include <stack>
#include <time.h>
#include <vector>
#include <complex>
#include <map>
#include <set>
#include <iomanip>
#include <math.h>
#include <stdlib.h>
#include <list>
#include <utility>
#include <memory>
#include <cstring>
#include <fstream>
#include <numeric>
#include <assert.h>
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll k,a,b;
int main(){
	cin>>k>>a>>b;
	if (b<=a){
		cout<<k+1;
		return 0;
	}
	if (k<=a-1){
		cout<<k+1;
		return 0;
	}
	k-=a-1;
	int el=k%2;
	int ee=k/2;
	cout<<max(a+ee*(b-a)+el,1+k+a-1);
}