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 <cstdio>
#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
using namespace std;
typedef long long ll;
ll bisket;
ll K,A,B; 
int main(){
	scanf("%lld %lld %lld",&K,&A,&B);
	bisket=1;
	if((A<B-2) && (K>A)){
		K-=(A-1); // 5
		bisket=A; // 1
		ll cnt=K/2; //
		bisket+=cnt*(B-A);
		if(K%2==1){
			bisket+=1;
		}
	}
	else{
		bisket=K+1;
	}
	printf("%lld\n",bisket);
	return 0;
}
// 53513332169120811
// 48518828981938099