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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdbool.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
typedef long long int ll;
#define mod 1000000007
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define m0(x) memset(x,0,sizeof(x))

int main(void)
{
	ll k,a,b;
	scanf("%lld %lld %lld",&k,&a,&b);
	ll nokori;
	ll max;
	if (a+2>=b) max=1+k;
	else if(a+1>k) max=1+k;
	else {
		max=b;
		nokori=k-(a+1);
		max+=(nokori/2)*(b-a);
		if(nokori%2==1) max++;
	}
	printf("%lld\n",max);
	return 0;
}