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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

int main(void){
	int k, a, b;
	int bis = 1, money = 0, i;

	scanf("%d %d %d", &k, &a, &b);
	if(b-a <= 1 || a+1 >= b-a){
		bis += k;
		bis++;
	}
	else{
		for(i=0; i<k; i++){
			bis++;//トンカチ
			if(bis == a || i<k){//ビスケット→金
				i++;
				bis -= a;
				money++;
			}
			while(money > 1 || i<k){
				if(money >= 1 || i<k){ //金→ビスケット	
					i++;
					bis += b;
					money--;
				}
				if(bis >= a || i<k-1){//ビスケット→金
					i++;
					bis -= a;
					money++;
				}
				else if(i<k){//トンカチ
					bis++;
				}
			}
			
		}
	}
	printf("%d\n", bis-1);
	return 0;
}