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: Output Limit Exceeded)

#include <stdio.h>
int main(void){
    int K,A,B,i=0,bis=1,yen=0;
    scanf("%d",&K);
    scanf("%d",&A);
    scanf("%d",&B);
    if(B-A<=1||K+1<A){
        printf("%d",K+1);
        return 0;
    }
    while(i<K){
        if(bis<A){
            bis=A;
            i+=A-bis;
        }
        else{
            if(i==K-1) bis++;
            else{
                
            }
        }
        printf("i:%d\nyen:%d\nbis:%d\n\n",i,yen,bis);
    }
    printf("%d",bis);
    return 0;
}