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 Python (3.4.3) (judge verdict: Accepted)

K,A,B = map(int, input().split())
bis=1
nokori_kaisuu=K
if A+3<B:
    tataki_onechange_max=K-2
    if tataki_onechange_max+1>=A:
        bis+=((A-1)+(B-A))
        nokori_kaisuu-=((A-1)+2)
        more_change_kaisuu=nokori_kaisuu//2
        bis+=(B-A)*more_change_kaisuu
        nokori_kaisuu-=2*more_change_kaisuu
        if nokori_kaisuu==1:
            bis+=1
    else:
        bis+=K
else:
    bis+=K
print(bis)