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: Wrong Answer)

KAB = [int(x) for x in input().split()]
K = KAB[0]
A = KAB[1]
B = KAB[2]
count = 1
if (B - A <= 1) or K <= A:
    print(K + 1)
    #print(1)
    #print(A - B)
    #print(A - K)
else:
    count = A
    K = K - A + 1
    if K % 2 == 1:
        #print(2)
        print(B - A, K // 2)
        count = count + 1 + (B - A) * (K // 2)
    else:
        #print(3)
        count += (B - A) * K // 2
    print(count)