Problem Description

Snuke initially has 1 biscuit and no Japanese yen. Snuke can perform the following operations in any order, totaling exactly $ K $ times:

• Hit the biscuits to increase the count by 1
• Exchange $ A $ biscuits for 1 yen
• Exchange 1 yen for $ B $ biscuits

Determine the maximum number of biscuits Snuke can have after $ K $ operations.

Input Format

The input is given from the standard input in the following format:

$ K $ $ A $ $ B $

Output Format

Output the maximum number of biscuits Snuke can have after $ K $ operations.

Sample Input and Output

Sample Input #1

4 2 6

Sample Output #1

7

Sample Input #2

7 3 4

Sample Output #2

8

Sample Input #3

314159265 35897932 384626433

Sample Output #3

48518828981938099

Notes/Hints

Constraints

• $1 \leq K, A, B \leq 10^9$
• $ K, A, B $ are integers

Sample Explanation 1

The following operations maximize the number of biscuits after $ K $ operations:
- Hit the biscuits. Snuke has 2 biscuits and 0 yen.
- Exchange 2 biscuits for 1 yen. Snuke has 0 biscuits and 1 yen.
- Hit the biscuits. Snuke has 1 biscuit and 1 yen.
- Exchange 1 yen for 6 biscuits. Snuke has 7 biscuits and 0 yen.

见题面 Input 部分

见题面 Output 部分