Number 1 is written on the whiteboard. Perform exactly $$c$$ operations on the written number. In each step, you can do one of the following operations:

Multiply the number on the board by $$a$$
Add $$b$$ to the number on the board

Determine the maximum number you can reach after exactly $$c$$ operations.

Input format

The first line of input contains $$a, b, c$$ respectively.

Note: $$a$$ is a decimal number and $$b$$ and $$c$$ are integers.

Output format

If the correct answer of the problem is $$Ans$$, then you must print $$\log_{2}{Ans}$$. If your answer is $$O$$, then your answer is considered correct if $$\frac{|(\log_{2}{Ans}) - O|}{\log_{2}{Ans}} \le 10^{-6}$$.

Note: The output should only consist of digits and dot. For example 235653455.5277 is correct and 2.356534555277e+8 is not correct. (You can use setpresicion function in C++.)

Constraints

$$0 \le a \le 10^{3}$$

$$1 \le b, c \le 10^{18}$$

$$1 \le b \times c \le 10^{18}$$