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

$0 \le  a \le 10^{3}$

$1 \le  b, c \le 10^{18}$

$1 \le  b \times c \le 10^{18}$