Find the positive integer $k$ for which the coefficient of $x^k$ in the expansion of $(x + 3)^{50}$ is maximized.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the positive integer $k$ for which the coefficient of $x^k$ in the expansion of $(x + 3)^{50}$ is maximized.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
12
Find the positive integer $k$ for which the coefficient of $x^k$ in the expansion of $(x + 3)^{50}$ is maximized.
train