<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 At a recent math contest, Evan was asked to find $2^{2016}(\bmod p)$ for a given prime number $p$ with $100<p<500$. Evan has forgotten what the prime $p$ was, but still remembers how he solved it: - Evan first tried taking 2016 modulo $p-1$, but got a value $e$ larger than 100. - However, Evan noted that $e-\frac{1}{2}(p-1)=21$, and then realized the answer was $-2^{21}(\bmod p)$. What was the prime $p$? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
211
At a recent math contest, Evan was asked to find $2^{2016}(\bmod p)$ for a given prime number $p$ with $100<p<500$. Evan has forgotten what the prime $p$ was, but still remembers how he solved it: - Evan first tried taking 2016 modulo $p-1$, but got a value $e$ larger than 100. - However, Evan noted that $e-\frac{1}{2}(p-1)=21$, and then realized the answer was $-2^{21}(\bmod p)$. What was the prime $p$?
test