CF986C AND Graph

You are given a set of size $ m $ with integer elements between $ 0 $ and $ 2^{n}-1 $ inclusive. Let's build an undirected graph on these integers in the following way: connect two integers $ x $ and $ y $ with an edge if and only if $ x \& y = 0 $ . Here $ \& $ is the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Count the number of connected components in that graph.

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Graph from first sample:  Graph from second sample: