Bin sizes for non-uniform discrete Fourier transforms
The notion of a "frequency bin" is somewhat misleading. In general a sine wave of a single frequency will show up in ALL frequency "bins" of the Time discrete Fourier Transform. It will generate the highest value where $f_k$ is closest to the signal frequency and but the values at any other Fourier frequency are not zero, just smaller.

The only exception is if the signal frequency is an exact integer multiple of $f_k$ and not windowing is applied.