There are $64$ booths arranged around a circular table, each containing a chip. The chips and booths are numbered from $1$ to $64$. At the center of the table, there are $1996$ light bulbs, all initially turned off. 

Every minute, the chips move simultaneously in a circular pattern as follows: chip $1$ moves one booth forward, chip $2$ moves two booths forward, and so on, such that multiple chips can occupy the same booth at the same time. 

A bulb is lit whenever chip $1$ shares a booth with any other chip. 

Determine the position of chip $1$ on the first minute when all $1996$ bulbs are lit.

Let's think step by step and output the final answer within \boxed{}.
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