If a hash function, represented by

$,$ is defined in the following way, which of the following properties are satisfied by

:

Hint: The

operation truncates an integer and set its length to $64$ bits. Here is why: since the remainder is always less than the divisor, the output of the operation is less than

which makes the result's binary representation a $64-$bit or shorter number. If the representation is shorter than $64$ bits, padding the result with some leading zeros can adjust the length to $64$ bits.

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