Hints:

$$ Use long long or long long int for C$++$

$$ Use numpy.int$64$ if using Python $2.$ In Python $3$ using int will automatically give you long

integer.

$$ Look at example below. Instead of iterating i from $1$ to $16,$ we can jump i from $6$ to $8$

because we know all the quotients are the same. Similarly we can jump I from $9$ to $16$

because we know all the quotients are the same. Can we compute the last day the quotient

will stay the same, given the current day?

$$ To analyze the time complexity concretely, you need to observe that n$/$sqrt$($n$)=$sqrt$($n$).$ Our tutor gave this hints. Your given code does not execute within $4$ sec for $10^12$