Holiday Madness: Draw a line through all the gifts

Question

Can you collect all the gifts?
The rules:

Start from the star
At each intersection are arrows. You can only move through the intersection in accordance with the direction of the arrow. (e.g If you hit an intersection with an arrow pointing down and to the left, when you hit that intersection you can only continue moving down or to the left) You must then continue on to the next intersection. (Meaning, you can't go through an intersection, hit the gift, then go back to that intersection.)
Can only draw in between the gray squares.
Can not pick up the pen/pencil from the maze. Meaning: the line you are drawing must be continuous.
Can not draw a line over any gift twice. (you can draw over a previous drawn line)
Goal: Collect all the gifts using the above rules and win!

GentlePurpleRain · Answer

Here is my solution.  I found it mostly by trial and error.
I made the line change colour every once in a while so that it would be easier to distinguish different lines when they overlap.  Start at the star, with the green line.
(Thanks to Ben Barden, who pointed out a small error in my original solution (and the way to fix it!))

npkllr · Answer

I was trying to get as much progress as possible just by using logical deduction.
This is how far I got:

I solved the remaining path with a mix of trial and error, and logical deduction. I managed to find a path that begins and terminates at the star.
My solution:

Holiday Madness: Draw a line through all the gifts

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