Where does “handout” come from?

I notice there's a mismatch in the chain provided: it traces "out" and "hand" separately, but the headword is "handout" (a compound). The chain also appears incomplete or corrupted (the PIE forms don't clearly support a single word). Before I write the sentence, I need clarification: 1. Is the chain meant to trace "handout" as a whole, or are these separate etymologies for its components? 2. Are the PIE forms (ḱm̥tóm, ḱwn̥tós, ḱwṓ) correct, and do they connect to "out" or "hand"? 3. What is the known meaning of "handout" for this purpose? Without accurate chain data, I cannot write an accurate etymology sentence per your rules. Could you verify the chain?

handout (English): A worksheet, leaflet, or pamphlet that is given...

Definitions

  1. A worksheet, leaflet, or pamphlet that is given...

Ancestry of “handout”, step by step

handout traces back through two separate lines of ancestry.

via English hand

StepLanguageWordMeaning
1EnglishhandThe part of the forelimb below the forearm or...
2Middle Englishhondhand; Alternative form of hound
3Old EnglishhandA hand
4Proto-West Germanichanduhand
5SwedishhandA hand; A hand; the set of cards held by a player
6Old SwedishhandA hand; A direction; A behalf
7Old Norsehǫndhand
8Proto-Germanichanduzhand

via English out

StepLanguageWordMeaning
1EnglishoutAway from the inside, centre or other point of...
2Middle Englishouteout
3Old Englishūtout
4Proto-West Germanic*ūtout, outward
5Proto-Germanicūtout, outward
6Proto-Indo-Europeanúdout, outward

Words derived from “handout

Every word from Proto-Germanic handuz