For YouTube to have the video start at a specific time code utilize the urlargs(URL arguments) parameter. Take the rest of the URL arguments from the custom URL and place them into the urlargs. Please note that not all video services support extra URL arguments or may have different keys for their URL arguments.
(α → β) → α
<math> \forall x \exists y P(x,y) \nVdash \exists y \forall x P(x,y) </math>