Check if the Rectangle Corner Is Reachable

Determine whether there's a path inside the rectangle from (0,0) to (xCorner,yCorner) that stays strictly inside the rectangle (touches it only at the two corners) and does not touch or lie inside any given circles. Core challenge: model circles (and the rectangle sides/corners) as nodes in a graph/union-find where edges represent touching/overlap, then check whether any connected obstacle component covers a corner or forms a continuous barrier that blocks the two corners.