CF1714F Build a Tree and That Is It

A tree is a connected undirected graph without cycles. Note that in this problem, we are talking about not rooted trees. You are given four positive integers $ n, d_{12}, d_{23} $ and $ d_{31} $ . Construct a tree such that: - it contains $ n $ vertices numbered from $ 1 $ to $ n $ , - the distance (length of the shortest path) from vertex $ 1 $ to vertex $ 2 $ is $ d_{12} $ , - distance from vertex $ 2 $ to vertex $ 3 $ is $ d_{23} $ , - the distance from vertex $ 3 $ to vertex $ 1 $ is $ d_{31} $ . Output any tree that satisfies all the requirements above, or determine that no such tree exists.

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