CF1003E Tree Constructing

You are given three integers $ n $ , $ d $ and $ k $ . Your task is to construct an undirected tree on $ n $ vertices with diameter $ d $ and degree of each vertex at most $ k $ , or say that it is impossible. An undirected tree is a connected undirected graph with $ n - 1 $ edges. Diameter of a tree is the maximum length of a simple path (a path in which each vertex appears at most once) between all pairs of vertices of this tree. Degree of a vertex is the number of edges incident to this vertex (i.e. for a vertex $ u $ it is the number of edges $ (u, v) $ that belong to the tree, where $ v $ is any other vertex of a tree).

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