CF1844G Tree Weights

You are given a tree with $ n $ nodes labelled $ 1,2,\dots,n $ . The $ i $ -th edge connects nodes $ u_i $ and $ v_i $ and has an unknown positive integer weight $ w_i $ . To help you figure out these weights, you are also given the distance $ d_i $ between the nodes $ i $ and $ i+1 $ for all $ 1 \le i \le n-1 $ (the sum of the weights of the edges on the simple path between the nodes $ i $ and $ i+1 $ in the tree). Find the weight of each edge. If there are multiple solutions, print any of them. If there are no weights $ w_i $ consistent with the information, print a single integer $ -1 $ .

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In the first sample, the tree is as follows: In the second sample, note that $ w_2 $ is not allowed to be $ 0 $ because it must be a positive integer, so there is no solution. In the third sample, the tree is as follows: