CF839E Mother of Dragons

There are $ n $ castles in the Lannister's Kingdom and some walls connect two castles, no two castles are connected by more than one wall, no wall connects a castle to itself. Sir Jaime Lannister has discovered that Daenerys Targaryen is going to attack his kingdom soon. Therefore he wants to defend his kingdom. He has $ k $ liters of a strange liquid. He wants to distribute that liquid among the castles, so each castle may contain some liquid (possibly zero or non-integer number of liters). After that the stability of a wall is defined as follows: if the wall connects two castles $ a $ and $ b $ , and they contain $ x $ and $ y $ liters of that liquid, respectively, then the strength of that wall is $ x·y $ . Your task is to print the maximum possible sum of stabilities of the walls that Sir Jaime Lannister can achieve.

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In the first sample, we can assign $ 0.5,0.5,0 $ liters of liquid to castles $ 1,2,3 $ , respectively, to get the maximum sum ( $ 0.25 $ ). In the second sample, we can assign $ 1.0,1.0,1.0,1.0 $ liters of liquid to castles $ 1,2,3,4 $ , respectively, to get the maximum sum ( $ 4.0 $ )