{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eTo seek candies for Maomao, Dudu comes to a maze. There are $n$ rooms numbered from $1$ to $n$ and $m$ undirected roads.\u003c/p\u003e\n\u003cp\u003eThere are two kinds of rooms in the maze -- candy room and monster room. There is one candy in each candy room, and candy room is safe. Dudu can take the only candy away when entering the room. After he took the candy, this candy room will be empty. A empty room is also safe. If Dudu is in safe, he can choose any one of adjacent rooms to go, whatever it is. Two rooms are adjacent means that at least one road connects the two rooms.\u003c/p\u003e\n\u003cp\u003eIn another kind of rooms, there are fierce monsters. Dudu can\u0027t beat these monsters, but he has a magic portal. The portal can show him a randomly chosen road which connects the current room and the other room.\u003c/p\u003e\n\u003cp\u003eThe chosen road is in the map so Dudu know where it leads to. Dudu can leave along the way to the other room, and those monsters will not follow him. He can only use the portal once because the magic energy is not enough.\u003c/p\u003e\n\u003cp\u003eDudu can leave the maze whenever he wants. That\u0027s to say, if he enters a monster room but he doesn\u0027t have enough energy to use the magic portal, he will choose to leave the maze immediately so that he can save the candies he have. If he leave the maze, the maze will never let him in again. If he try to fight with the monsters, he will be thrown out of the maze (never let in, of course). He remembers the map of the maze, and he is a clever guy who can move wisely to maximum the expection of candies he collected.\u003c/p\u003e\n\u003cp\u003eMaomao wants to know the expected value of candies Dudu will bring back. Please tell her the answer. He will start his adventure in room 1, and the room 1 is always a candy room. Since there may be more than one road connect the current room and the room he wants to go to, he can choose any of the roads.\u003c/p\u003e\n\u003ch2\u003eInput\u003c/h2\u003e\n\u003cp\u003eFirst line a integer $t$, means $t$ cases. $1 \\le t \\le 5$\u003c/p\u003e\n\u003cp\u003eFor each case:\u003c/p\u003e\n\u003cp\u003eFirst line 3 integer $n$, $m$, $k$, $n$ means the number of rooms, $m$ means the number of roads, $k$ means the number of monster rooms. $1 \\le n \\le 100000$, $n-1 \\le m \\le 2*n$, $0 \\le k \\le n$\u003c/p\u003e\n\u003cp\u003eNext $m$ lines, for each line there are two integer $a$ and $b$, separated by a space, means there is a road between $a$ and $b$. There may be repeated edges, but won\u0027t be self loop. $1 \\le a,b \\le n$\u003c/p\u003e\n\u003cp\u003eIn the last line there are $k$ distinct numbers, the $i$-th number $x_i$ means the number of the $i$-th monster room is $x_i$, and room 1 won\u0027t be monster room. $1 \\le i \\le k$\u003c/p\u003e\n\u003ch2\u003eOutput\u003c/h2\u003e\n\u003cp\u003eFor each case output a real number. The absolute error of the answer should not exceed $10^{-6}$.\u003c/p\u003e"}},{"title":"Sample 1","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2\n7 6 2\n1 2\n1 3\n2 5\n2 4\n3 6\n4 7\n2 3\n7 7 2\n1 2\n1 3\n2 5\n2 4\n3 6\n4 7\n2 4\n2 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2.000000\n2.250000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cbr /\u003e"}}]}