시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

2N명이 두 팀으로 나누어서 축구를 하고 있다. 각 플레이어는 자기 팀의 유니폼을 입고 있고, 등번호는 1번부터 N번까지이다.

각 플레이어는 자신의 정확도를 알고 있고, 패스를 할 수 있는 팀 동료의 집합 F와 자신의 공을 빼았을 수 있는 상대팀 선수의 집합 E를 알고 있다.

플레이어가 공을 소유하게 되면, 그 순간부터 1초동안 아래 세 가지 중 하나의 사건이 발생한다.

  1. F에 속해있는 동료 중 한 명에게 패스를 한다. (랜덤)
  2. E에 속해있는 상대팀 선수 중 한 명에게 공을 빼앗긴다. (랜덤)
  3. 골대를 향해서 슛을 쏜다.

플레이어가 골대를 향해서 슛을 쏠 때, 득점할 확률은 자신의 정확도와 같다. 슛을 쏜 이후에는 결과에 상관없이 상대편 1번 선수가 공을 소유하게 된다.

위의 각 사건이 발생할 확률은 |F| : |E| : 1이고, 이전에 일어났던 사건은 여기에 영향을 미치지 않는다. (|S|는 집합 S의 크기이다) 각 사건의 설명 중에 랜덤은 각 집합에 포함되는 한 선수를 선택할 확률이 모두 같다는 것을 의미한다. 선수가 공을 소유하고 있지 않는 시간은 무시할 수 있을 만큼 매우 작다.

경기는 첫 번째 팀의 1번 선수가 공을 소유하면서 시작한다. 경기는 R 골을 득점한 팀이 있거나, 경기가 시작한지 T초가 지나면 끝나게 된다. 가능한 모든 최종 스코어에 대해서, 그 스코어로 경기가 끝날 확률을 계산하는 프로그램을 작성하시오.

아래 그림은 예제를 그림으로 나타낸 것이다.

입력

첫째 줄에 N, R, T가 주어진다. (1 ≤ N ≤ 100, 1 ≤ R ≤ 10, 1 ≤ T ≤ 500)

다음 N개 줄에는 첫 번째 팀에 속하는 각 선수의 설명이 주어지며, 그 다음 N개 줄에는 두 번째 팀에 속하는 각 선수의 설명이 주어진다.

선수의 설명에서 첫 번째 숫자는 그 선수의 정확도 p이다. (0 ≤ p ≤ 1) 그 다음에는 두 양의 정수 집합 F의 크기 nF와 집합 E의 크기 nE가 주어진다. (0 ≤ nF ≤ N-1, 0 ≤ nE ≤ N) 다음 nF+nE개 숫자는 각각 집합 F와 E에 포함되는 선수의 번호가 순서대로 주어지며, 공백으로 구분되어져 있다. 집합 F에는 자기 자신 번호를 포함하지 않는다.

출력

이론상 가능한 최종 스코어는 R*(R+2)개이다. 각 스코어에 대해서 그 결과가 나올 확률을 한 줄에 하나씩 출력한다.

출력하는 순서는 첫 번째 팀의 점수가 증가하는 순서로, 같은 경우에는 두 번째 팀의 점수가 증가하는 순서로 출력한다.

확률의 오차는 0.000001까지 허용한다.

예제 입력 1

2 2 5
0.0 1 2 2 1 2
1.0 0 0
0.5 1 0 2
0.5 1 0 1

예제 출력 1

0.2578125
0.2812500
0.0703125
0.1718750
0.1640625
0.0234375
0.0156250
0.0156250
[{"problem_id":"5216","problem_lang":"0","title":"\ucd95\uad6c","description":"<p>2N\uba85\uc774 \ub450 \ud300\uc73c\ub85c \ub098\ub204\uc5b4\uc11c \ucd95\uad6c\ub97c \ud558\uace0 \uc788\ub2e4. \uac01 \ud50c\ub808\uc774\uc5b4\ub294 \uc790\uae30 \ud300\uc758 \uc720\ub2c8\ud3fc\uc744 \uc785\uace0 \uc788\uace0, \ub4f1\ubc88\ud638\ub294 1\ubc88\ubd80\ud130 N\ubc88\uae4c\uc9c0\uc774\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud50c\ub808\uc774\uc5b4\ub294 \uc790\uc2e0\uc758 \uc815\ud655\ub3c4\ub97c \uc54c\uace0 \uc788\uace0, \ud328\uc2a4\ub97c \ud560 \uc218 \uc788\ub294 \ud300 \ub3d9\ub8cc\uc758 \uc9d1\ud569 F\uc640 \uc790\uc2e0\uc758 \uacf5\uc744 \ube7c\uc558\uc744 \uc218 \uc788\ub294 \uc0c1\ub300\ud300 \uc120\uc218\uc758 \uc9d1\ud569 E\ub97c \uc54c\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud50c\ub808\uc774\uc5b4\uac00 \uacf5\uc744 \uc18c\uc720\ud558\uac8c \ub418\uba74, \uadf8 \uc21c\uac04\ubd80\ud130 1\ucd08\ub3d9\uc548 \uc544\ub798 \uc138 \uac00\uc9c0 \uc911 \ud558\ub098\uc758 \uc0ac\uac74\uc774 \ubc1c\uc0dd\ud55c\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>F\uc5d0 \uc18d\ud574\uc788\ub294 \ub3d9\ub8cc \uc911 \ud55c \uba85\uc5d0\uac8c \ud328\uc2a4\ub97c \ud55c\ub2e4. (\ub79c\ub364)<\/li>\r\n\t<li>E\uc5d0 \uc18d\ud574\uc788\ub294 \uc0c1\ub300\ud300 \uc120\uc218 \uc911 \ud55c \uba85\uc5d0\uac8c \uacf5\uc744 \ube7c\uc557\uae34\ub2e4. (\ub79c\ub364)<\/li>\r\n\t<li>\uace8\ub300\ub97c \ud5a5\ud574\uc11c \uc29b\uc744 \uc3dc\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\ud50c\ub808\uc774\uc5b4\uac00 \uace8\ub300\ub97c \ud5a5\ud574\uc11c \uc29b\uc744 \uc3e0 \ub54c, \ub4dd\uc810\ud560 \ud655\ub960\uc740 \uc790\uc2e0\uc758 \uc815\ud655\ub3c4\uc640 \uac19\ub2e4. \uc29b\uc744 \uc3dc \uc774\ud6c4\uc5d0\ub294 \uacb0\uacfc\uc5d0 \uc0c1\uad00\uc5c6\uc774 \uc0c1\ub300\ud3b8 1\ubc88 \uc120\uc218\uac00 \uacf5\uc744 \uc18c\uc720\ud558\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc704\uc758 \uac01 \uc0ac\uac74\uc774 \ubc1c\uc0dd\ud560 \ud655\ub960\uc740 |F| : |E| : 1\uc774\uace0, \uc774\uc804\uc5d0 \uc77c\uc5b4\ub0ac\ub358 \uc0ac\uac74\uc740 \uc5ec\uae30\uc5d0 \uc601\ud5a5\uc744 \ubbf8\uce58\uc9c0 \uc54a\ub294\ub2e4. (|S|\ub294 \uc9d1\ud569 S\uc758 \ud06c\uae30\uc774\ub2e4) \uac01 \uc0ac\uac74\uc758 \uc124\uba85 \uc911\uc5d0 \ub79c\ub364\uc740 \uac01 \uc9d1\ud569\uc5d0 \ud3ec\ud568\ub418\ub294 \ud55c \uc120\uc218\ub97c \uc120\ud0dd\ud560 \ud655\ub960\uc774 \ubaa8\ub450 \uac19\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. \uc120\uc218\uac00 \uacf5\uc744 \uc18c\uc720\ud558\uace0 \uc788\uc9c0 \uc54a\ub294 \uc2dc\uac04\uc740 \ubb34\uc2dc\ud560 \uc218 \uc788\uc744 \ub9cc\ud07c \ub9e4\uc6b0 \uc791\ub2e4.<\/p>\r\n\r\n<p>\uacbd\uae30\ub294 \uccab \ubc88\uc9f8 \ud300\uc758 1\ubc88 \uc120\uc218\uac00 \uacf5\uc744 \uc18c\uc720\ud558\uba74\uc11c \uc2dc\uc791\ud55c\ub2e4. \uacbd\uae30\ub294 R \uace8\uc744 \ub4dd\uc810\ud55c \ud300\uc774 \uc788\uac70\ub098, \uacbd\uae30\uac00 \uc2dc\uc791\ud55c\uc9c0 T\ucd08\uac00 \uc9c0\ub098\uba74 \ub05d\ub098\uac8c \ub41c\ub2e4. \uac00\ub2a5\ud55c \ubaa8\ub4e0 \ucd5c\uc885 \uc2a4\ucf54\uc5b4\uc5d0 \ub300\ud574\uc11c, \uadf8 \uc2a4\ucf54\uc5b4\ub85c \uacbd\uae30\uac00 \ub05d\ub0a0 \ud655\ub960\uc744 \uacc4\uc0b0\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc544\ub798 \uadf8\ub9bc\uc740 \uc608\uc81c\ub97c \uadf8\ub9bc\uc73c\ub85c \ub098\ud0c0\ub0b8 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/soccer.png\" style=\"height:206px; width:514px\" \/><\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 N, R, T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; N &le; 100, 1 &le; R &le; 10, 1 &le; T &le; 500)<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \uccab \ubc88\uc9f8 \ud300\uc5d0 \uc18d\ud558\ub294 \uac01 \uc120\uc218\uc758 \uc124\uba85\uc774 \uc8fc\uc5b4\uc9c0\uba70, \uadf8 \ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \ub450 \ubc88\uc9f8 \ud300\uc5d0 \uc18d\ud558\ub294 \uac01 \uc120\uc218\uc758 \uc124\uba85\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc120\uc218\uc758 \uc124\uba85\uc5d0\uc11c \uccab \ubc88\uc9f8 \uc22b\uc790\ub294 \uadf8 \uc120\uc218\uc758 \uc815\ud655\ub3c4 p\uc774\ub2e4. (0 &le; p &le; 1) \uadf8 \ub2e4\uc74c\uc5d0\ub294 \ub450 \uc591\uc758 \uc815\uc218 \uc9d1\ud569 F\uc758 \ud06c\uae30 nF\uc640 \uc9d1\ud569 E\uc758 \ud06c\uae30 nE\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; nF &le; N-1, 0 &le; nE &le; N) \ub2e4\uc74c nF+nE\uac1c \uc22b\uc790\ub294 \uac01\uac01 \uc9d1\ud569 F\uc640 E\uc5d0 \ud3ec\ud568\ub418\ub294 \uc120\uc218\uc758 \ubc88\ud638\uac00 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c0\uba70, \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4\uc838 \uc788\ub2e4. \uc9d1\ud569 F\uc5d0\ub294 \uc790\uae30 \uc790\uc2e0 \ubc88\ud638\ub97c \ud3ec\ud568\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","output":"<p>\uc774\ub860\uc0c1 \uac00\ub2a5\ud55c \ucd5c\uc885 \uc2a4\ucf54\uc5b4\ub294 R*(R+2)\uac1c\uc774\ub2e4. \uac01 \uc2a4\ucf54\uc5b4\uc5d0 \ub300\ud574\uc11c \uadf8 \uacb0\uacfc\uac00 \ub098\uc62c \ud655\ub960\uc744 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ucd9c\ub825\ud558\ub294 \uc21c\uc11c\ub294 \uccab \ubc88\uc9f8 \ud300\uc758 \uc810\uc218\uac00 \uc99d\uac00\ud558\ub294 \uc21c\uc11c\ub85c, \uac19\uc740 \uacbd\uc6b0\uc5d0\ub294 \ub450 \ubc88\uc9f8 \ud300\uc758 \uc810\uc218\uac00 \uc99d\uac00\ud558\ub294 \uc21c\uc11c\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud655\ub960\uc758 \uc624\ucc28\ub294 0.000001\uae4c\uc9c0 \ud5c8\uc6a9\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5216","problem_lang":"1","title":"MNOGOMET","description":"<p>2N people are playing football (soccer), divided into two teams. Each player wears a dress with the team logo and a unique (in the team) positive integer between 1 and N, inclusive. For each player, we know his precision, the set of teammates whom he can pass the ball to (F) and the set of opponents who can take the ball from him (E). When a player comes into possession of the ball, after exactly one second one of the following events will happen:<\/p>\r\n\r\n<ul>\r\n\t<li>the player passes the ball to a random teammate from the set F,<\/li>\r\n\t<li>a random opponent from the set E takes the ball from him,<\/li>\r\n\t<li>the player attempts a shot at the goal.<\/li>\r\n<\/ul>\r\n\r\n<p>If the player attempts a shot, the probability of scoring a goal is equal to his precision. After the shot, whether it was successful or not, the ball is awarded to the player number 1 from the opposing team.<\/p>\r\n\r\n<p>The probabilities of different events are in the proportion |F| : |E| : 1, in order, and depend only on the player currently in possession of the ball (|S| determines the size of the set S corresponding to the current player), not on any previous events in the game. The word &ldquo;random&rdquo; means that all players from the set F (or E) have the same probability of being passed (or taking) the ball by (from) the player that is currently in the ball&#39;s possession. The time that a ball spends outside of a player&#39;s possession is negligible.<\/p>\r\n\r\n<p>The match begins with player 1 from the first team in possession of the ball and ends either when one team has scored R goals or when T seconds have elapsed, whichever happens first. For each possible final score, determine the probability that the match will end with it.<\/p>\r\n\r\n<p>The following image illustrates the player arrangement for the second test example:<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/soccer.png\" style=\"height:206px; opacity:0.9; width:514px\" \/><\/p>\r\n","input":"<p>The first line of input contains three positive integers: N (1 &le; N &le; 100), the number of players in each team, R (1 &le; R &le; 10), the number of goals needed for victory, and T (1 &le; T &le; 500), the maximum duration of the match.<\/p>\r\n\r\n<p>The following N lines contain descriptions of the first team&#39;s players, one per line, while the next N lines after that contain descriptions of the second team&#39;s players. A description of a single player consists of a real number p (0 &le; p &le; 1), the player&#39;s precision, followed by two positive integers, nF (0 &le; nF &le; N - 1) and nE (0 &le; nE &le; N), the sizes of the sets F and E, respectively, followed by nF + nE player labels representing the sets F and E themselves (in that order), all space-separated. Note that the labels from F represent players from one team, and labels from E the other team. The set F will not contain the label of the player currently being described.<\/p>\r\n","output":"<p>The match can theoretically end with one of R * (R + 2) different final results. For each result, output the probability of its realization as a real number, one per line. Order the results first by the number of goals scored by the first team, then by the number of goas scored by the second team, in ascending order. The permitted difference from the exact value for each probability is 0.000001.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]