시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 6 4 4 100.000%

문제

월드 방송국에서 유선으로 방송을 하고자 한다. 방송망의 형태는 방송국이 루트인 트리의 형태가 될 것이다. 트리의 터미널 노드들은 사용자를 의미하며 트리에서 터미널을 제외한 노드는 송신기 역할을 하게 된다. (루트는 방송국이면서 송신기이며, 루트와 터미널이 아닌 노드들은 중간 송신기라고 불려진다)

한 노드에서 다른 노드로 방송 라인을 설치할 때 드는 비용이 주어진다. 총 방송 비용이란 설치한 방송 라인의 비용을 모두 더한 값이다.

같은 방송망에 있지만 각각의 사용자가 내는 돈은 다를 수 있으며 각각 사용자가 방송을 보게 될 때 지불할 돈이 미리 주어진다.

방송국에서는 방송 라인을 하나 설치할 때 지출을 하게 된다. 또한 방송망이 방송국에서 사용자까지 도달되면 방송국은 그 사용자에게서 시청료를 받게 된다.

방송라인을 적절히 설치해서 방송국이 손해를 보지 않으면서 방송을 해줄 수 있는 최대 사용자는 몇 명인가? (손해를 보지 않는다는 말은 총 시청료 - 총 방송 비용 ≥ 0 임을 의미한다)

입력

첫 줄에 N M이 입력된다. (2 ≤ N ≤ 3,000, 1 ≤ M ≤ N-1)
N은 트리의 노드 개수이고 M은 트리의 터미널 노드 개수이다.
노드의 번호는 트리의 루트가 1이며, 루트가 아닌 다른 송신기들은 2부터 N-M까지, 사용자들(터미널노드들)의 번호는 N-M+1부터 N까지 이다.
두 번째 줄부터 N-M개의 줄에 다음과 같은 형식으로 송신기 정보가 주어진다.
K A1 C1 A2 C2 ... Ak Ck
K는 그 송신기가 송신하는 노드의 개수이며 A는 그 노드의 이름 C는 그 비용을 의미한다.
그 이후의 M개의 라인에는 M명의 사용자의 시청료가 각각 입력된다.

출력

최대 사용자 수를 출력한다.

예제 입력 1

5 3
2 2 2 5 3
2 3 2 4 3
3 4 2

예제 출력 1

2
[{"problem_id":"1815","problem_lang":"0","title":"\ubc29\uc1a1\uad6d","description":"<p>\uc6d4\ub4dc \ubc29\uc1a1\uad6d\uc5d0\uc11c \uc720\uc120\uc73c\ub85c \ubc29\uc1a1\uc744 \ud558\uace0\uc790 \ud55c\ub2e4. \ubc29\uc1a1\ub9dd\uc758 \ud615\ud0dc\ub294 \ubc29\uc1a1\uad6d\uc774 \ub8e8\ud2b8\uc778 \ud2b8\ub9ac\uc758 \ud615\ud0dc\uac00 \ub420 \uac83\uc774\ub2e4. \ud2b8\ub9ac\uc758 \ud130\ubbf8\ub110 \ub178\ub4dc\ub4e4\uc740 \uc0ac\uc6a9\uc790\ub97c \uc758\ubbf8\ud558\uba70 \ud2b8\ub9ac\uc5d0\uc11c \ud130\ubbf8\ub110\uc744 \uc81c\uc678\ud55c \ub178\ub4dc\ub294 \uc1a1\uc2e0\uae30 \uc5ed\ud560\uc744 \ud558\uac8c \ub41c\ub2e4. (\ub8e8\ud2b8\ub294 \ubc29\uc1a1\uad6d\uc774\uba74\uc11c \uc1a1\uc2e0\uae30\uc774\uba70, \ub8e8\ud2b8\uc640 \ud130\ubbf8\ub110\uc774 \uc544\ub2cc \ub178\ub4dc\ub4e4\uc740 \uc911\uac04 \uc1a1\uc2e0\uae30\ub77c\uace0 \ubd88\ub824\uc9c4\ub2e4) <br \/>\r\n<br \/>\r\n\ud55c \ub178\ub4dc\uc5d0\uc11c \ub2e4\ub978 \ub178\ub4dc\ub85c \ubc29\uc1a1 \ub77c\uc778\uc744 \uc124\uce58\ud560 \ub54c \ub4dc\ub294 \ube44\uc6a9\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ucd1d \ubc29\uc1a1 \ube44\uc6a9\uc774\ub780 \uc124\uce58\ud55c \ubc29\uc1a1 \ub77c\uc778\uc758 \ube44\uc6a9\uc744 \ubaa8\ub450 \ub354\ud55c \uac12\uc774\ub2e4.<br \/>\r\n<br \/>\r\n\uac19\uc740 \ubc29\uc1a1\ub9dd\uc5d0 \uc788\uc9c0\ub9cc \uac01\uac01\uc758 \uc0ac\uc6a9\uc790\uac00 \ub0b4\ub294 \ub3c8\uc740 \ub2e4\ub97c \uc218 \uc788\uc73c\uba70 \uac01\uac01 \uc0ac\uc6a9\uc790\uac00 \ubc29\uc1a1\uc744 \ubcf4\uac8c \ub420 \ub54c \uc9c0\ubd88\ud560 \ub3c8\uc774 \ubbf8\ub9ac \uc8fc\uc5b4\uc9c4\ub2e4.<br \/>\r\n<br \/>\r\n\ubc29\uc1a1\uad6d\uc5d0\uc11c\ub294 \ubc29\uc1a1 \ub77c\uc778\uc744 \ud558\ub098 \uc124\uce58\ud560 \ub54c \uc9c0\ucd9c\uc744 \ud558\uac8c \ub41c\ub2e4. \ub610\ud55c \ubc29\uc1a1\ub9dd\uc774 \ubc29\uc1a1\uad6d\uc5d0\uc11c \uc0ac\uc6a9\uc790\uae4c\uc9c0 \ub3c4\ub2ec\ub418\uba74 \ubc29\uc1a1\uad6d\uc740 \uadf8 \uc0ac\uc6a9\uc790\uc5d0\uac8c\uc11c \uc2dc\uccad\ub8cc\ub97c \ubc1b\uac8c \ub41c\ub2e4.<br \/>\r\n<br \/>\r\n\ubc29\uc1a1\ub77c\uc778\uc744 \uc801\uc808\ud788 \uc124\uce58\ud574\uc11c \ubc29\uc1a1\uad6d\uc774 \uc190\ud574\ub97c \ubcf4\uc9c0 \uc54a\uc73c\uba74\uc11c \ubc29\uc1a1\uc744 \ud574\uc904 \uc218 \uc788\ub294 \ucd5c\ub300 \uc0ac\uc6a9\uc790\ub294 \uba87 \uba85\uc778\uac00? (\uc190\ud574\ub97c \ubcf4\uc9c0 \uc54a\ub294\ub2e4\ub294 \ub9d0\uc740 \ucd1d \uc2dc\uccad\ub8cc - \ucd1d \ubc29\uc1a1 \ube44\uc6a9 &ge; 0 \uc784\uc744 \uc758\ubbf8\ud55c\ub2e4)","input":"<p>\uccab \uc904\uc5d0 N M\uc774 \uc785\ub825\ub41c\ub2e4. (2 &le; N &le; 3,000, 1 &le; M &le; N-1)<br \/>\r\nN\uc740 \ud2b8\ub9ac\uc758 \ub178\ub4dc \uac1c\uc218\uc774\uace0 M\uc740 \ud2b8\ub9ac\uc758 \ud130\ubbf8\ub110 \ub178\ub4dc \uac1c\uc218\uc774\ub2e4.<br \/>\r\n\ub178\ub4dc\uc758 \ubc88\ud638\ub294 \ud2b8\ub9ac\uc758 \ub8e8\ud2b8\uac00 1\uc774\uba70, \ub8e8\ud2b8\uac00 \uc544\ub2cc \ub2e4\ub978 \uc1a1\uc2e0\uae30\ub4e4\uc740 2\ubd80\ud130 N-M\uae4c\uc9c0, \uc0ac\uc6a9\uc790\ub4e4(\ud130\ubbf8\ub110\ub178\ub4dc\ub4e4)\uc758 \ubc88\ud638\ub294 N-M+1\ubd80\ud130 N\uae4c\uc9c0 \uc774\ub2e4.<br \/>\r\n\ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 N-M\uac1c\uc758 \uc904\uc5d0 \ub2e4\uc74c\uacfc \uac19\uc740 \ud615\uc2dd\uc73c\ub85c \uc1a1\uc2e0\uae30 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<br \/>\r\nK A1 C1 A2 C2 ... Ak Ck<br \/>\r\nK\ub294 \uadf8 \uc1a1\uc2e0\uae30\uac00 \uc1a1\uc2e0\ud558\ub294 \ub178\ub4dc\uc758 \uac1c\uc218\uc774\uba70 A\ub294 \uadf8 \ub178\ub4dc\uc758 \uc774\ub984 C\ub294 \uadf8 \ube44\uc6a9\uc744 \uc758\ubbf8\ud55c\ub2e4.<br \/>\r\n\uadf8 \uc774\ud6c4\uc758 M\uac1c\uc758 \ub77c\uc778\uc5d0\ub294 M\uba85\uc758 \uc0ac\uc6a9\uc790\uc758 \uc2dc\uccad\ub8cc\uac00 \uac01\uac01 \uc785\ub825\ub41c\ub2e4.","output":"<p>\ucd5c\ub300 \uc0ac\uc6a9\uc790 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"1815","problem_lang":"1","title":"Telephone Lines","description":"<p>A TV-network plans to broadcast an important football match. Their network of transmitters and users can be represented as a tree. The root of the tree is a transmitter that emits the football match, the leaves of the tree are the potential users and other vertices in the tree are relays (transmitters).&nbsp;<\/p>\r\n\r\n<p>The price of transmission of a signal from one transmitter to another or to the user is given. A price of the entire broadcast is the sum of prices of all individual signal transmissions.&nbsp;<\/p>\r\n\r\n<p>Every user is ready to pay a certain amount of money to watch the match and the TV-network then decides whether or not to provide the user with the signal.&nbsp;<\/p>\r\n\r\n<p>Write a program that will find the maximal number of users able to watch the match so that the TVnetwork&rsquo;s doesn&rsquo;t lose money from broadcasting the match.<\/p>\r\n","input":"<p>The first line of the input file contains two integers N and M, 2 &le; N &le; 3000, 1 &le; M &le; N-1, the number of vertices in the tree and the number of potential users.&nbsp;<\/p>\r\n\r\n<p>The root of the tree is marked with the number 1, while other transmitters are numbered 2 to N-M and potential users are numbered N-M+1 to N.&nbsp;<\/p>\r\n\r\n<p>The following N-M lines contain data about the transmitters in the following form:&nbsp;<\/p>\r\n\r\n<p>K A<sub>1<\/sub> C<sub>1<\/sub> A<sub>2<\/sub> C<sub>2<\/sub> ... A<sub>K<\/sub> C<sub>K<\/sub><\/p>\r\n\r\n<p>Means that a transmitter transmits the signal to K transmitters or users, every one of them described by the pair of numbers A and C, the transmitter or user&rsquo;s number and the cost of transmitting the signal to them.&nbsp;<\/p>\r\n\r\n<p>The last line contains the data about users, containing M integers representing respectively the price every one of them is willing to pay to watch the match.&nbsp;<\/p>\r\n","output":"<p>The first and the only line of the output file should contain the maximal number of users described in the above text.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]