트리와 쿼리

$1$부터 $N$까지 $N$개의 정점으로 이루어진 트리가 있다. $i$번째 간선은 서로 다른 두 정점 $A_i$, $B_i$를 잇는다. ($1 ≤ i ≤ N - 1$)

$N$개의 정점 중 몇 개를 골라, 그 고른 정점들을 $S = \{s_1, s_2, \dots , s_K\}$라고 하자. 또한, $s_i = v$를 만족하는 $i$ ($1 ≤ i ≤ K$)가 존재할 때, 정점 $v$가 $S$에 속한다고 부르자.

$S$에 속하는 서로 다른 두 정점 $u$, $v$에 대하여, $S$에 속하는 정점만을 이용하여 트리 위에서 $u$, $v$ 사이를 오갈 수 있다면, “$u$와 $v$는 $S$ 위에서 연결되어 있다”고 하자.

예를 들어, 아래와 같은 트리를 생각하자. ($N = 7$)

만일, $K = 6$, $S = \{1, 2, 3, 4, 5, 6\}$라면, “$1$과 $2$”, “$3$과 $5$”, “$4$와 $6$”은 각각 서로 $S$ 위에서 연결되어 있다. 그러나, “$1$과 $6$”, “$2$와 $7$”은 각각 서로 $S$ 위에서 연결되어 있지 않다.

다음 조건을 모두 만족하는 정점쌍 $(u, v)$의 개수를 $S$의 연결 강도라고 하자.

1. $u$와 $v$는 서로 다른 두 정점.
2. $1 ≤ u < v ≤ N$.
3. $u$와 $v$는 $S$ 위에서 연결되어 있다.

고른 정점들 $S$가 주어질 때, $S$의 연결 강도를 계산하는 프로그램을 작성하라. 여러분은 이러한 질의 $Q$개에 대하여 모두 답해야 한다.

Limit

• $2 ≤ N ≤ 250\,000$
• $1 ≤ Q ≤ 100\,000$
• 모든 $i$ ($1 ≤ i ≤ N - 1$)에 대해, $1 ≤ A_i ≤ N$.
• 모든 $i$ ($1 ≤ i ≤ N - 1$)에 대해, $1 ≤ B_i ≤ N$.
• 모든 $i$ ($1 ≤ i ≤ N - 1$)에 대해, $A_i ≠ B_i$.
• 주어지는 그래프는 트리이다.
• 모든 질의에 대해, $1 ≤ K ≤ N$.
• 각 질의에서, 모든 $i$ ($1 ≤ i ≤ K$)에 대해, $1 ≤ s_i ≤ N$.
• 각 질의에서, 고른 $K$개의 정점 $s_1, \dots , s_K$는 서로 다르다.
• $Q$개의 질의에서 주어지는 $K$들의 합은 $1\,000\,000$ 이하이다.

Subtask

Lang Base64

[{"problem_id":"25402","problem_lang":"0","title":"\ud2b8\ub9ac\uc640 \ucffc\ub9ac","description":"<p>$1$\ubd80\ud130 $N$\uae4c\uc9c0 $N$\uac1c\uc758 \uc815\uc810\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ud2b8\ub9ac\uac00 \uc788\ub2e4. $i$\ubc88\uc9f8 \uac04\uc120\uc740 \uc11c\ub85c \ub2e4\ub978 \ub450 \uc815\uc810 $A_i$, $B_i$\ub97c \uc787\ub294\ub2e4. ($1 &le; i &le; N - 1$)<\/p>\r\n\r\n<p>$N$\uac1c\uc758 \uc815\uc810 \uc911 \uba87 \uac1c\ub97c \uace8\ub77c, \uadf8 \uace0\ub978 \uc815\uc810\ub4e4\uc744 $S = \\{s_1, s_2, \\dots , s_K\\}$\ub77c\uace0 \ud558\uc790. \ub610\ud55c, $s_i = v$\ub97c \ub9cc\uc871\ud558\ub294 $i$ ($1 &le; i &le; K$)\uac00 \uc874\uc7ac\ud560 \ub54c, \uc815\uc810 $v$\uac00 $S$\uc5d0 \uc18d\ud55c\ub2e4\uace0 \ubd80\ub974\uc790.<\/p>\r\n\r\n<p>$S$\uc5d0 \uc18d\ud558\ub294 \uc11c\ub85c \ub2e4\ub978 \ub450 \uc815\uc810 $u$, $v$\uc5d0 \ub300\ud558\uc5ec, $S$\uc5d0 \uc18d\ud558\ub294 \uc815\uc810\ub9cc\uc744 \uc774\uc6a9\ud558\uc5ec \ud2b8\ub9ac \uc704\uc5d0\uc11c $u$, $v$ \uc0ac\uc774\ub97c \uc624\uac08 \uc218 \uc788\ub2e4\uba74, &ldquo;$u$\uc640 $v$\ub294 $S$ \uc704\uc5d0\uc11c \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4&rdquo;\uace0 \ud558\uc790.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, \uc544\ub798\uc640 \uac19\uc740 \ud2b8\ub9ac\ub97c \uc0dd\uac01\ud558\uc790. ($N = 7$)<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/718e7c6d-b718-45a0-84b7-0ed67bd01c22\/-\/preview\/\" style=\"width: 259px; height: 145px;\" \/><\/p>\r\n\r\n<p>\ub9cc\uc77c, $K = 6$, $S = \\{1, 2, 3, 4, 5, 6\\}$\ub77c\uba74, &ldquo;$1$\uacfc $2$&rdquo;, &ldquo;$3$\uacfc $5$&rdquo;, &ldquo;$4$\uc640 $6$&rdquo;\uc740 \uac01\uac01 \uc11c\ub85c $S$ \uc704\uc5d0\uc11c \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4. \uadf8\ub7ec\ub098, &ldquo;$1$\uacfc $6$&rdquo;, &ldquo;$2$\uc640 $7$&rdquo;\uc740 \uac01\uac01 \uc11c\ub85c $S$ \uc704\uc5d0\uc11c \uc5f0\uacb0\ub418\uc5b4 \uc788\uc9c0 \uc54a\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\ud558\ub294 \uc815\uc810\uc30d $(u, v)$\uc758 \uac1c\uc218\ub97c $S$\uc758 \uc5f0\uacb0 \uac15\ub3c4\ub77c\uace0 \ud558\uc790.<\/p>\r\n\r\n<ol>\r\n\t<li>$u$\uc640 $v$\ub294 \uc11c\ub85c \ub2e4\ub978 \ub450 \uc815\uc810.<\/li>\r\n\t<li>$1 &le; u &lt; v &le; N$.<\/li>\r\n\t<li>$u$\uc640 $v$\ub294 $S$ \uc704\uc5d0\uc11c \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uace0\ub978 \uc815\uc810\ub4e4 $S$\uac00 \uc8fc\uc5b4\uc9c8 \ub54c, $S$\uc758 \uc5f0\uacb0 \uac15\ub3c4\ub97c \uacc4\uc0b0\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\ub77c. \uc5ec\ub7ec\ubd84\uc740 \uc774\ub7ec\ud55c \uc9c8\uc758 $Q$\uac1c\uc5d0 \ub300\ud558\uc5ec \ubaa8\ub450 \ub2f5\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \uc815\uc218 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c ($N - 1$)\uac1c\uc758 \uc904\uc5d0 \uac01 \uac04\uc120\uc5d0 \ub300\ud55c \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc911 $i$ ($1 &le; i &le; N - 1$)\ubc88\uc9f8 \uc904\uc5d0\ub294 \ub450 \uc815\uc218 $A_i$, $B_i$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0 \uc815\uc218 $Q$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $Q$\uac1c\uc758 \uc904\uc5d0 \uac01 \uc9c8\uc758\uc5d0 \ub300\ud55c \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc911 $i$ ($1 &le; i &le; Q$)\ubc88\uc9f8 \uc904\uc740 $i$\ubc88\uc9f8 \uc9c8\uc758\ub97c \ub098\ud0c0\ub0b4\uba70, \uc815\uc218 $K$\uc640 $K$\uac1c\uc758 \uc815\uc218 $s_1, \\dots , s_K$\uac00 \ucc28\ub840\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uccab \ubc88\uc9f8 \uc904\ubd80\ud130 $Q$\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0, \uac01 \uc9c8\uc758\uc5d0 \ub300\ud55c \ub2f5\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc774 \uc911 $i$ ($1 &le; i &le; Q$)\ubc88\uc9f8 \uc904\uc5d0\ub294 $i$\ubc88\uc9f8 \uc9c8\uc758\uc5d0\uc11c \uc8fc\uc5b4\uc9c4 $S$\uc5d0 \ub300\ud558\uc5ec, $S$\uc758 \uc5f0\uacb0 \uac15\ub3c4\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$2 &le; N &le; 250\\,000$<\/li>\r\n\t<li>$1 &le; Q &le; 100\\,000$<\/li>\r\n\t<li>\ubaa8\ub4e0 $i$ ($1 &le; i &le; N - 1$)\uc5d0 \ub300\ud574, $1 &le; A_i &le; N$.<\/li>\r\n\t<li>\ubaa8\ub4e0 $i$ ($1 &le; i &le; N - 1$)\uc5d0 \ub300\ud574, $1 &le; B_i &le; N$.<\/li>\r\n\t<li>\ubaa8\ub4e0 $i$ ($1 &le; i &le; N - 1$)\uc5d0 \ub300\ud574, $A_i &ne; B_i$.<\/li>\r\n\t<li>\uc8fc\uc5b4\uc9c0\ub294 \uadf8\ub798\ud504\ub294 \ud2b8\ub9ac\uc774\ub2e4.<\/li>\r\n\t<li>\ubaa8\ub4e0 \uc9c8\uc758\uc5d0 \ub300\ud574, $1 &le; K &le; N$.<\/li>\r\n\t<li>\uac01 \uc9c8\uc758\uc5d0\uc11c, \ubaa8\ub4e0 $i$ ($1 &le; i &le; K$)\uc5d0 \ub300\ud574, $1 &le; s_i &le; N$.<\/li>\r\n\t<li>\uac01 \uc9c8\uc758\uc5d0\uc11c, \uace0\ub978 $K$\uac1c\uc758 \uc815\uc810 $s_1, \\dots , s_K$\ub294 \uc11c\ub85c \ub2e4\ub974\ub2e4.<\/li>\r\n\t<li>$Q$\uac1c\uc758 \uc9c8\uc758\uc5d0\uc11c \uc8fc\uc5b4\uc9c0\ub294 $K$\ub4e4\uc758 \ud569\uc740 $1\\,000\\,000$ \uc774\ud558\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N = 3$.<\/p>\r\n","subtask2":"<p>$N &le; 50$, $Q &le; 50$.<\/p>\r\n","subtask3":"<p>$N &le; 2\\,500$, $Q &le; 2\\,500$.<\/p>\r\n","subtask4":"<p>\uac01 \uc9c8\uc758\uc5d0\uc11c, $K = 3$.<\/p>\r\n","subtask5":"<p>\ucd94\uac00 \uc81c\uc57d \uc870\uac74 \uc5c6\uc74c.<\/p>\r\n"},{"problem_id":"25402","problem_lang":"1","title":"Query on a Tree","description":"<p>You are given a tree where vertices are labeled with integers $1, 2, \\ldots, N$.&nbsp;<\/p>\r\n\r\n<p>For a subset of vertices $S \\subseteq \\{1, 2, \\ldots, N\\}$, we say two vertices $(u, v)$ are <em>connected under<\/em>&nbsp;$S$ if there exists a path that only passes through the vertices in $S$. Note that this includes endpoints of the path, so $u, v \\in S$ should hold.<\/p>\r\n\r\n<p>For example, consider the following tree and the set $S = \\{1, 2, 3, 4, 5, 6\\}$.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/00507a6e-b27b-4a92-b3d3-f2ca18b87750\/-\/preview\/\" style=\"width: 259px; height: 145px;\" \/><\/p>\r\n\r\n<p>In this case, $(1, 2)$, $(3, 5)$ and $(4, 6)$ are connected under $S$, while $(1, 6)$ and $(2, 7)$ are not connected under~$S$.<\/p>\r\n\r\n<p>Let $\\mathit{strength}(S)$ be the number of pairs of vertices $(u, v)$ such that $u \\neq v$ and $(u, v)$ are connected under $S$. You are given $Q$ queries, where each query contains a set $S$. For each query, you should compute the quantity $\\mathit{strength}(S)$.<\/p>\r\n","input":"<p>The first line contains a single integer $N$, the number of vertices ($2 \\le N \\le 250\\,000$).<\/p>\r\n\r\n<p>Each of the next $N - 1$ lines contains two space-separated integers $a$ and $b$: the vertices connected by an edge ($1 \\le a, b \\le N$). Together, the edges form a tree.<\/p>\r\n\r\n<p>The next line contains a single integer $Q$, the number of queries ($1 \\le Q \\le 100\\,000$).<\/p>\r\n\r\n<p>Each of the next $Q$ lines contains a query, denoted by space-separated integers. A query starts with an integer $K$, the size of the set ($1 \\le K \\le N$). It is followed by $K$ distinct integers from $1$ to $N$ in arbitrary order: the vertices of set $S$.<\/p>\r\n\r\n<p>The sum of $K$ in each test case is at most $1\\,000\\,000$.<\/p>\r\n","output":"<p>For each of the $Q$ queries, print a single line with the integer $\\mathit{strength}(S)$ as defined above.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","subtask1":"<p>$N = 3$.<\/p>\r\n","subtask2":"<p>$N &le; 50$, $Q &le; 50$.<\/p>\r\n","subtask3":"<p>$N &le; 2\\,500$, $Q &le; 2\\,500$.<\/p>\r\n","subtask4":"<p>\uac01 \uc9c8\uc758\uc5d0\uc11c, $K = 3$.<\/p>\r\n","subtask5":"<p>\ucd94\uac00 \uc81c\uc57d \uc870\uac74 \uc5c6\uc74c.<\/p>\r\n"}]

채점 및 기타 정보

• 예제는 채점하지 않는다.

첫 번째 줄에 정수 $N$이 주어진다.

다음 ($N - 1$)개의 줄에 각 간선에 대한 정보가 주어진다. 이 중 $i$ ($1 ≤ i ≤ N - 1$)번째 줄에는 두 정수 $A_i$, $B_i$가 주어진다.

다음 줄에 정수 $Q$가 주어진다.

다음 $Q$개의 줄에 각 질의에 대한 정보가 주어진다. 이 중 $i$ ($1 ≤ i ≤ Q$)번째 줄은 $i$번째 질의를 나타내며, 정수 $K$와 $K$개의 정수 $s_1, \dots , s_K$가 차례대로 주어진다.

첫 번째 줄부터 $Q$개의 줄에 걸쳐, 각 질의에 대한 답을 출력한다. 이 중 $i$ ($1 ≤ i ≤ Q$)번째 줄에는 $i$번째 질의에서 주어진 $S$에 대하여, $S$의 연결 강도를 출력한다.