문제
흐즈로는 그래프 이론을 공부하다가 흥미로운 그래프를 발견했습니다. 다음의 특징을 가지는 단순 무향 그래프를 Y라고 부릅시다.
- 4ドル$개의 정점과 3ドル$개의 간선을 가집니다.
- 하나의 정점을 루트라고 부르며, 나머지 3ドル$개의 정점을 리프라고 부릅니다.
- 3ドル$개의 간선은 각각의 리프와 루트를 연결합니다.
흐즈로는 Y의 성질이 매우 특이하다고 생각하여, 어떤 그래프 안에 Y가 몇 개나 존재하는지 세어 보기로 했습니다. 단순 무향 그래프에서 Y의 개수를 다음과 같이 정의합시다.
- 그래프에서 3ドル$개의 간선을 순서 없이 골랐을 때, 그 간선과 간선이 연결하는 정점들이 이루는 그래프가 Y가 되는 경우의 수를 그래프의 Y의 개수로 정의합니다.
단순 무향 그래프가 입력으로 주어질 때, 주어진 그래프의 Y의 개수를 출력하세요. 단, 개수가 너무 많을 수 있으니 개수를 소수 10ドル^9+7$로 나눈 나머지를 출력하세요.
출력
주어진 그래프의 Y의 개수를 10ドル^9 + 7$로 나눈 나머지를 출력하세요.
그래프에서 간선 3ドル$개를 선택해 만들어진 부분 그래프가 Y가 되는 경우는 다음과 같습니다.
- $(1,2),ドル $(1,3),ドル $(1,4)$를 선택합니다.
- $(1,2),ドル $(2,3),ドル $(2,4)$를 선택합니다.
- $(1,3),ドル $(2,3),ドル $(3,4)$를 선택합니다.
- $(1,4),ドル $(2,4),ドル $(3,4)$를 선택합니다.
따라서 예제의 그래프의 Y의 개수는 4ドル$입니다. 4ドル \equiv 4 \pmod{10^9+7}$이므로 4ドル$를 출력해야 합니다.
[{"problem_id":"31217","problem_lang":"0","title":"Y","description":"<p>\ud750\uc988\ub85c\ub294 \uadf8\ub798\ud504 \uc774\ub860\uc744 \uacf5\ubd80\ud558\ub2e4\uac00 \ud765\ubbf8\ub85c\uc6b4 \uadf8\ub798\ud504\ub97c \ubc1c\uacac\ud588\uc2b5\ub2c8\ub2e4. \ub2e4\uc74c\uc758 \ud2b9\uc9d5\uc744 \uac00\uc9c0\ub294 \ub2e8\uc21c \ubb34\ud5a5 \uadf8\ub798\ud504\ub97c <strong>Y<\/strong>\ub77c\uace0 \ubd80\ub985\uc2dc\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$4$\uac1c\uc758 \uc815\uc810\uacfc $3$\uac1c\uc758 \uac04\uc120\uc744 \uac00\uc9d1\ub2c8\ub2e4.<\/li>\r\n\t<li>\ud558\ub098\uc758 \uc815\uc810\uc744 <strong>\ub8e8\ud2b8<\/strong>\ub77c\uace0 \ubd80\ub974\uba70, \ub098\uba38\uc9c0 $3$\uac1c\uc758 \uc815\uc810\uc744 <strong>\ub9ac\ud504<\/strong>\ub77c\uace0 \ubd80\ub985\ub2c8\ub2e4.<\/li>\r\n\t<li>$3$\uac1c\uc758 \uac04\uc120\uc740 \uac01\uac01\uc758 \ub9ac\ud504\uc640 \ub8e8\ud2b8\ub97c \uc5f0\uacb0\ud569\ub2c8\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ud750\uc988\ub85c\ub294 <strong>Y<\/strong>\uc758 \uc131\uc9c8\uc774 \ub9e4\uc6b0 \ud2b9\uc774\ud558\ub2e4\uace0 \uc0dd\uac01\ud558\uc5ec, \uc5b4\ub5a4 \uadf8\ub798\ud504 \uc548\uc5d0 <strong>Y<\/strong>\uac00 \uba87 \uac1c\ub098 \uc874\uc7ac\ud558\ub294\uc9c0 \uc138\uc5b4 \ubcf4\uae30\ub85c \ud588\uc2b5\ub2c8\ub2e4. \ub2e8\uc21c \ubb34\ud5a5 \uadf8\ub798\ud504\uc5d0\uc11c <strong>Y\uc758 \uac1c\uc218<\/strong>\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud569\uc2dc\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uadf8\ub798\ud504\uc5d0\uc11c $3$\uac1c\uc758 \uac04\uc120\uc744 \uc21c\uc11c \uc5c6\uc774 \uace8\ub790\uc744 \ub54c, \uadf8 \uac04\uc120\uacfc \uac04\uc120\uc774 \uc5f0\uacb0\ud558\ub294 \uc815\uc810\ub4e4\uc774 \uc774\ub8e8\ub294 \uadf8\ub798\ud504\uac00 <strong>Y<\/strong>\uac00 \ub418\ub294 \uacbd\uc6b0\uc758 \uc218\ub97c \uadf8\ub798\ud504\uc758 <strong>Y\uc758 \uac1c\uc218<\/strong>\ub85c \uc815\uc758\ud569\ub2c8\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub2e8\uc21c \ubb34\ud5a5 \uadf8\ub798\ud504\uac00 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c8 \ub54c, \uc8fc\uc5b4\uc9c4 \uadf8\ub798\ud504\uc758 <strong>Y\uc758 \uac1c\uc218<\/strong>\ub97c \ucd9c\ub825\ud558\uc138\uc694. \ub2e8, \uac1c\uc218\uac00 \ub108\ubb34 \ub9ce\uc744 \uc218 \uc788\uc73c\ub2c8 \uac1c\uc218\ub97c \uc18c\uc218 $10^9+7$\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud558\uc138\uc694.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \uc815\uc810\uc758 \uac1c\uc218 $n$\uacfc \uac04\uc120\uc758 \uac1c\uc218 $m$\uc774 \uacf5\ubc31\uc73c\ub85c \ubd84\ub9ac\ub418\uc5b4 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. ($1 \\le n \\le 10^5$, $0 \\le m \\le \\min(\\frac{n(n-1)}{2},2\\times 10^5)$)<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 $m$\uac1c\uc758 \uc904\uc5d0 $i$\ubc88\uc9f8 \uac04\uc120\uc774 \uc5f0\uacb0\ud558\ub294 \uc815\uc810 $u$\uc640 $v$\uac00 \uacf5\ubc31\uc73c\ub85c \ubd84\ub9ac\ub418\uc5b4 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. ($1 \\le u,v \\le n$, $u \\neq v$)<\/p>\r\n\r\n<p>\uc8fc\uc5b4\uc9c4 \uadf8\ub798\ud504\ub294 \uc911\ubcf5 \uac04\uc120\uc774\ub098 \uc591 \ub05d\uc810\uc774 \uac19\uc740 \uac04\uc120\uc744 \uac00\uc9c0\uc9c0 \uc54a\uc74c\uc774 \ubcf4\uc7a5\ub429\ub2c8\ub2e4.<\/p>\r\n","output":"<p>\uc8fc\uc5b4\uc9c4 \uadf8\ub798\ud504\uc758 <strong>Y\uc758 \uac1c\uc218<\/strong>\ub97c $10^9 + 7$\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud558\uc138\uc694.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p>\uadf8\ub798\ud504\uc5d0\uc11c \uac04\uc120 $3$\uac1c\ub97c \uc120\ud0dd\ud574 \ub9cc\ub4e4\uc5b4\uc9c4 \ubd80\ubd84 \uadf8\ub798\ud504\uac00&nbsp;<strong>Y<\/strong>\uac00 \ub418\ub294 \uacbd\uc6b0\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$(1,2)$, $(1,3)$, $(1,4)$\ub97c \uc120\ud0dd\ud569\ub2c8\ub2e4.<\/li>\r\n\t<li>$(1,2)$, $(2,3)$, $(2,4)$\ub97c \uc120\ud0dd\ud569\ub2c8\ub2e4.<\/li>\r\n\t<li>$(1,3)$, $(2,3)$, $(3,4)$\ub97c \uc120\ud0dd\ud569\ub2c8\ub2e4.<\/li>\r\n\t<li>$(1,4)$, $(2,4)$, $(3,4)$\ub97c \uc120\ud0dd\ud569\ub2c8\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub530\ub77c\uc11c \uc608\uc81c\uc758 \uadf8\ub798\ud504\uc758 <strong>Y\uc758 \uac1c\uc218<\/strong>\ub294 $4$\uc785\ub2c8\ub2e4. $4 \\equiv 4 \\pmod{10^9+7}$\uc774\ubbc0\ub85c $4$\ub97c \ucd9c\ub825\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\r\n"},{"problem_id":"31217","problem_lang":"1","title":"Y","description":"<p>While studying graph theory, Chromate found an interesting type of graphs. Let us call a simple undirected graph <strong>Y<\/strong> if it has the following properties.<\/p>\r\n\r\n<ul>\r\n\t<li>It contains $4$ vertices and $3$ edges.<\/li>\r\n\t<li>One vertex is called the <strong>root<\/strong>, and the $3$ other vertices are called the <strong>leaves<\/strong>.<\/li>\r\n\t<li>Each of the $3$ edges connect the root and one leaf.<\/li>\r\n<\/ul>\r\n\r\n<p>Chromate, thinking that the property of <strong>Y<\/strong> is very unique, decided to count how many <strong>Y<\/strong>&nbsp;are contained in some graph. Let us define the <strong>cardinality of Y<\/strong> of a simple undirected graph as follows.<\/p>\r\n\r\n<ul>\r\n\t<li>When we select $3$ different edges without order in the graph, the number of cases such that the graph consisting of the edges and all incident vertices is <strong>Y<\/strong>, is called the <strong>cardinality of Y<\/strong>&nbsp;of that graph.<\/li>\r\n<\/ul>\r\n\r\n<p>Given a simple undirected graph as input, output the <strong>cardinality of Y<\/strong>&nbsp;of the given graph. As the answer can be too large, you should output the answer modulo $10^9+7$.<\/p>\r\n","input":"<p>On the first line, two integers $n$ and $m$ &mdash; the number of vertices and edges &mdash; are given. ($1 \\le n \\le 10^5$, $0 \\le m \\le \\min(\\frac{n(n-1)}{2},2\\times 10^5)$)<\/p>\r\n\r\n<p>Each of the following $m$ lines contain two vertices $u$ and $v$ connected by the $i$-th edge. ($1 \\le u,v \\le n$, $u \\neq v$)<\/p>\r\n\r\n<p>It is guaranteed that the given graph does not contain duplicate edges or self loops.<\/p>\r\n","output":"<p>On one line, output the <strong>cardinality of Y<\/strong> of the given graph modulo $10^9+7$.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","sample_explain_1":"<p>The cases that the subgraph constructed by selecting $3$ edges is <strong>Y<\/strong>&nbsp;is as follows.<\/p>\r\n\r\n<ul>\r\n\t<li>Select&nbsp;$(1,2)$, $(1,3)$, $(1,4)$.<\/li>\r\n\t<li>Select $(1,2)$, $(2,3)$, $(2,4)$.<\/li>\r\n\t<li>Select $(1,3)$, $(2,3)$, $(3,4)$.<\/li>\r\n\t<li>Select $(1,4)$, $(2,4)$, $(3,4)$.<\/li>\r\n<\/ul>\r\n\r\n<p>Therefore, the <strong>cardinality of Y<\/strong> of the graph given in the examples is $4$. As $4 \\equiv 4 \\pmod{10^9+7}$, you should output $4$.<\/p>\r\n"}]