{"trustable":false,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cscript type\u003d\u0027text/x-mathjax-config\u0027\u003eMathJax.Hub.Config({tex2jax: { inlineMath: [[\u0027$\u0027,\u0027$\u0027]] } }); \u003c/script\u003e\n\u003cscript type\u003d\u0027text/javascript\u0027 src\u003d\u0027https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\u0027\u003e\u003c/script\u003e\n\u003cscript type\u003d\u0027text/javascript\u0027\u003esetTimeout(function(){MathJax.Hub.Queue([\u0027Typeset\u0027, MathJax.Hub, \u0027left_view\u0027]);}, 2000);\u003c/script\u003e\n\u003cdiv class\u003d\"panel_content\"\u003e\n In the mathematical discipline of graph theory, a matching in a graph is a set of edges without common vertices. \n \u003cbr\u003eYou are given an undirected graph with $n$ vertices, labeled by $1,2,...,n$. Initially the graph has no edges. \n \u003cbr\u003eThere are $2$ kinds of operations : \n \u003cbr\u003e + u v, add an edge $(u,v)$ into the graph, multiple edges between same pair of vertices are allowed. \n \u003cbr\u003e - u v, remove an edge $(u,v)$, it is guaranteed that there are at least one such edge in the graph. \n \u003cbr\u003eYour task is to compute the number of matchings with exactly $k$ edges after each operation for $k\u003d1,2,3,...,\\frac{n}{2}$. Note that multiple edges between same pair of vertices are considered different. \n \u003cbr\u003e \n给你n个点，m个操作，每种操作要么加一条边要么减一条边，紧接着询问当前选出1条无公共端点的边，2条无公共端点的边，3条.....n/2条无公共端点边时分别有多少种不同的选择。（n\u003c\u003d10） \n\n\u003c/div\u003e\n"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains an integer $T(1\\leq T\\leq10)$, denoting the number of test cases. \n\u003cbr\u003eIn each test case, there are $2$ integers $n,m(2\\leq n\\leq 10,n \\bmod 2\u003d0,1\\leq m\\leq 30000)$, denoting the number of vertices and operations. \n\u003cbr\u003eFor the next $m$ lines, each line describes an operation, and it is guaranteed that $1\\leq u\u0026lt;v\\leq n$. \n\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each operation, print a single line containing $\\frac{n}{2}$ integers, denoting the answer for $k\u003d1,2,3,...,\\frac{n}{2}$. Since the answer may be very large, please print the answer modulo $10^9+7$. \n\u003cbr\u003e"}},{"title":"Sample Input","value":{"format":"HTML","content":"\u003cpre\u003e1\t\t\n4 8\t\n+ 1 2\n+ 3 4\n+ 1 3\n+ 2 4\n- 1 2\n- 3 4\n+ 1 2\n+ 3 4\u003c/pre\u003e"}},{"title":"Sample Output","value":{"format":"HTML","content":"\u003cpre\u003e1 0\n2 1\n3 1\n4 2\n3 1\n2 1\n3 1\n4 2\u003c/pre\u003e"}}]}