{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\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.\u003cbr\u003eYou are given an undirected graph with $n$ vertices, labeled by $1,2,...,n$. Initially the graph has no edges.\u003cbr\u003eThere are $2$ kinds of operations :\u003cbr\u003e + u v, add an edge $(u,v)$ into the graph, multiple edges between same pair of vertices are allowed.\u003cbr\u003e - u v, remove an edge $(u,v)$, it is guaranteed that there are at least one such edge in the graph.\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.\u003cbr\u003e\n\u003c/div\u003e"}},{"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.\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.\u003cbr\u003eFor the next $m$ lines, each line describes an operation, and it is guaranteed that $1\\leq u\u0026lt;v\\leq n$.\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 $10^9+7$.\u003cbr\u003e"}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e\u003cpre\u003e1\t\t\r\n4 8\t\r\n+ 1 2\r\n+ 3 4\r\n+ 1 3\r\n+ 2 4\r\n- 1 2\r\n- 3 4\r\n+ 1 2\r\n+ 3 4\u003c/pre\u003e\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e\u003cpre\u003e1 0\r\n2 1\r\n3 1\r\n4 2\r\n3 1\r\n2 1\r\n3 1\r\n4 2\u003c/pre\u003e\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}