{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":" \n \u003cp\u003eThere are N colored nodes, numbered from 1 to N. Initially, the color of Node i is Color i. There are M edges between some pairs of nodes.\u003c/p\u003e \n \u003cp\u003eAt the beginning of the (i+kN)\u003csup\u003eth\u003c/sup\u003e minute, the colors of the nodes that adjacent to Node i will be set to the same color as Node i, where k is a non-negative integer.\u003c/p\u003e \n \u003cp\u003eThe following pictures are examples.\u003c/p\u003e \n \u003cp\u003e\u003cimg src\u003d\"CDN_BASE_URL/482ce84477be3aa0af786e90d510d903?v\u003d1657373523\" title\u003d\"i.png\"\u003e\u003cbr\u003e\u003c/p\u003e \n \u003cp\u003eAt the beginning of the 1\u003csup\u003est\u003c/sup\u003e minute, the color of Node 2 is set to 1.\u003c/p\u003e \n \u003cp\u003eAt the beginning of the 2\u003csup\u003end\u003c/sup\u003e minute, the color of Node 1 and 5 is set to 1. \u003c/p\u003e \n \u003cp\u003eAt the beginning of the 3\u003csup\u003erd\u003c/sup\u003e minute, the color of Node 4 and 5 is set to 3. \u003c/p\u003e \n \u003cp\u003eAt the beginning of the 4\u003csup\u003eth\u003c/sup\u003e minute, the color of Node 3 and 5 is set to 3. \u003c/p\u003e \n \u003cp\u003eAt the beginning of the 5\u003csup\u003eth\u003c/sup\u003e minute, the color of Node 2, 3 and 4 is set to 3.\u003c/p\u003e \n \u003cp\u003eAt the beginning of the 6\u003csup\u003eth\u003c/sup\u003e minute, the color of Node 2 is set to 1.\u003c/p\u003e \n \u003cp\u003e……\u003c/p\u003e \n \u003cp\u003eAssume the number of nodes that are color i during the j\u003csup\u003eth\u003c/sup\u003e minute is D(i,j). And assume\u003c/p\u003e \n \u003cp\u003e\u003cimg src\u003d\"CDN_BASE_URL/67d03de733e22e802db3d7354d2bcf39?v\u003d1657373523\" title\u003d\"i2.png\"\u003e\u003cbr\u003e\u003c/p\u003e \n \u003cp\u003eYour task is to calculate F(i) for all i range from 1 to N.\u003c/p\u003e \n "}},{"title":"Input","value":{"format":"HTML","content":" \n \u003cp\u003eThe input consists of multiple test cases. (Up to 20)\u003c/p\u003e \n \u003cp\u003eFor each test case:\u003c/p\u003e \n \u003cp\u003eThe first line contains two integers N and M, indicating the number of nodes and the number of edges. (1≤N,M≤10\u003csup\u003e5\u003c/sup\u003e)\u003c/p\u003e \n \u003cp\u003eM lines follow, each line contains two integers a and b, indicating that there is an edge between Node a and Node b. (1≤a,b≤N)\u003c/p\u003e \n "}},{"title":"Output","value":{"format":"HTML","content":" \n \u003cp\u003e\u003cspan\u003eFor each test case, output all F(i) that satisfy F(i)≠0, rounded to six decimal places and sorted in descending order.\u003c/span\u003e\u003c/p\u003e \n \u003c/div\u003e \n "}},{"title":"Sample Input","value":{"format":"HTML","content":" \n \u003cpre\u003e5 5\r\n1 2\r\n2 5\r\n3 4\r\n4 5\r\n3 5\r\n5 4\r\n1 2\r\n2 5\r\n5 4\r\n4 3\u003c/pre\u003e \n "}},{"title":"Sample Output","value":{"format":"HTML","content":" \n \u003cpre\u003e3.000000\r\n2.000000\r\n2.800000\r\n2.200000\u003c/pre\u003e \n "}}]}