# Troublemakers

[after seeing that the room is on fire; Ted has a needle in his hand while holding the leg of a dead woman; Sara has a bottle of champagne in her hand, and Juancho is smoking] Man: Did they misbehave? Robert Rodrigues, “The Misbehavers.” Every school class has its troublemakers — those kids who can make the teacher’s life miserable. On his own, a troublemaker is manageable, but when you put certain pairs of troublemakers together in the same room, teaching a class becomes very hard. There are n kids in Mrs. Shaida’s math class, and there are m pairs of troublemakers among them. The situation has gotten so bad that Mrs. Shaida has decided to split the class into two classes. Help her do it in such a way that the number of troublemaker pairs is reduced by at least a half. Input The first line of input gives the number of cases, N. N test cases follow. Each one starts with a line containing n (0 ≤ n ≤ 100) and m (0 < m < 5000). The next m lines will contain a pair of integers u and v meaning that when kids u and v are in the same room, they make a troublemaker pair. Kids are numbered from 1 to n. Output For each test case, output one line containing ‘Case #x:’ followed by L — the number of kids who will be moved to a different class (in a different room). The next line should list those kids. The total number of troublemaker pairs in the two rooms must be at most m/2. If that is impossible, print ‘Impossible.’ instead of L and an empty line afterwards. Sample Input 2 43 12 23 34 46 12 13 14 23 24 34 Sample Output Case #1: 3 134 Case #2: 2 12