F. Group Divisiontime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIn the 31st lyceum, there were two groups of olympiad participants: computer science and mathematics. The number of computer scientists was n_1, and the number of mathematicians was n_2. It is not known for certain who belonged to which group, but it is known that there were friendly connections between some pairs of people (these connections could exist between a pair of people from the same group or from different groups).The connections were so strong that even if one person is removed along with all their friendly connections, any pair of people still remains acquainted either directly or through mutual friends.^{\dagger} More formally, two people (x, y) are acquainted in the following case: there are people a_1, a_2, \ldots,a_n (1 \le a_i \le n_1 + n_2) such that the following conditions are simultaneously met:\bullet Person x is directly acquainted with a_1.\bullet Person a_n is directly acquainted with y.\bullet Person a_i is directly acquainted with a_{i + 1} for any (1 \le i \le n - 1).The teachers were dissatisfied with the fact that computer scientists were friends with mathematicians and vice versa, so they decided to divide the students into two groups in such a way that the following two conditions are met:\bullet There were n_1 people in the computer science group, and n_2 people in the mathematics group.\bullet Any pair of computer scientists should be acquainted (acquaintance involving mutual friends, who must be from the same group as the people in the pair, is allowed), the same should be true for mathematicians.Help them solve this problem and find out who belongs to which group.InputEach test consists of several test cases. The first line contains a single integer t (1 \le t \le 1000) — the number of test cases. Then follows the description of the test cases.The first line of each test case contains three integers n_1, n_2, and m (1 \le n_1, n_2 \le 2000, 1 \le m \le 5000). n_1, n_2 are the sizes of the two groups described in the problem, and m is the number of friendly connections initially.The following m lines describe the friendly connections: in the i-th (1 \le i \le m) line, a pair of numbers (a, b) is given, which means that the person with number a is friends with the person with number b (and vice versa).It is guaranteed that for each test case, all friendly connections are distinct.It is guaranteed that the sum of n_1 + n_2 for all test cases does not exceed 2000, and the sum of m for all test cases does not exceed 5000.It is also guaranteed that for each test case, a solution exists.If there are several answers, print any of them.OutputFor each test case, output two lines.In the first line, output n_1 distinct numbers a_i (1 \le a_i \le n_1 + n_2) — the people belonging to the first group.In the second line, output n_2 distinct numbers b_i (1 \le b_i \le n_1 + n_2) — the people belonging to the second group.All numbers must be distinct.If there are several possible answers, print any one.ExampleInput
31 2 32 31 31 21 4 72 53 42 41 23 54 51 53 3 71 21 62 32 53 44 54 6Output
3 
1 2 
5 
1 2 3 4 
4 5 6 
1 2 3 
NoteConsider the third test case. The division into groups looks as follows:    The students selected as computer scientists are colored in green, and those selected as mathematicians are colored in blue.Consider all pairs of computer scientists and how they are acquainted:Pairs (4, 5), (4, 6) are directly acquainted.Pair (5, 6) is acquainted through the computer scientist with number 4.Consider all pairs of mathematicians and how they are acquainted:Pairs (1, 2), (2, 3) are directly acquainted.Pair (1, 3) is acquainted through the mathematician with number 2.We conclude that any pair of people belonging to the same group is acquainted with each other, thus the division into two groups is correct.
31 2 32 31 31 21 4 72 53 42 41 23 54 51 53 3 71 21 62 32 53 44 54 6
3  1 2  5  1 2 3 4  4 5 6  1 2 3  
['constructive algorithms', 'dfs and similar', 'graphs', 'greedy', '*2900']