Rope Pulling, also known as Tug of War, is a classic game. After acquiring a very very very large tie under suspicious circumstances, Zhang3 is using it to organize such a game between mathies and engineers.
There are ~n~ mathies and ~m~ engineers. Participant ~i~ has strength ~w_i~ and meme value ~v_i~.
To make the game more interesting, Zhang3 wants to choose the teams to have same total strengths, while maximizing the total meme values of all participants.
Output the maximum meme value possible. Note that empty teams are also allowed.
The first line of the input gives the number of test cases, ~T~ ~(1 \le T \le 30)~. ~T~ test cases follow.
For each test case, the first line contains two integers ~n,m~ ~(1 \le n,m \le 1\,000)~, representing the number of mathies and engineers respectively.
Then ~(n + m)~ lines follow, describing the students. The ~i~th line contains two integers ~w_i, v_i~ ~(1 \le w_i \le 1\,000, -10^9 \le v_i \le 10^9)~, representing the strength and the meme value by the ~i~th participant. The first ~n~ are mathies, while the other ~m~ are engineers. The sum of ~(n + m)~ in all test cases doesn't exceed ~10^4~.
For each test case, print a line with an integer, representing the maximum total meme value of two teams with the same total strength values.
2 3 4 4 7 3 8 2 2 1 4 5 8 1 3 4 4 1 2 1000 -10000 200 3000 800 5000
Problem Resource: 2020 Multi-University Training Contest 4, Hangzhou Xuejun Contest, Problem C