A9479 | Predict Outcome of the Game

There are $n$ games in a football tournament. Three teams are participating in it. Currently $k$ games had already been played.

You are an avid football fan, but recently you missed the whole $k$ games. Fortunately, you remember a guess of your friend for these $k$ games. Your friend did not tell exact number of wins of each team, instead he thought that absolute difference between number of wins of first and second team will be $d_{1}$ and that of between second and third team will be $d_{2}$ .

You don't want any of team win the tournament, that is each team should have the same number of wins after $n$ games. That's why you want to know: does there exist a valid tournament satisfying the friend's guess such that no team will win this tournament?

Note that outcome of a match can not be a draw, it has to be either win or loss.

The first line of the input contains a single integer corresponding to number of test cases $t$ $(1<=t<=10^{5})$ .

Each of the next $t$ lines will contain four space-separated integers $n,k,d_{1},d_{2}$ $(1<=n<=10^{12}; 0<=k<=n; 0<=d_{1},d_{2}<=k)$ — data for the current test case.

For each test case, output a single line containing either "yes" if it is possible to have no winner of tournament, or "no" otherwise (without quotes).