Predict Outcome of the Game

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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).

输入输出样例

输入样例 #1

5
3 0 0 0
3 3 0 0
6 4 1 0
6 3 3 0
3 3 3 2

输出样例 #1

yes
yes
yes
no
no

说明

Sample 1. There has not been any match up to now $ (k=0,d_{1}=0,d_{2}=0) $ . If there will be three matches (1-2, 2-3, 3-1) and each team wins once, then at the end each team will have 1 win. Sample 2. You missed all the games $ (k=3) $ . As $ d_{1}=0 $ and $ d_{2}=0 $ , and there is a way to play three games with no winner of tournament (described in the previous sample), the answer is "yes". Sample 3. You missed 4 matches, and $ d_{1}=1,d_{2}=0 $ . These four matches can be: 1-2 (win 2), 1-3 (win 3), 1-2 (win 1), 1-3 (win 1). Currently the first team has 2 wins, the second team has 1 win, the third team has 1 win. Two remaining matches can be: 1-2 (win 2), 1-3 (win 3). In the end all the teams have equal number of wins (2 wins).