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). 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).