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 d1 and that of between second and third team will be d2.

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.

Input

The first line of the input contains a single integer corresponding to number of test cases t (1 ≤ t ≤ 105).

Each of the next t lines will contain four space-separated integers n, k, d1, d2 (1 ≤ n ≤ 1012; 0 ≤ k ≤ n; 0 ≤ d1, d2 ≤ k) — data for the current test case.

Output

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).

Examples

Input

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


Output

yes
yes
yes
no
no

Note

Sample 1. There has not been any match up to now (k = 0, d1 = 0, d2 = 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 d1 = 0 and d2 = 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 d1 = 1, d2 = 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).
import sys
from functools import lru_cache, cmp_to_key
from heapq import merge, heapify, heappop, heappush
from math import *
from collections import defaultdict as dd, deque, Counter as C
from itertools import combinations as comb, permutations as perm
from bisect import bisect_left as bl, bisect_right as br, bisect
from time import perf_counter
from fractions import Fraction
import copy
import time
starttime = time.time()
mod = int(pow(10, 9) + 7)
mod2 = 998244353
# from sys import stdin
# input = stdin.readline
def data(): return sys.stdin.readline().strip()
def out(*var, end="\n"): sys.stdout.write(' '.join(map(str, var))+end)
def L(): return list(sp())
def sl(): return list(ssp())
def sp(): return map(int, data().split())
def ssp(): return map(str, data().split())
def l1d(n, val=0): return [val for i in range(n)]
def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)]
try:
    # sys.setrecursionlimit(int(pow(10,6)))
    sys.stdin = open("input.txt", "r")
    # sys.stdout = open("../output.txt", "w")
except:
    pass

for _ in range(L()[0]):
    n,k,d1,d2=L()
    if n%3!=0:
        print('no')
        continue
    #C1
    a=(2*d1+d2+k)
    a=(a*(-1 if a%3 else 1))//3
    b=a-d1
    c=b-d2
    if 0<=a<=n//3 and 0<=b<=n//3 and 0<=c<=n//3: 
        # print(1,a,b,c)
        print("yes")
        continue
    #C2
    b=(d1+d2+k)
    b=(b*(-1 if b%3 else 1))//3
    a=b-d1
    c=b-d2
    if 0<=a<=n//3 and 0<=b<=n//3 and 0<=c<=n//3: 
        # print(2,a,b,c)
        print("yes")
        continue
    #C3
    b=(k-d1-d2)
    if b<0:
        b=n**2
    b=(b*(-1 if b%3 else 1))//3
    a=b+d1
    c=b+d2
    if 0<=a<=n//3 and 0<=b<=n//3 and 0<=c<=n//3: 
        # print(3,a,b,c)
        print("yes")
        continue
    #C1
    b=(+d1-d2+k)
    if b<0:
        b=n**2
    b=(b*(-1 if b%3 else 1))//3
    a=b-d1
    c=b+d2
    if 0<=a<=n//3 and 0<=b<=n//3 and 0<=c<=n//3: 
        # print(4,a,b,c)
        print("yes")
        continue
    print("no")


endtime = time.time()
# print(f"Runtime of the program is {endtime - starttime}")