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.


-----Input-----

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.


-----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, 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).

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "t = int(input())\nret = []\nwhile t>0:\n    t-=1\n    n,k,d1,d2 = map(int,input().split())\n\n    # ans = []\n\n    y1 = (k-(d1-d2))//3\n    x1 = y1+d1\n    z1 = y1-d2\n    # ans = [y1,z1,x1]\n    # ans = sorted(ans)\n    # ans1 = 2*ans[2]-(ans[0]+ans[1])\n    ans1 = 2*x1-(z1+y1)\n    if x1+y1+z1==k and min(z1,y1)>=0 and ans1<=n-k and (n-k-ans1)%3==0:\n        ret.append('yes')\n        continue\n    \n    # ans = []\n\n    y1 = (k-(d1+d2))//3\n    x1 = y1+d1\n    z1 = y1+d2\n    if d1>=d2:\n        # ans = [y1,z1,x1]\n        ans1 = 2*x1-(y1+z1)\n    else:\n        # ans = [y1,x1,z1]\n        ans1 = 2*z1-(y1+x1)\n    # ans = sorted(ans)\n    # ans1 = 2*ans[2]-(ans[0]+ans[1])\n    if x1+y1+z1==k and y1>=0 and ans1<=n-k and (n-k-ans1)%3==0:\n        ret.append('yes')\n        continue\n    \n    y1 = (k-(d2-d1))//3\n    x1 = y1-d1\n    z1 = y1+d2\n    # ans = [x1,y1,z1]\n    # ans = sorted(ans)\n    ans1 = 2*z1-(x1+y1)\n    if x1+y1+z1==k and min(x1,y1)>=0 and ans1<=n-k and (n-k-ans1)%3==0:\n        ret.append('yes')\n        continue\n    \n    y1 = (k+(d2+d1))//3\n    x1 = y1-d1\n    z1 = y1-d2\n    # ans = [x1,y1,z1]\n    # ans = sorted(ans)\n    ans1 = 2*y1-(x1+z1)\n    if x1+y1+z1==k and min(x1,z1)>=0 and ans1<=n-k and (n-k-ans1)%3==0:\n        ret.append('yes')\n        continue\n\n\n\n\n\n    # if d1>=d2:\n    #     ans.append(2*d1-d2)\n    #     ans.append(d2+2*(d1-d2))\n    # else:\n    #     ans.append(2*d2-d1)\n    #     ans.append(d1+2*(d2-d1))\n\n    # ans+=[d1+2*d2,d2+2*d1,d1+d2]\n    # done = False\n    # print(ans)\n    # for a in ans:\n    #     # if (a==0 and (n-k)%3==0) or (a!=0 and (n-k)//a>1 and (n-k)%a==0):\n    #     if (a<=n-k) and (n-k-a)%3==0:\n    #         print(a)\n    #         done = True\n    #         break\n\n    # if done:\n    #     print('yes')\n    # else:\n    ret.append('no')\n\nprint(*ret, sep = '\\n')\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13809