CF1294A.Collecting Coins

Polycarp has three sisters: Alice, Barbara, and Cerene. They're collecting coins. Currently, Alice has $a$ coins, Barbara has $b$ coins and Cerene has $c$ coins. Recently Polycarp has returned from the trip around the world and brought $n$ coins.

He wants to distribute all these $n$ coins between his sisters in such a way that the number of coins Alice has is equal to the number of coins Barbara has and is equal to the number of coins Cerene has. In other words, if Polycarp gives $A$ coins to Alice, $B$ coins to Barbara and $C$ coins to Cerene ($A+B+C=n$), then $a + A = b + B = c + C$.

Note that A, B or C (the number of coins Polycarp gives to Alice, Barbara and Cerene correspondingly) can be 0.

Your task is to find out if it is possible to distribute all $n$ coins between sisters in a way described above.

You have to answer $t$ independent test cases.

波利卡普有三个姐妹：爱丽丝（Alice）、芭芭拉（Barbara）和塞琳（Cerene）。她们正在收集硬币。目前，爱丽丝有 $a$ 枚硬币，芭芭拉有 $b$ 枚硬币，塞琳有 $c$ 枚硬币。最近，波利卡普环游世界归来，带回了 $n$ 枚硬币。

他希望将这 $n$ 枚硬币全部分给他的姐妹们，使得分配后爱丽丝、芭芭拉和塞琳各自拥有的硬币数量相等。换句话说，若波利卡普分别给爱丽丝、芭芭拉和塞琳 $A$、$B$、$C$ 枚硬币（满足 $A+B+C=n$），则需满足 $a + A = b + B = c + C$。

注意：$A$、$B$ 或 $C$（即波利卡普分别给爱丽丝、芭芭拉和塞琳的硬币数）可以为 0。

你的任务是判断：是否可能按上述方式将全部 $n$ 枚硬币分给三位姐妹。

你需要回答 $t$ 个相互独立的测试用例。

The first line of the input contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The next $t$ lines describe test cases. Each test case is given on a new line and consists of four space-separated integers $a, b, c$ and $n$ ($1 \le a, b, c, n \le 10^8$) — the number of coins Alice has, the number of coins Barbara has, the number of coins Cerene has and the number of coins Polycarp has.

输入的第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

接下来的 $t$ 行描述各个测试用例。每个测试用例占一行，包含四个由空格分隔的整数 $a, b, c$ 和 $n$（$1 \le a, b, c, n \le 10^8$）—— 分别表示爱丽丝、芭芭拉、塞琳和波利卡普所拥有的硬币数量。

For each test case, print "YES" if Polycarp can distribute all $n$ coins between his sisters and "NO" otherwise.

对于每个测试用例，如果 Polycarp 能够将全部 $n$ 枚硬币分发给他的姐妹们，则输出 "YES"；否则输出 "NO"。