CF1685B Linguistics

Alina 发现了一种只由 $\text{A, B, AB, BA}$ 四种单词组成的语言，这种语言不含有空格，书写句子时只需要将单词直接连接起来即可。 她很好奇是否可以用 $a$ 个 $\text{A}$，$b$ 个 $\text{B}$，$c$ 个 $\text{AB}$，$d$ 个 $\text{BA}$ 拼接形成句子 $s$。 换句话说，是否可以用 $a+b+c+d$ 个单词以某种顺序拼接出句子 $s$，这 $a+b+c+d$ 个单词都得被用到，他们的顺序可以由你决定。

第一行是一个数字 $t$，表示数据的组数。每一组的格式如下： 每组的第一行是四个数字 $a, b, c, d$（$0\leq a,b,c,d\leq2\cdot10^5$），它们分别代表本组单词 $\text{A, B, AB, BA}$ 需要使用的次数。 每组的第二行是一个字符串 $s$（$|s|\leq 2\cdot 10^5$），并且保证 $s$ 的总长和 $a$ 个 $\text{A}$，$b$ 个 $\text{B}$，$c$ 个 $\text{AB}$，$d$ 个 $\text{BA}$ 拼接形成的长度相同（$|s|=a+b+2c+2d$）。其中 $|s|$ 表示字符串 $s$ 的长度。 所有 $s$ 的总长度之和不会超过 $2\cdot 10^5$。

对于每组数据，如果该组数据的 $s$ 可以被 $a$ 个 $\text{A}$，$b$ 个 $\text{B}$，$c$ 个 $\text{AB}$，$d$ 个 $\text{BA}$ 不限顺序地拼接形成，那么输出一个字符串 `YES`，否则输出 `NO`。

In the first test case, the sentence $ s $ is $ \texttt{B} $ . Clearly, it can't consist of a single word $ \texttt{A} $ , so the answer is $ \texttt{NO} $ . In the second test case, the sentence $ s $ is $ \texttt{AB} $ , and it's possible that it consists of a single word $ \texttt{AB} $ , so the answer is $ \texttt{YES} $ . In the third test case, the sentence $ s $ is $ \texttt{ABAB} $ , and it's possible that it consists of one word $ \texttt{A} $ , one word $ \texttt{B} $ , and one word $ \texttt{BA} $ , as $ \texttt{A} + \texttt{BA} + \texttt{B} = \texttt{ABAB} $ . In the fourth test case, the sentence $ s $ is $ \texttt{ABAAB} $ , and it's possible that it consists of one word $ \texttt{A} $ , one word $ \texttt{AB} $ , and one word $ \texttt{BA} $ , as $ \texttt{A} + \texttt{BA} + \texttt{AB} = \texttt{ABAAB} $ . In the fifth test case, the sentence $ s $ is $ \texttt{BAABBABBAA} $ , and it's possible that it consists of one word $ \texttt{A} $ , one word $ \texttt{B} $ , two words $ \texttt{AB} $ , and two words $ \texttt{BA} $ , as $ \texttt{BA} + \texttt{AB} + \texttt{B} + \texttt{AB} + \texttt{BA} + \texttt{A}= \texttt{BAABBABBAA} $ .