CF1685B.Linguistics

Alina has discovered a weird language, which contains only $4$ words: $\texttt{A}$, $\texttt{B}$, $\texttt{AB}$, $\texttt{BA}$. It also turned out that there are no spaces in this language: a sentence is written by just concatenating its words into a single string.

Alina has found one such sentence $s$ and she is curious: is it possible that it consists of precisely $a$ words $\texttt{A}$, $b$ words $\texttt{B}$, $c$ words $\texttt{AB}$, and $d$ words $\texttt{BA}$?

In other words, determine, if it's possible to concatenate these $a+b+c+d$ words in some order so that the resulting string is $s$. Each of the $a+b+c+d$ words must be used exactly once in the concatenation, but you can choose the order in which they are concatenated.

阿丽娜发现了一种奇怪的语言，该语言仅包含 $4$ 个单词：$\texttt{A}$、$\texttt{B}$、$\texttt{AB}$ 和 $\texttt{BA}$。此外，这种语言中没有空格：一个句子通过将其所有单词直接连接成一个字符串来书写。

阿丽娜找到了这样一个句子 $s$，她很好奇：它是否恰好由 $a$ 个单词 $\texttt{A}$、$b$ 个单词 $\texttt{B}$、$c$ 个单词 $\texttt{AB}$ 和 $d$ 个单词 $\texttt{BA}$ 组成？

换言之，请判断：能否将这 $a+b+c+d$ 个单词以某种顺序连接起来，使得最终得到的字符串恰好为 $s$？这 $a+b+c+d$ 个单词必须全部且仅使用一次，但你可以自由选择它们的连接顺序。

The first line of the input contains a single integer $t$ ($1 \le t \le 10^5$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains four integers $a$, $b$, $c$, $d$ ($0\le a,b,c,d\le 2\cdot 10^5$) — the number of times that words $\texttt{A}$, $\texttt{B}$, $\texttt{AB}$, $\texttt{BA}$ respectively must be used in the sentence.

The second line contains the string $s$ ($s$ consists only of the characters $\texttt{A}$ and $\texttt{B}$, $1\le |s| \le 2\cdot 10^5$, $|s|=a+b+2c+2d$) — the sentence. Notice that the condition $|s|=a+b+2c+2d$ (here $|s|$ denotes the length of the string $s$) is equivalent to the fact that $s$ is as long as the concatenation of the $a+b+c+d$ words.

The sum of the lengths of $s$ over all test cases doesn't exceed $2\cdot 10^5$.

输入的第一行包含一个整数 $t$（$1 \le t \le 10^5$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含四个整数 $a$、$b$、$c$、$d$（$0\le a,b,c,d\le 2\cdot 10^5$），分别表示句子中必须使用的单词 $\texttt{A}$、$\texttt{B}$、$\texttt{AB}$、$\texttt{BA}$ 的次数。

每个测试用例的第二行包含字符串 $s$（$s$ 仅由字符 $\texttt{A}$ 和 $\texttt{B}$ 组成，$1\le |s| \le 2\cdot 10^5$，且满足 $|s|=a+b+2c+2d$），即该句子。注意：条件 $|s|=a+b+2c+2d$（其中 $|s|$ 表示字符串 $s$ 的长度）等价于 $s$ 的长度恰好等于这 $a+b+c+d$ 个单词拼接后的总长度。

所有测试用例中字符串 $s$ 的长度之和不超过 $2\cdot 10^5$。

For each test case output $\texttt{YES}$ if it is possible that the sentence $s$ consists of precisely $a$ words $\texttt{A}$, $b$ words $\texttt{B}$, $c$ words $\texttt{AB}$, and $d$ words $\texttt{BA}$, and $\texttt{NO}$ otherwise. You can output each letter in any case.

对于每个测试用例，如果句子 $s$ 恰好由 $a$ 个单词 $\texttt{A}$、$b$ 个单词 $\texttt{B}$、$c$ 个单词 $\texttt{AB}$ 和 $d$ 个单词 $\texttt{BA}$ 组成是可能的，则输出 $\texttt{YES}$；否则输出 $\texttt{NO}$。你可以以任意大小写形式输出每个字母。

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 $\texttt{BA} + \texttt{AB} + \texttt{B} + \texttt{AB} + \texttt{BA} + \texttt{A}= \texttt{BAABBABBAA}$.

在第一个测试用例中，句子 $s$ 为 $\texttt{B}$。显然，它无法由单个单词 $\texttt{A}$ 构成，因此答案为 $\texttt{NO}$。

在第二个测试用例中，句子 $s$ 为 $\texttt{AB}$，它有可能由单个单词 $\texttt{AB}$ 构成，因此答案为 $\texttt{YES}$。

在第三个测试用例中，句子 $s$ 为 $\texttt{ABAB}$，它有可能由一个单词 $\texttt{A}$、一个单词 $\texttt{B}$ 和一个单词 $\texttt{BA}$ 构成，因为 $\texttt{A} + \texttt{BA} + \texttt{B} = \texttt{ABAB}$。

在第四个测试用例中，句子 $s$ 为 $\texttt{ABAAB}$，它有可能由一个单词 $\texttt{A}$、一个单词 $\texttt{AB}$ 和一个单词 $\texttt{BA}$ 构成，因为 $\texttt{A} + \texttt{BA} + \texttt{AB} = \texttt{ABAAB}$。

在第五个测试用例中，句子 $s$ 为 $\texttt{BAABBABBAA}$，它有可能由一个单词 $\texttt{A}$、一个单词 $\texttt{B}$、两个单词 $\texttt{AB}$ 和两个单词 $\texttt{BA}$ 构成，因为 $\texttt{BA} + \texttt{AB} + \texttt{B} + \texttt{AB} + \texttt{BA} + \texttt{A}= \texttt{BAABBABBAA}$。