1685B · Linguistics

Problem: 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.

Input Format: 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 $2\cdot 10^5$.

Output Format: 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.

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