B. Linguisticstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputAlina 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.InputThe 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.OutputFor 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.ExampleInput
8
1 0 0 0
B
0 0 1 0
AB
1 1 0 1
ABAB
1 0 1 1
ABAAB
1 1 2 2
BAABBABBAA
1 1 2 3
ABABABBAABAB
2 3 5 4
AABAABBABAAABABBABBBABB
1 3 3 10
BBABABABABBBABABABABABABAABABA
Output
NO
YES
YES
YES
YES
YES
NO
YES
NoteIn 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}.
8
1 0 0 0
B
0 0 1 0
AB
1 1 0 1
ABAB
1 0 1 1
ABAAB
1 1 2 2
BAABBABBAA
1 1 2 3
ABABABBAABAB
2 3 5 4
AABAABBABAAABABBABBBABB
1 3 3 10
BBABABABABBBABABABABABABAABABA

NO YES YES YES YES YES NO YES 
['greedy', 'implementation', 'sortings', 'strings', '*2000']