[Solution] Linguistics Codeforces Solution | Codeforces Problem Solution 2022

[Solution] Linguistics Codeforces Solution | Codeforces Problem Solution 2022

D. Linguistics

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Alina has discovered a weird language, which contains only 4$4$ words: A$\mathtt{\text{A}}$, B$\mathtt{\text{B}}$, AB$\mathtt{\text{AB}}$, BA$\mathtt{\text{BA}}$. 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$s$ and she is curious: is it possible that it consists of precisely a$a$ words A$\mathtt{\text{A}}$, b$b$ words B$\mathtt{\text{B}}$, c$c$ words AB$\mathtt{\text{AB}}$, and d$d$ words BA$\mathtt{\text{BA}}$?

In other words, determine, if it's possible to concatenate these a+b+c+d$a+b+c+d$ words in some order so that the

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 resulting string is s$s$. Each of the a+b+c+d$a+b+c+d$ words must be used exactly once in the concatenation, but you can choose the order in which they are concatenated.

Input

The first line of the input contains a single integer t$t$ (1≤t≤105$1\le t\le {10}^5$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains four integers a$a$, b$b$, c$c$, d$d$ (0≤a,b,c,d≤2⋅105$0\le a,b,c,d\le 2\cdot {10}^5$) — the number of times that words A$\mathtt{\text{A}}$, B$\mathtt{\text{B}}$, AB$\mathtt{\text{AB}}$, BA$\mathtt{\text{BA}}$ respectively must be used in the sentence.

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The second line contains the string s$s$ (s$s$ consists only of the characters A$\mathtt{\text{A}}$ and B$\mathtt{\text{B}}$, 1≤|s|≤2⋅105$1\le |s|\le 2\cdot {10}^5$, |s|=a+b+2c+2d$|s|=a+b+2c+2d$)  — the sentence. Notice that the condition |s|=a+b+2c+2d$|s|=a+b+2c+2d$ (here |s|$|s|$ denotes the length of the string s$s$) is equivalent to the fact that s$s$ is as long as the concatenation of the a+b+c+d$a+b+c+d$ words.

The sum of the lengths of s$s$ over all test cases doesn't exceed 2⋅105$2\cdot {10}^5$.

Output

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