P15498 [ICPC 2025 APC] Corrupted File

The WannaLaugh malware is a new computer malware that is spreading on the internet. If a computer is infected by this malware, then the malware will corrupt all files in the computer. A file in a computer contains zero or more bits. The malware corrupts a file by performing zero or more operations. In one operation, the malware randomly picks two consecutive bits and replaces them with a single bit. The new bit is $1$ if both of the replaced bits are $1$, or $0$ otherwise. For example, the malware might corrupt a file with bits $11011011$ as follows: 1. The malware picks the first and second bits: $11011011 \rightarrow 1011011$. 2. The malware picks the second and third bits: $1011011 \rightarrow 101011$. 3. The malware picks the third and fourth bits: $101011 \rightarrow 10011$. Alternatively, the malware might first pick the third and fourth bits: $11011011 \rightarrow 1101011$. At the start of the day, you have a file containing $n$ bits, denoted by $B$. You spend the day surfing the internet, including checking on your favorite programming contest website, just like many ICPC contestants would do. At the end of the day, the same file contains $m$ bits, denoted by $C$. You want to determine whether this file could have been corrupted by the WannaLaugh malware, or if it must have changed for other reasons.

The first line of input contains one integer $t$ ($1 \leq t \leq 10\,000$) representing the number of test cases. After that, $t$ test cases follow. Each of them is presented as follows. The first line of input contains two integers $n$ and $m$ ($1 \leq m \leq n \leq 100\,000$). The second line contains a string with $n$ characters, each is either $0$ or $1$, representing the bits $B$. The third line contains a string with $m$ characters, each is either $0$ or $1$, representing the bits $C$. The sum of $n$ across all test cases in one input file does not exceed $100\,000$.

For each test case, output **yes** if the file with bits $B$ could have been corrupted by the WannaLaugh malware into bits $C$, or **no** otherwise.

**Explanation for the sample input/output #1** The first test case corresponds to the example from the problem description. For the second test case, it is possible that the malware performs zero operations. For the third test case, it is impossible for the malware to corrupt a file with bits $101$ so that it has bits $00$.