Three Bit Computer Strikes Back

Byteland's scientists have moved on from the Three Bit Computer (TBC) to a new and far more powerful design: the Quantum Three Bit Computer (QTBC). On a quantum machine, initializing the memory is a completely different challenge, because every operation you perform has side effects that influence all of the memory at once.

To cope with this, the scientists use large-scale controlled impulses (LSCI). A single impulse acts on every memory bit at the same time and in exactly the same way, so it can be described by a function $f : \{0, 1, \ldots, n-1\} \to \{0, 1, \ldots, n-1\}$: when impulse $f$ is emitted, every bit currently in state $s$ moves to state $f(s)$. For example, $f(3) = 5$ means every bit in state $3$ becomes state $5$.

The scientists can emit $k$ different impulses $f_1, f_2, \ldots, f_k$. You may emit them in any order and repeat them as many times as you like; emitting a sequence of impulses applies the corresponding functions one after another to every bit simultaneously.

Determine whether there exists a sequence of impulses that drives every memory bit to state $0$, no matter which state each bit started in. In other words, decide whether some composition of the given functions sends every state in $\{0, 1, \ldots, n-1\}$ to $0$.

The first line contains a single integer $T$ ($1 \le T \le 10$), the number of test cases.

Each test case begins with a line containing two integers $n$ and $k$ ($1 \le n \le 200$, $1 \le k \le 5$), where $n$ is the number of possible states of a memory bit and $k$ is the number of available impulses.

Each of the next $k$ lines describes one impulse: the $i$-th of these lines contains $n$ integers $f_i(0)\ f_i(1)\ \ldots\ f_i(n-1)$, separated by single spaces, where each value lies in $\{0, 1, \ldots, n-1\}$.

For each test case, print a single line containing YES if it is possible to bring every memory bit to state $0$, or NO otherwise.