P12414 「YLLOI-R1-T3」Northward along the way
Background
Description
Given $n$ queues, each containing $m$ positive integers, all of which are less than or equal to $n$, the $i$-th queue's $j$-th element is $a_{i,j}$, where $a_{i,1}$ is the head of the queue and $a_{i,m}$ is the tail of the queue.
Now, you hold the number $0$. You need to select one queue, place $0$ at its tail, and take the head of the queue into your hand.
Next, you will repeat the operation until you take $0$ back into your hand:
- Let the number in your hand be $p$. Place it at the tail of the $p$-th queue and take the head of the $p$-th queue into your hand.
Now, Little Y wants to know if, over an infinite amount of time, you can avoid taking back $0$. If you can, output `Yes`, otherwise, output `No`.
Input Format
There are multiple test cases for this problem.
The first line contains an integer $T$, representing the number of test cases.
For each test case:
- The first line contains two integers $n$ and $m$.
- The next $n$ lines, each containing $m$ integers, represent the $i$-th queue's elements $a_{i,j}$.
Output Format
For each test case, output one line containing `Yes` if you can avoid taking back $0$, otherwise output `No`.
Explanation/Hint
### Explanation
**Sample 1:**
Below is a simulation where $0$ is initially placed into the first queue.
```php
// Number in hand:
0
// Queue contents (leftmost is the head, rightmost is the tail):
2 2
3 3
1 1
```
```
// Number in hand:
2
// Queue contents:
2 0
3 3
1 1
```
```
// Number in hand:
3
// Queue contents:
2 0
3 2
1 1
```
```
// Number in hand:
1
// Queue contents:
2 0
3 2
1 3
```
```
// Number in hand:
2
// Queue contents:
0 1
3 2
1 3
```
```
// Number in hand:
3
// Queue contents:
0 1
2 2
1 3
```
```
// Number in hand:
1
// Queue contents:
0 1
2 2
3 3
```
```
// Number in hand:
0
// Queue contents:
1 1
2 2
3 3
```
**Sample 2:**
By simulation, we can see that only when $0$ is initially placed into the first queue can it never be picked up again.
This is because after several rounds, the second queue will be filled with the number $2$, and the number in hand will also be $2$, so the process will loop indefinitely within the second queue.
### Constraints
**This problem uses subtask scoring.**
- Subtask 1 (20 points): $n \leq 2$.
- Subtask 2 (10 points): $\forall a_{i,j} = i$.
- Subtask 3 (20 points): $n \times m \leq 1000$.
- Subtask 4 (50 points): No special restrictions.
For all data:
- $1 \leq T \leq 10$.
- $1 \leq n \times m \leq 10^5$.
- $1 \leq a_{i,j} \leq n$.