34481번 - Herding Cats 다국어

You are opening a cat cafe in Baku and would like to take a promotional photograph of all the cats sitting in the front window. Unfortunately, getting cats to do what you want is a famously hard problem. But you have a plan: you have bought a collection of $m$ catnip plants, each of a different variety, knowing that each cat likes some of these varieties. There is a row of $m$ pots in the window, numbered $1$ to $m$ in order, and you will place one plant in each pot. Each cat will then be persuaded (by means of a toy on a string) to walk along the row of pots from $1$ to $m$. As soon as a cat reaches a pot with a catnip plant that it likes, it will stop there, even if there already are other cats at that plant.

Figure F.1: One possible plant ordering for the first sample test case.

You know which pot you would like each cat to stop beside. Can you find a way in which to place the plants in the pots to achieve this?

The first line of input contains an integer $t$ ($1 ≤ t ≤ 10\, 000$), which is the number of test cases. The descriptions of $t$ test cases follow.

The first line of each test case contains two integers $n$ and $m$, where $n$ ($1 ≤ n ≤ 2 \cdot 10^5$) is the number of cats, and $m$ ($1 ≤ m ≤ 2 \cdot 10^5$) is the number of catnip plants (and also the number of pots). Catnip plants are numbered from $1$ to $m$.

The following $n$ lines each describe one cat. The line starts with two integers $p$ and $k$, where $p$ ($1 ≤ p ≤ m$) is the pot at which the cat should stop, and $k$ ($1 ≤ k ≤ m$) is the number of catnip plants the cat likes. The remainder of the line contains $k$ distinct integers, which are the numbers of the plants that the cat likes.

Over all test cases, the sum of $n$ is at most $2 \cdot 10^5$, the sum of $m$ is at most $2 \cdot 10^5$, and the sum of all $k$ is at most $5 \cdot 10^5$.

For each test case, output either yes if it is possible to arrange the catnip plants as described above, or no if not.