Description

There is a sequence $A$ of length $m$ where all elements equal to $0$. We will then execute $n$ operations on $A$ in order. The $i$-th operation can be denoted as $p_i$ distinct integers $b_{i, 1}, b_{i, 2}, \cdots, b_{i, p_i}$, indicating that we'll change the value of the $b_{i, j}$-th element in the sequence to $i$ for all $1 \le j \le p_i$. Let $R$ be the resulting sequence after all operations.

We now require you to rearrange the operations but still produce the same result. More formally, let $q_1, q_2, \cdots, q_n$ be a permutation of $n$ that differs from $1, 2, \cdots, n$. You'll execute the $q_1$-th, $q_2$-th, ..., $q_n$-th operation on sequence $A$ in order, and the final resulting sequence must equal to $R$. Your task is to find such permutation or state that it does not exist.

Recall that a permutation of $n$ is a sequence of length $n$ in which each integer from $1$ to $n$ (both inclusive) appears exactly once. Let $x_1, x_2, \cdots, x_n$ and $y_1, y_2, \cdots, y_n$ be two permutations of $n$. We say they're different if there exists an integer $k$ such that $1 \le k \le n$ and $x_k \ne y_k$.

Input Format

There are multiple test cases. The first line of the input contains an integer $T$ indicating the number of test cases. For each test case:

The first line contains two integers $n$ and $m$ ($1 \leq n, m \leq 10^5$) indicating the number of operations and the length of the sequence.

For the following $n$ lines, the $i$-th line first contains an integer $p_i$ ($1 \le p_i \le m$) indicating the number of elements changed by the $i$-th operation. Then $p_i$ distinct integers $b_{i,1}, b_{i,2}, \cdots, b_{i,p_i}$ follow ($1 \le b_{i,j} \le m$) indicating the index of the elements to be changed.

It is guaranteed that the sum of $(n + m)$ of all test cases will not exceed $2 \times 10^6$, and the sum of $p_i$ of all test cases will not exceed $10^6$.

Output Format

For each test case, if such permutation exists, first output $\texttt{Yes}$ in one line. Then output $n$ integers $q_1, q_2, \cdots, q_n$ separated by a space in the second line indicating the answer. If there are multiple valid answers, you can output any of them.

If there is no such permutation, simply output $\texttt{No}$ in one line.

Please, DO NOT output extra spaces at the end of each line, or your solution may be considered incorrect!

3
3 6
3 3 1 5
2 5 3
2 2 6
2 3
3 1 3 2
2 3 1
1 3
2 2 1

Yes
3 1 2
No
No

Hint

For the first sample test case, by executing the operations in either order of $\{1, 2, 3\}$ or $\{3, 1, 2\}$ yields the same resulting sequence $\{1, 3, 2, 0, 2, 3\}$.