Sulfox the fennec fox gives you $n$ sets $S_1,S_2,\ldots,S_n$, each containing distinct integers between $0$ and $2^m-1$.

You may perform the following operation any number (possibly zero) of times: choose an integer $x$ with $0\le x< 2^m$, and for every $i=1,2,\ldots,n$, insert $x$ into $S_i$ if it is not already present.

A set $S$ is called XOR-closed if, for every $x,y\in S$, we have $x\oplus y\in S$, where $\oplus$ denotes the bitwise exclusive-OR operation.

Find the minimum number of operations required to make all $S_i$ XOR-closed, and construct any sequence of operations achieving this minimum.

Input

The first line contains two integers $n$ ($1\le n\le 2 \times 10^5$) and $m$ ($1\le m\le 20$).

The $i$-th of the next $n$ lines contains an integer $c_i$ ($c_i \ge 1$), followed by $c_i$ distinct integers $a_{i,1},a_{i,2},\ldots,a_{i,c_i}$ ($0\le a_{i,j}< 2^m$), representing the elements of $S_i$.

It is guaranteed that the sum of $c_i$ does not exceed $10^6$.

Output

On the first line, print the minimum number of operations $k$.

On the second line, print $k$ integers $x_1,x_2,\ldots,x_k$, where $x_i$ denotes the integer chosen in the $i$-th operation.

If there are multiple optimal solutions, output any of them.

Examples

Input 1

3 3
1 1
3 0 1 7
6 1 2 3 4 5 7

Output 1

3
0 7 6

Input 2

1 4
4 11 5 14 0

Output 2

0

Note

For the first example, after performing the shown operations, $S_1$ and $S_2$ become $\{0,1,6,7\}$, while $S_3$ becomes $\{0,1,2,3,4,5,6,7\}$. It can be proved that it is impossible to make all sets XOR-closed using less than $3$ operations.

For the second example, the only set is already XOR-closed, so no operation is needed.