The "Byte-cell" is a primitive organism inhabiting abandoned central processing units. It is an ordered sequence of cells, each of which can be one of $n$ types, numbered for simplicity from $1$ to $n$. A characteristic feature of the Byte-cell is its ability to replicate very rapidly.

In the first minute of its life, the Byte-cell consists of a single cell of type $1$. Every minute, cell replication occurs: each cell divides into a sequence of at least two cells. As a result of the division, cells of different types may be produced, but the division of a cell of type $k$ always results in the same sequence of cells $H(k) = h_{k,1}, h_{k,2}, \dots, h_{k,l_k}$. If in the $i$-th minute the Byte-cell consists of a sequence of cells $c_1, c_2, \dots, c_p$, then in the $(i+1)$-th minute it will consist of the sequence of cells formed by concatenating the sequences $H(c_1), H(c_2), \dots, H(c_p)$.

The Byte-cell reaches maturity when its sequence of cells contains a contiguous fragment that is a fixed sequence $S$ of consecutive cells of specific types.

Bytean scientists would like to study the life of the Byte-cell more closely, and in particular, to determine the time that elapses from the beginning of the Byte-cell's life until it reaches maturity.

Input

The first line of input contains two integers $n$ and $m$ ($1 \le n \le 500$, $1 \le m \le 1000$), representing the number of possible cell types and the length of the sequence of cells $S$ that must appear as a contiguous fragment of the Byte-cell's sequence for it to be considered mature, respectively.

This is followed by $n$ lines describing the cell replications: the $i$-th of these lines starts with an integer $l_i$ ($l_i \ge 2$), followed by $l_i$ integers $h_{i,1}, h_{i,2}, \dots, h_{i,l_i}$ ($1 \le h_{i,j} \le n$) representing the sequence $H(i)$. The sum of all values $l_i$ does not exceed $1000$.

The last line contains $m$ integers in the range from $1$ to $n$ representing the types of consecutive cells that make up the sequence $S$.

Output

Your program should output the number of the first minute of the Byte-cell's life in which it reaches maturity. If the Byte-cell never reaches maturity, output $-1$.

Examples

Input 1

3 2
2 2 3
3 1 3 3
2 1 2
3 1

Output 1

3

Note

In the second minute of its life, the Byte-cell consists of the sequence of cells $H(1) = 2, 3$. In the third minute, it takes the form $H(2), H(3) = 1, 3, 3, 1, 2$, and thus reaches maturity because it contains the fragment $S = 3, 1$.