Problem Statement

We have a rooted tree with $N$ vertices numbered $1$ to $N$. Vertex $1$ is the root, and the parent of vertex $i$ is vertex $P_i$. There are $N$ coins with heads and tails, one on each vertex. Additionally, there are $N$ buttons numbered $1$ to $N$. Pressing button $n$ flips all coins on the vertices in the subtree rooted at vertex $n$.

Process $Q$ queries described below.

In the $i$-th query, you are given a vertex set of size $M_i$: $S_i = \lbrace v_{i,1}, v_{i,2},\dots, v_{i,M_i} \rbrace$. Now, the coins on the vertices in $S_i$ are facing heads-up, and the others are facing tails-up. In order to make all $N$ coins face tails-up by repeatedly choosing a button and pressing it, at least how many button presses are needed? Print the answer, or $-1$ if there is no way to make all the coins face tails-up.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq P_i \lt i$
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq M_i$
• $\displaystyle \sum_{i=1}^Q M_i \leq 2 \times 10^5$
• $1 \leq v_{i,j} \leq N$
• $v_{i,1}, v_{i,2},\dots,v_{i,M_i}$ are pairwise different.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N Q
P_2 P_3 \dots P_N
M_1 v_{1,1} v_{1,2} \dots v_{1,M_1}
M_2 v_{2,1} v_{2,2} \dots v_{2,M_2}
\vdots
M_Q v_{Q,1} v_{Q,2} \dots v_{Q,M_Q}

Output

Print $Q$ lines. The $i$-th line should contain the answer to the $i$-th query.