You are given a tree consisting of \(N\) nodes. You have to answer \(Q\) queries. The \(q^{th}\) query consists of a node \(x_q\) and a set of \(k_q\) distinct nodes \(\{v_1, v_2,\dots, v_{k_q}\}\). The answer to the  \(q^{th}\) query is the number of pairs \((i, j)\) such that \(1 \le i \lt j \le k_q\) and the node \(x_q\) lies on the path between the nodes \(v_i\) and \(v_j\).

Input format

• The first line of input contains two integers \(N\) denoting the number of nodes in the tree and \(Q\) denoting the number of queries.
• \(N-1\) lines follow. The \(i^{th}\) line contains two integers \(X_i, Y_i\) denoting an edge between the nodes \(X_i,Y_i\). It is guaranteed that the given nodes and edges form a tree.
• \(2 \cdot Q\) lines follow. The \((2 \cdot q - 1)\)-th of these lines contains two integers \(x_q, k_q\), and the \(2 \cdot q\) -th line contains \(k_q\) space-separated distinct integers \(\{v_1, v_2,\dots, v_{k_q}\}\).

Output format

For each query, print the answer in a separate line.

Constraints

\(2 \leq N \leq 2\cdot10^5\\ 1 \leq Q \leq 2\cdot10^5 \\ 1 \le X_i \lt Y_i\le N \\ 1 \le k_q, x_q, v_q\le N\\\\ \sum k_q \le 3.5 * 10^5 \\\)