You are given a tree comprising $n$ nodes numbered from $1$ to $n$. You have to answer $q$ queries each consisting of three numbers – $r$, $d_1$ and $d_2$. 

For each query, print the number of nodes whose depth is between $d_1$ and $d_2$ (inclusive) if the tree is rooted at node $r$. The depth of root node itself is $0$, the depth of all its children is $1$ and so on.

Input format

First line: $n$ (the number of nodes) and $q$ (the number of queries)

Next $n-1$ lines: $u_i$ and $v_i$denoting an edge between the nodes $u_i$ and $v_i$.The next $q$ lines consist of three integers $r$ , $d_1$ and $d_2$ .

Output format

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

input Constraints

$1 \le n \le 100000\\1 \le q \le 150000\\ 0 \le d_1 \le d_2 \le n\\1 \le r \le n$