Description

Given an unrooted tree with $n$ nodes, there are $q$ queries.

Each query provides a parameter triple $(a,b,c)$. You need to find how many nodes $i$ satisfy that, when the tree is rooted at $i$, the LCA of $a$ and $b$ is $c$.

Input Format

The first line contains $2$ integers, $n$ and $q$.

The next $n-1$ lines each contain $2$ integers, describing an edge of the tree.

The next $q$ lines each contain $3$ integers, which are $(a,b,c)$.

Output Format

Output $q$ lines. Each line contains one integer: for each triple, the number of valid nodes $i$.

10 5
1 2
1 3
2 4
2 5
2 10
5 6
3 7
7 8
7 9
4 6 2
4 10 1
6 8 3
9 10 2
4 10 5

7
0
1
4
0

5 3
1 3
1 5
3 4
3 2
5 2 3
5 2 1
2 4 5

2
1
0

20 10
1 2
1 3
1 4
2 5
2 6
3 10
4 13
4 14
6 7
6 8
10 11
4 15
4 16
8 9
11 12
16 17
16 18
16 19
17 20
15 19 16
1 12 1
20 20 20
7 7 8
1 8 3
5 20 2
2 9 6
9 12 1
9 12 2
9 12 3

4
16
20
0
0
5
2
10
2
1

Hint

Explanation for Sample 2

For the first query, the valid $i$ are $3$ and $4$.

For the second query, the valid $i$ is $1$.

Constraints

This problem is tested by subtasks:

$subtask1 (20pts)$: $1 \leq n \leq 1000$, $1 \leq q \leq 500$.

$subtask2 (15pts)$: $1 \leq n \leq 10^{5}$, $1 \leq q \leq 10^{5}$, the tree degenerates into a chain.

$subtask3 (25pts)$: $1 \leq n \leq 5 \times 10^{5}$, $1 \leq q \leq 10^{5}$, the testdata is not random.

$subtask4 (40pts)$: $1 \leq n \leq 5 \times 10^{5}$, $1 \leq q \leq 2 \times 10^{5}$.

For all testdata: $1 \leq n \leq 5 \times 10^{5}$, $1 \leq q \leq 2 \times 10^{5}$.

Note: the testdata is not very strong, so there is no need to micro-optimize or use fast input/output.

Translated by ChatGPT 5