题面翻译

给定一颗从1到n编号的n个结点的树

同时给定m个约束，诸如$(a_i,b_i)$

给每一条边定向，使得对于每一对约束对存在一条从$a_i$到$b_i$或从$b_i$到$a_i$的路径。

求可行的方案数，答案对$10^9 + 7$取模

$1 \le n,m \le 5 \times 10^5$

给定一颗从1到n编号的n个结点的树

同时给定m个约束，诸如$(a_i,b_i)$

给每一条边定向，使得每一对约束对存在一条从$a_i$到$b_i$或从$b_i$到$a_i$的路径。

求可行的方案数，答案对$10^9 + 7$取模

$1 \le n,m \le 5 \times 10^5$

题目描述

We are given a tree with N nodes denoted with different positive integers from 1 to N. Additionally, you are given M node pairs from the tree in the form of ($a_1$ , $b_1$ ), ($a_2$ , $b_2$ ), …, ($a_M$ , $b_M$ ).

We need to direct each edge of the tree so that for each given node pair ($a_i$ , $b_i$ ) there is a path from $a_i$ to $b_i$ or from $b_i$ to $a_i$ . How many different ways are there to achieve this? Since the solution can be quite large, determine it modulo $10^{9}+7$.

输入格式

The first line of input contains the positive integers N and M (1 ≤ N, M ≤ $3*10^5$), the number of nodes in the tree and the number of given node pairs, respectively.

Each of the following N - 1 lines contains two positive integers, the labels of the nodes connected with an edge.

The $i_{th}$ of the following M lines contains two different positive integers $a_{i}$ and $b_{i}$ , the labels of the nodes from the $i_{th}$ node pair. All node pairs will be mutually different.

输出格式

You must output a single line containing the total number of different ways to direct the edges of the tree that meet the requirement from the task, modulo $10^{9}+7$.

样例 #1

样例输入 #1

4 1
1 2
2 3
3 4
2 4

样例输出 #1

4

样例 #2

样例输入 #2

7 2
1 2
1 3
4 2
2 5
6 5
5 7
1 7
2 6

样例输出 #2

8

样例 #3

样例输入 #3

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

样例输出 #3

0

提示

In test cases worth 20% of total points, the given tree will be a chain. In other words, node i will be connected with an edge to node i + 1 for all i < N.

In additional test cases worth 40% of total points, it will hold N, M ≤ $5*10^3$.

A tree is a graph that consists of N nodes and N - 1 edges such that there exists a path from each node to each other node.