Problem Description
bobo has a tree, whose vertices are conveniently labeled by 1,2,…,n.
There are m paths on the tree. bobo would like to pick some paths while any two paths do not share common vertices.
Find the maximum number of paths bobo can pick.
Input
The input consists of several tests. For each tests:
The first line contains n,m (1≤n,m≤105). Each of the following (n - 1) lines contain 2 integers ai,bi denoting an edge between vertices ai and bi (1≤ai,bi≤n). Each of the following m lines contain 2 integers ui,vi denoting a path between vertices ui and vi (1≤ui,vi≤n).
Output
For each tests:
A single integer, the maximum number of paths.
Sample Input
3 2
1 2
1 3
1 2
1 3
7 3
1 2
1 3
2 4
2 5
3 6
3 7
2 3
4 5
6 7
Sample Output
1
2