You are given a weighted tree of n vertices rooted at 1.
There are q queries, each of the form (u,v), find weight of the heaviest edge on the simple path between u and v.
### Input
- The first line contain 2 integers n,q.
- The next n−1 lines, each line contains 3 integers u,v,w, there is an edge of weight w between u and v.
- The next q lines, each line contains 2 integers u,v, an query.
### Output
- Print q integers, the answers to q queries.
### Constraints
- 1≤n,q≤105.
- 1≤u,v≤n.
- 1≤w≤109.
### Example
Input:
73121132243252361373452621
Output:
321