Graph Stuff

You will be given a tree with $n$ node numbered 1 to $n$ with weighted edge.

You will be asked $q$ queries.

For each query you have to find the largest edge in path from $A$ to $B$.

Input

The first line contains two integers $n$ and $q$ ($1 \le n, q \le 10^5$). Each of the next $n-1$ lines contains three integer $u_i$, $v_i$, $w_i$, ($1 \le u_i$, $v_i \le n$ and $1 \le w_i \le 10^5$), meaning there is an edge between $u_i$ and $v_i$ with weight $w_i$.

Each of the next $q$ lines contains two integer $A$, $B$ ($1 \le A, B \le n$ and $A \ne B$) describing the query.

Output

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

Samples

Input	Output
5 5 2 1 40 3 2 21 4 1 23 5 2 50 1 2 3 5 3 1 2 3 2 1	40 50 40 21 40
In query 1, from 1 to 2, there is only one edge and so the answer is 40. In query 2, from 3 to 5, largest edge in path is 2 -- 5 with weight 50, so the answer is 50.

Input	Output
5 5 2 1 2 3 2 31 4 1 2 5 2 5 1 4 1 5 3 1 2 3 2 1	2 5 31 31 2