## The Problem

Time Limit: 5000 MS Memory Limit: 65536 K

The N cows (2 <= N <= 1,000) conveniently numbered 1..N are grazing
among the N pastures also conveniently numbered 1..N. Most conveniently
of all, cow i is grazing in pasture i.
Some pairs of pastures are connected by one of N-1 bidirectional
walkways that the cows can traverse. Walkway i connects pastures
A_i and B_i (1 <= A_i <= N; 1 <= B_i <= N) and has a length of L_i
(1 <= L_i <= 10,000).
The walkways are set up in such a way that between any two distinct
pastures, there is exactly one path of walkways that travels between
them. Thus, the walkways form a tree.
The cows are very social and wish to visit each other often. Ever
in a hurry, they want you to help them schedule their visits by
computing the lengths of the paths between Q (1 <= Q <= 1,000) pairs
of pastures (each pair given as a query p1,p2 (1 <= p1 <= N; 1 <=
p2 <= N).
## INPUT FORMAT:

* Line 1: Two space-separated integers: N and Q
* Lines 2..N: Line i+1 contains three space-separated integers: A_i,
B_i, and L_i
* Lines N+1..N+Q: Each line contains two space-separated integers
representing two distinct pastures between which the cows wish
to travel: p1 and p2
## SAMPLE INPUT:

4 2

2 1 2

4 3 2

1 4 3

1 2

3 2

## OUTPUT FORMAT:

* Lines 1..Q: Line i contains the length of the path between the two
pastures in query i.
## SAMPLE OUTPUT:

2

7

## OUTPUT DETAILS:

Query 1: The walkway between pastures 1 and 2 has length 2.
Query 2: Travel through the walkway between pastures 3 and 4, then the one
between 4 and 1, and finally the one between 1 and 2, for a total length of 7.