VPEX P4 - Etopika

Points: 12 (partial)
Time limit: 3.0s
Java 11 4.0s
Memory limit: 128M

Author:
Problem types

Bobliu the monkey is living on a tree. The tree can be modelled as a tree (a connected graph with nodes and edges). Bob is currently on the ground, marked node . Every day, new nodes (not always distinct) grow a banana, and Bob climbs from his current spot to the 2 bananas (in any order) and eats them. He then takes a nap where he is and sleeps until the next day. What is the least distance he must travel?

Input

The first line contains , the number of nodes, and , the number of days.

The next lines contain , , and , marking a branch between and of length .

The next lines contain and , the location of the 2 bananas that day.

Output

Output the minimum total distance the monkey must travel.

Sample Input

5 2
1 2 4
2 4 3
4 3 1
5 4 1
5 3
2 5

Sample Output

14

On the first day, Bob starts at node and travels to node and then node to eat the bananas.

On the second day, Bob is already at node and eats the banana before travelling to node .