FJ wants to create a list of "suggested videos" for every MooTube video. This way, cows will be recommended the videos most relevant to the ones they already watch.
FJ devises a metric of "relevance," which determines, as the name suggests, how relevant two videos are to each other. He picks N−1 pairs of videos and manually computes their pairwise relevance. Then, FJ visualizes his videos as a network, where each video is a node and the N−1 pairs of videos he manually considered are connected. Conveniently, FJ has picked his N−1 pairs so that any video can be reached from any other video along a path of connections in exactly one way. FJ decides that the relevance of any pair of videos should be defined as the minimum relevance of any connection along this path.
Farmer John wants to pick a value K so that next to any given MooTube video, all other videos with relevance at least K to that video will be suggested. However, FJ is worried that too many videos will be suggested to his cows, which could distract them from milk production! Therefore, he wants to carefully set an appropriate value of K. Farmer John would like your help answering a number of questions about the suggested videos for certain values of K.
The first line of input contains N and Q (1≤Q≤100,000).
The next N−1 lines each describe a pair of videos FJ manually compares. Each line includes three integers pi, qi, and ri (1≤pi,qi≤N,1≤ri≤1,000,000,000), indicating that videos pi and qi are connected with relevance ri.
The next Q lines describe Farmer John's Q questions. Each line contains two integers, ki and vi (1≤ki≤1,000,000,000,1≤vi≤N), indicating that FJ's iith question asks how many videos will be suggested to viewers of video vivi if K=ki.
Output Q lines. On line i, output the answer to FJ's ith question.