QTREE2  Query on a tree II
You are given a tree (an undirected acyclic connected graph) with N nodes, and edges numbered 1, 2, 3...N1. Each edge has an integer value assigned to it, representing its length.
We will ask you to perfrom some instructions of the following form:
 DIST a b : ask for the distance between node a and node b
or  KTH a b k : ask for the kth node on the path from node a to node b
Example:
N = 6
1 2 1 // edge connects node 1 and node 2 has cost 1
2 4 1
2 5 2
1 3 1
3 6 2
Path from node 4 to node 6 is 4 > 2 > 1 > 3 > 6
DIST 4 6 : answer is 5 (1 + 1 + 1 + 2 = 5)
KTH 4 6 4 : answer is 3 (the 4th node on the path from node 4 to node 6 is 3)
Input
The first line of input contains an integer t, the number of test cases (t <= 25). t test cases follow.
For each test case:
 In the first line there is an integer N (N <= 10000)
 In the next N1 lines, the ith line describes the ith edge: a line with three integers a b c denotes an edge between a, b of cost c (c <= 100000)
 The next lines contain instructions "DIST a b" or "KTH a b k"
 The end of each test case is signified by the string "DONE".
There is one blank line between successive tests.
Output
For each "DIST" or "KTH" operation, write one integer representing its result.
Print one blank line after each test.
Example
Input: 1 6 1 2 1 2 4 1 2 5 2 1 3 1 3 6 2 DIST 4 6 KTH 4 6 4 DONE Output: 5 3
hide comments
zengshiyuan:
20141002 10:48:37
Easy problem.Can use heavylight decomposition


Chandan Mittal:
20140718 20:25:02
can there be a case when k is greater than number of nodes between a and b, both inclusive? 

Mojtaba FayazBakhsh:
20130821 17:05:54
got AC using 32 bit integer 

Parit Agarwal:
20130716 07:52:46
getting SIGSEGV ....

Added by:  ThanhVy Hua 
Date:  20060827 
Time limit:  0.433s 
Source limit:  15000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  Special thanks to Ivan Krasilnikov for his alternative solution 