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
Ashwani Gautam:
20161029 21:07:15
can use hld, use long long int for anything related to summation of edges 

prudvinit:
20160922 15:01:07
Last edit: 20160922 15:02:31 

nk17kumar:
20160828 21:03:27
easy . sparse Matrix approach for LCA calculation. 

nonushikhar:
20160726 19:51:48
easy ;) confidence booster 

moss3011:
20160515 09:32:36
getting tle may be bcoz of method of finding ancestors ...plz help


sigma_poet225:
20160403 03:22:29
Get Wa and Don't know why. 

Abhinandan Agarwal:
20160326 14:13:56
@chandan Mittal No, I checked it. Last edit: 20160326 14:35:26 

latte0119:
20151022 11:03:20
I was using doubling algorithm to get lca.


paimon:
20150626 17:59:44
beware test cases "DIST a a" and "KTH a a 1" Last edit: 20150626 18:00:27 

Luis Manuel Dï¿½az Barï¿½n:
20141012 21:27:20
I was using a LCA algorithm with NlogN preprocess and O(1) query and received rte, I changed it to NlogN preprocess and logN query... now I received TLE, wdf is wrong with this problem? Finding the Kth ancestor ran in O(N) for the worst case. Help Please. My Mail:

Added by:  ThanhVy Hua 
Date:  20060827 
Time limit:  0.433s 
Source limit:  15000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JS NODEJS PERL 6 VB.net 
Resource:  Special thanks to Ivan Krasilnikov for his alternative solution 