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
an09mous:
20200311 17:31:40
Did it using binary lifting. A must do problem if you're learning LCA. 

fayedanik:
20200222 15:48:43
Updated:AC


hkyiitd:
20190803 09:02:01
Don't forget to print one blank line after each test case. 

viskey:
20190522 22:16:44
Easy to solve with sqrt decompostion, as there are no updates. 

tarungupta:
20190411 10:33:26
Don't forget to clear graph before each test case, if taken globally. Costed me many WA. :/


vickyand_27:
20190204 19:08:54
Took sosoo long 

hacker_sk:
20181229 23:17:51
No need to use long long, int is enough. 

alucard_01:
20181224 06:50:25
just use binary lifting Last edit: 20181224 08:01:13 

lamia2658:
20181113 20:16:11
a must do LCA problem after learning 

vaishcr7:
20180801 13:18:40
i am getting nzec error in this , i have tried taking input in many different ways. Is anybody else also facing the same problem ? 
Added by:  ThanhVy Hua 
Date:  20060827 
Time limit:  1s 
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 