Y Figures

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You are given a tree with N nodes, numbered from 1 to N. It is rooted at node 1, and each node i is labelled with a positive integer label_{i}.
‘Y Figures’ of a node X are defined as the number of ordered triplets of nodes (A, B, C) satisfying:
 label_{A} = label_{B} = label_{C} = label_{X}.
 A is an ancestor of X.
 B and C are in the subtree of X and LCA(B,C) = X.
 A, B, C, X are pairwise distinct.
You need to answer Q queries of the form ‘X Z’. For each query, Change the label of node X to Z and report the number of ‘Y Figures’ of the node X.
Note: Changes are not persistent. Each query is independent of every other query.
It is advised to use fast I/O methods.
Input
 First Line of Input consists of a single integer T, the number of test cases.
 First line of every test case contains of two Integers, N and Q, denoting number of nodes in the tree and the number of queries respectively.
 The second line of input consists of N integers, where the ith integer represents label_{i}, the label of node i (1indexed).
 The next N  1 lines contain two integers, a and b, denoting that an edge exists between node a and node b.
 The next Q lines contain two integers, X and Z where X is the node and Z is the new label of the node for the current query.
Output
 For every testcase, output Q lines, where each line is the answer to each query in the order of input.
Constraints
 1 ≤ T ≤ 1000
 1 ≤ Sum of all N ≤ 200000
 1 ≤ a, b ≤ N
 1 ≤ X ≤ N
 1 ≤ Sum of all Q ≤ 100000
 1 ≤ Z, label_{i} ≤ 1000000000
Example
Input: 1 6 2 1 1 1 1 1 1 1 2 2 3 3 4 2 5 2 6 2 1 2 2 Output: 10 0
Explanation
For query ‘2 1’, the satisfying triplets are (1,3,5), (1,3,6), (1,4,5), (1,4,6), (1,5,6), (1,5,3), (1,5,4), (1,6,5), (1,6,3) and (1,6,4).
For query ‘2 2’, there are no satisfying triplets.
Author:  kr_abhinav 
Editorial  https://discuss.codechef.com/problems/YFG 
Tags  codemelange, dsu, kr_abhinav, medium, sack 
Date Added:  26032018 
Time Limit:  1.5 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, COB, FS 
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