B. Dynamic Diametertime limit per test6 secondsmemory limit per test1024 megabytesinputstandard inputoutputstandard outputYou are given a weighted undirected tree on n vertices and a list of q updates. Each update changes the weight of one edge. The task is to output the diameter of the tree after each update.(The distance between two vertices is the sum of the weights on the unique simple path that connects them. The diameter is the largest of all those distances.)InputThe first line contains three space-separated integers n, q and w (2 \leq n \leq 100,000, 1 \leq q \leq 100,000, 1 \leq w \leq 20,000,000,000,000) – the number of vertices in the tree, the number of updates and the limit on the weights of edges. The vertices are numbered 1 through n.Next, n-1 lines describing the initial tree follow. The i-th of these lines contains three space-separated integers a_i, b_i, c_i (1 \leq a_i, b_i \leq n, 0 \leq c_i < w) meaning that initially, there is an edge between vertices a_i and b_i with weight c_i. It is guaranteed that these n-1 lines describe a tree.Finally, q lines describing queries follow. The j-th of these lines contains two space-separated integers d_j, e_j (0 \leq d_j < n - 1, 0 \leq e_j < w). These two integers are then transformed according to the following scheme:   d'_j = (d_j + last) \bmod (n - 1)  e'_j = (e_j + last) \bmod w  where last is the result of the last query (initially last=0). Tuple (d'_j, e'_j) represents a query which takes the d'_j+1-th edge from the input and sets its weight to e'_j.OutputOutput q lines. For each i, line i should contain the diameter of the tree after the i-th update.ScoringSubtask 1 (11 points): n,q \leq 100 and w \leq 10,000Subtask 2 (13 points): n,q \leq 5,000 and w \leq 10,000Subtask 3 (7 points): w \leq 10,000 and the edges of the tree are exactly all valid edges of the form \{1, i\} (Hence, the tree is a star centered at vertex 1.)Subtask 4 (18 points): w \leq 10,000, and the edges of the tree are exactly all valid edges of the forms \{i, 2i\} and \{i, 2i+1\} (Hence, if we were to root the tree at vertex 1, it would be a balanced binary tree.)Subtask 5 (24 points): it is guaranteed that after each update a longest simple path goes through vertex 1Subtask 6 (27 points): no additional constraintsExamplesInput
4 3 2000
1 2 100
2 3 1000
2 4 1000
2 1030
1 1020
1 890
Output
2030
2080
2050
Input
10 10 10000
1 9 1241
5 6 1630
10 5 1630
2 6 853
10 1 511
5 3 760
8 3 1076
4 10 1483
7 10 40
8 2051
5 6294
5 4168
7 1861
0 5244
6 5156
3 3001
8 5267
5 3102
8 3623
Output
6164
7812
8385
6737
6738
7205
6641
7062
6581
5155
NoteThe first sample is depicted in the figure below. The left-most picture shows the initial state of the graph. Each following picture depicts the situation after an update. The weight of the updated edge is painted green, and the diameter is red.The first query changes the weight of the 3rd edge, i.e. \{2, 4\}, to 1030. The largest distance between any pair of vertices is 2030 – the distance between 3 and 4.As the answer is 2030, the second query is d'_2 = (1 + 2030) \bmod 3 = 0 e'_2 = (1020 + 2030) \bmod 2000 = 1050 Hence the weight of the edge \{1, 2\} is changed to 1050. This causes the pair \{1, 4\} to be the pair with the greatest distance, namely 2080.The third query is decoded as d'_3 = (1 + 2080) \bmod 3 = 2 e'_3 = (890 + 2080) \bmod 2000 = 970 As the weight of the edge \{2, 4\} decreases to 970, the most distant pair is suddenly \{1, 3\} with 2050.
4 3 2000
1 2 100
2 3 1000
2 4 1000
2 1030
1 1020
1 890

2030 2080 2050 
['*special problem', 'data structures', 'dfs and similar', 'divide and conquer', 'trees']