Envy

给出一个$ n $ 个点$ m $条边的无向图，每条边有边权，共$ Q $次询问，每次给出$ k_i $条边，问这些边能否同时在一棵最小生成树上。 感谢@mengbierr 提供的翻译

For a connected undirected weighted graph $ G $ , MST (minimum spanning tree) is a subgraph of $ G $ that contains all of $ G $ 's vertices, is a tree, and sum of its edges is minimum possible. You are given a graph $ G $ . If you run a MST algorithm on graph it would give you only one MST and it causes other edges to become jealous. You are given some queries, each query contains a set of edges of graph $ G $ , and you should determine whether there is a MST containing all these edges or not.

The first line contains two integers $ n $ , $ m $ ( $ 2<=n,m<=5·10^{5} $ , $ n-1<=m $ ) — the number of vertices and edges in the graph and the number of queries. The $ i $ -th of the next $ m $ lines contains three integers $ u_{i} $ , $ v_{i} $ , $ w_{i} $ ( $ u_{i}≠v_{i} $ , $ 1<=w_{i}<=5·10^{5} $ ) — the endpoints and weight of the $ i $ -th edge. There can be more than one edges between two vertices. It's guaranteed that the given graph is connected. The next line contains a single integer $ q $ ( $ 1<=q<=5·10^{5} $ ) — the number of queries. $ q $ lines follow, the $ i $ -th of them contains the $ i $ -th query. It starts with an integer $ k_{i} $ ( $ 1<=k_{i}<=n-1 $ ) — the size of edges subset and continues with $ k_{i} $ distinct space-separated integers from $ 1 $ to $ m $ — the indices of the edges. It is guaranteed that the sum of $ k_{i} $ for $ 1<=i<=q $ does not exceed $ 5·10^{5} $ .

For each query you should print "YES" (without quotes) if there's a MST containing these edges and "NO" (of course without quotes again) otherwise.

5 7
1 2 2
1 3 2
2 3 1
2 4 1
3 4 1
3 5 2
4 5 2
4
2 3 4
3 3 4 5
2 1 7
2 1 2

YES
NO
YES
NO

This is the graph of sample: Weight of minimum spanning tree on this graph is $ 6 $ . MST with edges $ (1,3,4,6) $ , contains all of edges from the first query, so answer on the first query is "YES". Edges from the second query form a cycle of length $ 3 $ , so there is no spanning tree including these three edges. Thus, answer is "NO".