# Envy

## 题目描述

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.

## 输入输出格式

### 输入格式

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} \$ .

### 输出格式

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.

## 输入输出样例

### 输入样例 #1

``````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
``````

### 输出样例 #1

``````YES
NO
YES
NO
``````

## 说明

This is the graph of sample: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF891C/d7f37868e211da76f9c523f75a033c3f4d56f21c.png)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".