题目描述

To help capture criminals on the run, the police are introducing a new computer system. The area covered by the police contains N cities and E bidirectional roads connecting them. The cities are labelled 1 to N.

为了帮助抓捕逃犯，警方引进了一套新的电脑系统。警察的辖区包含N座城市和E条双向道路，城市的编号是1~N。

The police often want to catch criminals trying to get from one city to another. Inspectors, looking at a map, try to determine where to set up barricades and roadblocks. The new computer system should answer the following two types of queries:

警察常常要抓住那些逃往另一个城市的罪犯。侦查员看着地图，试着确定在哪里设置路障。新的计算机系统要回答以下两种问题：

1. Consider two cities A and B, and a road connecting cities G1 and G2. Can the criminals get from city A to city B if that one road is blocked and the criminals can't use it?

1.考虑城市$A$和$B$，以及连接城市$G_1$和$G_2$的道路。罪犯能否在那条路不通的情况下从$A$到逃到$B$？

2. Consider three cities A, B and C. Can the criminals get from city A to city B if the entire city C is cut off and the criminals can't enter that city?

2.考虑三个城市$A$、$B$、$C$。罪犯能否在$C$被切断的情况下从$A$逃到$B$?

Write a program that implements the described system.

写一个程序实现上述系统。

输入格式

The first line contains two integers N and E (2 ≤ N ≤ 100 000, 1 ≤ E ≤ 500 000), the number of cities and roads.

Each of the following E lines contains two distinct integers between 1 and N – the labels of two cities connected by a road. There will be at most one road between any pair of cities.

The following line contains the integer Q (1 ≤ Q ≤ 300 000), the number of queries the system is being tested on.

Each of the following Q lines contains either four or five integers. The first of these integers is the type of the query – 1 or 2.

If the query is of type 1, then the same line contains four more integers A, B, G1 and G2 as described earlier. A and B will be different. G1 and G2 will represent an existing road.

If the query is of type 2, then the same line contains three more integers A, B and C. A, B and C will be distinct integers.

The test data will be such that it is initially possible to get from each city to every other city.

保证图中每两个点相互连通。

输出格式

Output the answers to all Q queries, one per line. The answer to a query can be "yes" or "no".

13 15
1 2
2 3
3 5
2 4
4 6
2 6
1 4
1 7
7 8
7 9
7 10
8 11
8 12
9 12
12 13
5
1 5 13 1 2
1 6 2 1 4
1 13 6 7 8
2 13 6 7
2 13 6 8

yes
yes
yes
no
yes

提示

Croatian Olympiad in Informatics 2007 Task 2