Trip Advisor

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

There is a strange country somewhere which its transportation network was built following some weird rules: Consider the transportation network as a connected undirected graph G with N nodes and M edges(nodes indicate cities,and people can travel from cities to cities by roads connecting them),the condition that every node in G is in at most one simple cycle holds.

One day Q people of the country want to make a travel, i_th people is located at city Ui, wants to move to city Vi(Ui can be equal to Vi),and he especially loves city Pi,so he wonders if there is a path that:

  1. starts at Ui;
  2. ends at Vi;
  3. for every pair of adjacent cities in path,there is a road connecting them.
  4. visits every city at most once.
  5. visits city Pi;

As a trip advisor,your task is to tell everybody whether there is a path satsifying all his requirements.

Input

The input contains several test cases, terminated by EOF. Most of test cases are rather small.

Each testcase contains M + Q + 2 lines, first line contains two integers NM (1 ≤ N, M ≤ 200000), the number of cities and roads; next M lines each contains two integer be indicates that there is a bidrictional-road connecting city b and city e;next line an integer Q(1 ≤ Q ≤ 100000) indicating number of people in that country that want to make a travel, next Q lines each contains three integers UiViPi, denotes the query as we mentioned above.

Output

For each test case output Q lines, for i-th query, if there exists such path, output one line "Yes" without quotes, otherwise output one line "No" without quotes.

Sample Input

6 7
1 2
1 2
3 4
2 4
5 6
5 6
4 5
5
1 6 3
1 6 4
1 2 5
2 2 2
2 2 3

Sample Output

No
Yes
No
Yes
No

Hint

 

Source