### Trip Advisor

#### 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:

- starts at Ui;
- ends at Vi;
- for every pair of adjacent cities in path,there is a road connecting them.
- visits every city at most once.
*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 *N*, *M* (1 ≤ *N*, *M* ≤ 200000), the number of cities and roads; next *M* lines each contains two integer *b*, *e* 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 *U*_{i}, *V*_{i}, *P*_{i}, denotes the query as we mentioned above.

#### 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