Given an undirected graph with $n$ vertices and $m$ weighted edges. The weight of each edge can be expressed in the form $2^a \times 3^b$. For $q$ queries of the form $u,v,a,b$, check whether there exists a path from $u$ to $v$ such that the least common multiple (LCM) of the weights of the edges on the path equals $2^a \times 3^b$. A path can include repeated edges.
### Input
- The first line contains two integers $n$ and $m$.
- The next $m$ lines each contain four integers $u,v,a,b$, representing an edge from $u$ to $v$ with weight $2^a \times 3^b$.
- The next line contains an integer $q$.
- The next $q$ lines each contain four integers $u,v,a,b$, a query.
### Output
- For each query, print `Yes` if there exists a valid path; otherwise, print `No`.
### Constraints
- $1 \le n,q \le 5 \times 10^4$.
- $1 \le m \le 10^5$.
- $1 \le u,v \le n$.
- $1 \le a,b \le 10^9$.
### Sample Test
Input:
```
4 5
1 4 2 1
1 3 1 2
3 4 2 2
1 2 1 3
2 4 3 2
5
4 2 2 3
1 4 3 3
1 3 4 4
2 3 2 2
1 3 2 2
```
Output
```
Yes
Yes
No
No
Yes
```
