You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 4.0 seconds
Memory limit: 512.0 MB

# Problem
Gildong was hiking a mountain, walking by millions of trees. Inspired by them, he suddenly came up with an interesting idea for trees in data structures: What if we add another edge in a tree?

Then he found that such tree-like graphs are called 1-trees. Since Gildong was bored of solving too many tree problems, he wanted to see if similar techniques in trees can be used in 1-trees as well. Instead of solving it by himself, he's going to test you by providing queries on 1-trees.

First, he'll provide you a tree (not 1-tree) with $$$n$$$ vertices, then he will ask you $$$q$$$ queries. Each query contains $$$5$$$ integers: $$$x$$$, $$$y$$$, $$$a$$$, $$$b$$$, and $$$k$$$. This means you're asked to determine if there exists a path from vertex $$$a$$$ to $$$b$$$ that contains exactly $$$k$$$ edges after adding a bidirectional edge between vertices $$$x$$$ and $$$y$$$. A path can contain the same vertices and same edges multiple times. All queries are independent of each other; i.e. the added edge in a query is removed in the next query.

## Input Format
The first line contains an integer $$$n$$$ ($$$3 \le n \le 10^5$$$), the number of vertices of the tree.

Next $$$n-1$$$ lines contain two integers $$$u$$$ and $$$v$$$ ($$$1 \le u,v \le n$$$, $$$u \ne v$$$) each, which means there is an edge between vertex $$$u$$$ and $$$v$$$. All edges are bidirectional and distinct.

Next line contains an integer $$$q$$$ ($$$1 \le q \le 10^5$$$), the number of queries Gildong wants to ask.

Next $$$q$$$ lines contain five integers $$$x$$$, $$$y$$$, $$$a$$$, $$$b$$$, and $$$k$$$ each ($$$1 \le x,y,a,b \le n$$$, $$$x \ne y$$$, $$$1 \le k \le 10^9$$$) – the integers explained in the description. It is guaranteed that the edge between $$$x$$$ and $$$y$$$ does not exist in the original tree.

## Output Format
For each query, print "YES" if there exists a path that contains exactly $$$k$$$ edges from vertex $$$a$$$ to $$$b$$$ after adding an edge between vertices $$$x$$$ and $$$y$$$. Otherwise, print "NO".

You can print each letter in any case (upper or lower).

## Examples
```input
5
1 2
2 3
3 4
4 5
5
1 3 1 2 2
1 4 1 3 2
1 4 1 3 3
4 2 3 3 9
5 2 3 3 9
```
```output
YES
YES
NO
YES
NO
```

## Note
The image below describes the tree (circles and solid lines) and the added edges for each query (dotted lines).

Possible paths for the queries with "YES" answers are:

- $$$1$$$-st query: $$$1$$$ – $$$3$$$ – $$$2$$$
- $$$2$$$-nd query: $$$1$$$ – $$$2$$$ – $$$3$$$
- $$$4$$$-th query: $$$3$$$ – $$$4$$$ – $$$2$$$ – $$$3$$$ – $$$4$$$ – $$$2$$$ – $$$3$$$ – $$$4$$$ – $$$2$$$ – $$$3$$$

Now solve the problem and return the code.