D. Odd Mineral Resource
time limit per test
5 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

In Homer's country, there are $$$n$$$ cities numbered $$$1$$$ to $$$n$$$ and they form a tree. That is, there are $$$(n-1)$$$ undirected roads between these $$$n$$$ cities and every two cities can reach each other through these roads.

Homer's country is an industrial country, and each of the $$$n$$$ cities in it contains some mineral resource. The mineral resource of city $$$i$$$ is labeled $$$a_i$$$.

Homer is given the plans of the country in the following $$$q$$$ years. The plan of the $$$i$$$-th year is described by four parameters $$$u_i, v_i, l_i$$$ and $$$r_i$$$, and he is asked to find any mineral resource $$$c_i$$$ such that the following two conditions hold:

  • mineral resource $$$c_i$$$ appears an odd number of times between city $$$u_i$$$ and city $$$v_i$$$; and
  • $$$l_i \leq c_i \leq r_i$$$.

As the best friend of Homer, he asks you for help. For every plan, find any such mineral resource $$$c_i$$$, or tell him that there doesn't exist one.

Input

The first line contains two integers $$$n$$$ ($$$1 \leq n \leq 3 \cdot 10^5$$$) and $$$q$$$ ($$$1 \leq q \leq 3 \cdot 10^5$$$), indicating the number of cities and the number of plans.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \leq a_i \leq n$$$).

Then the $$$i$$$-th line of the following $$$(n-1)$$$ lines contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \leq x_i, y_i \leq n$$$) with $$$x_i \neq y_i$$$, indicating that there is a bidirectional road between city $$$x_i$$$ and city $$$y_i$$$. It is guaranteed that the given roads form a tree.

Then the $$$i$$$-th line of the following $$$q$$$ lines contains four integers $$$u_i$$$, $$$v_i$$$, $$$l_i$$$, $$$r_i$$$ ($$$1 \leq u_i \leq n$$$, $$$1 \leq v_i \leq n$$$, $$$1 \leq l_i \leq r_i \leq n$$$), indicating the plan of the $$$i$$$-th year.

Output

Print $$$q$$$ lines, the $$$i$$$-th of which contains an integer $$$c_i$$$ such that

  • $$$c_i = {-1}$$$ if there is no such mineral resource that meets the required condition; or
  • $$$c_i$$$ is the label of the chosen mineral resource of the $$$i$$$-th year. The chosen mineral resource $$$c_i$$$ should meet those conditions in the $$$i$$$-th year described above in the problem statement. If there are multiple choices of $$$c_i$$$, you can print any of them.
Example
Input
6 8
3 2 1 3 1 3
1 2
1 3
2 4
2 5
4 6
3 5 1 1
3 5 1 3
3 5 1 3
1 1 2 2
1 1 3 3
1 4 1 5
1 6 1 3
1 6 1 3
Output
-1
2
3
-1
3
2
2
3
Note

In the first three queries, there are four cities between city $$$3$$$ and city $$$5$$$, which are city $$$1$$$, city $$$2$$$, city $$$3$$$ and city $$$5$$$. The mineral resources appear in them are mineral resources $$$1$$$ (appears in city $$$3$$$ and city $$$5$$$), $$$2$$$ (appears in city $$$2$$$) and $$$3$$$ (appears in city $$$1$$$). It is noted that

  • The first query is only to check whether mineral source $$$1$$$ appears an odd number of times between city $$$3$$$ and city $$$5$$$. The answer is no, because mineral source $$$1$$$ appears twice (an even number of times) between city $$$3$$$ and city $$$5$$$.
  • The second and the third queries are the same but they can choose different mineral resources. Both mineral resources $$$2$$$ and $$$3$$$ are available.