A949. Milk Visits--Gold

Farmer John is planning to build $N$ ($1 \leq N \leq 10^5$) farms that will be
connected by $N-1$ roads, forming a tree (i.e., all farms are reachable from
each-other, and there are no cycles). Each farm contains a cow with an integer
type $T_i$ between $1$ and $N$ inclusive.
Farmer John's $M$ friends ($1 \leq M \leq 10^5$) often come to visit him.
During a visit with friend $i$, Farmer John will walk with his friend along
the unique path of roads from farm $A_i$ to farm $B_i$ (it may be the case
that $A_i = B_i$). Additionally, they can try some milk from any cow along the
path they walk. Since most of Farmer John's friends are also farmers, they
have very strong preferences regarding milk. Each of his friends will only
drink milk from a certain type of cow. Any of Farmer John's friends will only
be happy if they can drink their preferred type of milk during their visit.
Please determine whether each friend will be happy after visiting.

* Test case 2 is the second example case below.
* Test case 3 satisfies $N\le 10^3, M\le 2\cdot 10^3$.
* Test cases 4-7 satisfy $C_i\le 10$ ($C_i$ defined below).

The first line contains two integer $N$ and $M$.
The second line contains $N$ space-separated integers $T_1,T_2,\ldots, T_N.$
The type of the cow in the $i$-th farm is denoted by $T_i.$
The next $N-1$ lines each contain two distinct integers $X$ and $Y$ ($1 \leq
X, Y \leq N$), indicating that there is an edge between farms $X$ and $Y$.
The next $M$ lines contain integers $A_i$, $B_i$, and $C_i$. $A_i$ and $B_i$
represent the endpoints of the path walked during friend $i$'s visit, while
$C_i$ ($1\le C_i\le N$) indicates the type of cow whose milk the friend enjoys
drinking.

10110
In this example, the path from 1 and 4 involves farms 1, 2, and 4. All of