AQT is playing a game. The map in this game is a tree with $N$ nodes and $N-1$ edges. Since it's a tree, there is exactly one path to connect any two nodes. AQT has $M$ weapons and the weapon $i$ can block the path from node $a_i$ to node $b_i$ with a cost $c_i$. There are $T$ monsters living in the tree. A monster $j$ will travel from node $u_j$ to node $v_j$. AQT can catch a monster if the path he blocks is an exact subpath of the monster's path. AQT can reuse his weapon, and the path is automatically unblocked after he catches a monster. However, AQT thinks this game is not challenging enough. For each monster $j$, he wants to use the $k_j^{\text{th}}$ minimal cost weapon among all the weapons which can catch the monster $j$. Can you write a program to help him?

Input Specification

The first line contains $3$ integers, $N$, $M$, and $T$ $(N,M,T\le 40000)$, which represent the number of nodes, the number of weapons, and the number of monsters, respectively.

Each of the following $N-1$ lines contains $2$ integers, $a$ and $b$ $(1\le a,b\le N)$, representing an edge between node $a$ and node $b$.

Each of the following $M$ lines contains $3$ integers, $a$, $b$ and $c$ ($1\le a,b\le N$ and $a\ne b$, $0\le c\le {10}^9$), representing a weapon which can block the path from node $a$ to node $b$ with a cost of $c$.

Each of the following $T$ lines contains $3$ integers, $a$, $b$ and $k$ $(1\le a,b\le N)$, representing a monster's path from node $a$ to node $b$ and the $k^{\text{th}}$ min cost weapon AQT wants to choose. It's guaranteed the $k^{\text{th}}$ min cost weapon exists.

Output Specification

Output one line for each monster $j$, the $k_j^{\text{th}}$ min cost to catch the monster $j$.

Sample Input 1

6 4 2
1 2
2 3
2 4
3 5
3 6
1 5 2
2 4 3
3 6 5
2 3 4
5 6 1
5 4 2

Sample Output 1

5
4

Sample Input 2

10 10 10
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10
3 2 2
10 7 1
6 7 4
6 8 5
4 6 6
8 3 3
10 4 10
10 8 9
9 2 7
4 9 8
1 8 5
3 8 3
3 8 4
1 8 3
4 8 1
2 3 1
2 3 1
2 3 1
2 4 1
1 4 1

Sample Output 2

6
5
6
4
4
2
2
2
2
2