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 400\,000)~, 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