Spanning Tree Queries

Description:

Input:

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 50$$$; $$$n - 1 \le m \le 300$$$) — the number of vertices and the number of edges in the graph.

Each of the next $$$m$$$ lines contains a description of an undirected edge: three integers $$$v$$$, $$$u$$$ and $$$w$$$ ($$$1 \le v, u \le n$$$; $$$v \neq u$$$; $$$0 \le w \le 10^8$$$) — the vertices the edge connects and its weight. Note that there might be multiple edges between a pair of vertices. The edges form a connected graph.

The next line contains five integers $$$p, k, a, b$$$ and $$$c$$$ ($$$1 \le p \le 10^5$$$; $$$p \le k \le 10^7$$$; $$$0 \le a, b \le 10^8$$$; $$$1 \le c \le 10^8$$$) — the number of queries provided explicitly, the total number of queries and parameters to generate the queries.

The next line contains $$$p$$$ integers $$$q_1, q_2, \dots, q_p$$$ ($$$0 \le q_j < c$$$) — the first $$$p$$$ queries.

Output:

Print a single integer — the xor of answers to all queries.

Sample Input:

5 8
4 1 4
3 1 0
3 5 3
2 5 4
3 4 8
4 3 4
4 2 8
5 3 9
3 11 1 1 10
0 1 2

Sample Output:

4

Sample Input:

6 7
2 4 0
5 4 7
2 4 0
2 1 7
2 6 1
3 4 4
1 4 8
4 10 3 3 7
3 0 2 1

Sample Output:

5

Sample Input:

3 3
1 2 50
2 3 100
1 3 150
1 10000000 0 0 100000000
75

Sample Output:

164

Note:

The queries in the first example are $$$0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0$$$. The answers are $$$11, 9, 7, 3, 1, 5, 8, 7, 5, 7, 11$$$.

The queries in the second example are $$$3, 0, 2, 1, 6, 0, 3, 5, 4, 1$$$. The answers are $$$14, 19, 15, 16, 11, 19, 14, 12, 13, 16$$$.

The queries in the third example are $$$75, 0, 0, \dots$$$. The answers are $$$50, 150, 150, \dots$$$.