Travel

Time Limit: 1500/1000 MS (Java/Others)

Memory Limit: 131072/131072 K (Java/Others)

Description

Jack likes to travel around the world, but he doesn’t like to wait. Now, he is traveling in the Undirected Kingdom. There are $n$ cities and $m$ bidirectional roads connecting the cities. Jack hates waiting too long on the bus, but he can rest at every city. Jack can only stand staying on the bus for a limited time and will go berserk after that. Assuming you know the time it takes to go from one city to another and that the time Jack can stand staying on a bus is $x$ minutes, how many pairs of city $(a, b)$ are there that Jack can travel from city $a$ to $b$ without going berserk?

Input

The first line contains one integer $T, T \leq 5$, which represents the number of test case.

For each test case, the first line consists of three integers $n, m$ and $q$ where $n \leq 20000, m \leq 100000, q \leq 5000$. The Undirected Kingdom has $n$ cities and $m$ bidirectional roads, and there are $q$ queries.

Each of the following $m$ lines consists of three integers $a, b$ and $d$ where $a, b ∈ \{1, . . . , n\}$ and $d \leq 100000$. It takes Jack $d$ minutes to travel from city $a$ to city $b$ and vice versa.

Then $q$ lines follow. Each of them is a query consisting of an integer $x$ where $x$ is the time limit before Jack goes berserk.

Output

You should print $q$ lines for each test case. Each of them contains one integer as the number of pair of cities $(a, b)$ which Jack may travel from $a$ to $b$ within the time limit $x$.

Note that $(a, b)$ and $(b, a)$ are counted as different pairs and $a$ and $b$ must be different cities.

Sample Input

1 5 5 3 2 3 6334 1 5 15724 3 5 5705 4 3 12382 1 3 21726 6000 10000 13000

Sample Output

2 6 12

Hint

hujie

Source

2015 ACM/ICPC Asia Regional Changchun Onlin

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