There is a planet named “Ruizland” having $N$ cities, These cities are connected in the form of a tree by a bidirectional path of specified length(in miles). Cities are numbered from $1$ to $N$. City number $1$ is the capital city.

$M$ pilgrims started their journey from the capital city having initial energy $E_{1}, E_{2}, \ldots, E_{M}$ respectively which reduces on moving from one city to another by a certain amount$(A)$.
$A$ is calculated as follows:-
Consider two cities $U$ and $V$ having an edge length of $K$ miles.
The total number of distinct cities from the capital city to the city $U$ is $D$ (city $U$ and capital city both are inclusive).
If a pilgrim moves from city $U$ to $V$, then $A=K*D$.

Out of $N$ cities, There are some special cities (except the capital city) that are connected to only one city. All pilgrims want to reach any of the special cities. A pilgrim will stop his journey as soon as the energy of the pilgrims becomes $0$ or reaches any of the special cities.

Initially, all cities have $0$ pilgrims except the capital city.

Find the maximum count of special cities that is non-empty (at least one pilgrim is present) after the end of the journey of all the pilgrims given that pilgrims are allowed to take any path during their journey.

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains two integers $N$ and $M$ separated by space, where $N$ is the number of cities and $M$ is the number of pilgrims.
The second line contains $M$ integers separated by spaces, denoting the initial energy of the pilgrims.
Next, $N-1$ lines consists of three integers $U$, $V$ and $K$ separated by space where city $U$ and $V$ are connected by a bidirectional path whose length is $K$ miles

------ Output ------
For each test case, Print the maximum count of special cities that is non-empty (at least one pilgrim is present) after the end of the journey of all the pilgrims.

------ Constraints ------
$1 ≤ T ≤ 50$
$2 ≤ N ≤ 10^{5}$
$1 ≤ M ≤ 10^{5}$
$1 ≤ E_{i} ≤ 10^{18}$
$1 ≤ U, V ≤ N$
$1 ≤ K ≤ 10^{6}$
It is guaranteed that the sum of $N$ over all test cases does not exceed $10^{5}$.
It is guaranteed that the sum of $M$ over all test cases does not exceed $10^{5}$.

----- Sample Input 1 ------
1
6 4
100 20 10 50
1 2 10
2 3 20
2 4 30
4 5 40
1 6 50
----- Sample Output 1 ------
2
----- explanation 1 ------
There are $3$ special cities namely $3, 5$ and $6$. The energy expected to reach these special cities are $50, 190$ and $50$ respectively. Special city $5$ cannot be reached by any pilgrim. If Pilgrim $1$ goes to the special city $3$ and pilgrim $4$ goes to the special city $6$, then the maximum number of non-empty special cities is $2$.

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