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There are $N$ circles in a plane. Circle $i$ and circle $j$ form a good pair if it is possible to choose a point $P_{1}$ on the perimeter of circle $i$ and a point $P_{2}$ on the perimeter of circle $j$ such that the Euclidean distance between $P_{1}$ and $P_{2}$ is exactly $K$. (Note that $P_{1}$ and $P_{2}$ do not need to have integer coordinates.)

You should answer $Q$ queries. In each query, you are given the required distance $K$. Chef is interested in finding the number of good pairs of distinct circles for each query. Please help him.

Note: Circle $i$ and circle $j$ are distinct when $i \neq j$. There may be any number of circles that coincide (have identical centers and radii).

------ Input ------
The first line of the input contains two space-separated integers $N$ and $Q$ denoting the number of circles and the number of queries respectively.
Each of the following $N$ lines contains three space-separated integers $X$, $Y$ and $R$ describing a circle with radius $R$ and center $(X, Y)$.
Each of the next $Q$ lines contains one integer $K$ describing a query.

------ Output ------
For each query, print a single line containing one integer — the number of good pairs of circles.

------ Constraints ------
$2 ≤ N ≤ 10^{3}$
$1 ≤ Q ≤ 5\cdot 10^{5}$
$X, Y ≤ |2\cdot 10^{5}|$
$1 ≤ R ≤ 2\cdot 10^{5}$
$0 ≤ K ≤ 10^{6}$

------ Subtasks ------
Subtask #1 (30 points):
$2 ≤ N ≤ 10^{2}$
$1 ≤ Q ≤ 5\cdot 10^{2}$

Subtask #2 (70 points): original constraints

----- Sample Input 1 ------
2 3

0 0 5

8 3 2

0

10

20
----- Sample Output 1 ------
0

1

0
----- explanation 1 ------
The distance between the point $(0.00, -5.00)$ on circle $1$ and the point $(8.00, 1.00)$ on circle $2$ is $10$. There is no pair of points on these two circles with distance $0$ or $20$.

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