In this problem, you will be given N circles, and M points. You are required to find out how many circles each of the M points lies. None of the M points will lie on any of the N circle boundaries (they will either lie inside a circle or outside it, but not on the circle).

Input

The 1st line gives the number of test cases T.

Each of the next T test cases has a format as explained below.

The 1st line of each test case contains 2 integers N and M.

Each of next N lines contains 3 integers cx, cy, r. The circle is located at center (cx, cy) and has a radius r.

Each of the following M lines contain 2 integers (x, y), which are the location of a point.

Output

For each of test case, print M lines, each corresponding to the number of circles the point is inside.

Separate each test case with a blank line.

Example

Input:
1
2 3
3 3 2
1 1 2
1 1
2 2
3 3

Output:
1
2
1

Constraints

T ≤ 100
0 ≤ N ≤ 500
0 ≤ M ≤ 500
-1000 ≤ cx ≤ 1000
-1000 ≤ cy ≤ 1000
-1000 ≤ x ≤ 1000
-1000 ≤ y ≤ 1000
1 ≤ r ≤ 1000