Inspecting Radars 

Radars Inc. is a worldwide renowned radar maker, whose excellent reputation lies on strict quality assurance procedures and a large variety of radar models that fit all budgets. The company hired you to develop a detailed inspection that consists of a sequence of E experiments on a specific surveillance model.

There is a field represented with a polar coordinate plane that contains N objects placed at positions with integer polar coordinates. The inspected model is located at the origin (0, 0) of the field and can detect objects at a distance less than its detection range R through a scan area defined by four adjustment parameters $\alpha$, A, h, and H, whose meaning is illustrated with the following figure:

Formally, the scan area of the model is the region described by the set of polar points

{(r,$$\theta$$)| h $$\leq$$ r < h + H, $$\alpha$$ $$\leq$$ $$\theta$$ $$\leq$$ $$\alpha$$ + A}

$\alpha$, A, h and H are four integer values where:

• $\alpha$ specifies the start angle of the radar's scan area ( 0 $\leq$ $\alpha$ < 360);
• A specifies the opening angle of the radar's scan area ( 0 $\leq$ A < 360);
• h gives the internal radius of the radar's scan area ( 0 $\leq$ h < R); and
• H gives the height of the radar's scan area ( 1 $\leq$ H $\leq$ R).

An object placed at (r,$\theta$) will be displayed by the model if h $\leq$ r < h + H and $\alpha$ $\leq$ $\theta$ $\leq$ $\alpha$ + A, where the last inequality should be understood modulo 360^o (i.e., adding and comparing angles in a circle).

Given N objects placed on the field, you must develop an inspection of the surveillance model through the implementation of E experiments with specific parameterizations. For each experiment you have to find the maximal number of objects on the field that the radar should display if the parameters $\alpha$ ( 0 $\leq$ $\alpha$ < 360) and h ( 0 $\leq$ h < R) are free to set (as integer numbers), and the parameters H ( 1 $\leq$ H $\leq$ R) and A ( 0 $\leq$ A < 360) are given.

Input 

The input consists of several test cases. Each test case is described as follows:

• A line with two integer numbers N and R separated by blanks, representing (respectively) the number of objects located on the field and the detection range of the model ( 1 $\leq$ N $\leq$ 10⁴, 2 $\leq$ R $\leq$ 10²).
• Each one of the following N lines contains two integer numbers r_i and $\theta_{i}^{}$ separated by blanks, specifying the integer polar coordinates (r_i,$\theta_{i}^{}$) of the i-th object ( 1 $\leq$ r_i < R, 0 $\leq$ $\theta_{i}^{}$ < 360, 1 $\leq$ i $\leq$ N).
• The next line has an integer number E indicating the number of experiments of the inspection ( 1 $\leq$ E $\leq$ 10²).
• Each one of the following E lines contains two integer numbers H_j and A_j separated by blanks, representing (respectively) the fixed height and the fixed opening angle that parameterize the j-th experiment ( 1 $\leq$ H_j $\leq$ R, 0 $\leq$ A_j < 360, 1 $\leq$ j $\leq$ E).

For each test case you can suppose that there are not two different objects placed at the same integer polar coordinate. The last test case is followed by a line containing two zeros.

Output 

For each test case of the input, print E lines where the j-th line contains the maximal number of objects on the field that the radar should display according to the parameterization given for the j-th experiment ( 1 $\leq$ j $\leq$ E).

Sample Input 

6 100
15 7
15 60
40 15
50 15
45 30
45 90
2
2 1
100 359
9 100
15 7
15 60
40 15
50 15
45 30
45 90
40 45
50 45
78 100
6
100 359
11 30
10 30
11 29
5 30
11 10
0 0

Sample Output 

1
6
9
5
3
3
2
2