### PROBLEM LINK:

**Author:** Vitalij Kozhukhivskij

**Tester:** Praveen Dhinwa and Hiroto Sekido

**Editorialist:** Lalit Kundu

### DIFFICULTY:

Easy

### PREREQUISITES:

None at all

### PROBLEM:

- Initially the robot is at position
**(0, 0)**. - In the beginning it goes
**1**step to the East (i.e. In a single step, its x coordinate will increase by 1 unit.) - then
**2**steps to the North, (i.e. In a single step, its y coordinate will increase by 1 unit.) - then
**3**steps to the West, (i.e. In a single step, its x coordinate will decrease by 1 unit.) - then
**4**steps to the South, (i.e. In a single step, its y coordinate will decrease by 1 unit.) - then
**5**steps to the East, - and so on.

^{5}queries of form (X,Y). You have to tell if robot ever visiter the coordinate (X,Y).

### EXPLANATION:

Since number of queries is high, we need to solve all queries in O(1).

Letâ€™s consider the vertical line as y-axis and other as x-axis. If we extend the path of the robot, we can clearly observe from the path that

. Robot visits all lines of form:

x=2*k+1 //k>=0; y ranges from -2*k to 2*k+2 (both inclusive)

x=-2*k //k>=1; y ranges from -2*k to 2*k (both inclusive)

y=2*k //k>=0; x ranges from -2*k to 2*k+1 (both inclusive)

y=-2*k //k>=1; x ranges from -2*k to 2*k+1 (both inclusive)

Now, itâ€™s very trivial to find if a point (X,Y) lies on these possible lines.