Car

HZ is driving a car along a straight road of length $L$. Now the car is at one end of the road, and HZ wants to go to the other end.

There are $N$ speed measuring points on the road. The distance between the start point and the $i$-th speed measuring point is $S_i$. The speed limit of the $i$-th speed measuring point is $V_i$, which means that when the car passes the point, its velocity should not exceed $V_i$.

The initial velocity of the car is zero, and the car must ${\bf stop}$ at the other end. The absolute value of acceleration of the car can not exceed $A$.

HZ wants you to calculate the shortest time to go to the other end of the road, but Zayin thinks it's too easy. Therefore, they come up with new problems for you.

Initially, there is no speed measuring point on the road. Then, the $N$ speed measuring points will be built one by one in order from $1$ to $N$. After each one is built, you need to answer whether the shortest time becomes longer or not.

There are multiple test cases.

For each test case, the first line contains $3$ integers $L$, $A$ and $N$ $(1\leq L \leq 10^5,~ 1\leq A \leq 9,~ 1\leq N \leq 10^5)$.

In the next $n$ lines, each line contains $2$ integers $S_i$ and $V_i$ $(0\leq S_i \leq L,~ 1 \leq V_i \leq 10^3)$, denoting a speed measuring point. And they will be built in order of input.

It's guaranteed that the sum of $N$ of all the test cases is not larger than $2 \cdot 10^5$.

For each test case, print $N$ lines.

In the $i$-th line of each test case, if the shortest time becomes longer after building the $i$-th one, print $1$. Otherwise, print $0$.

6 2 5
2 1
4 1
3 3
1 1
1 1

1
1
0
1
0

2021“MINIEYE杯”中国大学生算法设计超级联赛-热身赛（2021湘潭全国邀请赛-重现）