D. Unmanned Interceptors
time limit per test
2.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

In a future autonomous interception drill, commander Alice uses $$$n$$$ unmanned interceptors (denoted as $$$A_1, A_2, \ldots, A_n$$$) to surround an intruding target $$$B$$$ controlled by Bob. All units move on a two-dimensional plane. Whether the interception succeeds depends not only on the initial layout, but also on the path planning strategies of both participants.

You are given the initial coordinates $$$A_i(x_i, y_i)$$$ of the $$$n$$$ interceptors and the starting position $$$(x_0, y_0)$$$ of target $$$B$$$ on the 2D plane.

Game Rules:

  1. Equal speed movement: All interceptors $$$A_i$$$ and target $$$B$$$ move at a constant speed $$$v$$$ ($$$v \gt 0$$$) at all times. They can change direction instantly at any moment.
  2. Interception rule: If at any moment $$$t \ge 0$$$, any interceptor $$$A_i$$$ coincides with target $$$B$$$ in position, the interception succeeds and Alice wins.
  3. Optimal play: Alice controls all interceptors cooperatively to complete the interception, while Bob controls target $$$B$$$ to avoid being caught by any $$$A_i$$$ permanently. Both sides can track each other's positions in real time and will adopt optimal strategies.

There are $$$q$$$ independent queries. For each query, a new initial position $$$(x_0, y_0)$$$ of target $$$B$$$ is given. For every query, determine whether Alice is able to catch Bob under optimal play from both sides.

Input

The first line contains two positive integers $$$n, q$$$ ($$$1 \le n,q \le 2 \times 10^5$$$).

The next $$$n$$$ lines each contain two integers $$$x_i, y_i$$$, representing the coordinates of $$$A_i$$$ ($$$-10^9 \le x_i, y_i \le 10^9$$$).

The next $$$q$$$ lines each contain two integers $$$x_0, y_0$$$, representing the initial position of target $$$B$$$ in the corresponding query.

Output

Print $$$q$$$ lines in total. For each line, output either Yes or No. Print Yes if Alice can catch Bob, otherwise print No. The answer is case-insensitive.

Example
Input
5 5
0 0
6 0
0 6
1 0
0 1
1 0
0 1
2 0
1 1
-1 0
Output
YES
YES
NO
YES
NO