Classic problems in competitive programming are problems frequently appearing in programming contests. This problem is also a very classic one in the field of computational geometry.

It asks to determine which points are covered by a given simple polygon.

To state the problem precisely, we first give the definition of a polygon.

A polygon of \(n\) edges is described by \(n\) straight line segments \(e_1, e_2, \dots, e_n\) connected to form a closed chain.

That is, there exists a sequence of vertices \(v_1 = (x_1, y_1), v_2 = (x_2, y_2), \dots, v_n = (x_n, y_n)\) such that:

• \(e_n = v_n v_1\)
• \(e_i = v_i v_{i+1}\) for \(1 \le i < n\)

So a polygon can be defined by the sequence of vertices \(v_1, v_2, \dots, v_n\).

A simple polygon is a polygon that does not intersect itself. That is, any two line segments may only meet at their endpoints.

Therefore, a simple polygon encloses a region called its interior.

A point \(p\) is covered by a simple polygon \(P\) if and only if:

• \(p\) lies on some edge of \(P\), or
• \(p\) lies inside the interior of \(P\).

Task

You are given:

• A simple polygon with \(n\) edges defined by a sequence of vertices.
• \(m\) points on the \(2D\) plane.

Determine for each point whether it is covered by the given simple polygon.

Input

The first line contains two space-separated positive integers:

• \(n\) — number of edges of the simple polygon
• \(m\) — number of query points

Then \(n + m\) lines follow.

For \(1 \le i \le n\), the \((i+1)\)-th line contains two space-separated integers \(x_i\) and \(y_i\), where \(v_i = (x_i, y_i)\).

For \(1 \le j \le m\), the \((1 + n + j)\)-th line contains two space-separated integers \(X_j\) and \(Y_j\), where \(p_j = (X_j, Y_j)\).

Output

Output \(m\) lines. On the \(j\)-th line:

• Print YES if \(p_j\) is covered by the polygon.
• Otherwise, print NO.

Constraints

• \(3 \le n \le 10^5\)
• \(1 \le m \le 10^5\)
• The sequence \(v_1, v_2, \dots, v_n\) always defines a simple polygon.
• \(x_i, y_i \in [-10^9, 10^9]\) for \(1 \le i \le n\)
• \(X_j, Y_j \in [-10^9, 10^9]\) for \(1 \le j \le m\)

Example

3 3
0 0
5 5
5 0
1 1
1 2
2 1

YES
NO
YES

4 4
0 0
1 1
2 0
1 5
1 0
1 1
1 2
1 3

NO
YES
YES
YES