Task

You are given K points with positive integer coordinates. You are also given M triangles, each of them having one vertex in the origin and the other 2 vertices with non-negative integer coordinates.

You are asked to determine for each triangle whether it has at least one of the K given points inside. (None of the K points are on any edge of any triangle.)

Input

The first line of the input file will contain K and M. The following K lines will contain 2 positive integers x y separated by one space that represent the coordinates of each point. The next M lines have 4 non-negative integers separated by one space, (x1, y1) and (x2, y2), that represent the other 2 vertices of each triangle, except the origin.

Output

The output file should contain exactly M lines. The k-th line should contain the character Y if the k-th triangle (in the order of the input file) contains at least one point inside it, or N otherwise.

Constraints

• 1 ≤ K,M ≤ 100 000
• 1 ≤ each coordinate of the K points ≤ 10⁹
• 0 ≤ each coordinate of the triangle vertices ≤ 10⁹
• Triangles are not degenerate (they all have nonzero area).
• In 50% of the test cases, all triangles have vertices with coordinates x1=0 and
  y2=0. That is, one edge of the triangle is on the x-axis, and another is on the y-axis.

Sample input 1

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

Sample output 1

Y
N
Y

Explanation for sample 1

Sample input 2

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

Sample output 2

N
Y

Explanation for sample 2

CEOI 2009 - Tîrgu Mureş, Romania