Problem Description

Given a pair of numbers $(a,b)$, you may use any of the vectors $(a,b)$, $(a,-b)$, $(-a,b)$, $(-a,-b)$, $(b,a)$, $(b,-a)$, $(-b,a)$, $(-b,-a)$ in arbitrary quantities. Determine whether you can form another vector $(x,y)$.

Note: Here, “form” means that the sum of the vectors you choose equals $(x,y)$.

Input Format

The first line contains the number of test cases $t$ ($t \le 50000$).

The next $t$ lines each contain four integers $a, b, x, y$ ($-2\times 10^9 \le a, b, x, y \le 2\times 10^9$).

Output Format

Output $t$ lines. Each line is Y if it is possible, or N if it is not.

3
2 1 3 3
1 1 0 1
1 0 -2 3

Y
N
Y

Hint

Sample Explanation

Group 1: $(2,1) + (1,2) = (3,3)$.

Group 3: $(-1,0) + (-1,0) + (0,1) + (0,1) + (0,1) = (-2,3)$.

Translated by ChatGPT 5