Given 2 points in 2 dimensional space (xs, ys) and (xd, yd), your task is to find whether (xd, yd) can be reached from (xs, ys) by making a sequence of zero or more operations.

From a given point (x, y), the operations possible are:

• Move to point (y, x)
• Move to point (x, -y)
• Move to point (x + y, y)
• Move to point (2 * x, y)

Input

The first line of input contains T, the number of test cases. T lines follow, one for each test case. For each test case, the input contains one line denoting the 4 integers xs, ys, xd, yd

Output

Output T lines, one for each test case. For each test case, output "YES" if (xd, yd) is reachable from (xs, ys) and "NO" otherwise. (quotes for clarity)

Example

Input:
1
1 1 2 2

Output:
YES

Constraints

T <= 25

-10^10 <= xs, ys, xd, yd <= 10^10

Note that, although the input values are constrained by the above inequality, the coordinates of the points at the intermediate steps need not be.

Explanation

Test case 1: We can move in the following manner: (1,1) → (2,1), using the operation (x, y) → (2 * x, y). Then, move from (2, 1) → (1, 2), using the operation (x, y) → (y, x). Finally use the operation (x, y) → (2 * x, y) to move from (1, 2) → (2, 2).