E. Graduation Decorations
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

$$$Nowar$$$ and $$$Abodeh$$$ are organizing their graduation party. To make the place look more festive, they decided to prepare a large rectangular decoration board of size $$$n \times m$$$.

They have collected several decorative pieces that can be placed on the board:

  • $$$s$$$ square tiles of size $$$1 \times 1$$$;
  • $$$r$$$ rectangular tiles of size $$$1 \times 2$$$;
  • $$$t$$$ right triangular tiles with legs of length $$$1$$$ and $$$1$$$.

Tiles may be rotated by any multiple of $$$90^\circ$$$. Each tile may be used at most once.

$$$Nowar$$$ has a specific design in mind. He wants the decorations to cover exactly a fraction $$$\frac{a}{b}$$$ of the total board area. $$$Abodeh$$$ is not sure whether this can be achieved using the available tiles, so he asks for your help.

No two tiles may overlap.

Determine whether it is possible to choose and place some of the available tiles so that the total covered area is exactly $$$\frac{a}{b}$$$ of the board's area.

Input

The first line contains a single integer $$$T$$$ — the number of test cases.

Each test case consists of seven integers: $$$[n\ m\ s\ r\ t\ a\ b]$$$

  • $$$1 \le T \le 10^4$$$
  • $$$1 \le n, m \le 10^4$$$
  • $$$0 \le s, r, t \le 10^9$$$
  • $$$0 \le a \le 10^4$$$
  • $$$1 \le b \le 10^4$$$
  • $$$a \le b $$$

where:

  • $$$n$$$ and $$$m$$$ are the dimensions of the board;
  • $$$s$$$ is the number of square tiles;
  • $$$r$$$ is the number of rectangular tiles;
  • $$$t$$$ is the number of triangular tiles;
  • $$$\frac{a}{b}$$$ is the required fraction of the board area.
Output

For each test case, print: YES if it is possible to obtain exactly the required area, or NO otherwise.

You may print each letter in any case.

Example
Input
4
2 2 2 1 0 1 1
3 3 1 1 1 1 2
1 1 0 0 1 1 2
2 3 1 1 0 5 6
Output
YES
NO
YES
NO