Carving Pumpkins (part 1)

Note: This problem statement is identical to Carving Pumpkins (part 2), but requires rectangular eye and mouth shapes.

Now that we've bought some pumpkins, it's time to carve them into Jack-o'-lanterns.

A pumpkin can be considered an ellipse:

pumpkin-ellipse

Let's place the pumpkin on a coordinate axis, with its center exactly in $(0, 0)$ . Note that a point $(x, y)$ is strictly inside an ellipse with width $2 \cdot a$ and height $2 \cdot b$ if:

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} < 1.

(If this formula seems off-putting, make sure to check out the pumpkin carving simulator!)

We want to carve a pair of eyes and a mouth into our pumpkin, according to the following rules:

The area of each eye must be exactly $E$ .
The area of the mouth must be exactly $M$ .
The eyes and the mouth must be rectangles with sides parallel to the coordinate axes.
The vertices of each shape must be in integer coordinates.
The left eye, the right eye, and the mouth cannot touch or intersect each other.
The eyes and the mouth cannot touch or go beyond the pumpkin shape (the ellipse).
The mouth must reside strictly below the x-axis.
Both eyes must reside strictly above the x-axis.
The left eye must reside strictly to the left of y-axis.
The right eye must reside strictly to the right of y-axis.

Given the width $W$ and height $H$ of the pumpkin, find a carving that satisfies the above constraints.

Input

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

Each test case contains 4 integers $W$ , $H$ , $E$ , $M$ .

Constraints

$10 \leq H, W \leq 100$
$1 \leq E, M \leq 2000$
The input data will be chosen in such a way that at least one valid carving exists.

Output

For each test case, print Case #i:, followed by 3 lines.

On the first line, print 4 integers leftX topY rightX bottomY, where $(l e f tX, t o p Y)$ are the coordinates of the left eye's top left corner, and $(r i g h tX, b o tt o mY)$ are the coordinates of the left eye's bottom right corner.

The second line must define the right eye in the same format.

The third line must define the mouth in the same format.

Any carving that satisfies the rules will be accepted.

Examples

Input

2
33 24 8 56
33 24 10 10

Output

Case #1:
-6 1 -2 3
2 1 6 3
-7 -5 7 -1
Case #2:
-7 3 -2 1
4 6 6 1
-3 -3 2 -5

Explanation

Case 1. We have a pumpkin with height 24 and width 33, and need to carve out eyes with area 8 and mouth with area 56. The sample output makes them perfectly symmetric (as a good Jack o'lantern should be).

sample1

Case 2. We have a pumpkin with height 24 and width 33, and need to carve out eyes with area 10 and mouth with area 10. The sample output specifies a rather terrible carving, but it fits our rules regardless.

sample1

Feel free to try different carvings with the following simulator.