Scientists who specialize in witchcraft have recently discovered a new elementary particle called a magion. Studying the laws of magions’ movement, a group of three scientists conducts the following experiment.

The scientists created positvie homogeneous aura in the laboratory. The force of interaction with this aura has constant value and is up-directed. If no other force affects the magion, the aura will make the magion move with constant acceleration (0,0,a).

A magion with initial speed equal to zero is placed to the point M₁ = (0,0,0). At the beginning the first scientist creates a bundle of mana at the point O₁. Magion is immediately affected by the bundle and while the latter exists it will be at the distance O₁M₁ from the point O₁. As a result, the magion starts moving up along the arc of the circle omega₁ with the center at O₁.

At some moment the first scientist annihilates the bundle of mana at O₁, and the second scientist at the same time creates his own bundle at the point O₂. The moment for this is being chosen in the following way.

The position of the point O₂ is being chosen so that the point M₂ is uniquely determined and does not coincide with the point M₁. Affected by the second bundle, the magion continues its movement along the circle omega₂ with the center at the point O₂ and with the point M₂ on it.

After that the procedure is repeated, i. e. the second scientist annihilates his bundle of mana, and the third one creates his own bundle at the point O₃. The magion, being at this moment at the point M₃, now starts moving along the circle omega₃ with the center in O₃. The third scientist waits until the magion finishes the full circle along omega₃ and returns to the point M₃. This moment is considered the end of the experiment.

All scientists choose moments and points to create bundles of mana so that the point M_i does not coincide neither with M_i−1 nor O_i, and the distance from O_i to any point of the circle omega_i−1, other than M_i, is strictly greater than O_iM_i. Apart from that, at every moment except the initial one the scientists don’t allow the magion’s speed to be zero.

At any moment of time the magion is affected by exactly two forces: the force of interaction with the bundle of mana and the force of interaction with the aura. The first one is always directed perpendicularly to the magion’s path of motion and therefore doesn’t affect the absolute value of magion’s speed.

Knowing the coordinates of the points O_i and the value of the acceleration a being imparted to the magion by the positive aura, will you be able to define the overall length of the magion’s path segments where its speed is not less than v?

The first line contains an integer t that is the number of experiments (1 ≤ t ≤ 1000). Then the description of the experiments follows, each of them is described by a block of four lines.

The first line of each block contains integers v and a (1 ≤ v ≤ 50 000; 1 ≤ a ≤ 1000). Each of the following three lines contains integers x_i, y_i, z_i, which are the coordinates of the point O_i (−10⁶ ≤ x_i, y_i, z_i ≤ 10⁶; x₁² + y₁² > 0). It is guaranteed that the magion’s path won’t have a horizontal arc it will follow with the speed exactly v.

For each experiment output in a separate line the overall length of the magion’s path segments where its speed is not less than v. The answers should be output with an absolute of relative error not more than 10⁻⁶.

There is one experiment in the example. The path looks the following way:
from point (0,0,0) to point (4,0,2): an arc with measure equal to arcsin(0.8) of the circle with the radius 5;
from point (4,0,2) to point (20,16,2): a quarter of the circle with the radius 16;
from point (20,16,2) to point (20,16,2): a full circle with the radius 1.