Ali Mansour was having a breakfast with his friends at the dorm. He will pour tea in their cups. He wanted to make the breakfast more exciting, so he decided to throw a drop of tea at their cups.
Ali will throw the drop randomly from point $(0, 0)$ at a random (formally random) angle between $L$ and $R$ with initial speed $V$.
He has $N$ friends, and each has a cup of different width. Let's assume that each cup has a $0$ height and is placed on the ground (The $X$ Axis). Given each cup's position, for each cup calculate the probability that the drop will fall in this cup. Note: it's possible for two cups to overlap or intersect.
First line of input will be $T$ the number of test cases.
Each test case is described by $4$ space separated integers, $N, V, L, R$ ($1 <= N <= 1000$), ($1 <= V <= 10^9$), ($0 <= L <= R <= 90$).
Then $N$ lines, the positions of the cups ($X 1_i$, $X 2_i$), ($0 <= X 1_i < X 2_i <= 10^9$)
For each test case print $N$ lines. in the $I_{t h}$ line print the probability that the drop will fall in the $I_{t h}$ cup.
Print the probability rounded to exactly $4$ digits
Consider $g$ = $10$ $m$.$s^(-2)$
## Input
First line of input will be $T$ the number of test cases.Each test case is described by $4$ space separated integers, $N, V, L, R$ ($1 <= N <= 1000$), ($1 <= V <= 10^9$), ($0 <= L <= R <= 90$).Then $N$ lines, the positions of the cups ($X 1_i$, $X 2_i$), ($0 <= X 1_i < X 2_i <= 10^9$)
## Output
For each test case print $N$ lines. in the $I_(t h)$ line print the probability that the drop will fall in the $I_(t h)$ cup.Print the probability rounded to exactly $4$ digits
[samples]
## Note
Consider $g$ = $10$ $m$.$s^(-2)$
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case:
- Let $ N \in \mathbb{Z} $ be the number of cups.
- Let $ V > 0 $ be the initial speed (m/s).
- Let $ L, R \in \mathbb{R} $ be the lower and upper bounds of the launch angle (degrees), with $ 0 \le L < R \le 90 $.
- For $ i \in \{1, \dots, N\} $, let $ [x_{1,i}, x_{2,i}] \subset \mathbb{R}_{\ge 0} $ be the interval on the x-axis representing the $ i $-th cup’s width, with $ 0 \le x_{1,i} < x_{2,i} \le 10^9 $.
- Let $ g = 10 \, \text{m/s}^2 $ be the gravitational acceleration.
**Constraints**
1. $ 1 \le T \le \text{unknown} $ (implied by input format)
2. $ 1 \le N \le 1000 $
3. $ 1 \le V \le 10^9 $
4. $ 0 \le L < R \le 90 $
5. $ 0 \le x_{1,i} < x_{2,i} \le 10^9 $ for all $ i \in \{1, \dots, N\} $
**Objective**
For each cup $ i $, compute the probability $ P_i $ that a projectile launched from $ (0,0) $ with speed $ V $ and angle $ \theta \sim \text{Uniform}(L^\circ, R^\circ) $ lands within $ [x_{1,i}, x_{2,i}] $.
The horizontal range of a projectile is:
$$
x(\theta) = \frac{V^2 \sin(2\theta)}{g}, \quad \theta \in [L^\circ, R^\circ]
$$
Convert angles to radians: $ \theta_{\text{rad}} = \theta \cdot \frac{\pi}{180} $.
Let $ \Theta \sim \text{Uniform}(L, R) $ in degrees. Define the range function:
$$
f(\theta) = \frac{V^2}{g} \sin\left(2 \cdot \theta \cdot \frac{\pi}{180}\right)
$$
Then:
$$
P_i = \mathbb{P}\left( x_{1,i} \le f(\Theta) \le x_{2,i} \right) = \frac{1}{R - L} \cdot \mu\left( \left\{ \theta \in [L, R] : f(\theta) \in [x_{1,i}, x_{2,i}] \right\} \right)
$$
where $ \mu $ denotes Lebesgue measure (length) of the set of angles satisfying the condition.
**Output**
For each test case, output $ N $ lines, each containing $ P_i $ rounded to exactly 4 decimal places.