Orig Description
Problem J: SolveMe
In each room, a picture of a rabbit is drawn. If you stand up and lean to the right ear in room $r$, you can instantly move to the room $A[r]$ written there. Similarly, if you stand up and lean to the left ear, you can instantly move to the room $B[r]$.
Integers $X$, $Y$, and $Z$ are given. You are trying to set up instant teleportation so that the following conditions are met. How many ways are there to set up instant teleportation to meet the conditions? Output the remainder when the answer is divided by $1,000,000,007$.
Condition: Stand in a certain room $r$, lean your right ear $X$ times, lean your left ear once, lean your right ear $Y$ times, lean your left ear once, and then return to the original room $r$.
Constraints
$N$ is an integer between $1$ and $1,000$ inclusive.
$X$, $Y$, and $Z$ are integers between $0$ and $1,000,000,000,000,000,000$ inclusive.
Input format
The input is given in the following format:
$N$ $X$ $Y$ $Z$
Output format
Output the number of ways to set it up, divided by $1,000,000,007$, on one line.
Sample Input 1
3 1 0 1
Sample Output 1
18
Sample Input 2
5 8 5 8
Sample Output 2
120
Extracted Specification
Canonicalized Input Description:
An integer N (1 ≤ N ≤ 1,000), representing some quantity or size.
An integer X (0 ≤ X ≤ 1e18).
An integer Y (0 ≤ Y ≤ 1e18).
An integer Z (0 ≤ Z ≤ 1e18).
### Example Input:
```
3 1 0 1
```
### Function Signature:
Write a function f(N, X, Y, Z) that takes in the input.
def f(N: int, X: int, Y: int, Z: int):
'''
N: an integer
X: an integer
Y: an integer
Z: an integer
'''
Test Case Generator
Certainly! Let's start by breaking down the problem statement for Problem J: SolveMe and then create a test case generator for it.
### Problem Understanding
**Problem Description:**
You have a network of rooms with specific rules for moving between them:
- Each room has two possible teleportation destinations: one for leaning right and one for leaning left.
- You're given parameters \(X\), \(Y\), and \(Z\) which describe a sequence of movements:
1. Lean right \(X\) times.
2. Lean left once.
3. Lean right \(Y\) times.
4. Lean left once.
5. Return to the original room \(r\).
**Constraints:**
- \(N\): Number of rooms (1 ≤ \(N\) ≤ 1000)
- \(X\), \(Y\), \(Z\): Large integers up to \(10^{18}\)
**Input:**
- \(N\)
- \(X\), \(Y\), \(Z\)
- Two lists \(A\) and \(B\) of length \(N\) where:
- \(A[r]\) indicates the room you move to when leaning right in room \(r\)
- \(B[r]\) indicates the room you move to when leaning left in room \(r\)
**Output:**
- The number of ways to set up the teleportation paths such that the conditions are met, modulo 1,000,000,007.
### Test Case Generator
Here's how we can write a test case generator for this problem:
```python
import random
def tcgen():
MOD = 1_000_000_007
# Step 1: Randomly generate N within the problem constraints
N = random.randint(1, 1000)
# Step 2: Randomly generate X, Y, Z within the problem constraints
X = random.randint(0, 10**18)
Y = random.randint(0, 10**18)
Z = random.randint(0, 10**18)
# Step 3: Generate random lists A and B of size N
A = [random.randint(0, N-1) for _ in range(N)]
B = [random.randint(0, N-1) for _ in range(N)]
return N, X, Y, Z, A, B
# Example of generating a test case
test_case = tcgen()
print(test_case)
```
### Explanation of the Generator:
1. **N**: Generate a random integer between 1 and 1000 (inclusive).
2. **X, Y, Z**: Generate random integers between 0 and \(10^{18}\) (inclusive).
3. **A and B**: Generate two lists of size \(N\) where each element is a random integer from 0 to \(N-1\). This ensures each room has a valid teleportation destination within the range of rooms available.
This generator can be used to produce a variety of test cases, covering the bounds and general cases expected in the problem. Each output from the `tcgen` function provides a complete set of inputs as required by the problem statement.
Extract Arguments
def extract_arguments(fh):
N, X, Y, Z = map(int, fh.readline().strip().split())
return N, X, Y, Z