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.
Three integers X, Y, and Z, each between 0 and 1e18 inclusive.
### Example Input:
```
3 1 0 1
```
### Function Signature:
Write a function f(N, X, Y, Z) that takes in the input.
```python
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
Sure! Here's a Python function to generate test cases for the given problem statement for "SolveMe":
```python
import random
def tcgen():
# Generate random values for N, X, Y, and Z within the specified constraints
N = random.randint(1, 1000)
X = random.randint(0, 10**18)
Y = random.randint(0, 10**18)
Z = random.randint(0, 10**18)
return N, X, Y, Z
# Example of generating a test case
N, X, Y, Z = tcgen()
print(f"{N} {X} {Y} {Z}")
```
This function randomly generates the values for \(N\), \(X\), \(Y\), and \(Z\) within their respective constraints. Each time you call `tcgen()`, it will return a new set of input parameters for the problem.
Here is how you might use this function:
```python
for _ in range(5): # Generate 5 test cases
N, X, Y, Z = tcgen()
print(f"Test Case: N={N}, X={X}, Y={Y}, Z={Z}")
```
You can adjust the loop to generate as many test cases as you need. The generated values will help ensure your solution is robust and can handle a variety of inputs within the specified constraints.
Extract Arguments
def extract_arguments(fh):
N, X, Y, Z = map(int, fh.readline().strip().split())
return N, X, Y, Z