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 ≤ 1000).
Three integers X, Y, and Z (0 ≤ X, Y, Z ≤ 1e18).
### 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, I can help you with that. Here's a test case generator for the given problem statement "SolveMe":
```python
import random
def tcgen():
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 usage:
N, X, Y, Z = tcgen()
print(f"{N} {X} {Y} {Z}")
```
This function generates random test cases within the specified constraints:
- \(N\) is a random integer between 1 and 1000 inclusive.
- \(X\), \(Y\), and \(Z\) are random integers between 0 and \(10^{18}\) inclusive.
The `tcgen` function returns these values as a tuple, which you can use to test your solution to the "SolveMe" problem. Here is an example of how you could use the generated values:
```python
# Example usage:
N, X, Y, Z = tcgen()
print(f"Generated Test Case: N={N}, X={X}, Y={Y}, Z={Z}")
```
By running this code multiple times, you will get different test cases that you can use for your competitive programming problem.
Extract Arguments
def extract_arguments(fh):
N, X, Y, Z = map(int, fh.readline().strip().split())
return N, X, Y, Z