Orig Description
Zero AND Subsets
Given a multiset of non-negative integers a_1, a_2, ..., a_N.
How many non-empty subsets of this multiset have a bitwise AND value of 0?
Output the answer modulo 10^9+7.
Input
N
a_1 a_2...a_N
Output
Output the answer modulo 10^9+7.
Constraints
1 \leq N \leq 10^5
0 \leq a_i \leq 2^{20}-1
Input Example
6
8 6 9 1 2 1
Output Example
51
Extracted Specification
Canonicalized Input Description:
An integer N (1 ≤ N ≤ 10^5), representing some quantity or size.
A list of integers A of size N, where each integer is between 0 and 2^20 - 1.
### Example Input:
```
6
8 6 9 1 2 1
```
### Function Signature:
Write a function f(N, A) that takes in the input.
```python
def f(N: int, A: List[int]):
'''
N: an integer
A: a list of integers
'''
```
Test Case Generator
Sure, I can help you write a test case generator for the "Zero AND Subsets" problem. The generator will produce random inputs that adhere to the constraints provided in the problem statement. Here is a Python function for generating such test cases:
```python
import random
def tcgen():
N = random.randint(1, 10**5)
A = [random.randint(0, 2**20 - 1) for _ in range(N)]
return N, A
# Example usage:
N, A = tcgen()
print(N)
print(' '.join(map(str, A)))
```
### Explanation:
1. **N Generation**:
- `N` is chosen randomly between 1 and \(10^5\), inclusive, as specified in the problem constraints.
2. **A Generation**:
- The list `A` of size `N` is generated where each element is a random integer between 0 and \(2^{20} - 1\) (inclusive), also as per the problem constraints.
### Example Output:
Running the `tcgen` function might produce an output like this:
```
5
542 12345 678 9 1024
```
This represents:
- **N = 5**
- **A = [542, 12345, 678, 9, 1024]**
You can run the function multiple times to generate different test cases for your problem. This function ensures that all generated test cases adhere to the provided constraints.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
A = list(map(int, fh.readline().strip().split()))
return N, A