Problem p02194 - Generation 3

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

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, let's write a test case generator for the "Zero AND Subsets" problem. This generator will create a random number of elements in the multiset, generate random integers within the specified range, and return them in the required format.

Here's the Python test case generator:

```python
import random

def tcgen():
    # Constraints
    N = random.randint(1, 10**5)
    A = [random.randint(0, 2**20 - 1) for _ in range(N)]
    
    return N, A

# Example of using the test case generator
if __name__ == "__main__":
    N, A = tcgen()
    print(N)
    print(" ".join(map(str, A)))
```

This code snippet does the following:
1. Randomly selects `N`, the number of elements in the multiset, within the range \([1, 10^5]\).
2. Generates a list `A` of `N` integers, each randomly selected from the range \([0, 2^{20} - 1]\).
3. Returns the values of `N` and `A`.

To see the generated test case, you can run the script. It prints the number of elements and the elements themselves in the format required by the problem statement.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    A = list(map(int, fh.readline().strip().split()))
    return N, A