Problem p01976 - Generation 1

Orig Description

C: Matching
Problem
Given a sequence of integers $a_i$ of length $N$, output all integers $K (1 \le K \le N)$ that satisfy the following condition:
Condition:
By arranging $a_1, \cdots, a_K$ appropriately, it matches with $a_{N-K+1}, \cdots, a_N$.
Constraints
$1 \le N \le 10^5$
$1 \le a_i \le 10^9$
All inputs are integers.
Input:
$N$
$a_1 \cdots a_N$
Output:
Output all $K$ that satisfies the condition in ascending order, separated by a space. Print a newline character at the end.
Sample
Sample Input 1
8
5 2 4 9 4 9 2 5
Sample Output 1
1 2 4 6 7 8
Sample Input 2
3
5 7 5
Sample Output 2
1 2 3
Sample Input 3
9
118 118 97 116 97 97 114 110 101
Sample Output 3
9

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 1 and 1e9.

### Example Input:

```
8
5 2 4 9 4 9 2 5
```

### Function Signature:
Write a function f(N, A) that takes in the input.
def f(N: int, A: List[int]):
    '''
    N: an integer
    A: a list of integers
    '''

Test Case Generator

Sure! Below is a test case generator for the given problem statement "C: Matching."

```python
import random

def tcgen():
    # Generate a random value for N within the given range
    N = random.randint(1, 10**5)
    
    # Generate a list of N random integers between 1 and 10^9
    A = [random.randint(1, 10**9) for _ in range(N)]
    
    return N, A

# Example usage:
N, A = tcgen()
print(N)
print(' '.join(map(str, A)))
```

### Explanation:

1. **N Generation**: We randomly pick an integer `N` such that `1 ≤ N ≤ 10^5`.
2. **List A Generation**: We generate a list `A` of size `N` where each element is a random integer between `1` and `10^9`.
3. **Output**: The function returns `N` and the list `A`.

You can execute this generator to create random test cases for this problem. Here's an example of how you might use it:

```python
N, A = tcgen()
print(N)
print(' '.join(map(str, A)))
```

### Example Output:

```
8
123456789 987654321 123456789 987654321 123456789 987654321 123456789 987654321
```

This would generate the input for the problem. You can then run your solution on this input to validate its correctness.

Extract Arguments

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

# if __name__ == "__main__":
#     input_path = sys.argv[1]
#     with open(input_path, 'r') as fh:
#         N, A = extract_arguments(fh)
#         f(N, A)