Problem p01976 - Generation 2

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 10^9.

### Example Input:

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

### 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

Certainly! I'll provide a test case generator for the given problem "C: Matching".

### Problem Statement: C: Matching

**Description**

Given a sequence of integers \(a_i\) of length \(N\), output all integers \(K\) (1 ≤ \(K\) ≤ \(N\)) 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**

- \(1 \le N \le 10^5\)
- \(1 \le a_i \le 10^9\)

**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.

**Examples**

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

_Output_  
```
1 2 4 6 7 8
```

_Input_  
```
3
5 7 5
```

_Output_  
```
1 2 3
```

_Input_  
```
9
118 118 97 116 97 97 114 110 101
```

_Output_  
```
9
```

### Test Case Generator

Here's a Python function to generate test cases for this problem:

```python
import random

def tcgen():
    # Generate N
    N = random.randint(1, 10**5)
    
    # Generate the array A of length N with elements 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)))
```

This function generates a random test case as follows:

1. The length of the array \(N\) is chosen randomly between 1 and \(10^5\).
2. Each element of the array \(A\) is chosen randomly between 1 and \(10^9\).

You can call this function to generate different test cases for the problem. The output will be printed in the required format.

Extract Arguments

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