Problem p02357 - Generation 2

Orig Description

Sliding Minimum Element
  For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\{1, 7, 7, 4, 8, 1, 6\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\{1, 7, 7\}$, $\{7, 7, 4\}$, $\{7, 4, 8\}$, $\{4, 8, 1\}$, $\{8, 1, 6\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.
Constraints
 $1 \leq N \leq 10^6$ 
 $1 \leq L \leq 10^6$
 $1 \leq a_i \leq 10^9$
 $L \leq N$ 
Input
The input is given in the following format.
$N$ $L$
$a_1$ $a_2$ ... $a_N$
Output
  Print a sequence of the minimum in a line. Print a space character between adjacent elements.
Sample Input 1
7 3
1 7 7 4 8 1 6
Sample Output 1
1 4 4 1 1

Extracted Specification

An integer N (1 ≤ N ≤ 10^6), representing some quantity or size.
An integer L (1 ≤ L ≤ 10^6), also representing some quantity or size.
A list of integers A of size N, where each integer is between 1 and 1e9.

### Example Input:

```
7 3
1 7 7 4 8 1 6
```

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

Test Case Generator

Sure! Below is the test case generator for the given problem statement "Sliding Minimum Element":

```python
import random

def tcgen():
    # Generate N such that 1 <= N <= 10^6
    N = random.randint(1, 10**6)
    
    # Generate L such that 1 <= L <= N (if N is 1, L must be 1)
    L = random.randint(1, N)
    
    # Generate array A of size N with elements between 1 and 10^9
    A = [random.randint(1, 10**9) for _ in range(N)]
    
    return N, L, A

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

### Explanation
- **N**: Randomly generated integer between 1 and \(10^6\).
- **L**: Randomly generated integer between 1 and \(N\).
- **A**: List of \(N\) integers, each between 1 and \(10^9\).

The function `tcgen()` generates a random test case for the problem which can be used for testing solutions. The values for \(N\), \(L\), and the list \(A\) are printed in the format specified by the problem statement. 

This test case generator adheres to the constraints of the problem and ensures that the size of the sub-array \(L\) is always less than or equal to \(N\).

Extract Arguments

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