Sure! Here is a test case generator for the given problem statement:

```python
import random

def tcgen():
    # Constraints
    N = random.randint(1, 2 * 10**5)
    
    # Generate a permutation of the integers from 1 to N
    P = list(range(1, N+1))
    random.shuffle(P)
    
    return N, P

# Example usage:
N, P = tcgen()
print(N)
for p in P:
    print(p)
```

This generator creates a random test case by:
1. Randomly choosing a value \( N \) within the constraint \( 1 \leq N \leq 2 \times 10^5 \).
2. Generating a permutation of the integers from 1 to \( N \).
3. Shuffling the permutation to ensure it's in a random order.

You can run this generator to create different test cases for the given problem. Make sure to handle large input sizes within the constraints when using this in a competitive programming environment.