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

```python
import random

def tcgen():
    # Generate a random integer N in the range 1 to 2 × 10^5
    N = random.randint(1, 2 * 10**5)
    
    # Initialize lists A and B
    A = []
    B = []
    
    # Generate a random sum S for both lists (let's keep S small for simplicity)
    S = random.randint(1, N * 10)
    
    # Distribute the sum S across N elements for both A and B
    for _ in range(N):
        if _ == N - 1:  # For the last element, just add the remaining sum to ensure the total sum is S
            A.append(S)
            B.append(S)
        else:
            a_i = random.randint(0, S)
            b_i = random.randint(0, S)
            A.append(a_i)
            B.append(b_i)
            S -= a_i
            S -= b_i
    
    # Adjust the last element to ensure the sums of A and B are equal
    A[-1] += S
    B[-1] += S
    
    return N, A, B

# Example usage
N, A, B = tcgen()
print(N)
for a, b in zip(A, B):
    print(a, b)
```

This code generates random test cases for the problem with the following constraints:
1. \( N \) is a random integer between 1 and 200,000.
2. Sequences \( A \) and \( B \) are both of length \( N \) and their sums are equal.
3. Each element \( A[i] \) and \( B[i] \) is a non-negative integer, and their sums match the total sum \( S \).

The generated test case ensures that the conditions specified in the problem statement are met. You can run the generator multiple times to get different random test cases.