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

```python
import random

def tcgen():
    X = random.randint(1, 10**9)
    K = random.randint(1, 10**5)
    
    # Generate unique random times for r_1, r_2, ..., r_K in increasing order
    r = sorted(random.sample(range(1, 10**9 + 1), K))
    
    Q = random.randint(1, 10**5)
    
    queries = []
    for _ in range(Q):
        t_i = random.randint(0, 10**9)
        a_i = random.randint(0, X)
        queries.append((t_i, a_i))
    
    return X, K, r, Q, queries

def main():
    X, K, r, Q, queries = tcgen()
    
    # Print the generated test case
    print(X)
    print(K)
    print(" ".join(map(str, r)))
    print(Q)
    for t_i, a_i in queries:
        print(f"{t_i} {a_i}")

if __name__ == "__main__":
    main()
```

Explanation:
1. **X**: Total grams of sand, randomly chosen between 1 and \(10^9\).
2. **K**: Number of times the sandglass will be turned over, randomly chosen between 1 and \(10^5\).
3. **r**: A list of K distinct integers representing the times when the sandglass is turned. These are sorted to ensure they are in increasing order.
4. **Q**: Number of queries, randomly chosen between 1 and \(10^5\).
5. **Queries**: Each query consists of \(t_i\) (time) and \(a_i\) (initial sand in bulb A). The time \(t_i\) is chosen randomly between 0 and \(10^9\), and the sand amount \(a_i\) is chosen randomly between 0 and X.

This test case generator ensures that all constraints are respected and generates valid input for the problem.