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Find K Smallest Pairs

Write a Python function `k_smallest_pairs(nums1, nums2, k)` that takes two lists of integers `nums1` and `nums2`, and an integer `k`. The function should return the `k` smallest pairs (in terms of their sums) where each pair consists of one element from `nums1` and one element from `nums2`.

If there are fewer than `k` pairs possible, return all possible pairs.

#### Example Usage
```python [main.nopy]
nums1 = [1, 3, 7]
nums2 = [2, 4, 6]
k = 2
print(k_smallest_pairs(nums1, nums2, k))
# Output: [[1, 2], [1, 4]]

nums1 = [1, 3, 7]
nums2 = [2, 4, 6]
k = 7
print(k_smallest_pairs(nums1, nums2, k))
# Output: [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [3, 6], [7, 2]]
```

#### Constraints
- Both `nums1` and `nums2` are sorted in ascending order.
- `k` is a non-negative integer.
- The function should aim for efficiency, especially for large inputs.
import heapq

def k_smallest_pairs(nums1, nums2, k):
    """
    Find the k smallest pairs from two sorted arrays.

    Args:
        nums1 (List[int]): First sorted list of integers.
        nums2 (List[int]): Second sorted list of integers.
        k (int): Number of smallest pairs to find.

    Returns:
        List[List[int]]: List of k smallest pairs.
    """
    # Placeholder for the solution
    pass
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