Implement sparse matrix addition and multiplication

Implement sparse-matrix operations with explicit error handling. ### Sparse matrix A matrix `A` has dimensions `r x c` and is **sparse**, meaning most entries are zero. You may choose a representation (e.g., hashmap/dictionary keyed by `(row, col)` for non-zero values, or compressed rows), but your implementation should be efficient for sparse inputs. ### Tasks Implement: 1. `add(A, B)` → returns `A + B` 2. `mul(A, B)` → returns `A * B` ### Requirements - If dimensions are incompatible: - For addition: `A` and `B` must have the same shape. - For multiplication: `A` is `r x k`, `B` must be `k x c`. - Incompatible dimensions must trigger clear error handling (e.g., raise an exception or return an error value, as specified by your interface). - Preserve sparsity: avoid iterating over all `r*c` cells. ### Input/Output (one reasonable interface) - Input: two sparse matrices - Output: a sparse matrix (or error) ### Constraints (reasonable interview constraints) - Up to `10^5` non-zero entries per matrix. - Dimensions can be large (e.g., up to `10^9`), so dense storage is not allowed.