Qualitative Numerical Planning (QNP) extends classical planning with numerical variables that can be changed by arbitrary amounts. FOND+ extends Fully Observable Non-Deterministic (FOND) planning by introducing explicit fairness assumptions, resulting in a more expressive model that can also capture QNP as a special case. However, existing QNP and FOND+ solvers still face significant scalability challenges. To address this, we propose a novel framework for solving QNP and FOND+ by generating strong cyclic solutions of the associated FOND problem, testing their validity, and forbidding non-solutions in conducting further searches. For this, we propose a procedure called SIEVE*, which generalizes the QNP termination testing algorithm SIEVE to determine whether a strong cyclic solution is a FOND+ solution. Additionally, we propose several optimization techniques to further improve the performance of our basic framework. We implemented our approach based on the advanced FOND solver PRP; experimental results show that our solver shows superior scalability over the existing QNP and FOND+ solvers.