# Problem related to set partitioning

Let $$A_j=\{(a^i_j,b^i_j)~:~ 0 \leq i \leq n,\text{and } a^i_j,b^i_j \in \mathbb{Z}^+\}$$

Given sets $$A_1,\ldots, A_{p}$$ and a positive integer $$k$$, the problem is to check whether there exists one element $$(a^{i_j}_j,b^{i_j}_j)$$ from each $$A_j$$ such that $$\sum_{j}^{} a^{i_j}_j \geq k$$ and $$\sum_{j}^{} b^{i_j}_j \geq k$$.

It looks like the problem is related to set partitioning problem, however, I am not sure how to get a reduction from set partitioning problem. Can someone help me to find the algorithm to solve this problem?