Virtual Verification Technology

Hyundai AutoEver's virtual verification technology virtualizes vehicles, systems, and controllers, and provides a virtual driving environment and verification tools. It lets engineers run function-level verification, cross-function verification, and system-level verification without hardware. Virtual verification secures quality through early verification and simulates adverse conditions that cannot be tested in the real world. As the computing complexity of vehicles grows in the SDV era, virtual verification is an effective way to secure vehicle safety and performance against software quality risks of a different kind.

Dohun, a senior researcher, and Sanghyuk, a new researcher, are in charge of virtual verification for vehicle models $A$ and $B$. One virtual verification simulation for model $A$ takes $T_A$ time, and one for model $B$ takes $T_B$ time. Model $A$ needs $V_A$ verification items tested, and model $B$ needs $V_B$ items tested. Each simulation tests exactly one verification item.

Dohun is a senior researcher who can run virtual verification for both models $A$ and $B$. Sanghyuk is a new researcher who can run verification only for model $A$. Dohun and Sanghyuk each run one simulation at a time, and they cannot simulate the same verification item. They assume no time is needed to prepare the next simulation after finishing one. A simulation cannot be stopped once it starts.

The work is complete when all simulations for both models are finished. Find the minimum time Dohun and Sanghyuk need to complete the virtual verification work.

The first line contains the number of test cases $Q$. $(1 \leq Q \leq 1\,000)$

From the second line onward, each test case is given on one line as $T_A$, $T_B$, $V_A$, and $V_B$, separated by spaces. Here $T_A$ and $T_B$ are the time for one simulation of models $A$ and $B$, and $V_A$ and $V_B$ are the numbers of verification items for models $A$ and $B$. $(1 \leq T_A, T_B, V_A, V_B \leq 100)$

For each test case, print on its own line the minimum time needed to complete the work.