Exit K

Mog and Lunarity play the Exit $K$ game in an endless underground passage. They start at exit $0$. A correct action advances them from exit $i$ to exit $i+1$, while a wrong action immediately sends them back to exit $0$.

At every exit, one of $A$ normal phenomena and $B$ abnormal phenomena appears uniformly at random. Mog acts correctly on a normal phenomenon, and Lunarity acts correctly on an abnormal phenomenon.

The players alternate after every action. Returning to exit $0$ after a wrong action does not reset whose turn comes next. Mog takes the first action.

Find the expected number of actions required to reach exit $K$ for the first time.

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$

Each case consists of three positive integers $A$, $B$, and $K$ on one line.

For each test case, write the expectation as a reduced fraction $p/q$ and print $p \times q^{-1} \bmod 998\,244\,353$.

• $1 \leq T \leq 100\,000$
• $1 \leq A,B,K \leq 10^6$
• The sum of $K$ over all test cases does not exceed $10^6$.