[USACO15DEC] Fruit Feast G

现在Bessie的饱食度为 $0$ ，她每吃一个橙子，饱食度就会增加 $A$ ；每吃一个柠檬，饱食度就会增加 $B$ 。Bessie还有一次喝水的机会，如果Bessie喝水前饱食度为 $x$ ，喝水后饱食度会变为 $\left\lfloor\dfrac{x}{2}\right\rfloor$ 。 Bessie的饱食度不能超过 $T$ ，否则肚子会爆炸。试求Bessie的饱食度最大能达到多少。 Translated by @Planet6174

Bessie has broken into Farmer John's house again! She has discovered a pile of lemons and a pile of oranges in the kitchen (effectively an unlimited number of each), and she is determined to eat as much as possible. Bessie has a maximum fullness of $T$ $(1 ≤ T ≤ 5,000,000)$. Eating an orange increases her fullness by $A$, and eating a lemon increases her fullness by $B$ ($1 ≤ A,B ≤ T$). Additionally, if she wants, Bessie can drink water at most one time, which will instantly decrease her fullness by half (and will round down). Help Bessie determine the maximum fullness she can achieve!

The first (and only) line has three integers $T$, $A$, and $B$.

A single integer, representing the maximum fullness Bessie can achieve.

8 5 6

8

Problem credits: Nathan Pinsker