Loot Chest

Your favorite online game has a prize system. After each match you win, you receive a prize with probability $P\%$. The value of $P$ changes over time as follows:

• Every time you lose a match, $P$ increases by $\Delta_L$.
• Every time you win a match but do not receive a prize, $P$ increases by $\Delta_W$.
• Every time you win a match and receive a prize, $P$ is set to $0$.

Whenever $P$ increases, it is capped at $100$. That is, if $P$ is increased by $\Delta$, then $P$ becomes $\min(P+\Delta, 100)$.

The developers have just revealed that one of the prizes this season is a silverback gorilla suit with star-shaped sunglasses. You want it! Each prize is this gorilla suit with probability $G\%$.

You start with $P = 0\%$. Each match you play has a $L\%$ chance of being a loss. Given $\Delta_L, \Delta_W, G,$ and $L$, compute the expected number of matches you will play until you obtain the silverback gorilla suit.

For example, in the first sample case you win every match and are guaranteed to receive a prize every 2 matches. Each prize is the gorilla suit with probability $50\%$. So you expect to obtain the gorilla suit after receiving 2 prizes. Thus, in expectation, it takes 4 matches to obtain the gorilla suit.

The input consists of a single line containing four integers $\Delta_L$ ($1 \leq \Delta_L \leq 100$), $\Delta_W$ ($1 \leq \Delta_W \leq 100$), $G$ ($1 \leq G \leq 100$), and $L$ ($0 \leq L \leq 99$), which are described above.

Display the expected number of matches you will play before you obtain the gorilla suit. Your answer should have an absolute or relative error of at most $10^{-6}$.