Problem Statement

Iroha is into a game where you keep pets.

Iroha's pet is Takahashi. Initially, Takahashi's STR and EXP are $X$ and $0$, respectively. These parameters increase in the following two kinds of training:

• Go to Kakomon Gym: the STR gets multiplied by $A$, and the EXP increases by $1$.
• Go to AtCoder Gym: the STR increases by $B$, and the EXP increases by $1$.

Takahashi evolves when his STR becomes $Y$ or greater, but Iroha thinks that makes him less cute.

Find the maximum possible EXP of Takahashi when he is trained without letting him evolve.

Constraints

• $1 \leq X < Y \leq 10^{18}$
• $2 \leq A \leq 10^9$
• $1 \leq B \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y A B

Output

Print the maximum possible EXP of Takahashi under the given situation.