101803: [AtCoder]ABC180 D - Takahashi Unevolved

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.

Sample Input 1

4 20 2 10

Sample Output 1

2

Initially, Takahashi's STR is $4$. We can make his EXP $2$ in the following course of training:

• First, go to Kakomon Gym, which makes his STR $8$ and his EXP $1$.
• Then, go to AtCoder Gym, which makes his STR $18$ and his EXP $2$.

On the other hand, there is no way to train him so that his EXP becomes greater than $2$.

Sample Input 2

1 1000000000000000000 10 1000000000

Sample Output 2

1000000007

Watch out for overflows.