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.

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.

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.

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.

见题面 Input 部分

见题面 Output 部分