Problem Statement

There is a container with A cyan balls. Takahashi will do the following operation as many times as he likes (possibly zero times):

• add B cyan balls and C red balls into the container.

Takahashi's objective is to reach a situation where the number of cyan balls in the container is at most D times the number of red balls in it.
Determine whether the objective is achievable. If it is achievable, find the minimum number of operations needed to achieve it.

Input

Input is given from Standard Input in the following format:
A B C D

Output

If Takahashi's objective is achievable, print the minimum number of operations needed to achieve it. Otherwise, print -1.

Constraints

• $1 \leq A,B,C,D \leq 10^5$
• All values in input are integers.

Sample Input 1

5 2 3 2

Sample Output 1

2

Before the first operation, the container has 5 cyan balls and 0 red balls. Since 5 is greater than 0 multiplied by D=2, Takahashi's objective is not yet achieved.
Just after the first operation, the container has 7 cyan balls and 3 red balls. Since 7 is greater than 3 multiplied by 2, the objective is still not achieved.
Just after the second operation, the container has 9 cyan balls and 6 red balls. Since 9 is not greater than 6 multiplied by 2, the objective is achieved.
Thus, the answer is 2.

Sample Input 2

6 9 2 3

Sample Output 2

-1

No matter how many times Takahashi repeats the operation, his objective will never be achieved.

见题面 Input 部分

见题面 Output 部分