Generalized Knights

On an infinitely large grid, a generalized knight stands at position $(0, 0)$. The knight is allowed to move in $8$ ways. First, it may move either $\pm a$ or $\pm b$ steps horizontally, and then $\pm a$ or $\pm b$ steps vertically.

Compute the minimum number of moves the knight must make to reach the position $(x, y)$.

Input

The first and only line contains the four integers $a, b, x, y$ from the statement ($1 \le a \neq b \le 10^{9}$, $0 \le x, y \le 10^9$). It is guaranteed that the knight can reach $(x, y)$, and $(x, y)$ is not $(0, 0)$.

Output

Output a single integer – the minimum number of moves from position $(0, 0)$ to $(x, y)$.

2 1 1 1

2

2 1 1 0

3

123 321 123456 321456

1036