Torus Sea

Sanggeun is sailing the Doughnut Sea. The sea has the shape of a torus and is divided into $N \times M$ cells.

(Image by YassineMrabet from Wikimedia Commons, licensed under CC BY-SA 3.0.)

Every cell has coordinates $(n, m)$ with $0 \le n < N$ and $0 \le m < M$. Coordinates are always kept as remainders modulo $N$ and $M$, so the sea wraps around in both directions. Increasing the first coordinate from $N-1$ gives $0$, and decreasing it from $0$ gives $N-1$. The second coordinate wraps the same way modulo $M$.

Sanggeun starts at $(0, 0)$ and wants to reach $(x, y)$. He moves once per day. From $(n, m)$ he goes to $((n+1) \bmod N, (m+1) \bmod M)$ or to $((n-1) \bmod N, (m-1) \bmod M)$, each with probability $1/2$. Here $a \bmod b$ is the remainder in $[0, b)$.

Write a program that computes the expected number of days until Sanggeun first reaches $(x, y)$.

The first line contains $N$, $M$, $x$, $y$, separated by spaces. ($2 \le N, M \le 10$, $0 \le x \le N-1$, $0 \le y \le M-1$)

$(x, y)$ is not $(0, 0)$.

Print the expected number of days until Sanggeun first reaches $(x, y)$. This expected value is always an integer, so print a single integer with no decimal point and no trailing digits.

If $(x, y)$ cannot be reached, print -1.