CF982E.Billiard

Consider a billiard table of rectangular size $n \times m$ with four pockets. Let's introduce a coordinate system with the origin at the lower left corner (see the picture).

There is one ball at the point $(x, y)$ currently. Max comes to the table and strikes the ball. The ball starts moving along a line that is parallel to one of the axes or that makes a $45^{\circ}$ angle with them. We will assume that:

1. the angles between the directions of the ball before and after a collision with a side are equal,
2. the ball moves indefinitely long, it only stops when it falls into a pocket,
3. the ball can be considered as a point, it falls into a pocket if and only if its coordinates coincide with one of the pockets,
4. initially the ball is not in a pocket.

Note that the ball can move along some side, in this case the ball will just fall into the pocket at the end of the side.

Your task is to determine whether the ball will fall into a pocket eventually, and if yes, which of the four pockets it will be.

考虑一个尺寸为 $n \times m$ 的矩形台球桌（billiard table），其四个角各有一个袋口。我们建立一个坐标系，原点位于左下角（参见下图）。

当前，桌面上在点 $(x, y)$ 处有一个球。Max 走到桌边击打该球。球开始沿一条直线运动，该直线要么平行于某条坐标轴，要么与坐标轴成 $45^{\circ}$ 夹角。我们作如下假设：

1. 球在与桌边碰撞前后的运动方向与法线（或边）的夹角相等（即满足反射定律）；
2. 球将无限运动下去，仅当落入袋口时才停止；
3. 球可视为一个质点；当且仅当球的坐标恰好与某一袋口坐标重合时，球才算落入该袋口；
4. 初始时刻，球不在任何袋口中。

注意：球可能沿着某条边运动，此时球将直接落入该边端点处的袋口。

你的任务是判断球最终是否会落入某个袋口；若会，则指出它将落入四个袋口中的哪一个。

The only line contains $6$ integers $n$, $m$, $x$, $y$, $v_x$, $v_y$ ($1 \leq n, m \leq 10^9$, $0 \leq x \leq n$; $0 \leq y \leq m$; $-1 \leq v_x, v_y \leq 1$; $(v_x, v_y) \neq (0, 0)$) — the width of the table, the length of the table, the $x$-coordinate of the initial position of the ball, the $y$-coordinate of the initial position of the ball, the $x$-component of its initial speed and the $y$-component of its initial speed, respectively. It is guaranteed that the ball is not initially in a pocket.

唯一的一行包含 $6$ 个整数 $n$、$m$、$x$、$y$、$v_x$、$v_y$（$1 \leq n, m \leq 10^9$；$0 \leq x \leq n$；$0 \leq y \leq m$；$-1 \leq v_x, v_y \leq 1$；$(v_x, v_y) \neq (0, 0)$），分别表示球桌的宽度、球桌的长度、球初始位置的 $x$ 坐标、球初始位置的 $y$ 坐标、球初始速度的 $x$ 分量以及球初始速度的 $y$ 分量。保证球初始时不在袋口内。

Print the coordinates of the pocket the ball will fall into, or $-1$ if the ball will move indefinitely.

输出球将落入的球袋的坐标；如果球将永远运动，则输出 $-1$。

The first sample:

The second sample:

In the third sample the ball will never change its $y$ coordinate, so the ball will never fall into a pocket.

第一个样例：

第二个样例：

在第三个样例中，小球的 $y$ 坐标永远不会改变，因此小球永远不会落入袋中。