CF1200C.Round Corridor

Amugae is in a very large round corridor. The corridor consists of two areas. The inner area is equally divided by $n$ sectors, and the outer area is equally divided by $m$ sectors. A wall exists between each pair of sectors of same area (inner or outer), but there is no wall between the inner area and the outer area. A wall always exists at the 12 o'clock position.

The inner area's sectors are denoted as $(1,1), (1,2), \dots, (1,n)$ in clockwise direction. The outer area's sectors are denoted as $(2,1), (2,2), \dots, (2,m)$ in the same manner. For a clear understanding, see the example image above.

Amugae wants to know if he can move from one sector to another sector. He has $q$ questions.

For each question, check if he can move between two given sectors.

Amugae 位于一条非常大的圆形走廊中。该走廊由两个区域组成：内圈区域被均分为 $n$ 个扇形区域，外圈区域被均分为 $m$ 个扇形区域。在同一区域（内圈或外圈）的任意两个相邻扇形之间都有一堵墙，但内圈区域与外圈区域之间没有墙。在 12 点钟方向始终有一堵墙。

内圈区域的扇形按顺时针方向依次记为 $(1,1), (1,2), \dots, (1,n)$；外圈区域的扇形同样按顺时针方向依次记为 $(2,1), (2,2), \dots, (2,m)$。为便于理解，请参见上方示例图。

Amugae 想知道他能否从一个扇形区域移动到另一个扇形区域。他共有 $q$ 个询问。

对每个询问，请判断给定的两个扇形区域之间是否可以互相通行。

The first line contains three integers $n$, $m$ and $q$ ($1 \le n, m \le 10^{18}$, $1 \le q \le 10^4$) — the number of sectors in the inner area, the number of sectors in the outer area and the number of questions.

Each of the next $q$ lines contains four integers $s_x$, $s_y$, $e_x$, $e_y$ ($1 \le s_x, e_x \le 2$; if $s_x = 1$, then $1 \le s_y \le n$, otherwise $1 \le s_y \le m$; constraints on $e_y$ are similar). Amague wants to know if it is possible to move from sector $(s_x, s_y)$ to sector $(e_x, e_y)$.

第一行包含三个整数 $n$、$m$ 和 $q$（$1 \le n, m \le 10^{18}$，$1 \le q \le 10^4$）—— 分别表示内圈区域的扇区数量、外圈区域的扇区数量以及询问次数。

接下来的 $q$ 行每行包含四个整数 $s_x$、$s_y$、$e_x$、$e_y$（$1 \le s_x, e_x \le 2$；若 $s_x = 1$，则 $1 \le s_y \le n$，否则 $1 \le s_y \le m$；对 $e_y$ 的约束类似）。Amague 想知道是否可以从扇区 $(s_x, s_y)$ 移动到扇区 $(e_x, e_y)$。

For each question, print "YES" if Amugae can move from $(s_x, s_y)$ to $(e_x, e_y)$, and "NO" otherwise.

You can print each letter in any case (upper or lower).

对于每个问题，如果 Amugae 能够从 $(s_x, s_y)$ 移动到 $(e_x, e_y)$，则输出 "YES"；否则输出 "NO"。

您可以以任意大小写（大写或小写）输出每个字母。

Example is shown on the picture in the statement.

示例见题目描述中的图片。