Round Corridor

题意翻译

走廊有两部分构成：内圈和外圈。内圈有$n(n\le10^{18})$个部分组成，外圈有$m(m\le10^{18})$个部分组成。如下图，有墙在每个部分中阻隔。但是内圈和外圈之间没有墙。并且在走廊的12点钟方向始终有一堵墙。  里圈的各个部分被$(1,1),(1,2)...(1,n)$这种方式来表示。同理，外圈则被$(2,1),(2,2)...(2,m)$这种方式来表示。上图即使一个表达方式的样例。 现在，有个人想要知道从$(sx,sy)$出发能否到达$(ex,ey)$.他有$q\le10^4$个疑问。 对于每个疑问，回答是否能从给出的两个区间中的一个到达另一个。

题目描述

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.

输入输出格式

输入格式

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) $ .

输出格式

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).

输入输出样例

输入样例 #1

4 6 3
1 1 2 3
2 6 1 2
2 6 2 4

输出样例 #1

YES
NO
YES

说明

Example is shown on the picture in the statement.