27483번 - Round Corridor 스페셜 저지다국어

문제

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.

입력

The first line contains three integers $n,ドル $m$ and $q$ (1ドル\le n,m\le 10^{18},ドル 1ドル\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,ドル $s_y,ドル $e_x,ドル $e_y$ (1ドル\le s_x,e_x\le 2$; if $s_x=1,ドル then 1ドル\le s_y\le n,ドル otherwise 1ドル\le s_y\le m$; constraints on $e_y$ are similar). Amague wants to know if it is possible to move from sector $(s_x,s_y)$ to sector $(e_x,e_y)$.

출력

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

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

제한

노트

Example is shown on the picture in the statement.