A12848. 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.

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 $(e_x, e_y)$ .

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).

Example is shown on the picture in the statement.