Archery

Korea is famous for archery: its national teams have swept nearly every gold, silver, and bronze medal at the Olympic Games.

An archery exhibition will be held in Korea. As a ceremonial event, a master archer will try to shoot a single arrow that passes through every one of several paper target boards at once. Because an arrow flies in a straight line, whether the master can pierce all targets depends on where along the archer line he stands.

The picture below is a top-down view of the field. Every target is a line segment parallel to the archer line. Set up a coordinate system whose origin is the leftmost point of the archer line, with the archer line lying on the positive $x$-axis.

In the figure, the master can pierce all targets from position B, but never from position A, because any ray from A meets at most 3 targets.

Given the width of the archer line and the positions of the targets, decide whether there is a spot on the archer line from which the master can pierce every target with one straight shot. You may assume the $y$-coordinates of the targets are all different. If an arrow passes exactly through an endpoint of a target, it still counts as hitting that target.

The first line contains the number of test cases $T$ ($1 \le T \le 30$).

Each test case begins with a line holding an integer $W$ ($2 \le W \le 10{,}000{,}000$), the width of the archer line. The next line holds an integer $N$ ($2 \le N \le 5{,}000$), the number of target boards. Each of the following $N$ lines contains three integers $D_i$, $L_i$, $R_i$ ($1 \le D_i \le W$, $0 \le L_i < R_i \le W$): $D_i$ is the $y$-coordinate of the $i$-th target, and $L_i$ and $R_i$ are the $x$-coordinates of its leftmost and rightmost points. All $D_i$ are distinct.

For each test case, print exactly one line: YES if some position on the archer line lets the master pierce every target with a single straight shot, otherwise NO.