Ringworld

The world is actually neither a disc or a sphere. It is a ring! There are $m$ cities there, conveniently called $0,1,2,\ldots ,m-1$, and arranged on the ring in the natural order: first $0$, then $1$, then $2$, ..., then $m-1$, and then again $0$ (as the world is a ring, remember?). You are given a collection of contiguous ranges of cities. Each of them starts at some city $x$, and contains also cities $x+1$, $x+2$, ..., $y-1,y$, for some city $y$. Note that the range can wrap around, for instance if $m=5$, then $[3,4,0]$ is a valid range, and so are $[1]$, $[2,3,4]$, or even $[3,4,0,1,2]$. Your task is to choose a single city inside each range so that no city is chosen twice for two different ranges.

The input consists of several lines. The first line contains $1\le T\le 20$, the number of test cases. Each test case consists of a number of lines. The first line contains two integers $1\le m\le 10^9$ and $1\leq n \le 10^5$ denoting the number of cities and the number of requests, respectively. The next $n$ lines define the ranges: the $i$-th row contains two integers $0\leq x_ i, y_ i < m$ describing the $i$-th range $[x_ i,x_ i+1 \mod m,\ldots ,y_ i]$.

For each test case, output one line containing YES if it is possible to assign a unique city to each request, and NO otherwise.

Sample Input 1 | Sample Output 1 |
---|---|

4 3 3 0 1 1 2 2 0 200000 3 100000 100000 100001 100001 100000 100001 6 6 0 1 1 2 2 3 3 4 4 5 5 0 6 6 0 0 1 2 2 3 4 4 4 5 5 0 |
YES NO YES NO |