Code for fun!

#### Start

2020-07-19 06:00 AKDT

## Code for fun!

#### End

2020-07-19 10:00 AKDT
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# Problem LRingworld

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.

## Input

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 $[x_ i,x_ i+1 \mod m,\ldots ,y_ i]$.

## Output

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