litte-jhool-and-world-tour-1

Little Jhool is just not a smart algorithmic coder, he regularly contributes to open source, too. This year, he's managed to be selected for a project in the prestigious Google Summer of Code, too. More than the project, he's happy about the money he's going to receive. He's already started day dreaming about what he will do with the money, - he's settled on for going to a tour of couple of countries. Now, he's a bit confused about which countries he wants to consider, so he buys a globe, and starts rotating it like some boss.

The globe has n different countries on it, and let's say they are labeled as 0, 1, 2, 3, 4... n-1, but since it is a globe, after n-1, country order follows again. That is to say, if there are n countries - 0, 1, 2, 3, 4, . . . , n-1, then, their arrangement would be: first 0, then 1, then 2, ..., then n-1, and then again 0... 

Let us take m = 6, then {4, 5, 0} can be a valid range of countries, {2} can be a valid range, too, {3, 4, 5, 0, 1, 2} is a valid range, too. Since it is a globe, the range can  wrap around itself. 

Now, his girlfriend decides a range of countries. Since, his girlfriend is confusing him a lot, he just wants to pick up ONLY ONE country from a range. He does NOT want to any country to be chosen more than once for different ranges.

Given number of countries, and number of ranges (And their range!) - help Little Jhool figure out if he'll be able to do this.

Input format:
The first line contains test cases, tc, followed by two integers N,M- the first one depicting the number of countries on the globe, the second one depicting the number of ranges his girlfriend has given him. After which, the next M lines will have two integers describing the range, X and Y. If (X ≤ Y), then range covers countries [X,X+1... Y] else range covers [X,X+1,.... N-1,0,1..., Y].

Output format:
Print "YES" if it is possible for Little Jhool to do so, print "NO", if it is not.

Constraints:
1 ≤ TC ≤ 30
1 ≤ N ≤ 10^9
1 ≤ M ≤ 10^5
0 ≤ Xi, Yi < N

SAMPLE INPUT
2
4 3
0 1
1 2
2 0
5 5
0 0
1 2
2 3
4 4
4 0

SAMPLE OUTPUT
YES
NO

Source: hackerearth | Difficulty: HARD
Tags: Data structures


Solutions: