You are given an axis-aligned rectangle in a 2D Cartesian plane. The bottom left corner of this rectangle has coordinates (0,0)$(0, 0)$ and the top right corner has coordinates (N−1,N−1)$(N-1, N-1)$. You are also given K$K$ light sources; each light source is a point inside or on the perimeter of the rectangle.
For each light source, let's divide the plane into four quadrants by a horizontal and a vertical line passing through this light source. The light source can only illuminate one of these quadrants (including its border, i.e. the point containing the light source and two half-lines), but the quadrants illuminated by different light sources may be different.
You want to assign a quadrant to each light source in such a way that when they illuminate their respective quadrants, the entire rectangle (including its perimeter) is illuminated. Find out whether it is possible to assign quadrants to light sources in such a way.

-----Input-----
- The first line of the input contains an integer T$T$ denoting the number of test cases. The description of the test cases follows.
- The first line of each test case contains two space-separated integers K$K$ and N$N$.
- Each of the next K$K$ lines contains two space-separated integers x$x$ and y$y$ denoting a light source with coordinates (x,y)$(x, y)$.

-----Output-----
For each test case, print a single line containing the string "yes" if it is possible to illuminate the whole rectangle or "no" if it is impossible.

-----Constraints-----
- 1≤T≤5,000$1 \le T \le 5,000$
- 1≤K≤100$1 \le K \le 100$
- 1≤N≤109$1 \le N \le 10^9$
- 0≤x,y≤N−1$0 \le x, y \le N-1$
- no two light sources coincide

-----Example Input-----
2
2 10
0 0
1 0
2 10
1 2
1 1

-----Example Output-----
yes
no

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
def assess(sq, points):
	EWct = 0
	NSct = 0
	for (a, b) in points:
		EW = a == 0 or a == sq
		NS = b == 0 or b == sq
		if EW and NS:
			return 'yes'
		EWct += EW
		NSct += NS
	if NSct + EWct == 0 or len(points) == 1:
		return 'no'
	if EWct >= 2 or NSct >= 2:
		return 'yes'
	if len(points) == 2:
		return 'no'
	if NSct == 1 and EWct == 1:
		return 'yes'
	x = -1
	for (a, b) in points:
		if EWct > 0:
			if a == 0 or a == sq:
				e = b
			elif x == -1:
				x = b
			else:
				y = b
		elif b == 0 or b == sq:
			e = a
		elif x == -1:
			x = a
		else:
			y = a
	if (e - x) * (e - y) < 0:
		return 'no'
	else:
		return 'yes'
for ti in range(int(input())):
	(k, n) = map(int, input().split())
	if k > 3:
		for ki in range(k):
			input()
		print('yes')
	else:
		pos = [tuple(map(int, input().split())) for ki in range(k)]
		print(assess(n - 1, pos))


t = int(input())
while t:
	(k, n) = map(int, input().split())
	l = []
	j = 0
	h = k
	while h:
		p = list(map(int, input().split()))
		l.append(p)
		h -= 1
	if k > 3:
		j = 1
	elif k == 1:
		if l[0][0] == 0 and l[0][1] == n - 1 or (l[0][0] == 0 and l[0][1] == 0) or (l[0][0] == n - 1 and l[0][1] == 0) or (l[0][0] == n - 1 and l[0][1] == n - 1):
			j = 1
	elif k == 2:
		for q in range(2):
			if l[q][0] == 0 and l[q][1] == n - 1 or (l[q][0] == 0 and l[q][1] == 0) or (l[q][0] == n - 1 and l[q][1] == 0) or (l[q][0] == n - 1 and l[q][1] == n - 1):
				j = 1
		if l[0][0] == 0 or l[0][0] == n - 1:
			if l[1][0] == 0 or l[1][0] == n - 1:
				j = 1
		if l[0][1] == 0 or l[0][1] == n - 1:
			if l[1][1] == 0 or l[1][1] == n - 1:
				j = 1
	elif k == 3:
		for q in range(3):
			if l[q][0] == 0 and l[q][1] == n - 1 or (l[q][0] == 0 and l[q][1] == 0) or (l[q][0] == n - 1 and l[q][1] == 0) or (l[q][0] == n - 1 and l[q][1] == n - 1):
				j = 1
		for q in range(2):
			for w in range(q + 1, 3):
				if l[q][0] == 0 or l[q][0] == n - 1:
					if l[w][0] == 0 or l[w][0] == n - 1:
						j = 1
				if l[q][1] == 0 or l[q][1] == n - 1:
					if l[w][1] == 0 or l[w][1] == n - 1:
						j = 1
				if l[q][0] == 0 or l[q][0] == n - 1:
					if l[w][1] == 0 or l[w][1] == n - 1:
						j = 1
				if l[q][1] == 0 or l[q][1] == n - 1:
					if l[w][0] == 0 or l[w][0] == n - 1:
						j = 1
		for q in range(3):
			w = (q + 1) % 3
			r = (q + 2) % 3
			if l[q][0] == 0 or l[q][0] == n - 1:
				if (l[q][1] - l[w][1]) * (l[q][1] - l[r][1]) >= 0:
					j = 1
			if l[q][1] == 0 or l[q][1] == n - 1:
				if (l[q][0] - l[w][0]) * (l[q][0] - l[r][0]) >= 0:
					j = 1
	if j:
		print('yes')
	else:
		print('no')
	t -= 1