R = xrange
def solve():
	p = 10**9+7
	Comb = [[0]*76 for i in R(76)]
	Comb[0][0] = 1
	cx = [0]*5; cy = [0]*5; cN = [0]*5; use = [0]*5
	Gx,Gy,K = map(int,raw_input().split())
	assert -10**5 <= Gx <= 10**5
	assert -10**5 <= Gy <= 10**5
	assert 1 <= K <= 5
	check_set = set()
	for i in R(K):
		cx[i],cy[i],cN[i] = map(int,raw_input().split())
		assert -10**4 <= cx[i] <= 10**4
		assert -10**4 <= cy[i] <= 10**4
		assert 1 <= cN[i] <= 15
		assert (cx[i],cy[i]) not in check_set
		check_set.add((cx[i],cy[i]))
	for i in R(K*15):
		for j in R(i+2):
			Comb[i+1][j] = (Comb[i][j] + (Comb[i][j-1] if j > 0 else 0)) % p
	ans = 0
	for i in R(cN[0]+1):
		use[0] = i
		for j in R(cN[1]+1):
			use[1] = j
			for k in R(cN[2]+1):
				use[2] = k
				for l in R(cN[3]+1):
					use[3] = l
					for m in R(cN[4]+1):
						use[4] = m
						x =sum(cx[n]*use[n] for n in R(5))
						y =sum(cy[n]*use[n] for n in R(5))
						if Gx != x or Gy != y:
							continue  
						total = sum(use)
						cnt = 1
						for n in xrange(5):
							cnt = cnt * Comb[total][use[n]] % p
							total -= use[n]
						ans = (ans + cnt) % p
	print ans
solve()