Buggy python submission (verdict: Time Limit Exceeded):
H,W=map(int,input().split())
hlen = list(map(int,input().split()))
wlen =	list(map(int,input().split()))
hlen.sort(reverse=True)
wlen.sort(reverse=True)
hhlen =[0 for _ in range(H*W+1)]
wwlen =[0 for _ in range(H*W+1)]
for x,xx in zip([hlen,wlen],[hhlen,wwlen]):
	c = 1
	for y in x:
		if xx[y] != 0:
			print(0)
			exit()
		else:
			xx[y] = c


def Count(x,l):
	ret = 0
	while l[ret] > x :
		ret += 1
		if ret == len(l):
			break
	return ret	

m = max(hlen[0],wlen[0])
count = 1
for num in range(1,H*W+1)[::-1]:
	if hhlen[num] and wwlen[num]:
		count *= 1
	elif hhlen[num]:
		count *= Count(num,wlen)
	elif wwlen[num]:
		count *= Count(num,hlen)
	else:
		count *= Count(num,hlen)*Count(num,wlen) - (m-num)
	#print(num,flagh,flagw,count)
	count %= (10**9+7)
print(count % (10**9+7))

Fixed submission:
H,W=map(int,input().split())
hlen = list(map(int,input().split()))
wlen =	list(map(int,input().split()))
hlen.sort(reverse=True)
wlen.sort(reverse=True)
hlen.append(0)
wlen.append(0)

m = H*W
count = 1
h=0
w=0
for num in range(1,H*W+1)[::-1]:
	if hlen[h] == num and wlen[w] == num:
		count *= 1
		h += 1
		w += 1
	elif hlen[h] == num:
		count *= w
		h += 1
	elif wlen[w] == num:
		count *= h
		w += 1
	else:
		count *= h*w - (m-num)
	#print(num,flagh,flagw,count)
	count %= (10**9+7)
print(count)

Buggy python submission (verdict: Runtime Error):
H,W=map(int,input().split())
hlen= list(map(int,input().split()))
wlen =	list(map(int,input().split()))
def is_unique(l):
    return len(l) == len(set(l))
if not is_unique(hlen) or not is_unique(wlen):
	print(0)
	exit()
def Count(x,l):
	ret = 0
	while l[ret] > x :
		ret += 1
		if ret == len(l):
			break
	return ret	
hlen.sort(reverse=True)
wlen.sort(reverse=True)

m = max(hlen[0],wlen[0])
count = 1
for num in range(1,H*W+1)[::-1]:
	flagh = 0
	flagw = 0
	if num in hlen:
		flagh = 1
	if num in wlen:
		flagw = 1
	if flagh and flagw:
		count *= 1
	elif flagh:
		count *= Count(num,wlen)
	elif flagw:
		count *= Count(num,hlen)
	else:
		count *= Count(num,hlen)*Count(num,wlen) - (m-num)
    count %= (10**9+7)
	#print(num,flagh,flagw,count)
print(count % (10**9+7))

Fixed submission:
H,W=map(int,input().split())
hlen = list(map(int,input().split()))
wlen =	list(map(int,input().split()))
hlen.sort(reverse=True)
wlen.sort(reverse=True)
hlen.append(0)
wlen.append(0)

m = H*W
count = 1
h=0
w=0
for num in range(1,H*W+1)[::-1]:
	if hlen[h] == num and wlen[w] == num:
		count *= 1
		h += 1
		w += 1
	elif hlen[h] == num:
		count *= w
		h += 1
	elif wlen[w] == num:
		count *= h
		w += 1
	else:
		count *= h*w - (m-num)
	#print(num,flagh,flagw,count)
	count %= (10**9+7)
print(count)

Buggy python submission (verdict: Runtime Error):
H,W=map(int,input().split())
hlen = list(map(int,input().split()))
wlen =	list(map(int,input().split()))
hlen.sort(reverse=True)
wlen.sort(reverse=True)
hhlen =[0 for _ in range(H*W+1)]
wwlen =[0 for _ in range(H*W+1)]
for x,xx in zip([hlen,wlen],[hhlen,wwlen]):
	c = 1
	for y in x:
		if xx[y] != 0:
			print(0)
			exit()
		else:
			xx[y] = c
			c += 1

def Count(x,l):
	ret = 0
	for ll in l[x:]:
		if ll > 0:
			return ll

m = max(hlen[0],wlen[0])
count = 1
for num in range(1,H*W+1)[::-1]:
	flagh = 0
	flagw = 0
	if hhlen[num]:
		flagh = 1
	if wwlen[num]:
		flagw = 1
	if flagh and flagw:
		count *= 1
	elif flagh:
		count *= Count(num,wwlen)
	elif flagw:
		count *= Count(num,hhlen)
	else:
		count *= Count(num,hhlen)*Count(num,wwlen) - (m-num)
	#print(num,flagh,flagw,count)
	count %= (10**9+7)
print(count % (10**9+7))

Fixed submission:
H,W=map(int,input().split())
hlen = list(map(int,input().split()))
wlen =	list(map(int,input().split()))
hlen.sort(reverse=True)
wlen.sort(reverse=True)
hlen.append(0)
wlen.append(0)

m = H*W
count = 1
h=0
w=0
for num in range(1,H*W+1)[::-1]:
	if hlen[h] == num and wlen[w] == num:
		count *= 1
		h += 1
		w += 1
	elif hlen[h] == num:
		count *= w
		h += 1
	elif wlen[w] == num:
		count *= h
		w += 1
	else:
		count *= h*w - (m-num)
	#print(num,flagh,flagw,count)
	count %= (10**9+7)
print(count)

Buggy python submission (verdict: Time Limit Exceeded):
H,W=map(int,input().split())
hlen = list(map(int,input().split()))
wlen =	list(map(int,input().split()))
hlen.sort(reverse=True)
wlen.sort(reverse=True)
hhlen =[0 for _ in range(H*W+1)]
wwlen =[0 for _ in range(H*W+1)]
for x,xx in zip([hlen,wlen],[hhlen,wwlen]):
	for y in x:
		if xx[y] == 1:
			print(0)
			exit()
		else:
			xx[y] = 1

def is_unique(l):
    return len(l) == len(set(l))
if not is_unique(hlen) or not is_unique(wlen):
	print(0)
	exit()

def Count(x,l):
	ret = 0
	while l[ret] > x :
		ret += 1
		if ret == len(l):
			break
	return ret	


m = max(hlen[0],wlen[0])
count = 1
for num in range(1,H*W+1)[::-1]:
	flagh = 0
	flagw = 0
	if hhlen[num]:
		flagh = 1
	if wwlen[num]:
		flagw = 1
	if flagh and flagw:
		count *= 1
	elif flagh:
		count *= wwlen[num:].count(1)
	elif flagw:
		count *= hhlen[num:].count(1)
	else:
		count *= hhlen[num:].count(1)*wwlen[num:].count(1) - (m-num)
	#print(num,flagh,flagw,count)
print(count % (10**9+7))

Fixed submission:
H,W=map(int,input().split())
hlen = list(map(int,input().split()))
wlen =	list(map(int,input().split()))
hlen.sort(reverse=True)
wlen.sort(reverse=True)
hlen.append(0)
wlen.append(0)

m = H*W
count = 1
h=0
w=0
for num in range(1,H*W+1)[::-1]:
	if hlen[h] == num and wlen[w] == num:
		count *= 1
		h += 1
		w += 1
	elif hlen[h] == num:
		count *= w
		h += 1
	elif wlen[w] == num:
		count *= h
		w += 1
	else:
		count *= h*w - (m-num)
	#print(num,flagh,flagw,count)
	count %= (10**9+7)
print(count)

Buggy python submission (verdict: Time Limit Exceeded):
H,W=map(int,input().split())
hlen= list(map(int,input().split()))
wlen =	list(map(int,input().split()))
def is_unique(l):
    return len(l) == len(set(l))
if not is_unique(hlen) or not is_unique(wlen):
	print(0)
	exit()
def Count(x,l):
	ret = 0
	while l[ret] > x :
		ret += 1
		if ret == len(l):
			break
	return ret	
hlen.sort(reverse=True)
wlen.sort(reverse=True)

m = max(hlen[0],wlen[0])
count = 1
for num in range(1,H*W+1)[::-1]:
	flagh = 0
	flagw = 0
	if num in hlen:
		flagh = 1
	if num in wlen:
		flagw = 1
	if flagh and flagw:
		count *= 1
	elif flagh:
		count *= Count(num,wlen)
	elif flagw:
		count *= Count(num,hlen)
	else:
		count *= Count(num,hlen)*Count(num,wlen) - (m-num)
	#print(num,flagh,flagw,count)
print(count % (10**9+7))

Fixed submission:
H,W=map(int,input().split())
hlen = list(map(int,input().split()))
wlen =	list(map(int,input().split()))
hlen.sort(reverse=True)
wlen.sort(reverse=True)
hlen.append(0)
wlen.append(0)

m = H*W
count = 1
h=0
w=0
for num in range(1,H*W+1)[::-1]:
	if hlen[h] == num and wlen[w] == num:
		count *= 1
		h += 1
		w += 1
	elif hlen[h] == num:
		count *= w
		h += 1
	elif wlen[w] == num:
		count *= h
		w += 1
	else:
		count *= h*w - (m-num)
	#print(num,flagh,flagw,count)
	count %= (10**9+7)
print(count)