Buggy python submission (verdict: Time Limit Exceeded):
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
A.sort(reverse=True)
B.sort(reverse=True)

aloop = 0
bloop = 0

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if C == 0:
            break
        if k in A and k in B:
            continue
        elif (k in A and k not in B):
            C *= len([x for x in B if x > k])
        elif (k not in A and k in B):
            C *= len([x for x in A if x > k])
        else:
            C *= (len([x for x in A if x > k]) *
                  len([x for x in B if x > k]) - (N*M-k))

        C = C % (10**9+7)
print(C)


Fixed submission:
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
A.sort(reverse=True)
B.sort(reverse=True)

aloop = 0
bloop = 0

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if aloop < N and bloop < M and k == A[aloop] and k == B[bloop]:
            aloop += 1
            bloop += 1
        elif aloop < N and k == A[aloop]:
            C *= bloop
            aloop += 1
        elif bloop < M and k == B[bloop]:
            C *= aloop
            bloop += 1
        else:
            C *= (aloop * bloop - (N * M - k))

        C = C % (10**9+7)
print(C)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
A.sort(reverse=True)
B.sort(reverse=True)

aloop = 0
bloop = 0

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if C == 0:
            break
        if k in A and k in B:
            continue
        elif (k in A and k not in B):
            C *= len([x for x in B if x > k])
        elif (k not in A and k in B):
            C *= len([x for x in A if x > k])
        else:
            C *= (len([x for x in A if x > k]) *
                  len([x for x in B if x > k]) - (N * M - k))

        C %= (10**9+7)

print(C)

Fixed submission:
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
A.sort(reverse=True)
B.sort(reverse=True)

aloop = 0
bloop = 0

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if aloop < N and bloop < M and k == A[aloop] and k == B[bloop]:
            aloop += 1
            bloop += 1
        elif aloop < N and k == A[aloop]:
            C *= bloop
            aloop += 1
        elif bloop < M and k == B[bloop]:
            C *= aloop
            bloop += 1
        else:
            C *= (aloop * bloop - (N * M - k))

        C = C % (10**9+7)
print(C)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
A.sort(reverse=True)
B.sort(reverse=True)

aloop = 0
bloop = 0

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if aloop < N and bloop < M and k == A[aloop] and k == B[bloop]:
            aloop += 1
            bloop += 1
        elif aloop < N and k == A[aloop]:
            C *= bloop
            aloop += 1
        elif bloop < M and k == B[bloop]:
            C *= aloop
            bloop += 1
        else:
            C *= (aloop*bloop-(N*M-k))

print(C % (10**9+7))

Fixed submission:
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
A.sort(reverse=True)
B.sort(reverse=True)

aloop = 0
bloop = 0

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if aloop < N and bloop < M and k == A[aloop] and k == B[bloop]:
            aloop += 1
            bloop += 1
        elif aloop < N and k == A[aloop]:
            C *= bloop
            aloop += 1
        elif bloop < M and k == B[bloop]:
            C *= aloop
            bloop += 1
        else:
            C *= (aloop * bloop - (N * M - k))

        C = C % (10**9+7)
print(C)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
A.sort(reverse=True)
B.sort(reverse=True)

aloop = 0
bloop = 0

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if C == 0:
            break
        if aloop < N and bloop < M and k == A[aloop] and k == B[bloop]:
            aloop += 1
            bloop += 1
        elif aloop < N and k == A[aloop]:
            C *= bloop
            aloop += 1
        elif bloop < M and k == B[bloop]:
            C *= aloop
            bloop += 1
        else:
            C *= (aloop*bloop-(N*M-k))

print(C % (10**9+7))

Fixed submission:
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
A.sort(reverse=True)
B.sort(reverse=True)

aloop = 0
bloop = 0

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if aloop < N and bloop < M and k == A[aloop] and k == B[bloop]:
            aloop += 1
            bloop += 1
        elif aloop < N and k == A[aloop]:
            C *= bloop
            aloop += 1
        elif bloop < M and k == B[bloop]:
            C *= aloop
            bloop += 1
        else:
            C *= (aloop * bloop - (N * M - k))

        C = C % (10**9+7)
print(C)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
#A_S = sorted(A, reverse=True)
#B_S = sorted(B, reverse=True)
A.sort(reverse=True)
B.sort(reverse=True)

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if C == 0:
            break
        if k in A and k in B:
            continue
        elif (k in A and k not in B):
            C *= len([x for x in B if x > k])
        elif (k not in A and k in B):
            C *= len([x for x in A if x > k])
        else:
            C *= (len([x for x in A if x > k]) *
                  len([x for x in B if x > k]) - (N*M-k))

print(C % (10**9+7))

Fixed submission:
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
A.sort(reverse=True)
B.sort(reverse=True)

aloop = 0
bloop = 0

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if aloop < N and bloop < M and k == A[aloop] and k == B[bloop]:
            aloop += 1
            bloop += 1
        elif aloop < N and k == A[aloop]:
            C *= bloop
            aloop += 1
        elif bloop < M and k == B[bloop]:
            C *= aloop
            bloop += 1
        else:
            C *= (aloop * bloop - (N * M - k))

        C = C % (10**9+7)
print(C)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if C == 0:
            break
        if k in A and k in B:
            continue
        elif (k in A and k not in B):
            C *= len([x for x in B if x > k])
        elif (k not in A and k in B):
            C *= len([x for x in A if x > k])
        elif (k not in A and k not in B):
            C *= (len([x for x in A if x > k]) *
                  len([x for x in B if x > k]) - (N*M-k))
        else:
            C = 0
            break

print(C % (10**9+7))


Fixed submission:
N, M = (map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))

C = 1
A.sort(reverse=True)
B.sort(reverse=True)

aloop = 0
bloop = 0

if len(set(A)) != len(A) or len(set(B)) != len(B):
    C = 0

else:
    for k in range(N * M, 0, -1):
        if aloop < N and bloop < M and k == A[aloop] and k == B[bloop]:
            aloop += 1
            bloop += 1
        elif aloop < N and k == A[aloop]:
            C *= bloop
            aloop += 1
        elif bloop < M and k == B[bloop]:
            C *= aloop
            bloop += 1
        else:
            C *= (aloop * bloop - (N * M - k))

        C = C % (10**9+7)
print(C)