Buggy python submission (verdict: Time Limit Exceeded):
n, m = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]

a.sort(reverse=True); b.sort(reverse=True)

def k(a, b, n, m):
    c, s = 0, 1
    if (n * m not in a) or (n * m not in b):
        return 0
    for i in reversed(range(n * m)):
        try:
            x = a.index(i + 1) + 1
            row = 1
        except ValueError:
            row = 0
        try:
            y = b.index(i + 1) + 1
            column = 1
        except ValueError:
            column = 0

        if row * column:
            s *= 1
        elif not row * column and row + column:
            s *= column * x + row * y
        else:
            if x * y - c > 0:
                s *= x * y - c
            else:
                s = 0
                break
        c += 1
        if s > 10 ** 9 + 7:
            s %= 10 ** 9 + 7
    return s

if len(a) != n or len(b) != m:
    print(0)
else:
    print(k(a, b, n, m))


Fixed submission:
n, m = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]

a = set(a); b = set(b)
#print(a, b)

def k(a, b, n, m):
    s = 1
    x, y = 0, 0
    if (n * m not in a) or (n * m not in b):
        return 0
    for i, j in enumerate(reversed(range(n * m))):

        if (j + 1 in a) and (j + 1 in b):
            x += 1; y += 1
            #continue
        elif j + 1 in a:
            y += 1
            s *= x
        elif j + 1 in b:
            x += 1
            s *= y
        else:
            if x * y - i > 0:
                s *= x * y - i
            else:
                s = 0
                break
        if s > 10 ** 9 + 7:
            s %= 10 ** 9 + 7
        #print(i, j + 1, 'x=', x, 'y=', y, 's=', s)
    return s

if len(a) != n or len(b) != m:
    print(0)
else:
    print(k(a, b, n, m))

# TimeLimitExceeded
# indexで一個ずつ見つけていくのは時間がかかるということ。

Buggy python submission (verdict: Time Limit Exceeded):
n, m = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]

a.sort(reverse=True); b.sort(reverse=True)

def k(a, b, n, m):
    c, s = 0, 1
    if (n * m not in a) or (n * m not in b):
        return 0
    for i in reversed(range(n * m)):
        try:
            x = a.index(i + 1) + 1
            row = 1
        except ValueError:
            row = 0
        try:
            y = b.index(i + 1) + 1
            column = 1
        except ValueError:
            column = 0

        if row * column:
            s *= 1
        elif not row * column and row + column:
            s *= column * x + row * y
        else:
            if x * y - c > 0:
                s *= x * y - c
            else:
                s = 0
                break
        c += 1
        if s > 10 ** 9 + 7:
            s %= 10 ** 9 + 7
    return s

print(k(a, b, n, m))


Fixed submission:
n, m = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]

a = set(a); b = set(b)
#print(a, b)

def k(a, b, n, m):
    s = 1
    x, y = 0, 0
    if (n * m not in a) or (n * m not in b):
        return 0
    for i, j in enumerate(reversed(range(n * m))):

        if (j + 1 in a) and (j + 1 in b):
            x += 1; y += 1
            #continue
        elif j + 1 in a:
            y += 1
            s *= x
        elif j + 1 in b:
            x += 1
            s *= y
        else:
            if x * y - i > 0:
                s *= x * y - i
            else:
                s = 0
                break
        if s > 10 ** 9 + 7:
            s %= 10 ** 9 + 7
        #print(i, j + 1, 'x=', x, 'y=', y, 's=', s)
    return s

if len(a) != n or len(b) != m:
    print(0)
else:
    print(k(a, b, n, m))

# TimeLimitExceeded
# indexで一個ずつ見つけていくのは時間がかかるということ。

Buggy python submission (verdict: Runtime Error):
n, m = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]

a.sort(reverse=True); b.sort(reverse=True)
c, s = 0, 1

for i in reversed(range(n * m)):
    try:
        x = a.index(i + 1) + 1
        row = 1
    except ValueError:
        row = 0
    try:
        y = b.index(i + 1) + 1
        column = 1
    except ValueError:
        column = 0

    if row * column:
        s *= 1
    elif not row * column and row + column:
        s *= column * x + row * y
    else:
        if x * y - c > 0:
            s *= x * y - c
        else:
            s = 0
            break
    c += 1
    if s > 10 ** 9 + 7:
        s %= 10 ** 9 + 7

print(s)


Fixed submission:
n, m = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]

a = set(a); b = set(b)
#print(a, b)

def k(a, b, n, m):
    s = 1
    x, y = 0, 0
    if (n * m not in a) or (n * m not in b):
        return 0
    for i, j in enumerate(reversed(range(n * m))):

        if (j + 1 in a) and (j + 1 in b):
            x += 1; y += 1
            #continue
        elif j + 1 in a:
            y += 1
            s *= x
        elif j + 1 in b:
            x += 1
            s *= y
        else:
            if x * y - i > 0:
                s *= x * y - i
            else:
                s = 0
                break
        if s > 10 ** 9 + 7:
            s %= 10 ** 9 + 7
        #print(i, j + 1, 'x=', x, 'y=', y, 's=', s)
    return s

if len(a) != n or len(b) != m:
    print(0)
else:
    print(k(a, b, n, m))

# TimeLimitExceeded
# indexで一個ずつ見つけていくのは時間がかかるということ。