n, m, k = list(map(int, input().split()))

mod = 10 ** 9 + 7

MAX = n * m





class ModInt:

    def __init__(self, num):

        self.num = num



    def __str__(self):

        return str(self.num)



    def __repr__(self):

        return "ModInt(num: {}, mod: {}".format(self.num, mod)



    def __add__(self, other):

        ret = self.num + other.num

        ret %= mod

        return ModInt(ret)



    def __sub__(self, other):

        ret = self.num - other.num

        ret %= mod

        return ModInt(ret)



    def __mul__(self, other):

        ret = self.num * other.num

        ret %= mod

        return ModInt(ret)



    def pow(self, times):

        pw = pow(self.num, times, mod)

        return ModInt(pw)



    def inverse(self):

        return ModInt(inv[self.num])



    def __truediv__(self, other):

        num = self * other.inverse()

        return ModInt(num)





def comb(n, k):

    return fact[n] * inv[n-k] * inv[k]





fact = [None] * (MAX + 1)

fact[0] = ModInt(1)

for i in range(1, MAX + 1):

    fact[i] = fact[i-1] * ModInt(i)



inv = [None] * (MAX + 1)

inv[MAX] = fact[MAX].pow(mod - 2)

for i in range(MAX, 0, -1):

    inv[i-1] = inv[i] * ModInt(i)



ans = ModInt(0)

for i in range(n):

    for j in range(m):

        add = ModInt(n - i) * ModInt(m - j) * ModInt(i + j)

        if i != 0 and j != 0:

            add *= ModInt(2)



        ans += add



ans *= comb(n * m - 2, k - 2)

print(ans)

n, m, k = list(map(int, input().split()))



mod = 10 ** 9 + 7

MAX = n * m



fact = [1] * (MAX + 1)

for i in range(1, MAX + 1):

    fact[i] = (fact[i-1] * i) % mod



inv = [1] * (MAX + 1)

inv[MAX] = pow(fact[MAX], mod - 2, mod)

for i in range(MAX, 0, -1):

    inv[i-1] = (inv[i] * i) % mod





def comb(n, k):

    return fact[n] * inv[n-k] * inv[k] % mod





ans = 0

for i in range(n):

    for j in range(m):

        add = (n - i) * (m - j) * (i + j) % mod

        if i != 0 and j != 0:

            add *= 2

            add %= mod



        ans += add

        ans %= mod



ans *= comb(MAX - 2, k - 2)

ans %= mod

print(ans)

n, m, k = list(map(int, input().split()))
mod = 10**9 + 7
MAX = n * m


class ModInt:
    def __init__(self, num):
        self.num = num

    def __str__(self):
        return str(self.num)

    def __repr__(self):
        return "ModInt(num: {}, mod: {}".format(self.num, mod)

    def __add__(self, other):
        ret = self.num + other.num
        ret %= mod
        return ModInt(ret)

    def __sub__(self, other):
        ret = self.num - other.num
        ret %= mod
        return ModInt(ret)

    def __mul__(self, other):
        ret = self.num * other.num
        ret %= mod
        return ModInt(ret)

    def pow(self, times):
        pw = pow(self.num, times, mod)
        return ModInt(pw)

    def inverse(self):
        return ModInt(inv[self.num])

    def __truediv__(self, other):
        num = self * other.inverse()
        return ModInt(num)


def comb(n, k):
    return fact[n] * inv[n - k] * inv[k]


fact = [None] * (MAX + 1)
fact[0] = ModInt(1)
for i in range(1, MAX + 1):
    fact[i] = fact[i - 1] * ModInt(i)
inv = [None] * (MAX + 1)
inv[MAX] = fact[MAX].pow(mod - 2)
for i in range(MAX, 0, -1):
    inv[i - 1] = inv[i] * ModInt(i)
ans = ModInt(0)
for i in range(n):
    for j in range(m):
        add = ModInt(n - i) * ModInt(m - j) * ModInt(i + j)
        if i != 0 and j != 0:
            add *= ModInt(2)
        ans += add
ans *= comb(n * m - 2, k - 2)
print(ans)

n, m, k = list(map(int, input().split()))
mod = 10**9 + 7
MAX = n * m
fact = [1] * (MAX + 1)
for i in range(1, MAX + 1):
    fact[i] = (fact[i - 1] * i) % mod
inv = [1] * (MAX + 1)
inv[MAX] = pow(fact[MAX], mod - 2, mod)
for i in range(MAX, 0, -1):
    inv[i - 1] = (inv[i] * i) % mod


def comb(n, k):
    return fact[n] * inv[n - k] * inv[k] % mod


ans = 0
for i in range(n):
    for j in range(m):
        add = (n - i) * (m - j) * (i + j) % mod
        if i != 0 and j != 0:
            add *= 2
            add %= mod
        ans += add
        ans %= mod
ans *= comb(MAX - 2, k - 2)
ans %= mod
print(ans)

- - -class ModInt: -    def __init__(self, num): -        self.num = num - -    def __str__(self): -        return str(self.num) - -    def __repr__(self): -        return "ModInt(num: {}, mod: {}".format(self.num, mod) - -    def __add__(self, other): -        ret = self.num + other.num -        ret %= mod -        return ModInt(ret) - -    def __sub__(self, other): -        ret = self.num - other.num -        ret %= mod -        return ModInt(ret) - -    def __mul__(self, other): -        ret = self.num * other.num -        ret %= mod -        return ModInt(ret) - -    def pow(self, times): -        pw = pow(self.num, times, mod) -        return ModInt(pw) - -    def inverse(self): -        return ModInt(inv[self.num]) - -    def __truediv__(self, other): -        num = self * other.inverse() -        return ModInt(num) +fact = [1] * (MAX + 1) +for i in range(1, MAX + 1): +    fact[i] = (fact[i - 1] * i) % mod +inv = [1] * (MAX + 1) +inv[MAX] = pow(fact[MAX], mod - 2, mod) +for i in range(MAX, 0, -1): +    inv[i - 1] = (inv[i] * i) % mod -    return fact[n] * inv[n - k] * inv[k] +    return fact[n] * inv[n - k] * inv[k] % mod -fact = [None] * (MAX + 1) -fact[0] = ModInt(1) -for i in range(1, MAX + 1): -    fact[i] = fact[i - 1] * ModInt(i) -inv = [None] * (MAX + 1) -inv[MAX] = fact[MAX].pow(mod - 2) -for i in range(MAX, 0, -1): -    inv[i - 1] = inv[i] * ModInt(i) -ans = ModInt(0) +ans = 0 -        add = ModInt(n - i) * ModInt(m - j) * ModInt(i + j) +        add = (n - i) * (m - j) * (i + j) % mod -            add *= ModInt(2) +            add *= 2 +            add %= mod -ans *= comb(n * m - 2, k - 2) +        ans %= mod +ans *= comb(MAX - 2, k - 2) +ans %= mod