# inverse x^(-1)
def inv(x):
    global mod
    return pow(x, mod - 2, mod)

# factorial x!
def fact(x):
    global mod
    res=1
    for i in range(2 , x + 1):
        res=res * i % mod
    return res

# combination nCr
def combi(n,r):
    if r < 0 or r > n:
        return 0
    else:
        return fact(n) * inv(fact(r)) * inv(fact(n - r)) % mod

mod = 10 ** 9 + 7
N, M, K = map(int,input().split())
x = (N - 1) * N * (N + 1) * inv(6) % mod
x = x * M * M % mod
y = (M - 1) * M * (M + 1) * inv(6) % mod
y = y * N * N % mod
z = combi(M * N - 2, K - 2)
ans = (x + y) * z % mod
print(ans) def inv(x):
    global mod
    return pow(x, mod - 2, mod)

# factorial x! inv global mod return pow(x, mod - 2, mod) pow(x, mod - 2, mod) pow x mod - 2 mod 2 mod x x def fact(x):
    global mod
    res=1
    for i in range(2 , x + 1):
        res=res * i % mod
    return res

# combination nCr fact global mod res=1 res 1 for i in range(2 , x + 1):
        res=res * i % mod
     i range(2 , x + 1) range 2 x + 1 x 1 res=res * i % mod res res * i % mod res * i res i mod return res res x x def combi(n,r):
    if r < 0 or r > n:
        return 0
    else:
        return fact(n) * inv(fact(r)) * inv(fact(n - r)) % mod combi if r < 0 or r > n:
        return 0
    else:
        return fact(n) * inv(fact(r)) * inv(fact(n - r)) % mod r < 0 or r > n r < 0 r 0 r > n r n return 0 0 return fact(n) * inv(fact(r)) * inv(fact(n - r)) % mod fact(n) * inv(fact(r)) * inv(fact(n - r)) % mod fact(n) * inv(fact(r)) * inv(fact(n - r)) fact(n) * inv(fact(r)) fact(n) fact n inv(fact(r)) inv fact(r) fact r inv(fact(n - r)) inv fact(n - r) fact n - r n r mod n n r r mod = 10 ** 9 + 7 mod 10 ** 9 + 7 10 ** 9 10 9 7 N, M, K = map(int,input().split()) N map(int,input().split()) map int input().split() ().split () input split M K x = (N - 1) * N * (N + 1) * inv(6) % mod x (N - 1) * N * (N + 1) * inv(6) % mod (N - 1) * N * (N + 1) * inv(6) (N - 1) * N * (N + 1) (N - 1) * N N - 1 N 1 N N + 1 N 1 inv(6) inv 6 mod x = x * M * M % mod x x * M * M % mod x * M * M x * M x M M mod y = (M - 1) * M * (M + 1) * inv(6) % mod y (M - 1) * M * (M + 1) * inv(6) % mod (M - 1) * M * (M + 1) * inv(6) (M - 1) * M * (M + 1) (M - 1) * M M - 1 M 1 M M + 1 M 1 inv(6) inv 6 mod y = y * N * N % mod y y * N * N % mod y * N * N y * N y N N mod z = combi(M * N - 2, K - 2) z combi(M * N - 2, K - 2) combi M * N - 2 M * N M N 2 K - 2 K 2 ans = (x + y) * z % mod ans (x + y) * z % mod (x + y) * z x + y x y z mod print(ans) print ans ans = (x + y) * z % mod (x + y) * z % mod ans x = (N - 1) * N * (N + 1) * inv(6) % mod (N - 1) * N * (N + 1) * inv(6) % mod x N, M, K = map(int,input().split()) map(int,input().split()) N y = (M - 1) * M * (M + 1) * inv(6) % mod (M - 1) * M * (M + 1) * inv(6) % mod y def fact(x):
    global mod
    res=1
    for i in range(2 , x + 1):
        res=res * i % mod
    return res

# combination nCr def fact(x):
    global mod
    res=1
    for i in range(2 , x + 1):
        res=res * i % mod
    return res

# combination nCr fact M, K = map(int,input().split()) map(int,input().split()) M def combi(n,r):
    if r < 0 or r > n:
        return 0
    else:
        return fact(n) * inv(fact(r)) * inv(fact(n - r)) % mod def combi(n,r):
    if r < 0 or r > n:
        return 0
    else:
        return fact(n) * inv(fact(r)) * inv(fact(n - r)) % mod combi mod = 10 ** 9 + 7 10 ** 9 + 7 mod x = x * M * M % mod x * M * M % mod x z = combi(M * N - 2, K - 2) combi(M * N - 2, K - 2) z def inv(x):
    global mod
    return pow(x, mod - 2, mod)

# factorial x! def inv(x):
    global mod
    return pow(x, mod - 2, mod)

# factorial x! inv y = y * N * N % mod y * N * N % mod y K = map(int,input().split()) map(int,input().split()) K
# inverse x^(-1)
def inv(x):
    global mod
    return pow(x, mod - 2, mod)

# factorial x!
def fact(x):
    global mod
    res=1
    for i in range(2 , x + 1):
        res=res * i % mod
    return res

# combination nCr
def combi(n,r):
    if r < 0 or r > n:
        return 0
    else:
        return fact(n) * inv(fact(r)) * inv(fact(n - r)) % mod

mod = 10 ** 9 + 7
N, M, K = map(int,input().split())
x = (N - 1) * N * (N + 1) * inv(6) % mod
x = x * M * M % mod
y = (M - 1) * M * (M + 1) * inv(6) % mod
y = y * N * N % mod
z = combi(M * N - 2, K - 2)
ans = (x + y) * z % mod
print(ans)