def inverse(a, mod):
    while(a < 0):
        a += mod
    a %= mod
    p = mod
    ya = 0
    yp = 1
    while (a > 0):
        n = p // a
        r = p % a
        yr = ya - n * yp
        ya = yp
        yp = yr
        p = a
        a = r
    return ya % mod if ya >= 0 else ya + mod

mod = 1000000007

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

inv = 1
for i in range(1, k-1):
    inv = inv * i % mod
inv = inverse(inv, mod)

combination = inv
for i in range(n*m-k+1, n*m-1):
    combination = combination * i % mod


xn = n * (n + 1) * (n - 1) // 6 % mod * m % mod * m % mod
yn = m * (m + 1) * (m - 1) // 6 % mod * n % mod * n % mod
ans = (xn + yn) * combination % mod
print(ans)
 def inverse(a, mod):
    while(a < 0):
        a += mod
    a %= mod
    p = mod
    ya = 0
    yp = 1
    while (a > 0):
        n = p // a
        r = p % a
        yr = ya - n * yp
        ya = yp
        yp = yr
        p = a
        a = r
    return ya % mod if ya >= 0 else ya + mod inverse while(a < 0):
        a += mod
     a < 0 a 0 a += mod a mod a %= mod a mod p = mod p mod ya = 0 ya 0 yp = 1 yp 1 while (a > 0):
        n = p // a
        r = p % a
        yr = ya - n * yp
        ya = yp
        yp = yr
        p = a
        a = r
     a > 0 a 0 n = p // a n p // a p a r = p % a r p % a p a yr = ya - n * yp yr ya - n * yp ya n * yp n yp ya = yp ya yp yp = yr yp yr p = a p a a = r a r return ya % mod if ya >= 0 else ya + mod ya % mod if ya >= 0 else ya + mod ya >= 0 ya 0 ya % mod ya mod ya + mod ya mod a a mod mod mod = 1000000007 mod 1000000007 n, m, k = map(int, input().split()) n map(int, input().split()) map int input().split() ().split () input split m k inv = 1 inv 1 for i in range(1, k-1):
    inv = inv * i % mod i range(1, k-1) range 1 k-1 k 1 inv = inv * i % mod inv inv * i % mod inv * i inv i mod inv = inverse(inv, mod) inv inverse(inv, mod) inverse inv mod combination = inv combination inv for i in range(n*m-k+1, n*m-1):
    combination = combination * i % mod i range(n*m-k+1, n*m-1) range n*m-k+1 n*m-k n*m n m k 1 n*m-1 n*m n m 1 combination = combination * i % mod combination combination * i % mod combination * i combination i mod xn = n * (n + 1) * (n - 1) // 6 % mod * m % mod * m % mod xn n * (n + 1) * (n - 1) // 6 % mod * m % mod * m % mod n * (n + 1) * (n - 1) // 6 % mod * m % mod * m n * (n + 1) * (n - 1) // 6 % mod * m % mod n * (n + 1) * (n - 1) // 6 % mod * m n * (n + 1) * (n - 1) // 6 % mod n * (n + 1) * (n - 1) // 6 n * (n + 1) * (n - 1) n * (n + 1) n n + 1 n 1 n - 1 n 1 6 mod m mod m mod yn = m * (m + 1) * (m - 1) // 6 % mod * n % mod * n % mod yn m * (m + 1) * (m - 1) // 6 % mod * n % mod * n % mod m * (m + 1) * (m - 1) // 6 % mod * n % mod * n m * (m + 1) * (m - 1) // 6 % mod * n % mod m * (m + 1) * (m - 1) // 6 % mod * n m * (m + 1) * (m - 1) // 6 % mod m * (m + 1) * (m - 1) // 6 m * (m + 1) * (m - 1) m * (m + 1) m m + 1 m 1 m - 1 m 1 6 mod n mod n mod ans = (xn + yn) * combination % mod ans (xn + yn) * combination % mod (xn + yn) * combination xn + yn xn yn combination mod print(ans) print ans yn = m * (m + 1) * (m - 1) // 6 % mod * n % mod * n % mod m * (m + 1) * (m - 1) // 6 % mod * n % mod * n % mod yn inv = 1 1 inv xn = n * (n + 1) * (n - 1) // 6 % mod * m % mod * m % mod n * (n + 1) * (n - 1) // 6 % mod * m % mod * m % mod xn combination = combination * i % mod combination * i % mod combination mod = 1000000007 1000000007 mod n, m, k = map(int, input().split()) map(int, input().split()) n def inverse(a, mod):
    while(a < 0):
        a += mod
    a %= mod
    p = mod
    ya = 0
    yp = 1
    while (a > 0):
        n = p // a
        r = p % a
        yr = ya - n * yp
        ya = yp
        yp = yr
        p = a
        a = r
    return ya % mod if ya >= 0 else ya + mod def inverse(a, mod):
    while(a < 0):
        a += mod
    a %= mod
    p = mod
    ya = 0
    yp = 1
    while (a > 0):
        n = p // a
        r = p % a
        yr = ya - n * yp
        ya = yp
        yp = yr
        p = a
        a = r
    return ya % mod if ya >= 0 else ya + mod inverse k = map(int, input().split()) map(int, input().split()) k ans = (xn + yn) * combination % mod (xn + yn) * combination % mod ans combination = inv inv combination inv = inv * i % mod inv * i % mod inv inv = inverse(inv, mod) inverse(inv, mod) inv m, k = map(int, input().split()) map(int, input().split()) m
def inverse(a, mod):
    while(a < 0):
        a += mod
    a %= mod
    p = mod
    ya = 0
    yp = 1
    while (a > 0):
        n = p // a
        r = p % a
        yr = ya - n * yp
        ya = yp
        yp = yr
        p = a
        a = r
    return ya % mod if ya >= 0 else ya + mod

mod = 1000000007

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

inv = 1
for i in range(1, k-1):
    inv = inv * i % mod
inv = inverse(inv, mod)

combination = inv
for i in range(n*m-k+1, n*m-1):
    combination = combination * i % mod


xn = n * (n + 1) * (n - 1) // 6 % mod * m % mod * m % mod
yn = m * (m + 1) * (m - 1) // 6 % mod * n % mod * n % mod
ans = (xn + yn) * combination % mod
print(ans)

