import sys

readline = sys.stdin.readline

sys.setrecursionlimit(10**8)

mod = 10**9+7

#mod = 998244353

INF = 10**18

eps = 10**-7



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



def comb(n, r, mod):

    r = min(r, n-r)

    mol = 1

    deno = 1

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

        mol = mol * (n-r+i) % mod

        deno = deno * i % mod

    ret = mol * pow(deno, mod-2, mod) % mod

    return ret



def f1(x,y,a,b):

    return (a+b-x-y)*(a-x+1)*(b-y+1)//2



def f2(x,a):

    return (a-x)*(a-x+1)//2



ans = 0



for x in range(1,n+1):

    for y in range(1,m+1):

        a = n-x+1

        b = m-y+1

        c = m*(a*(a-1)+x*(x-1))

        d = n*(b*(b-1)+y*(y-1))

        ans += (c+d)//2

        ans %= mod



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

ans = ans*pow(2,mod-2,mod)%mod



print(ans)



import sys

readline = sys.stdin.readline

sys.setrecursionlimit(10**8)

mod = 10**9+7

#mod = 998244353

INF = 10**18

eps = 10**-7



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



def comb(n, r, mod):

    r = min(r, n-r)

    mol = 1

    deno = 1

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

        mol = mol * (n-r+i) % mod

        deno = deno * i % mod

    ret = mol * pow(deno, mod-2, mod) % mod

    return ret



ans = m*n*(m+n)*(m*n-1)//3



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

ans = ans*pow(2,mod-2,mod)%mod



print(ans)



import sys

readline = sys.stdin.readline
sys.setrecursionlimit(10**8)
mod = 10**9 + 7
# mod = 998244353
INF = 10**18
eps = 10**-7
m, n, k = list(map(int, readline().split()))


def comb(n, r, mod):
    r = min(r, n - r)
    mol = 1
    deno = 1
    for i in range(1, r + 1):
        mol = mol * (n - r + i) % mod
        deno = deno * i % mod
    ret = mol * pow(deno, mod - 2, mod) % mod
    return ret


def f1(x, y, a, b):
    return (a + b - x - y) * (a - x + 1) * (b - y + 1) // 2


def f2(x, a):
    return (a - x) * (a - x + 1) // 2


ans = 0
for x in range(1, n + 1):
    for y in range(1, m + 1):
        a = n - x + 1
        b = m - y + 1
        c = m * (a * (a - 1) + x * (x - 1))
        d = n * (b * (b - 1) + y * (y - 1))
        ans += (c + d) // 2
        ans %= mod
ans = (ans * comb(m * n - 2, k - 2, mod)) % mod
ans = ans * pow(2, mod - 2, mod) % mod
print(ans)

import sys

readline = sys.stdin.readline
sys.setrecursionlimit(10**8)
mod = 10**9 + 7
# mod = 998244353
INF = 10**18
eps = 10**-7
m, n, k = list(map(int, readline().split()))


def comb(n, r, mod):
    r = min(r, n - r)
    mol = 1
    deno = 1
    for i in range(1, r + 1):
        mol = mol * (n - r + i) % mod
        deno = deno * i % mod
    ret = mol * pow(deno, mod - 2, mod) % mod
    return ret


ans = m * n * (m + n) * (m * n - 1) // 3
ans = (ans * comb(m * n - 2, k - 2, mod)) % mod
ans = ans * pow(2, mod - 2, mod) % mod
print(ans)

-def f1(x, y, a, b): -    return (a + b - x - y) * (a - x + 1) * (b - y + 1) // 2 - - -def f2(x, a): -    return (a - x) * (a - x + 1) // 2 - - -ans = 0 -for x in range(1, n + 1): -    for y in range(1, m + 1): -        a = n - x + 1 -        b = m - y + 1 -        c = m * (a * (a - 1) + x * (x - 1)) -        d = n * (b * (b - 1) + y * (y - 1)) -        ans += (c + d) // 2 -        ans %= mod +ans = m * n * (m + n) * (m * n - 1) // 3