n, m, k = gets.split(" ").map(&:to_i)
## 二項係数 C(n,k) mod pの計算 (pは素数)##

#適切な値に設定する
MOD = 10**9 + 7
MAX = n*m-2

$fact = Array.new(MAX + 1) # i! mod p
$finv = Array.new(MAX + 1) # (i!)^(-1) mod p
$inv = Array.new(MAX + 1) # i^(-1) mod p

def com_init()
  $fact[0] = $fact[1] = 1
  $finv[0] = $finv[1] = 1
  $inv[1] = 1
  2.upto(MAX) do |i|
    $fact[i] = $fact[i-1] * i % MOD
    $inv[i] = MOD - $inv[MOD % i] * (MOD/i) % MOD
    $finv[i] = $finv[i-1] * $inv[i] % MOD
  end
end

# C(n,k) mod p
def com(n,k)
  return 0 if n < k || n < 0 || k < 0
  $fact[n] * (($finv[n-k] * $finv[k]) % MOD )% MOD
end

def f(n)
  ((n-1)*n*(n+1)/6) %MOD
end

com_init
puts (m**2 * f(n) + n**2 * f(m)) * com(m*n-2, k-2) %MOD
