module ModInt
  MOD = 10 ** 9 + 7

  def to_mod(a); a % MOD; end
  def add(a, b); (a + b) % MOD; end
  def mul(a, b); (a * b) % MOD; end
  def inv(a); a.pow(MOD - 2, MOD); end
  def div(a, b); mul(a, inv(b)); end
end

MOD = 10 ** 9 + 7

# MODを法とした階乗、組み合わせ
class ModCombination
  attr_reader :fac, :inv, :finv, :mod

  def initialize(n, mod: MOD)
    @mod = mod
    @fac = [1, 1]
    @inv = [1, 1]
    @finv = [1, 1]

    (2..n).each do |i|
      @fac[i] = fac[i - 1] * i % mod
      @inv[i] = mod - inv[mod % i] * (mod / i) % mod
      @finv[i] = finv[i - 1] * inv[i] % mod
    end
  end

  def combination(n, k)
    return 0 if n < k
    return 0 if n < 0 || k < 0

    fac[n] * (finv[k] * finv[n - k] % mod) % mod
  end

  def repeated_combination(n, k)
    combination(n + k - 1, k)
  end
end

n, m, k = gets.split.map(&:to_i)
ft = ModCombination.new(n * m)

# https://www.wolframalpha.com/input/?i=sum%28n*%28x-n%29%29%2C+n%3D1+to+x-1&lang=ja
def choose_pair(x)
  x * (x - 1) * (x + 1) / 6
end

include ModInt
x_sum = to_mod(choose_pair(n) * m * m)
y_sum = to_mod(choose_pair(m) * n * n)
pat = ft.combination(n*m-2,k-2)
ans = mul(x_sum + y_sum, pat)
puts ans
