MOD = 1_000_000_007

$fact = [1]
(1..220000).each do |i|
  $fact << $fact[-1] * i % MOD
end

def exp(n, k)
  x = 1
  while k > 0
    x = x * n % MOD if k & 1 == 1
    n = n * n % MOD
    k >>= 1
  end
  x
end

$inv = (0..220000).map {|i| exp($fact[i], MOD - 2) }

def comb(n, k)
  ($fact[n] * $inv[k] % MOD) * $inv[n-k] % MOD
end

n, m, k = gets.split.map(&:to_i)

answer = 0
(0..k).each do |ke|
  east  = ke == 0 ? 1 : (comb(n + ke * 2, ke) - comb(n + ke * 2, ke - 1)) % MOD
  kn = k - ke
  north = kn == 0 ? 1 : (comb(m + kn * 2, kn) - comb(m + kn * 2, kn - 1)) % MOD
  answer = (answer + east * north * comb(n + m + k * 2, n + ke * 2)) % MOD
end
p answer

