#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
ll MOD = 1000000007LL;
ll mod_pow(ll a, ll b) {
	if (b == 0) return 1;
	if (b % 2 == 0) {
		ll x = mod_pow(a, b / 2);
		return (x*x) % MOD;
	}
	return (a*mod_pow(a, b - 1)) % MOD;
}
ll fact[300001];
ll inv_fact[300001];
ll comb(ll n, ll k) {
	if (n < k) return 0;
	ll ret = fact[n];
	(ret *= inv_fact[k]) %= MOD;
	(ret *= inv_fact[n - k]) %= MOD;
	return ret;
}
int main() {
	fact[0] = inv_fact[0] = 1;
	for (int i = 1; i <= 300000; i++) {
		fact[i] = (fact[i - 1] * i) % MOD;
		inv_fact[i] = (inv_fact[i - 1] * mod_pow(i, MOD - 2)) % MOD;
	}
	int N, M, K;
	cin >> N >> M >> K;
	ll ans = 0;
	for (int i = 0; i <= K; i++) {
		ll sum = comb(N + M + 2 * K, N + 2 * i);
		ll X = comb(N + 2 * i, N + i);
		if (i > 0) (X += MOD - comb(N + 2 * i, i - 1)) %= MOD;
		ll Y = comb(M + 2 * (K - i), M + (K - i));
		if (K - i > 0) (Y += MOD - comb(M + 2 * (K - i), K - i - 1)) %= MOD;
		(sum *= X) %= MOD;
		(sum *= Y) %= MOD;
		(ans += sum) %= MOD;
	}
	cout << ans << endl;
}
