#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
using namespace std;
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
const ll mod = 1000000007;
typedef long double ld;
const ll INF = mod * mod;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef complex<ld> Point;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ld, ld> LDP;
typedef pair<ll, ll> LP;
#define fr first
#define sc second

struct perm {
private:
	int sz;
	vector<ll> p, invp;
public:
	perm(int n) {
		sz = n + 1;
		p.resize(sz), invp.resize(sz);
		p[0] = 1;
		rep1(i, sz - 1) {
			p[i] = p[i - 1] * i%mod;
		}
		invp[sz - 1] = 1;
		ll cop = mod - 2, x = p[sz - 1];
		while (cop) {
			if (cop % 2)invp[sz - 1] = invp[sz - 1] * x%mod;
			cop >>= 1; x = x * x % mod;
		}
		per(i, sz - 1) {
			invp[i] = invp[i + 1] * (i + 1) % mod;
		}
	}
	ll comb(ll x, ll y) {
		if (x < y || y < 0)return 0;
		ll ret = p[x];
		(ret *= invp[y]) %= mod;
		(ret *= invp[x - y]) %= mod;
		return ret;
	}
	ll combP(ll x, ll y) {
		if (x < y || y < 0)return 0;
		return p[x] * invp[x - y] % mod;
	}
};
void solve() {
	perm p(1 << 18);
	int n, m, k; cin >> n >> m >> k;
	ll ans = 0;
	vector<ll> s({ 1 });
	vector<ll> t({ 1 });
	rep1(i, k) {
		ll sum1 = p.comb(n + 2 * i, i) - p.comb(n + 2 * i, i - 1);
		if (sum1 < 0)sum1 += mod;
		ll sum2 = p.comb(m + 2 * i, i) - p.comb(m + 2 * i, i-1);
		if (sum2 < 0)sum2 += mod;
		s.push_back(sum1);
		t.push_back(sum2);
	}
	rep(i, k + 1) {
		ll csum = s[i] * t[k - i] % mod*p.comb(n + m + 2*k, n + 2*i) % mod;
		ans = (ans + csum) % mod;
	}
	cout << ans << endl;
}
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	solve();
	//stop
	return 0;
}
