#include <bits/stdc++.h>
using namespace std;
struct Fast {
    Fast() {
        std::cin.tie(0);
        ios::sync_with_stdio(false);
        cout.precision(20);
    }
} fast;

/* define */
#define FOR(I, X, Y) for(long long(I) = (X); (I) < (Y); (I)++)
#define REP(I, X, Y) for(long long(I) = (Y)-1; (I) >= (X); (I)--)
#define ALL(X) (X).begin(), (X).end()
#define pb push_back
#define COUNT(V, X)                                                            \
    (upper_bound((V).begin(), (V).end(), X) -                                  \
     lower_bound((V).begin(), (V).end(), X))
#define debug(x) cerr << #x << ':' << x << endl;
#define DEBUG(v)                                                               \
    {                                                                          \
        cerr << #v << ':';                                                     \
        for(auto xv : v) cerr << xv << ' ';                                    \
        cerr << endl;                                                          \
    }
#define Yes(X) cout << (X ? "Yes" : "No") << endl;
#define YES(X) cout << (X ? "YES" : "NO") << endl;
#define ctoi(C) (C - '0')
#define pow2(x) ((long long)((long long)1 << x))

/* alias */
using ll = long long;
using ld = long double;
using vi = vector<int>;
using vii = vector<vector<int>>;
using vl = vector<long long>;
using vll = vector<vector<long long>>;
using pi = pair<int, int>;
using pl = pair<long long, long long>;
template <typename T> using PQ = priority_queue<T>;
template <typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;

/* const */
const long long dx[] = {1, 0, -1, 0};
const long long dy[] = {0, 1, 0, -1};
const long long dx8[] = {1, 1, 0, -1, -1, -1, 0, 1};
const long long dy8[] = {0, 1, 1, 1, 0, -1, -1, -1};
const long long dx9[] = {1, 1, 0, -1, -1, -1, 0, 1, 0};
const long long dy9[] = {0, 1, 1, 1, 0, -1, -1, -1, 0};
const int INF = 1000000007;
const long long LINF = 1000000000000000007;

/* func */
template <typename T> inline bool chmin(T &a, const T &b) {
    if(a > b) a = b;
    return a > b;
}
template <typename T> inline bool chmax(T &a, const T &b) {
    if(a < b) a = b;
    return a < b;
}
long long max(long long x, int y) {
    return max(x, (long long)y);
}
long long max(int x, long long y) {
    return max((long long)x, y);
}
long long min(long long x, int y) {
    return min(x, (long long)y);
}
long long min(int x, long long y) {
    return min((long long)x, y);
}

/* liblary */

long long POW(long long x, long long n, long long mod) {
    long long ans = 1;
    while(n) {
        if(n % 2) ans *= x;
        x *= x;
        x %= mod;
        ans %= mod;
        n >>= 1;
    }
    return ans;
}
vector<long long> factorial(2, 1);
long long nckmodp(long long n, long long k, long long p) {
    if(n < k || n <= 0 || k < 0) return 0;
    while(factorial.size() <= n) {
        long long i = factorial.size();
        factorial.push_back(i * factorial[i - 1] % p);
    }
    return ((factorial[n] * POW(factorial[k], p - 2, p)) % p) *
           POW(factorial[n - k], p - 2, p) % p;
}

/* main */

ll solve(ll N, ll M, ll K) {
    int n[K + 1], m[K + 1];
    int DP[K + 1] = {0}, DP2[K + 1] = {0};
    DP[0] = 1;
    FOR(i, 1, max(N, M) + 2 * K + 1) {
        FOR(j, 0, K + 1) {
            DP2[j] = DP[j] + (j ? DP[j - 1] : 0);
            DP2[j] %= INF;
            if(!(i / 2 >= j)) DP2[j] = 0;
            if(N <= i && i <= N + 2 * K && (i - N) % 2 == 0 &&
               (i - N) / 2 == j) {
                n[(i - N) / 2] = DP2[j];
            }
            if(M <= i && i <= M + 2 * K && (i - M) % 2 == 0 &&
               (i - M) / 2 == j) {
                m[(i - M) / 2] = DP2[j];
            }
        }
        FOR(j, 0, K + 1) DP[j] = DP2[j];
    }
    ll ans = 0;
    FOR(i, 0, K + 1) {
        ans += (ll)(nckmodp(N + M + 2 * K, N + 2 * i, INF) * n[i]) % INF *
               m[K - i];
        ans %= INF;
    }
    return ans;
}

signed main() {
    ll N, M, K;
    cin >> N >> M >> K;
    cout << solve(N, M, K) << endl;
}


Measured memory_bytes: 5164