#include <bits/stdc++.h>
using namespace std;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) cout << #v << "=" << endl; REP(i_debug, v.size()){ cout << v[i_debug] << ","; } cout << endl;
#define mdebug(m) cout << #m << "=" << endl; REP(i_debug, m.size()){ REP(j_debug, m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;}
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; }
template<typename T> ostream &operator<<(ostream &os, vector<T> &v){ for(int i = 0; i < v.size(); i++) { cout << v[i]; if(i != v.size() - 1) cout << endl; }; return os; }
template<typename T> void Out(T x) { cout << x << endl; }
template<typename T1, typename T2> void Ans(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); }

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};
//char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
//const int mod = 998244353;
#define Add(x, y) x = (x + (y)) % mod
#define Mult(x, y) x = (x * (y)) % mod

template<long long MOD>
struct ModInt{

    using ll = long long;
    ll val;

    void setval(ll v) { val = v % MOD; };
    ModInt(): val(0) {}
    ModInt(ll v) { setval(v); };

    ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
    ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
    ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
    ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt operator+=(const ModInt &x) { return *this = *this + x; }
    ModInt operator-=(const ModInt &x) { return *this = *this - x; }
    ModInt operator*=(const ModInt &x) { return *this = *this * x; }
    ModInt operator/=(const ModInt &x) { return *this = *this / x; }

    friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; }
    friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; }

    ModInt pow(ll n) const {
        ModInt a = 1;
        if(n == 0) return a;
        int i0 = 64 - __builtin_clzll(n);
        for(int i = i0 - 1; i >= 0; i--){
            a = a * a;
            if((n >> i) & 1) a *= (*this); 
        }
        return a;
    }
    ModInt inv() const { return this->pow(MOD - 2); }
};

using mint = ModInt<mod>; mint pow(mint x, long long n) { return x.pow(n); }
//using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct Combination{

    vector<mint> fact, invfact;

    Combination(int N){
        fact = vector<mint>({mint(1)});
        invfact = vector<mint>({mint(1)});
        fact_initialize(N);
    }

    void fact_initialize(int N){
        int i0 = fact.size();
        if(i0 >= N + 1) return;
        fact.resize(N + 1);
        invfact.resize(N + 1);
        for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i;
        invfact[N] = (mint)1 / fact[N];
        for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1); 
    }

    mint nCr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if(fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[r] * invfact[n - r];
    }

    mint nPr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if(fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[n - r];
    }

};

int D = 100000;
int memo[10001]={1,457992974,107146451,373281933,559805077,154425679,679209364,526226141,644158465,730342129,641102369,99410016,363599536,361684231,539157852,448516387,309854856,95657988,663484182,311407840,578095319,229611066,765808214,142477924,585806050,119948046,579773866,816761238,861745250,639926530,5832229,630915411,242744764,932799119,899032987,929795683,150478174,609593566,627860803,358784546,259081142,57134788,544918953,8837465,907400235,59433257,421968194,500425006,278955367,248057675,974067448,293296655,996965954,212873022,473966292,261465122,479920311,214054614,752161465,719792849,316220877,224748329,1575312,652382508,620898940,663134272,405577532,116225742,956413299,257438891,690120224,437383740,24521750,596209708,576078970,304661605,929871923,412584039,14422365,604303898,251368199,808427728,582439362,55596303,220087090,704262886,98361446,295620142,763414075,927340096,980250487,248981102,618104354,839684660,398723029,386267146,764421236,558837848,476998749,345911460,682498929,58865407,152611299,37365474,345470378,681184885,403024660,947000742,140864216,22803916,134623568,733842728,373126171,337899910,461157687,427907847,363224613,642502601,526497651,759652538,95936601,173914411,19447777,382610562,584319463,140928835,569582206,226022701,9045328,784835785,933097914,76048860,959173997,780658683,559096347,391177708,12442609,40743573,508362944,781264818,167332441,33592533,75538458,714210512,275742306,739650465,137855279,889166166,60332461,798657991,598816162,464484063,31223863,344176836,767213175,292015879,564190300,296547306,222078457,977909564,336060741,474159159,632048012,952625711,895642779,810640932,171183381,305391286,851161246,209567103,248744620,551739578,635103992,526685249,605016577,892704918,853414712,566161015,546047842,894851390,626497524,433082692,867430659,512332467,904851726,118508240,475501650,815664143,298693437,652967545,288843364,865229790,52298443,803384326,743602491,406755567,479708090,643624459,125625755,316969704,491101308,708750650,662967999,571611259,385457627,668723114,482257159,899820643,393222011,401679067,245341950,587770205,474567292,725000295,196002818,560364972,754437203,498728445,542706821,970854495,565768255,246407879,524308015,724201825,545648343,913230882,58680787,702934318,792180189,131514392,246899319,192185054,99934426,98200674,788944266,756627904,676012445,734897886,610686655,130907341,968999,379198792,595032530,642903797,244819707,7998896,511710008,696896528,902492598,3525929,586350670,296000745,979137619,86414019,980655027,328019447,474700377,306429182,30153596,966484628,638587686,610696318,420932107,477267870,353049206,497857012,281562548,500956856,921459833,157600969,881746146,924389072,850268753,87892573,711117420,526658674,919203761,262557378,831442297,122316469,19426633,190298375,910061172,214146479,862345480,560607302,293462255,370787091,542955556,768910131,850500036,31318378,181909169,500033013,496532173,916364742,582702682,778006566,168757859,361307467,76479948,219226870,477639087,126712923,930180103,732041432,941723214,130794194,28581913,85186984,268124147,88516556,685075984,488636005,53790970,30473806,672818243,906976408,581968000,78103048,842267748,348586163,947532066,464777188,451116854,878381584,333707614,448457825,650009312,53500714,886294336,648763344,868829344,570443478,613566917,73995168,695702195,776902855,853242582,107560517,485348706,31109298,229827108,590398688,827117592,771153434,492711911,111567856,296974594,269232911,463847391,546178363,649090736,276477167,204857297,72518508,760019200,656049509,942731826,505080571,544075857,422316785,185735387,876081033,550588097,264638935,632593345,941126423,706629399,642498983,898187927,769005417,854821744,205765722,297803207,468116664,596729075,409898960,466541843,190009221,798967520,644759890,743420839,206187615,198998756,359622660,526623452,836550874,952046139,202071291,82926604,130808582,924044367,848688381,23777891,59761470,924258126,204012302,450837733,960862718,723816384,547639586,535478979,87226689,53975412,320608814,517436639,173809161,63932312,478679185,156530778,571781438,807928028,681452055,305569485,278224088,545662462,710807771,29493652,581977264,721996174,820229375,49456224,979809664,480391065,222176885,526281212,927482461,151117811,44756165,299085602,643484121,522961673,277106101,374481484,814440466,489252071,587318335,589831644,15753781,323604647,21771073,153393495,433729686,268164416,359932651,48301315,364347439,90383486,945599636,172827403,695951947,800588969,106892865,757146415,213590923,169338716,599312274,192601723,455503344,398699886,668865790,675113999,708394300,139831846,983975503,135840345,334346960,475501867,167226923,530389102,852493922,499294891,922898261,415376,619965361,114785958,146628257,576550918,635060378,294587621,55789549,714006296,103228118,457685563,221896631,875018827,971180026,254653019,274155554,813805606,9027036,172340144,518728060,498342367,676243000,258170000,496205651,43217172,714008239,67347853,912590546,909565792,54071151,16783532,557470122,495844744,953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mint mfact(int N){
    int n = N / D;
    mint t = memo[n];
    FOR(i, D * n + 1, N + 1) t *= i;
    return t;
}

mint nCr(int n, int r){
    int n1 = n % mod, n2 = n / mod;
    int r1 = r % mod, r2 = r / mod;

    mint c1 = mfact(n1) / mfact(r1) / mfact(n1 - r1);
    mint c2 = mfact(n2) / mfact(r2) / mfact(n2 - r2);
    return c1 * c2;
}

signed main(){

    int N, M, K; cin >> N >> M >> K;
    mvec s(N + M + 1, 0);
    FOR(i, 1, N + M + 1) s[i] = s[i - 1] + i;
    
    mint x = 0;
    REP(i, N){
        x += (s[i] + s[N - 1 - i]) * M;
    }
    x /= (mint)N;
    x /= (mint)(N * M - 1);

    mint y = 0;
    REP(i, M){
        y += (s[i] + s[M - 1 - i]) * N;
    }
    y /= (mint)M;
    y /= (mint)(N * M - 1);

    mint ans = (x + y) * (mint)(K * (K - 1) / 2);

    //Combination C(N * M);
    //ans *= C.nCr(N * M, K);
    ans *= nCr(N * M, K);
    

    Out(ans);

    return 0;
}


Measured memory_bytes: 1792