#include <bits/stdc++.h>
using namespace std;

using VS = vector<string>;    using LL = long long;
using VI = vector<int>;       using VVI = vector<VI>;
using PII = pair<int, int>;   using PLL = pair<LL, LL>;
using VL = vector<LL>;        using VVL = vector<VL>;

#define ALL(a)  begin((a)),end((a))
#define RALL(a) (a).rbegin(), (a).rend()
#define SZ(a) int((a).size())
#define SORT(c) sort(ALL((c)))
#define RSORT(c) sort(RALL((c)))
#define UNIQ(c) (c).erase(unique(ALL((c))), end((c)))
#define FOR(i, s, e) for (int(i) = (s); (i) < (e); (i)++)
#define FORR(i, s, e) for (int(i) = (s); (i) > (e); (i)--)
//#pragma GCC optimize ("-O3") 
#ifdef YANG33
#include "mydebug.hpp"
#else
#define DD(x) 
#endif
const int INF = 1e9;                          const LL LINF = 1e16;
const LL MOD = 1000000007;                    const double PI = acos(-1.0);

/* -----  2019/05/25  Problem: ABC 127 E / Link: http://abc127.contest.atcoder.jp/tasks/abc127_e  ----- */


template <std::uint_least32_t MODULO> class modint {
public:
using uint32 = std::uint_least32_t; using uint64 = std::uint_least64_t; using iint64 = std::int_fast64_t; class optimize_tag_t {}; static constexpr optimize_tag_t optimize_tag{}; public:using value_type = uint32; value_type a; static constexpr value_type cst(iint64 x) noexcept { x %= static_cast<iint64>(MODULO); if (x < static_cast<iint64>(0)) { x += static_cast<iint64>(MODULO); }return static_cast<value_type>(x); }constexpr modint(optimize_tag_t, const value_type &x) noexcept : a(x) {}constexpr modint() noexcept : a(static_cast<value_type>(0)) {}constexpr modint(const iint64 &x) noexcept : a(cst(x)) {}constexpr modint operator+(const modint &o) const noexcept { return modint(optimize_tag, a + o.a < MODULO ? a + o.a : a + o.a - MODULO); }constexpr modint operator-(const modint &o) const noexcept { return modint(optimize_tag, a < o.a ? a + MODULO - o.a : a - o.a); }constexpr modint operator*(const modint &o) const noexcept { return modint(optimize_tag, static_cast<value_type>(static_cast<uint64>(a) * static_cast<uint64>(o.a) % static_cast<uint64>(MODULO))); }constexpr modint operator/(const modint &o) const { return modint(optimize_tag, static_cast<value_type>(static_cast<uint64>(a) * static_cast<uint64>((~o).a) % static_cast<uint64>(MODULO))); }modint &operator+=(const modint &o) noexcept { if ((a += o.a) >= MODULO)a -= MODULO; return *this; }modint &operator-=(const modint &o) noexcept { if (a < o.a)a += MODULO; a -= o.a; return *this; }modint &operator*=(const modint &o) noexcept { a = static_cast<value_type>(static_cast<uint64>(a) * static_cast<uint64>(o.a) % static_cast<uint64>(MODULO)); return *this; }modint &operator/=(const modint &o) { a = static_cast<uint64>(a) * (~o).a % MODULO; return *this; }constexpr modint inverse() const noexcept { assert(a != static_cast<value_type>(0) && "0 does not have inverse"); return pow(static_cast<uint64>(MODULO - static_cast<value_type>(2))); }constexpr modint operator~() const noexcept { return inverse(); }constexpr modint operator-() const noexcept { if (a == static_cast<value_type>(0)) { return modint(optimize_tag, static_cast<value_type>(0)); } else { return modint(optimize_tag, MODULO - a); } }modint &operator++() noexcept { if (++a == MODULO) { a = static_cast<value_type>(0); }return *this; }modint &operator--() noexcept { if (a == static_cast<value_type>(0)) { a = MODULO; }--a; return *this; }constexpr bool operator==(const modint &o) const noexcept { return a == o.a; }constexpr bool operator!=(const modint &o) const noexcept { return a != o.a; }constexpr bool operator<(const modint &o) const noexcept { return a < o.a; }constexpr bool operator<=(const modint &o) const noexcept { return a <= o.a; }constexpr bool operator>(const modint &o) const noexcept { return a > o.a; }constexpr bool operator>=(const modint &o) const noexcept { return a >= o.a; }constexpr explicit operator bool() const noexcept { return a; }constexpr explicit operator value_type() const noexcept { return a; }modint pow(iint64 inx) const noexcept { if (inx < 0)assert(a != static_cast<value_type>(0) && "not pow index < 0"); uint64 x = inx; uint64 t = a, u = 1; while (x) { if (x & 1)u = u * t % MODULO; t = (t * t) % MODULO; x >>= 1; }return modint(optimize_tag, static_cast<value_type>(u)); }
constexpr value_type get() const noexcept { return a; }
};


using mint = modint<MOD>;
const mint mintzero = mint(0); const mint mintone = mint(1);
mint modinv(mint a) { return mintone / mint(a); }

vector<mint> fact, inv_fact;

void init_fact(int n) {
	fact.resize(n);
	fact[0] = mintone;
	for (int i = 1; i < n; i++) {
		fact[i] = fact[i - 1] * mint(i);
	}
	inv_fact.resize(n);
	inv_fact[n - 1] = modinv(fact[n - 1]);
	for (int i = n - 2; i >= 0; i--) {
		inv_fact[i] = mint(i + 1) * inv_fact[i + 1];
	}
}
mint nCr(int n, int r) {
	if (n < r || n < 0 || r < 0) return mintzero;
	return fact[n] * inv_fact[r] * inv_fact[n - r];
}

mint nPr(int n, int r) {
	if (n < r || n < 0 || r < 0) return mintzero;
	return fact[n] * inv_fact[n - r];
}

mint nHr(int n, int r) {
	if (n < 0 || r < 0) return mintzero;
	if (n == 0 && r == 0) return mintone;
	return nCr(n + r - 1, r);
}


void test(LL H, LL W) {
	//DD(de((nCr(W + 1, 3).get())));
	FOR(K, 2, H*W + 1) {
		LL ans = 0;
		FOR(p, 0, 1 << (H*W)) {
			if (__builtin_popcount(p) != K)continue;
			// K個おく
			vector<PLL>pos;
			FOR(i, 0, H*W) {
				if (p & 1LL << i) {
					pos.push_back(PLL(i / W, i%W));
				}
			}
			// 計算
			FOR(a, 0, K) {
				FOR(b, a + 1, K) {
					LL ret = abs(pos[a].first - pos[b].first);
					ret += abs(pos[a].second - pos[b].second);
					ans += ret;
				}
			}
		}
		DD(de(K, ans));
		mint h = H, w = W;

		mint base = h * w*(h + w)*(h*w - 1) / mint(6);
		mint ks = nCr(H*W - 2, K - 2);
		mint ans2 = base * ks;
		DD(de(K, ans, ans2.get()));
		//DD(de(K, ans, nCr(W + 1, 3).get()*nCr(W - 2, K - 2).get()));
		//DD(de(nCr(H * W - 2, K - 2).get()));
	}
}

int main() {
	init_fact(2e6 + 5);
	//FOR(W, 1, 11) {
	//	DD(de(W));
	//	test(1, W);
	//}
	//return 0;
	////FOR(W, 1, 11) {
	////	DD(de(W));
	////	test(2, W);
	////}
	////FOR(W, 1, 11) {
	////	DD(de(W*(W + 1)*(W + 2) / 6));
	////	DD(de(W));
	////	test(3, W);
	////}
	//FOR(W, 1, 11) {
	//	int k = 2, n = W;
	//	DD(de(k*n*(n + k)*(k*n - 1) / 6));
	//	DD(de(W));
	//	test(2, W);
	//}
	//DD(return 0;);
	cin.tie(0);
	ios_base::sync_with_stdio(false);

	LL H, W, K; cin >> H >> W >> K;
	mint h = H, w = W;
	mint base = 0;
	FOR(i, 1, H) {
		base += mint(i)*mint(H - i)*mint(W)*mint(W);
	}
	FOR(i, 1, W) {
		base += mint(i)*mint(W - i)*mint(H)*mint(H);
	}
	//mint base = h * w*(h + w)*(h*w - 1) / mint(6);
	mint ks = nCr(H*W - 2, K - 2);
	mint ans2 = base * ks;


	LL ans = ans2.get();


	cout << (ans) << "\n";

	return 0;
}


Measured memory_bytes: 15872