// Original C++ solution (slower):
#include <bits/stdc++.h>

using namespace std;

typedef long long   signed int LL;

typedef long long unsigned int LU;

#define incID(i, l, r) for(LL i = (l)    ; i <  (r); ++i)

#define incII(i, l, r) for(LL i = (l)    ; i <= (r); ++i)

#define decID(i, l, r) for(LL i = (r) - 1; i >= (l); --i)

#define decII(i, l, r) for(LL i = (r)    ; i >= (l); --i)

#define inc(i, n)  incID(i, 0, n)

#define inc1(i, n) incII(i, 1, n)

#define dec(i, n)  decID(i, 0, n)

#define dec1(i, n) decII(i, 1, n)

#define inID(v, l, r) ((l) <= (v) && (v) <  (r))

#define inII(v, l, r) ((l) <= (v) && (v) <= (r))

#define PB push_back

#define EB emplace_back

#define MP make_pair

#define FI first

#define SE second

#define  ALL(v)  v.begin(),  v.end()

#define RALL(v) v.rbegin(), v.rend()

template<typename T> bool setmin  (T & a, T b) { if(b <  a) { a = b; return true; } else { return false; } }

template<typename T> bool setmax  (T & a, T b) { if(b >  a) { a = b; return true; } else { return false; } }

template<typename T> bool setmineq(T & a, T b) { if(b <= a) { a = b; return true; } else { return false; } }

template<typename T> bool setmaxeq(T & a, T b) { if(b >= a) { a = b; return true; } else { return false; } }

LL mo(LL a, LL b) { assert(b > 0); a %= b; if(a < 0) { a += b; } return a; }

LL fl(LL a, LL b) { assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }

LL ce(LL a, LL b) { assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }

template<typename T> T gcd(T a, T b) { return (b == 0 ? a : gcd(b, a % b)); }

template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

#define bit(b, i) (((b) >> (i)) & 1)

#define BC __builtin_popcountll

#define SC static_cast

#define SI(v) SC<int>(v.size())

#define SL(v) SC<LL >(v.size())

#define RF(e, v) for(auto & e: v)

#define ef else if

#define UR assert(false)



// ---- ----



template<LL M> class ModInt {

private:

	LL v = 0;

public:

	ModInt() { }

	ModInt(LL vv) { setval(vv); }

	ModInt & setval(LL vv) { v = vv % M; if(v < 0) { v += M; } return (*this); }

	LL getval() const { return v; }

	ModInt & operator+=(const ModInt & b)       { return setval(v + b.v); }

	ModInt & operator-=(const ModInt & b)       { return setval(v - b.v); }

	ModInt & operator*=(const ModInt & b)       { return setval(v * b.v); }

	ModInt & operator/=(const ModInt & b)       { return setval(v * b.inv()); }

	ModInt & operator^=(            LU b)       { return setval(ex(v, b)); }

	ModInt   operator+ (                ) const { return ModInt(+v); }

	ModInt   operator- (                ) const { return ModInt(-v); }

	ModInt   operator+ (const ModInt & b) const { return ModInt(v + b.v); }

	ModInt   operator- (const ModInt & b) const { return ModInt(v - b.v); }

	ModInt   operator* (const ModInt & b) const { return ModInt(v * b.v); }

	ModInt   operator/ (const ModInt & b) const { return ModInt(v * b.inv()); }

	ModInt   operator^ (            LU b) const { return ModInt(ex(v, b)); }

	LL inv() const {

		LL x = (ex_gcd(v, M).FI + M) % M;

		assert(v * x % M == 1);

		return x;

	}

	LL ex(LL a, LU b) const {

		LL D = 64, x[64], y = 1;

		inc(i, D) { if((b >> i) == 0) { D = i; break; } }

		inc(i, D) { x[i] = (i == 0 ? a : x[i - 1] * x[i - 1]) % M; }

		inc(i, D) { if((b >> i) & 1) { (y *= x[i]) %= M; } }

		return y;

	}

	pair<LL, LL> ex_gcd(LL a, LL b) const {

		if(b == 0) { return MP(1, 0); }

		auto p = ex_gcd(b, a % b);

		return MP(p.SE, p.FI - (a / b) * p.SE);

	}

};

template<LL M> ModInt<M> operator+(LL a, const ModInt<M> & b) { return  b + a; }

template<LL M> ModInt<M> operator-(LL a, const ModInt<M> & b) { return -b + a; }

template<LL M> ModInt<M> operator*(LL a, const ModInt<M> & b) { return  b * a; }

template<LL M> ModInt<M> operator/(LL a, const ModInt<M> & b) { return  a * b.inv(); }

template<LL M> istream & operator>>(istream & is, ModInt<M> & b) { LL v; is >> v; b.setval(v); return is; }

template<LL M> ostream & operator<<(ostream & os, const ModInt<M> & b) { return (os << b.getval()); }



// ---- ----



typedef ModInt<1'000'000'007> MI;



LL n, m, k;



MI s1(MI x) { return x * (x + 1) / 2; }

MI s2(MI x) { return x * (x + 1) * (2 * x + 1) / 6; }

MI g(MI i, MI j) { return s2(i + j) - (s2(i) + j * s1(i)) - (s2(j - 1) + (i + 1) * s1(j - 1)); }



MI f(MI i, MI j) {

	MI I = n - 1 - i;

	MI J = m - 1 - j;

	

	MI s = 0;

	s += g(i, j);

	s += g(J, i);

	s += g(I, J);

	s += g(j, I);

	return s;

}



MI comb(LL x, LL y) {

	MI c = 1;

	inc(i, y) {

		c *= x - i;

		c /= i + 1;

	}

	return c;

}



int main() {

	cin >> n >> m >> k;

	

	MI a2 = 0;

	inc(i, n) {

	inc(j, m) {

		a2 += f(i, j);

	}

	}

	

	MI ans = a2 * comb(k, 2) * comb(n * m - 2, k - 2) / k / (k - 1);

	

	cout << ans << endl;

	

	return 0;

}


// Optimized solution to the same problem (faster):
#include <bits/stdc++.h>

using namespace std;

typedef long long   signed int LL;

typedef long long unsigned int LU;

#define incID(i, l, r) for(LL i = (l)    ; i <  (r); ++i)

#define incII(i, l, r) for(LL i = (l)    ; i <= (r); ++i)

#define decID(i, l, r) for(LL i = (r) - 1; i >= (l); --i)

#define decII(i, l, r) for(LL i = (r)    ; i >= (l); --i)

#define inc(i, n)  incID(i, 0, n)

#define inc1(i, n) incII(i, 1, n)

#define dec(i, n)  decID(i, 0, n)

#define dec1(i, n) decII(i, 1, n)

#define inID(v, l, r) ((l) <= (v) && (v) <  (r))

#define inII(v, l, r) ((l) <= (v) && (v) <= (r))

#define PB push_back

#define EB emplace_back

#define MP make_pair

#define FI first

#define SE second

#define  ALL(v)  v.begin(),  v.end()

#define RALL(v) v.rbegin(), v.rend()

template<typename T> bool setmin  (T & a, T b) { if(b <  a) { a = b; return true; } else { return false; } }

template<typename T> bool setmax  (T & a, T b) { if(b >  a) { a = b; return true; } else { return false; } }

template<typename T> bool setmineq(T & a, T b) { if(b <= a) { a = b; return true; } else { return false; } }

template<typename T> bool setmaxeq(T & a, T b) { if(b >= a) { a = b; return true; } else { return false; } }

LL mo(LL a, LL b) { assert(b > 0); a %= b; if(a < 0) { a += b; } return a; }

LL fl(LL a, LL b) { assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }

LL ce(LL a, LL b) { assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }

template<typename T> T gcd(T a, T b) { return (b == 0 ? a : gcd(b, a % b)); }

template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

#define bit(b, i) (((b) >> (i)) & 1)

#define BC __builtin_popcountll

#define SC static_cast

#define SI(v) SC<int>(v.size())

#define SL(v) SC<LL >(v.size())

#define RF(e, v) for(auto & e: v)

#define ef else if

#define UR assert(false)



// ---- ----



template<LL M> class ModInt {

private:

	LL v = 0;

public:

	ModInt() { }

	ModInt(LL vv) { setval(vv); }

	ModInt & setval(LL vv) { v = vv % M; if(v < 0) { v += M; } return (*this); }

	LL getval() const { return v; }

	ModInt & operator+=(const ModInt & b)       { return setval(v + b.v); }

	ModInt & operator-=(const ModInt & b)       { return setval(v - b.v); }

	ModInt & operator*=(const ModInt & b)       { return setval(v * b.v); }

	ModInt & operator/=(const ModInt & b)       { return setval(v * b.inv()); }

	ModInt & operator^=(            LU b)       { return setval(ex(v, b)); }

	ModInt   operator+ (                ) const { return ModInt(+v); }

	ModInt   operator- (                ) const { return ModInt(-v); }

	ModInt   operator+ (const ModInt & b) const { return ModInt(v + b.v); }

	ModInt   operator- (const ModInt & b) const { return ModInt(v - b.v); }

	ModInt   operator* (const ModInt & b) const { return ModInt(v * b.v); }

	ModInt   operator/ (const ModInt & b) const { return ModInt(v * b.inv()); }

	ModInt   operator^ (            LU b) const { return ModInt(ex(v, b)); }

	LL inv() const {

		LL x = (ex_gcd(v, M).FI + M) % M;

		assert(v * x % M == 1);

		return x;

	}

	LL ex(LL a, LU b) const {

		LL D = 64, x[64], y = 1;

		inc(i, D) { if((b >> i) == 0) { D = i; break; } }

		inc(i, D) { x[i] = (i == 0 ? a : x[i - 1] * x[i - 1]) % M; }

		inc(i, D) { if((b >> i) & 1) { (y *= x[i]) %= M; } }

		return y;

	}

	pair<LL, LL> ex_gcd(LL a, LL b) const {

		if(b == 0) { return MP(1, 0); }

		auto p = ex_gcd(b, a % b);

		return MP(p.SE, p.FI - (a / b) * p.SE);

	}

};

template<LL M> ModInt<M> operator+(LL a, const ModInt<M> & b) { return  b + a; }

template<LL M> ModInt<M> operator-(LL a, const ModInt<M> & b) { return -b + a; }

template<LL M> ModInt<M> operator*(LL a, const ModInt<M> & b) { return  b * a; }

template<LL M> ModInt<M> operator/(LL a, const ModInt<M> & b) { return  a * b.inv(); }

template<LL M> istream & operator>>(istream & is, ModInt<M> & b) { LL v; is >> v; b.setval(v); return is; }

template<LL M> ostream & operator<<(ostream & os, const ModInt<M> & b) { return (os << b.getval()); }



// ---- ----



typedef ModInt<1'000'000'007> MI;



MI comb(LL x, LL y) {

	MI p = 1;

	inc(i, y) {

		p *= x - i;

		p /= i + 1;

	}

	return p;

}



int main() {

	LL n, m, k;

	cin >> n >> m >> k;

	

	MI a2 = 0;

	incII(i, 0, n) { a2 += i * 2 * (n - i) * m * m; }

	incII(i, 0, m) { a2 += i * 2 * (m - i) * n * n; }

	a2 /= 2;

	

	MI ans = a2 * comb(n * m - 2, k - 2);

	

	cout << ans << endl;

	

	return 0;

}


// Fastest known solution for this problem: