#include using namespace std; #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) begin(v),end(v) template inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; } using ll = long long; using pii = pair; constexpr ll INF = 1ll<<30; constexpr ll longINF = 1ll<<60; constexpr ll MOD = 1000000007; constexpr bool debug = false; //---------------------------------// /** * @brief https://tkmst201.github.io/Library/Mathematics/ModInt.hpp */ template struct ModInt { static_assert(M > 0); using value_type = int; using calc_type = std::int_fast64_t; private: value_type val_; public: constexpr ModInt(calc_type val = 0) : val_(val < 0 ? (val % M + M) % M : val % M) {} constexpr value_type val() const noexcept { return val_; } constexpr static decltype(M) mod() noexcept { return M; } explicit constexpr operator bool() const noexcept { return val_; } constexpr bool operator !() const noexcept { return !static_cast(*this); } constexpr ModInt operator +() const noexcept { return *this; } constexpr ModInt operator -() const noexcept { return ModInt(-val_); } constexpr ModInt operator ++(int) noexcept { ModInt res = *this; ++*this; return res; } constexpr ModInt operator --(int) noexcept { ModInt res = *this; --*this; return res; } constexpr ModInt & operator ++() noexcept { val_ = val_ + 1 == M ? 0 : val_ + 1; return *this; } constexpr ModInt & operator --() noexcept { val_ = val_ == 0 ? M - 1 : val_ - 1; return *this; } constexpr ModInt & operator +=(const ModInt & rhs) noexcept { val_ += val_ < M - rhs.val_ ? rhs.val_ : rhs.val_ - M; return *this; } constexpr ModInt & operator -=(const ModInt & rhs) noexcept { val_ += val_ >= rhs.val_ ? -rhs.val_ : M - rhs.val_; return *this; } constexpr ModInt & operator *=(const ModInt & rhs) noexcept { val_ = static_cast(val_) * rhs.val_ % M; return *this; } constexpr ModInt & operator /=(const ModInt & rhs) noexcept { return *this *= rhs.inv(); } friend constexpr ModInt operator +(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) += rhs; } friend constexpr ModInt operator -(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) -= rhs; } friend constexpr ModInt operator *(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) *= rhs; } friend constexpr ModInt operator /(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) /= rhs; } friend constexpr bool operator ==(const ModInt & lhs, const ModInt & rhs) noexcept { return lhs.val_ == rhs.val_; } friend constexpr bool operator !=(const ModInt & lhs, const ModInt & rhs) noexcept { return !(lhs == rhs); } friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val_; } friend std::istream & operator >>(std::istream & is, ModInt & rhs) { calc_type x; is >> x; rhs = ModInt(x); return is; } constexpr ModInt pow(calc_type n) const noexcept { ModInt res = 1, x = val_; if (n < 0) { x = x.inv(); n = -n; } while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } constexpr ModInt inv() const noexcept { value_type a = val_, a1 = 1, b = M, b1 = 0; while (b > 0) { value_type q = a / b, r = a % b; value_type nb1 = a1 - q * b1; a = b; b = r; a1 = b1; b1 = nb1; } assert(a == 1); return a1; } }; using mint = ModInt; /** * @brief https://tkmst201.github.io/Library/Mathematics/Combination.hpp */ template struct Combination { using size_type = std::size_t; private: std::vector fact_, finv_, inv_; static constexpr size_type MAX_LIMIT = 50000000; public: Combination(size_type sz = 1) : fact_(1, 1), finv_(1, 1), inv_(1, 1) { build(sz); } T fact(size_type k) { if (k >= T::mod()) return 0; build(k); return fact_[k]; } T finv(size_type k) { assert(k < T::mod()); build(k); return finv_[k]; } T inv(size_type k) { assert(k > 0 && k < T::mod()); build(k); return inv_[k]; } T operator ()(int n, int r) { return c(n, r); } T c(int n, int r) { if (r < 0 || n < r) return 0; return fact(n) * finv(r) * finv(n - r); } private: void build(size_type k) { if (fact_.size() > k) return; assert(k < MAX_LIMIT); size_type sz = std::min({MAX_LIMIT, static_cast(T::mod()), std::max(fact_.size() * 2, k + 1)}); size_type presz = fact_.size(); fact_.resize(sz); finv_.resize(sz); inv_.resize(sz); for (size_type i = presz; i < sz; ++i) fact_[i] = fact_[i - 1] * i; finv_[sz - 1] = fact_[sz - 1].inv(); for (size_type i = sz - 1; i > presz; --i) { finv_[i - 1] = finv_[i] * i; inv_[i] = fact_[i - 1] * finv_[i]; } inv_[presz] = fact_[presz - 1] * finv_[presz]; } }; using Comb = Combination; Comb comb; int main() { int N, M, K; cin >> N >> M >> K; mint ans = 0; FOR(i, 1, min(N, M) + 1) { if (N + M - 2 * i < K) break; mint cur = comb(N - 1, i - 1) * comb(M - 1, i - 1) * 2; // ABAB or BABA if (i < N) cur += comb(N - 1, i) * comb(M - 1, i - 1); // ABA if (i < M) cur += comb(M - 1, i) * comb(N - 1, i - 1); // BAB ans += cur; } ans = ans * comb.fact(N) * comb.fact(M) * comb.inv(N + M); cout << ans << endl; }