#include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; typedef long long ll; typedef vector vl; typedef vector vvl; typedef vector vc; typedef vector vs; typedef vector vb; typedef vector vd; typedef pair P; typedef vector

vpl; typedef tuple tapu; #define rep(i,n) for(ll i=0; i<(n); i++) #define REP(i,a,b) for(int i=(a); i<(b); i++) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() const int inf = 1<<30; const ll linf = 1LL<<62; const int MAX = 510000; ll dy[8] = {0,1,0,-1,1,-1,1,-1}; ll dx[8] = {1,0,-1,0,1,-1,-1,1}; const double pi = acos(-1); const double eps = 1e-7; template inline bool chmin(T1 &a,T2 b){ if(a>b){ a = b; return true; } else return false; } template inline bool chmax(T1 &a,T2 b){ if(a inline void print2(T1 a, T2 b){cout << a << " " << b << "\n";} template inline void print3(T1 a, T2 b, T3 c){ cout << a << " " << b << " " << c << "\n"; } const int mod = 1e9 + 7; //const int mod = 998244353; template class modint { using u64 = std::uint_fast64_t; public: u64 a; constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {} constexpr u64 &value() noexcept { return a; } constexpr const u64 &value() const noexcept { return a; } constexpr modint operator+(const modint rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint rhs) const noexcept { return modint(*this) /= rhs; } constexpr modint &operator+=(const modint rhs) noexcept { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr modint &operator-=(const modint rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr modint &operator*=(const modint rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr modint &operator/=(modint rhs) noexcept { u64 exp = Modulus - 2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } }; using mint = modint; vector fac(MAX), finv(MAX), inv(MAX); void comInit(){ fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for(ll i=2; i> n >> m >> k; comInit(); mint ans = 0; for(ll i=0; i<=n+m-k; i+=2){ mint res = com(n,i/2) * fac[n-1] % mod * fac[m]; res *= com(m-1,i/2-1); ans += res; } cout << ans.value() << endl; }