#ifdef stderr_path #define LOCAL #endif #ifdef LOCAL #define _GLIBCXX_DEBUG #else #pragma GCC optimize("Ofast") #endif #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // #define NDEBUG #define debug_stream std::cerr #define iostream_untie true #define __precision__ 10 #define all(v) std::begin(v), std::end(v) #define rall(v) std::rbegin(v), std::rend(v) #define __odd(n) ((n)&1) #define __even(n) (not __odd(n)) #define __popcount(n) __builtin_popcountll(n) #define __clz32(n) __builtin_clz(n) #define __clz64(n) __builtin_clzll(n) #define __ctz32(n) __builtin_ctz(n) #define __ctz64(n) __builtin_ctzll(n) using i64 = int_fast64_t; using pii = std::pair; using pll = std::pair; template using heap = std::priority_queue; template using minheap = std::priority_queue, std::greater>; template constexpr T inf = std::numeric_limits::max() / T(2) - T(1123456); namespace execution { std::chrono::system_clock::time_point start_time, end_time; void print_elapsed_time() { end_time = std::chrono::system_clock::now(); std::cerr << "\n----- Exec time : "; std::cerr << std::chrono::duration_cast( end_time - start_time) .count(); std::cerr << " ms -----\n\n"; } struct setupper { setupper() { if(iostream_untie) { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); } std::cout << std::fixed << std::setprecision(__precision__); #ifdef stderr_path if(freopen(stderr_path, "a", stderr)) { std::cerr << std::fixed << std::setprecision(__precision__); } #endif #ifdef stdout_path if(not freopen(stdout_path, "w", stdout)) { freopen("CON", "w", stdout); std::cerr << "Failed to open the stdout file\n\n"; } std::cout << ""; #endif #ifdef stdin_path if(not freopen(stdin_path, "r", stdin)) { freopen("CON", "r", stdin); std::cerr << "Failed to open the stdin file\n\n"; } #endif #ifdef LOCAL std::cerr << "----- stderr at LOCAL -----\n\n"; atexit(print_elapsed_time); start_time = std::chrono::system_clock::now(); #else fclose(stderr); #endif } } __setupper; } // namespace execution class myclock_t { std::chrono::system_clock::time_point built_pt, last_pt; int built_ln, last_ln; std::string built_func, last_func; bool is_built; public: explicit myclock_t() : is_built(false) { } void build(int crt_ln, const std::string &crt_func) { is_built = true; last_pt = built_pt = std::chrono::system_clock::now(); last_ln = built_ln = crt_ln, last_func = built_func = crt_func; } void set(int crt_ln, const std::string &crt_func) { if(is_built) { last_pt = std::chrono::system_clock::now(); last_ln = crt_ln, last_func = crt_func; } else { debug_stream << "[ " << crt_ln << " : " << crt_func << " ] " << "myclock_t::set failed (yet to be built!)\n"; } } void get(int crt_ln, const std::string &crt_func) { if(is_built) { std::chrono::system_clock::time_point crt_pt( std::chrono::system_clock::now()); int64_t diff = std::chrono::duration_cast(crt_pt - last_pt) .count(); debug_stream << diff << " ms elapsed from" << " [ " << last_ln << " : " << last_func << " ]"; if(last_ln == built_ln) debug_stream << " (when built)"; debug_stream << " to" << " [ " << crt_ln << " : " << crt_func << " ]" << "\n"; last_pt = built_pt, last_ln = built_ln, last_func = built_func; } else { debug_stream << "[ " << crt_ln << " : " << crt_func << " ] " << "myclock_t::get failed (yet to be built!)\n"; } } }; #ifdef LOCAL myclock_t __myclock; #define build_clock() __myclock.build(__LINE__, __func__) #define set_clock() __myclock.set(__LINE__, __func__) #define get_clock() __myclock.get(__LINE__, __func__) #else #define build_clock() ((void)0) #define set_clock() ((void)0) #define get_clock() ((void)0) #endif namespace std { template void rsort(RAitr __first, RAitr __last) { sort(__first, __last, greater<>()); } template size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); } template struct hash> { size_t operator()(pair const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } }; template ::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine( tuple_hash_calc::apply(seed, t), get(t)); } }; template struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } }; template struct hash> { size_t operator()(tuple const &t) const { return tuple_hash_calc>::apply(0, t); } }; template istream &operator>>(std::istream &s, pair &p) { return s >> p.first >> p.second; } template ostream &operator<<(std::ostream &s, const pair p) { return s << p.first << " " << p.second; } template istream &operator>>(istream &s, vector &v) { for(T &e : v) { s >> e; } return s; } template ostream &operator<<(ostream &s, const vector &v) { bool is_front = true; for(const T &e : v) { if(not is_front) { s << ' '; } else { is_front = false; } s << e; } return s; } template struct tupleos { static ostream &apply(ostream &s, const tuple_t &t) { tupleos::apply(s, t); return s << " " << get(t); } }; template struct tupleos { static ostream &apply(ostream &s, const tuple_t &t) { return s << get<0>(t); } }; template ostream &operator<<(ostream &s, const tuple &t) { return tupleos, tuple_size>::value - 1>::apply( s, t); } template <> ostream &operator<<(ostream &s, const tuple<> &t) { return s; } string revstr(string str) { reverse(str.begin(), str.end()); return str; } } // namespace std #ifdef LOCAL #define dump(...) \ debug_stream << "[ " << __LINE__ << " : " << __FUNCTION__ << " ]\n", \ dump_func(#__VA_ARGS__, __VA_ARGS__) template void dump_func(const char *ptr, const T &x) { debug_stream << '\t'; for(char c = *ptr; c != '\0'; c = *++ptr) { if(c != ' ') debug_stream << c; } debug_stream << " : " << x << '\n'; } template void dump_func(const char *ptr, const T &x, rest_t... rest) { debug_stream << '\t'; for(char c = *ptr; c != ','; c = *++ptr) { if(c != ' ') debug_stream << c; } debug_stream << " : " << x << ",\n"; dump_func(++ptr, rest...); } #else #define dump(...) ((void)0) #endif template void read_range(P __first, P __second) { for(P i = __first; i != __second; ++i) std::cin >> *i; } template void write_range(P __first, P __second) { for(P i = __first; i != __second; std::cout << (++i == __second ? '\n' : ' ')) { std::cout << *i; } } // substitute y for x. template void subst(T &x, const T &y) { x = y; } // substitue y for x iff x > y. template bool chmin(T &x, const T &y) { return x > y ? x = y, true : false; } // substitue y for x iff x < y. template bool chmax(T &x, const T &y) { return x < y ? x = y, true : false; } template constexpr T minf(const T &x, const T &y) { return std::min(x, y); } template constexpr T maxf(const T &x, const T &y) { return std::max(x, y); } // binary search. template int_t bin(int_t ok, int_t ng, const F &f) { while(std::abs(ok - ng) > 1) { int_t mid = (ok + ng) / 2; (f(mid) ? ok : ng) = mid; } return ok; } // be careful that val is type-sensitive. template void init(A (&array)[N], const T &val) { std::fill((T *)array, (T *)(array + N), val); } void reset() { } template void reset(A &array, rest_t... rest) { memset(array, 0, sizeof(array)); reset(rest...); } // a integer uniformly and randomly chosen from the interval [l, r). template int_t rand_int(int_t l, int_t r) { static std::random_device seed_gen; static std::mt19937 engine(seed_gen()); std::uniform_int_distribution unid(l, r - 1); return unid(engine); } // a real number uniformly and randomly chosen from the interval [l, r). template real_t rand_real(real_t l, real_t r) { static std::random_device seed_gen; static std::mt19937 engine(seed_gen()); std::uniform_real_distribution unid(l, r); return unid(engine); } /* The main code follows. */ namespace math { template struct modint { int rep; constexpr modint() : rep(0) {} constexpr modint(int_fast64_t y) : rep(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} constexpr modint &operator+=(const modint &p) { return (rep += p.rep) < mod ? 0 : rep -= mod, *this; } constexpr modint &operator++() { return ++rep, *this; } constexpr modint operator++(int) { modint t = *this; return ++rep, t; } constexpr modint &operator-=(const modint &p) { return (rep += mod - p.rep) < mod ? 0 : rep -= mod, *this; } constexpr modint &operator--() { return --rep, *this; } constexpr modint operator--(int) { modint t = *this; return --rep, t; } constexpr modint &operator*=(const modint &p) { return rep = (int_fast64_t)rep * p.rep % mod, *this; } constexpr modint &operator/=(const modint &p) { return *this *= inverse(p); } // constexpr modint &operator%=(int m) { return rep %= m, *this; } constexpr modint operator-() const { return modint(-rep); } constexpr modint operator+(const modint &p) const { return modint(*this) += p; } constexpr modint operator-(const modint &p) const { return modint(*this) -= p; } constexpr modint operator*(const modint &p) const { return modint(*this) *= p; } constexpr modint operator/(const modint &p) const { return modint(*this) /= p; } // constexpr modint operator%(int m) const { return modint(*this) %= m; // } constexpr bool operator==(const modint &p) const { return rep == p.rep; } constexpr bool operator!=(const modint &p) const { return rep != p.rep; } constexpr bool operator!() const { return !rep; } // constexpr bool operator>(const modint &p) const { return rep > p.rep; } // constexpr bool operator<(const modint &p) const { return rep < p.rep; } // constexpr bool operator>=(const modint &p) const { return rep >= p.rep; } // constexpr bool operator<=(const modint &p) const { return rep <= p.rep; } constexpr friend modint inverse(const modint &p) { int a = p.rep, b = mod, u = 1, v = 0; while(b > 0) { int t = a / b; a -= t * b; a ^= b ^= a ^= b; u -= t * v; u ^= v ^= u ^= v; } return modint(u); } constexpr friend modint pow(modint p, int_fast64_t e) { if(e < 0) e = (e % (mod - 1) + mod - 1) % (mod - 1); modint ret = 1; while(e) { if(e & 1) ret *= p; p *= p; e >>= 1; } return ret; } friend std::ostream &operator<<(std::ostream &s, const modint &p) { return s << p.rep; } friend std::istream &operator>>(std::istream &s, modint &p) { int_fast64_t rep; p = modint((s >> rep, rep)); return s; } }; } // namespace math // require modint namespace math { constexpr int mod = 1000000007; constexpr size_t N = 2.5e5, ext_N = 2.2e6; class fact_impl { int _fact[N], _invfact[N], _inv[N]; static int _ext_fact[], _ext_invfact[], _ext_inv[]; static size_t fact_itr, invfact_itr, inv_itr; public: constexpr fact_impl() : _fact(), _invfact(), _inv() { _fact[0] = 1; for(size_t i = 1; i < N; ++i) _fact[i] = (int_fast64_t)_fact[i - 1] * i % mod; _inv[1] = 1; for(size_t i = 2; i < N && i < mod; ++i) _inv[i] = mod - (int_fast64_t)_inv[mod % i] * (mod / i) % mod; _invfact[0] = 1; for(size_t i = 1; i < N && i < mod; ++i) _invfact[i] = (int_fast64_t)_invfact[i - 1] * _inv[i] % mod; } int ext_fact(int x) const { assert(x < (int)ext_N); if(x < 0) return 0; if(not fact_itr) { _ext_fact[N - 1] = _fact[N - 1]; fact_itr = N; } for(size_t &i = fact_itr; (int)i <= x; ++i) { _ext_fact[i] = (int_fast64_t)_ext_fact[i - 1] * i % mod; } return x < (int)N ? _fact[x] : _ext_fact[x]; } int ext_inv(int x) const { assert(x < (int)ext_N and x % mod); for(size_t &i = inv_itr, r; (int)i <= x; ++i) { r = mod % i, _ext_inv[i] = mod - (r < N ? _inv[r] : _ext_inv[r]) * int_fast64_t(mod / i) % mod; } return x < (int)N ? _inv[x] : _ext_inv[x]; } int ext_invfact(int x) const { assert(x < (int)ext_N and x < mod); if(not invfact_itr) { _ext_invfact[N - 1] = _invfact[N - 1]; invfact_itr = N; } for(size_t &i = inv_itr, r; (int)i <= x; ++i) { r = mod % i, _ext_inv[i] = mod - (r < N ? _inv[r] : _ext_inv[r]) * int_fast64_t(mod / i) % mod; } for(size_t &i = invfact_itr; (int)i <= x; ++i) { _ext_invfact[i] = i < N ? _invfact[i] : _ext_invfact[i - 1] * _ext_inv[i] % mod; } return x < (int)N ? _invfact[x] : _ext_invfact[x]; } }; constexpr fact_impl _fact_impl; int fact_impl::_ext_fact[ext_N], fact_impl::_ext_inv[ext_N], fact_impl::_ext_invfact[ext_N]; size_t fact_impl::fact_itr, fact_impl::inv_itr = N, fact_impl::invfact_itr; template <> struct modint { int rep; constexpr modint() : rep(0) {} constexpr modint(int_fast64_t y) : rep(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} constexpr modint &operator+=(const modint &p) { return (rep += p.rep) < mod ? 0 : rep -= mod, *this; } constexpr modint &operator++() { return ++rep, *this; } constexpr modint operator++(int) { modint t = *this; return ++rep, t; } constexpr modint &operator-=(const modint &p) { return (rep += mod - p.rep) < mod ? 0 : rep -= mod, *this; } constexpr modint &operator--() { return --rep, *this; } constexpr modint operator--(int) { modint t = *this; return --rep, t; } constexpr modint &operator*=(const modint &p) { return rep = (int_fast64_t)rep * p.rep % mod, *this; } modint &operator/=(const modint &p) { return *this *= inverse(p); } // constexpr modint &operator%=(int m) { return rep %= m, *this; } constexpr modint operator-() const { return modint(-rep); } constexpr modint operator+(const modint &p) const { return modint(*this) += p; } constexpr modint operator-(const modint &p) const { return modint(*this) -= p; } constexpr modint operator*(const modint &p) const { return modint(*this) *= p; } modint operator/(const modint &p) const { return modint(*this) /= p; } // constexpr modint operator%(int m) const // { // return modint(*this) %= m; // } constexpr bool operator==(const modint &p) const { return rep == p.rep; } constexpr bool operator!=(const modint &p) const { return rep != p.rep; } constexpr bool operator!() const { return !rep; } // constexpr bool operator>(const modint &p) const { return rep > p.rep; } // constexpr bool operator<(const modint &p) const { return rep < p.rep; } // constexpr bool operator>=(const modint &p) const { return rep >= p.rep; } // constexpr bool operator<=(const modint &p) const { return rep <= p.rep; } friend modint inverse(const modint &p) { if(p.rep <= (int)ext_N) return _fact_impl.ext_inv(p.rep); int a = p.rep, b = mod, u = 1, v = 0; while(b > 0) { int t = a / b; a -= t * b; a ^= b ^= a ^= b; u -= t * v; u ^= v ^= u ^= v; } return modint(u); } constexpr friend modint pow(modint p, int_fast64_t e) { if(e < 0) e = (e % (mod - 1) + mod - 1) % (mod - 1); modint ret = 1; while(e) { if(e & 1) ret *= p; p *= p; e >>= 1; } return ret; } friend std::ostream &operator<<(std::ostream &s, const modint &p) { return s << p.rep; } friend std::istream &operator>>(std::istream &s, modint &p) { int_fast64_t rep; p = modint((s >> rep, rep)); return s; } }; modint fact(int x) { return modint(_fact_impl.ext_fact(x)); } modint invfact(int x) { return modint(_fact_impl.ext_invfact(x)); } modint binom(int x, int y) { if(y < 0 or x < y) return 0; return fact(x) * invfact(y) * invfact(x - y); } modint perm(int x, int y) { return binom(x, y) * fact(y); } } // namespace math using namespace std; using namespace math; signed main() { void __solve(); void __precalc(); unsigned int t = 1; // cin >> t; // __precalc(); #ifdef LOCAL t = 3; #endif while(t--) { __solve(); } } using mint=modint; void __solve() { int a, b, c; cin >> a >> b >> c; const int n=a+b+c; mint ans=0; mint po=pow(mint(2),c); for(int i = c; i <= n-2; ++i,po*=2) { ans+=(po-1)*binom(i-1,c-1)*binom(i-c,b-1); } std::cout << ans << "\n"; }