Problem p04004 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
// created [2020/02/01] 13:20:15
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"

using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
using uint = unsigned int;
using usize = std::size_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template <typename T, usize n> using arr = T (&)[n];
template <typename T, usize n> using c_arr = const T (&)[n];
template <typename T> using max_heap = std::priority_queue<T>;
template <typename T>
using min_heap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T> constexpr T popcount(const T u) {
  return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u)))
           : static_cast<T>(0);
}
template <typename T> constexpr T log2p1(const T u) {
  return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u)))
           : static_cast<T>(0);
}
template <typename T> constexpr T msbp1(const T u) { return log2p1(u); }
template <typename T> constexpr T lsbp1(const T u) {
  return __builtin_ffsll(u);
}
template <typename T> constexpr T clog(const T u) {
  return u ? log2p1(u - 1) : static_cast<T>(u);
}
template <typename T> constexpr bool ispow2(const T u) {
  return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0;
}
template <typename T> constexpr T ceil2(const T u) {
  return static_cast<T>(1) << clog(u);
}
template <typename T> constexpr T floor2(const T u) {
  return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1);
}
template <typename T> constexpr bool btest(const T mask, const usize ind) {
  return static_cast<bool>((static_cast<u64>(mask) >> ind) &
                           static_cast<u64>(1));
}
template <typename T> void bset(T &mask, const usize ind) {
  mask |= (static_cast<T>(1) << ind);
}
template <typename T> void breset(T &mask, const usize ind) {
  mask &= ~(static_cast<T>(1) << ind);
}
template <typename T> void bflip(T &mask, const usize ind) {
  mask ^= (static_cast<T>(1) << ind);
}
template <typename T> void bset(T &mask, const usize ind, const bool b) {
  (b ? bset(mask, ind) : breset(mask, ind));
}
template <typename T> constexpr T bcut(const T mask, const usize ind) {
  return ind == 0 ? static_cast<T>(0)
                  : static_cast<T>((static_cast<u64>(mask) << (64 - ind)) >>
                                   (64 - ind));
}
template <typename T> bool chmin(T &a, const T &b) {
  return (a > b ? a = b, true : false);
}
template <typename T> bool chmax(T &a, const T &b) {
  return (a < b ? a = b, true : false);
}
constexpr unsigned int mod = 1000000007;
template <typename T> constexpr T inf_v = std::numeric_limits<T>::max() / 4;
template <typename Real>
constexpr Real pi_v = Real{3.141592653589793238462643383279502884};
auto mfp = [](auto &&f) {
  return [=](auto &&...args) {
    return f(f, std::forward<decltype(args)>(args)...);
  };
};

template <typename T> T in() {
  T v;
  return std::cin >> v, v;
}
template <typename T, typename Uint, usize n, usize i>
T in_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type) {
  return in<T>();
}
template <typename T, typename Uint, usize n, usize i>
auto in_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type &szs) {
  const usize s = (usize)szs[i];
  std::vector<decltype(in_v<T, Uint, n, i + 1>(szs))> ans(s);
  for (usize j = 0; j < s; j++) {
    ans[j] = in_v<T, Uint, n, i + 1>(szs);
  }
  return ans;
}
template <typename T, typename Uint, usize n> auto in_v(c_arr<Uint, n> szs) {
  return in_v<T, Uint, n, 0>(szs);
}
template <typename... Types> auto in_t() {
  return std::tuple<std::decay_t<Types>...>{in<Types>()...};
}
struct io_init {
  io_init() {
    std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(20);
  }
  void clear() { std::cin.tie(), std::ios::sync_with_stdio(true); }
} io_setting;

int out() { return 0; }
template <typename T> int out(const T &v) { return std::cout << v, 0; }
template <typename T> int out(const std::vector<T> &v) {
  for (usize i = 0; i < v.size(); i++) {
    if (i > 0) {
      std::cout << ' ';
    }
    out(v[i]);
  }
  return 0;
}
template <typename T1, typename T2> int out(const std::pair<T1, T2> &v) {
  return out(v.first), std::cout << ' ', out(v.second), 0;
}
template <typename T, typename... Args>
int out(const T &v, const Args... args) {
  return out(v), std::cout << ' ', out(args...), 0;
}
template <typename... Args> int outln(const Args... args) {
  return out(args...), std::cout << '\n', 0;
}
template <typename... Args> int outel(const Args... args) {
  return out(args...), std::cout << std::endl, 0;
}
#define SHOW(...) static_cast<void>(0)
constexpr ull TEN(const usize n) { return n == 0 ? 1ULL : TEN(n - 1) * 10ULL; }

template <typename T, typename Uint, usize n, usize i>
auto make_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type,
            const T &v = T{}) {
  return v;
}
template <typename T, typename Uint, usize n, usize i>
auto make_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type szs,
            const T &v = T{}) {
  const usize s = (usize)szs[i];
  return std::vector<decltype(make_v<T, Uint, n, i + 1>(szs, v))>(
      s, make_v<T, Uint, n, i + 1>(szs, v));
}
template <typename T, typename Uint, usize n>
auto make_v(c_arr<Uint, n> szs, const T &t = T{}) {
  return make_v<T, Uint, n, 0>(szs, t);
}

template <typename T> T gcd(const T &a, const T &b) {
  return a < 0   ? gcd(-a, b)
         : b < 0 ? gcd(a, -b)
                 : (a > b    ? gcd(b, a)
                    : a == 0 ? b
                             : gcd(b % a, a));
}
template <typename T> T lcm(const T &a, const T &b) {
  return a / gcd(a, b) * b;
}
template <typename T> constexpr std::pair<T, T> extgcd(const T a, const T b) {
  if (b == 0) {
    return std::pair<T, T>{1, 0};
  }
  const auto g = gcd(a, b), da = std::abs(b) / g;
  const auto p = extgcd(b, a % b);
  const auto x = (da + p.second % da) % da, y = (g - a * x) / b;
  return {x, y};
}
template <typename T> constexpr T inverse(const T a, const T mod) {
  return extgcd(a, mod).first;
}
template <uint mod_value, bool dynamic = false> class modint_base {
public:
  template <typename UInt = uint>
  static std::enable_if_t<dynamic, const UInt> mod() {
    return mod_ref();
  }
  template <typename UInt = uint>
  static constexpr std::enable_if_t<not dynamic, const UInt> mod() {
    return mod_value;
  }
  template <typename UInt = uint>
  static void set_mod(const std::enable_if_t<dynamic, const UInt> mod) {
    mod_ref() = mod, inv_ref() = {1, 1};
  }
  modint_base() : v{0} {}
  modint_base(const ll val)
      : v{norm(static_cast<uint>(val % static_cast<ll>(mod()) +
                                 static_cast<ll>(mod())))} {}
  modint_base(const modint_base &n) : v{n()} {}
  explicit operator bool() const { return v != 0; }
  bool operator!() const { return not static_cast<bool>(*this); }
  modint_base &operator=(const modint_base &m) { return v = m(), (*this); }
  modint_base &operator=(const ll val) {
    return v = norm(
               uint(val % static_cast<ll>(mod()) + static_cast<ll>(mod()))),
           (*this);
  }
  friend modint_base operator+(const modint_base &m) { return m; }
  friend modint_base operator-(const modint_base &m) {
    return make(norm(mod() - m.v));
  }
  friend modint_base operator+(const modint_base &m1, const modint_base &m2) {
    return make(norm(m1.v + m2.v));
  }
  friend modint_base operator-(const modint_base &m1, const modint_base &m2) {
    return make(norm(m1.v + mod() - m2.v));
  }
  friend modint_base operator*(const modint_base &m1, const modint_base &m2) {
    return make(
        static_cast<uint>(static_cast<ll>(m1.v) * static_cast<ll>(m2.v) %
                          static_cast<ll>(mod())));
  }
  friend modint_base operator/(const modint_base &m1, const modint_base &m2) {
    return m1 * inv(m2.v);
  }
  friend modint_base operator+(const modint_base &m, const ll val) {
    return modint_base{static_cast<ll>(m.v) + val};
  }
  friend modint_base operator-(const modint_base &m, const ll val) {
    return modint_base{static_cast<ll>(m.v) - val};
  }
  friend modint_base operator*(const modint_base &m, const ll val) {
    return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))};
  }
  friend modint_base operator/(const modint_base &m, const ll val) {
    return modint_base{static_cast<ll>(m.v) * inv(val)};
  }
  friend modint_base operator+(const ll val, const modint_base &m) {
    return modint_base{static_cast<ll>(m.v) + val};
  }
  friend modint_base operator-(const ll val, const modint_base &m) {
    return modint_base{-static_cast<ll>(m.v) + val};
  }
  friend modint_base operator*(const ll val, const modint_base &m) {
    return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))};
  }
  friend modint_base operator/(const ll val, const modint_base &m) {
    return modint_base{val * inv(static_cast<ll>(m.v))};
  }
  friend modint_base &operator+=(modint_base &m1, const modint_base &m2) {
    return m1 = m1 + m2;
  }
  friend modint_base &operator-=(modint_base &m1, const modint_base &m2) {
    return m1 = m1 - m2;
  }
  friend modint_base &operator*=(modint_base &m1, const modint_base &m2) {
    return m1 = m1 * m2;
  }
  friend modint_base &operator/=(modint_base &m1, const modint_base &m2) {
    return m1 = m1 / m2;
  }
  friend modint_base &operator+=(modint_base &m, const ll val) {
    return m = m + val;
  }
  friend modint_base &operator-=(modint_base &m, const ll val) {
    return m = m - val;
  }
  friend modint_base &operator*=(modint_base &m, const ll val) {
    return m = m * val;
  }
  friend modint_base &operator/=(modint_base &m, const ll val) {
    return m = m / val;
  }
  friend modint_base operator^(const modint_base &m, const ll n) {
    return power(m.v, n);
  }
  friend modint_base &operator^=(modint_base &m, const ll n) {
    return m = m ^ n;
  }
  friend bool operator==(const modint_base &m1, const modint_base &m2) {
    return m1.v == m2.v;
  }
  friend bool operator!=(const modint_base &m1, const modint_base &m2) {
    return not(m1 == m2);
  }
  friend bool operator==(const modint_base &m, const ll val) {
    return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) +
                                         val % static_cast<ll>(mod())));
  }
  friend bool operator!=(const modint_base &m, const ll val) {
    return not(m == val);
  }
  friend bool operator==(const ll val, const modint_base &m) {
    return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) +
                                         val % static_cast<ll>(mod())));
  }
  friend bool operator!=(const ll val, const modint_base &m) {
    return not(m == val);
  }
  friend std::istream &operator>>(std::istream &is, modint_base &m) {
    ll v;
    return is >> v, m = v, is;
  }
  friend std::ostream &operator<<(std::ostream &os, const modint_base &m) {
    return os << m();
  }
  uint operator()() const { return v; }
  static modint_base small_inv(const usize n) {
    auto &in = inv_ref();
    if (n < in.size()) {
      return in[n];
    }
    for (usize i = in.size(); i <= n; i++) {
      in.push_back(-in[modint_base::mod() % i] * (modint_base::mod() / i));
    }
    return in.back();
  }
  std::pair<ll, ll> quad() const {
    const auto ans = quad_r(v, mod());
    ll x = std::get<0>(ans), y = std::get<1>(ans);
    if (y < 0) {
      x = -x, y = -y;
    }
    return {x, y};
  }

private:
  static std::tuple<ll, ll, ll>
  quad_r(const ll r, const ll p) // r = x/y (mod p), (x,y,z) s.t. x=yr+pz
  {
    if (std::abs(r) <= 1000) {
      return {r, 1, 0};
    }
    ll nr = p % r, q = p / r;
    if (nr * 2LL >= r) {
      nr -= r, q++;
    }
    if (nr * 2LL <= -r) {
      nr += r, q--;
    }
    const auto sub = quad_r(nr, r);
    const ll x = std::get<0>(sub), z = std::get<1>(sub), y = std::get<2>(sub);
    return {x, y - q * z, z};
  }

  template <typename UInt = uint>
  static std::enable_if_t<dynamic, UInt &> mod_ref() {
    static UInt mod = 0;
    return mod;
  }
  static uint norm(const uint x) { return x < mod() ? x : x - mod(); }
  static modint_base make(const uint x) {
    modint_base m;
    return m.v = x, m;
  }
  static modint_base power(modint_base x, ull n) {
    modint_base ans = 1;
    for (; n; n >>= 1, x *= x) {
      if (n & 1) {
        ans *= x;
      }
    }
    return ans;
  }
  static modint_base inv(const ll v) {
    return v <= 2000000 ? small_inv(static_cast<usize>(v))
                        : modint_base{inverse(v, static_cast<ll>(mod()))};
  }
  static std::vector<modint_base> &inv_ref() {
    static std::vector<modint_base> in{1, 1};
    return in;
  }
  uint v;
};
template <uint mod> using modint = modint_base<mod, false>;
template <uint id> using dynamic_modint = modint_base<id, true>;
template <uint mod_value, bool dynamic = false> class modcomb_base {
public:
  using value_type = modint_base<mod_value, dynamic>;
  modcomb_base() = delete;
  static void set_mod(const uint mod) {
    value_type::set_mod(mod), fact_ref() = {1, 1}, inv_fact_ref() = {1, 1};
  }
  static value_type fact(const usize n) {
    auto &f = fact_ref();
    if (n < f.size()) {
      return f[n];
    }
    for (usize i = f.size(); i <= n; i++) {
      f.push_back(f.back() * i);
    }
    return f.back();
  }
  static value_type inv_fact(const usize n) {
    auto &invf = inv_fact_ref();
    if (n < invf.size()) {
      return invf[n];
    }
    for (usize i = invf.size(); i <= n; i++) {
      invf.push_back(invf.back() * value_type::small_inv(i));
    }
    return invf.back();
  }
  static value_type perm(const usize n, const usize k) {
    return k > n ? value_type{0} : fact(n) * inv_fact(n - k);
  }
  static value_type comb(const usize n, const usize k) {
    return k > n ? value_type{0} : fact(n) * inv_fact(n - k) * inv_fact(k);
  }

private:
  static std::vector<value_type> &fact_ref() {
    static std::vector<value_type> f{1, 1};
    return f;
  }
  static std::vector<value_type> &inv_fact_ref() {
    static std::vector<value_type> invf{1, 1};
    return invf;
  }
};
template <uint mod> using modcomb = modcomb_base<mod, false>;
template <uint id> using dynamic_modcomb = modcomb_base<id, true>;
int main() {
  using mint = modint<mod>;
  using moc = modcomb<mod>;
  const auto N = in<int>(), M = in<int>(), K = in<int>();
  mint ans = 0;
  for (int L = N - 1; L <= (N - 1) + M + K; L++) {
    const int l = L - N + 1;
    mint sub = 0;
    for (int m = 0; m <= M; m++) {
      const int k = l - m;
      if (m <= M and k <= K) {
        sub += moc::comb(L, N - 1) * moc::comb(l, m);
      }
    }
    ans += sub * (mint(3) ^ (N + M + K - L - 1));
  }
  outln(ans);
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
// created [2020/02/01] 13:20:15
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"

using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
using uint = unsigned int;
using usize = std::size_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template <typename T, usize n> using arr = T (&)[n];
template <typename T, usize n> using c_arr = const T (&)[n];
template <typename T> using max_heap = std::priority_queue<T>;
template <typename T>
using min_heap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T> constexpr T popcount(const T u) {
  return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u)))
           : static_cast<T>(0);
}
template <typename T> constexpr T log2p1(const T u) {
  return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u)))
           : static_cast<T>(0);
}
template <typename T> constexpr T msbp1(const T u) { return log2p1(u); }
template <typename T> constexpr T lsbp1(const T u) {
  return __builtin_ffsll(u);
}
template <typename T> constexpr T clog(const T u) {
  return u ? log2p1(u - 1) : static_cast<T>(u);
}
template <typename T> constexpr bool ispow2(const T u) {
  return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0;
}
template <typename T> constexpr T ceil2(const T u) {
  return static_cast<T>(1) << clog(u);
}
template <typename T> constexpr T floor2(const T u) {
  return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1);
}
template <typename T> constexpr bool btest(const T mask, const usize ind) {
  return static_cast<bool>((static_cast<u64>(mask) >> ind) &
                           static_cast<u64>(1));
}
template <typename T> void bset(T &mask, const usize ind) {
  mask |= (static_cast<T>(1) << ind);
}
template <typename T> void breset(T &mask, const usize ind) {
  mask &= ~(static_cast<T>(1) << ind);
}
template <typename T> void bflip(T &mask, const usize ind) {
  mask ^= (static_cast<T>(1) << ind);
}
template <typename T> void bset(T &mask, const usize ind, const bool b) {
  (b ? bset(mask, ind) : breset(mask, ind));
}
template <typename T> constexpr T bcut(const T mask, const usize ind) {
  return ind == 0 ? static_cast<T>(0)
                  : static_cast<T>((static_cast<u64>(mask) << (64 - ind)) >>
                                   (64 - ind));
}
template <typename T> bool chmin(T &a, const T &b) {
  return (a > b ? a = b, true : false);
}
template <typename T> bool chmax(T &a, const T &b) {
  return (a < b ? a = b, true : false);
}
constexpr unsigned int mod = 1000000007;
template <typename T> constexpr T inf_v = std::numeric_limits<T>::max() / 4;
template <typename Real>
constexpr Real pi_v = Real{3.141592653589793238462643383279502884};
auto mfp = [](auto &&f) {
  return [=](auto &&...args) {
    return f(f, std::forward<decltype(args)>(args)...);
  };
};

template <typename T> T in() {
  T v;
  return std::cin >> v, v;
}
template <typename T, typename Uint, usize n, usize i>
T in_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type) {
  return in<T>();
}
template <typename T, typename Uint, usize n, usize i>
auto in_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type &szs) {
  const usize s = (usize)szs[i];
  std::vector<decltype(in_v<T, Uint, n, i + 1>(szs))> ans(s);
  for (usize j = 0; j < s; j++) {
    ans[j] = in_v<T, Uint, n, i + 1>(szs);
  }
  return ans;
}
template <typename T, typename Uint, usize n> auto in_v(c_arr<Uint, n> szs) {
  return in_v<T, Uint, n, 0>(szs);
}
template <typename... Types> auto in_t() {
  return std::tuple<std::decay_t<Types>...>{in<Types>()...};
}
struct io_init {
  io_init() {
    std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(20);
  }
  void clear() { std::cin.tie(), std::ios::sync_with_stdio(true); }
} io_setting;

int out() { return 0; }
template <typename T> int out(const T &v) { return std::cout << v, 0; }
template <typename T> int out(const std::vector<T> &v) {
  for (usize i = 0; i < v.size(); i++) {
    if (i > 0) {
      std::cout << ' ';
    }
    out(v[i]);
  }
  return 0;
}
template <typename T1, typename T2> int out(const std::pair<T1, T2> &v) {
  return out(v.first), std::cout << ' ', out(v.second), 0;
}
template <typename T, typename... Args>
int out(const T &v, const Args... args) {
  return out(v), std::cout << ' ', out(args...), 0;
}
template <typename... Args> int outln(const Args... args) {
  return out(args...), std::cout << '\n', 0;
}
template <typename... Args> int outel(const Args... args) {
  return out(args...), std::cout << std::endl, 0;
}
#define SHOW(...) static_cast<void>(0)
constexpr ull TEN(const usize n) { return n == 0 ? 1ULL : TEN(n - 1) * 10ULL; }

template <typename T, typename Uint, usize n, usize i>
auto make_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type,
            const T &v = T{}) {
  return v;
}
template <typename T, typename Uint, usize n, usize i>
auto make_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type szs,
            const T &v = T{}) {
  const usize s = (usize)szs[i];
  return std::vector<decltype(make_v<T, Uint, n, i + 1>(szs, v))>(
      s, make_v<T, Uint, n, i + 1>(szs, v));
}
template <typename T, typename Uint, usize n>
auto make_v(c_arr<Uint, n> szs, const T &t = T{}) {
  return make_v<T, Uint, n, 0>(szs, t);
}

template <typename T> T gcd(const T &a, const T &b) {
  return a < 0   ? gcd(-a, b)
         : b < 0 ? gcd(a, -b)
                 : (a > b    ? gcd(b, a)
                    : a == 0 ? b
                             : gcd(b % a, a));
}
template <typename T> T lcm(const T &a, const T &b) {
  return a / gcd(a, b) * b;
}
template <typename T> constexpr std::pair<T, T> extgcd(const T a, const T b) {
  if (b == 0) {
    return std::pair<T, T>{1, 0};
  }
  const auto g = gcd(a, b), da = std::abs(b) / g;
  const auto p = extgcd(b, a % b);
  const auto x = (da + p.second % da) % da, y = (g - a * x) / b;
  return {x, y};
}
template <typename T> constexpr T inverse(const T a, const T mod) {
  return extgcd(a, mod).first;
}
template <uint mod_value, bool dynamic = false> class modint_base {
public:
  template <typename UInt = uint>
  static std::enable_if_t<dynamic, const UInt> mod() {
    return mod_ref();
  }
  template <typename UInt = uint>
  static constexpr std::enable_if_t<not dynamic, const UInt> mod() {
    return mod_value;
  }
  template <typename UInt = uint>
  static void set_mod(const std::enable_if_t<dynamic, const UInt> mod) {
    mod_ref() = mod, inv_ref() = {1, 1};
  }
  modint_base() : v{0} {}
  modint_base(const ll val)
      : v{norm(static_cast<uint>(val % static_cast<ll>(mod()) +
                                 static_cast<ll>(mod())))} {}
  modint_base(const modint_base &n) : v{n()} {}
  explicit operator bool() const { return v != 0; }
  bool operator!() const { return not static_cast<bool>(*this); }
  modint_base &operator=(const modint_base &m) { return v = m(), (*this); }
  modint_base &operator=(const ll val) {
    return v = norm(
               uint(val % static_cast<ll>(mod()) + static_cast<ll>(mod()))),
           (*this);
  }
  friend modint_base operator+(const modint_base &m) { return m; }
  friend modint_base operator-(const modint_base &m) {
    return make(norm(mod() - m.v));
  }
  friend modint_base operator+(const modint_base &m1, const modint_base &m2) {
    return make(norm(m1.v + m2.v));
  }
  friend modint_base operator-(const modint_base &m1, const modint_base &m2) {
    return make(norm(m1.v + mod() - m2.v));
  }
  friend modint_base operator*(const modint_base &m1, const modint_base &m2) {
    return make(
        static_cast<uint>(static_cast<ll>(m1.v) * static_cast<ll>(m2.v) %
                          static_cast<ll>(mod())));
  }
  friend modint_base operator/(const modint_base &m1, const modint_base &m2) {
    return m1 * inv(m2.v);
  }
  friend modint_base operator+(const modint_base &m, const ll val) {
    return modint_base{static_cast<ll>(m.v) + val};
  }
  friend modint_base operator-(const modint_base &m, const ll val) {
    return modint_base{static_cast<ll>(m.v) - val};
  }
  friend modint_base operator*(const modint_base &m, const ll val) {
    return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))};
  }
  friend modint_base operator/(const modint_base &m, const ll val) {
    return modint_base{static_cast<ll>(m.v) * inv(val)};
  }
  friend modint_base operator+(const ll val, const modint_base &m) {
    return modint_base{static_cast<ll>(m.v) + val};
  }
  friend modint_base operator-(const ll val, const modint_base &m) {
    return modint_base{-static_cast<ll>(m.v) + val};
  }
  friend modint_base operator*(const ll val, const modint_base &m) {
    return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))};
  }
  friend modint_base operator/(const ll val, const modint_base &m) {
    return modint_base{val * inv(static_cast<ll>(m.v))};
  }
  friend modint_base &operator+=(modint_base &m1, const modint_base &m2) {
    return m1 = m1 + m2;
  }
  friend modint_base &operator-=(modint_base &m1, const modint_base &m2) {
    return m1 = m1 - m2;
  }
  friend modint_base &operator*=(modint_base &m1, const modint_base &m2) {
    return m1 = m1 * m2;
  }
  friend modint_base &operator/=(modint_base &m1, const modint_base &m2) {
    return m1 = m1 / m2;
  }
  friend modint_base &operator+=(modint_base &m, const ll val) {
    return m = m + val;
  }
  friend modint_base &operator-=(modint_base &m, const ll val) {
    return m = m - val;
  }
  friend modint_base &operator*=(modint_base &m, const ll val) {
    return m = m * val;
  }
  friend modint_base &operator/=(modint_base &m, const ll val) {
    return m = m / val;
  }
  friend modint_base operator^(const modint_base &m, const ll n) {
    return power(m.v, n);
  }
  friend modint_base &operator^=(modint_base &m, const ll n) {
    return m = m ^ n;
  }
  friend bool operator==(const modint_base &m1, const modint_base &m2) {
    return m1.v == m2.v;
  }
  friend bool operator!=(const modint_base &m1, const modint_base &m2) {
    return not(m1 == m2);
  }
  friend bool operator==(const modint_base &m, const ll val) {
    return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) +
                                         val % static_cast<ll>(mod())));
  }
  friend bool operator!=(const modint_base &m, const ll val) {
    return not(m == val);
  }
  friend bool operator==(const ll val, const modint_base &m) {
    return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) +
                                         val % static_cast<ll>(mod())));
  }
  friend bool operator!=(const ll val, const modint_base &m) {
    return not(m == val);
  }
  friend std::istream &operator>>(std::istream &is, modint_base &m) {
    ll v;
    return is >> v, m = v, is;
  }
  friend std::ostream &operator<<(std::ostream &os, const modint_base &m) {
    return os << m();
  }
  uint operator()() const { return v; }
  static modint_base small_inv(const usize n) {
    auto &in = inv_ref();
    if (n < in.size()) {
      return in[n];
    }
    for (usize i = in.size(); i <= n; i++) {
      in.push_back(-in[modint_base::mod() % i] * (modint_base::mod() / i));
    }
    return in.back();
  }
  std::pair<ll, ll> quad() const {
    const auto ans = quad_r(v, mod());
    ll x = std::get<0>(ans), y = std::get<1>(ans);
    if (y < 0) {
      x = -x, y = -y;
    }
    return {x, y};
  }

private:
  static std::tuple<ll, ll, ll>
  quad_r(const ll r, const ll p) // r = x/y (mod p), (x,y,z) s.t. x=yr+pz
  {
    if (std::abs(r) <= 1000) {
      return {r, 1, 0};
    }
    ll nr = p % r, q = p / r;
    if (nr * 2LL >= r) {
      nr -= r, q++;
    }
    if (nr * 2LL <= -r) {
      nr += r, q--;
    }
    const auto sub = quad_r(nr, r);
    const ll x = std::get<0>(sub), z = std::get<1>(sub), y = std::get<2>(sub);
    return {x, y - q * z, z};
  }

  template <typename UInt = uint>
  static std::enable_if_t<dynamic, UInt &> mod_ref() {
    static UInt mod = 0;
    return mod;
  }
  static uint norm(const uint x) { return x < mod() ? x : x - mod(); }
  static modint_base make(const uint x) {
    modint_base m;
    return m.v = x, m;
  }
  static modint_base power(modint_base x, ull n) {
    modint_base ans = 1;
    for (; n; n >>= 1, x *= x) {
      if (n & 1) {
        ans *= x;
      }
    }
    return ans;
  }
  static modint_base inv(const ll v) {
    return v <= 2000000 ? small_inv(static_cast<usize>(v))
                        : modint_base{inverse(v, static_cast<ll>(mod()))};
  }
  static std::vector<modint_base> &inv_ref() {
    static std::vector<modint_base> in{1, 1};
    return in;
  }
  uint v;
};
template <uint mod> using modint = modint_base<mod, false>;
template <uint id> using dynamic_modint = modint_base<id, true>;
template <uint mod_value, bool dynamic = false> class modcomb_base {
public:
  using value_type = modint_base<mod_value, dynamic>;
  modcomb_base() = delete;
  static void set_mod(const uint mod) {
    value_type::set_mod(mod), fact_ref() = {1, 1}, inv_fact_ref() = {1, 1};
  }
  static value_type fact(const usize n) {
    auto &f = fact_ref();
    if (n < f.size()) {
      return f[n];
    }
    for (usize i = f.size(); i <= n; i++) {
      f.push_back(f.back() * i);
    }
    return f.back();
  }
  static value_type inv_fact(const usize n) {
    auto &invf = inv_fact_ref();
    if (n < invf.size()) {
      return invf[n];
    }
    for (usize i = invf.size(); i <= n; i++) {
      invf.push_back(invf.back() * value_type::small_inv(i));
    }
    return invf.back();
  }
  static value_type perm(const usize n, const usize k) {
    return k > n ? value_type{0} : fact(n) * inv_fact(n - k);
  }
  static value_type comb(const usize n, const usize k) {
    return k > n ? value_type{0} : fact(n) * inv_fact(n - k) * inv_fact(k);
  }

private:
  static std::vector<value_type> &fact_ref() {
    static std::vector<value_type> f{1, 1};
    return f;
  }
  static std::vector<value_type> &inv_fact_ref() {
    static std::vector<value_type> invf{1, 1};
    return invf;
  }
};
template <uint mod> using modcomb = modcomb_base<mod, false>;
template <uint id> using dynamic_modcomb = modcomb_base<id, true>;
int main() {
  using mint = modint<mod>;
  using moc = modcomb<mod>;
  const auto N = in<int>(), M = in<int>(), K = in<int>();
  mint ans = 0;
  mint cs = 1;
  for (int L = N; L <= N + M + K; L++) {
    const mint coeff = moc::comb(L - 1, N - 1) / (mint(3) ^ L);
    // mint sum         = 0;
    // for (int m = 0; m <= M; m++) {
    //     const int k = L - N - m;
    //     if (k > K) { continue; }
    //     sum += moc::comb(L - N, m);
    // }
    // ans += sum * coeff;
    ans += cs * coeff;
    cs = (cs * 2) - moc::comb(L - N, M) -
         (L - N - K < 0 ? mint(0) : moc::comb(L - N, L - N - K));
  }
  ans *= (mint(3) ^ (N + M + K));
  outln(ans);
  return 0;
}