#405268 (C++14) No.940 ワープ ε=ε=ε=ε=ε=│;p>д＜│

• 問題: No.940 ワープ ε=ε=ε=ε=ε=│;p>д＜│
• ユーザー: hitonanode
• 提出日時: 2019-12-05 21:31:41
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 1,129 ms / 5,000 ms
• コード長: 7,067 bytes
• コンパイル時間: 1,826 ms
• コンパイル使用メモリ: 174,776 KB
• 実行使用メモリ: 20,352 KB
• 最終ジャッジ日時: 2024-12-23 00:06:58
• 合計ジャッジ時間: 10,982 ms
• ジャッジサーバーID （参考情報）: judge3 / judge4

ファイルパターン	結果
sample	AC * 5
other	AC * 22

ソースコード

#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((lint)(x).size())
#define POW2(n) (1LL << (n))
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool mmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool mmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
///// This part below is only for debug, not used /////
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
///// END /////
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
using namespace __gnu_pbds; // find_by_order(), order_of_key()
template<typename TK> using pbds_set = tree<TK, null_type, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename TK, typename TV> using pbds_map = tree<TK, TV, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
*/


constexpr lint MOD = 1000000007;
template <int mod>
struct ModInt
{
    using lint = long long;
    int val;
    constexpr ModInt() : val(0) {}
    constexpr void _setval(lint v) { v = (v % mod) + mod; val = v >= mod ? v - mod : v; }
    constexpr ModInt(lint v) { _setval(v); }
    constexpr ModInt operator+(const ModInt &x) const { return ModInt((lint)val + x.val); }
    constexpr ModInt operator-(const ModInt &x) const { return ModInt((lint)val - x.val); }
    constexpr ModInt operator*(const ModInt &x) const { return ModInt((lint)val * x.val); }
    constexpr ModInt operator/(const ModInt &x) const { return ModInt((lint)val * x.inv()); }
    constexpr ModInt operator-() const { return ModInt(-val); }
    constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a % mod + x.val); }
    friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a % mod - x.val); }
    friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a % mod * x.val); }
    friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a % mod * x.inv()); }
    constexpr bool operator==(const ModInt &x) { return val == x.val; }
    constexpr bool operator!=(const ModInt &x) { return val != x.val; }
    friend istream &operator>>(istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }
    friend ostream &operator<<(ostream &os, const ModInt &x) { os << x.val;  return os; }

    constexpr lint power(lint n) const {
        lint ans = 1, tmp = this->val;
        while (n) {
            if (n & 1) ans = ans * tmp % mod;
            tmp = tmp * tmp % mod;
            n /= 2;
        }
        return ans;
    }
    constexpr lint inv() const { return this->power(mod - 2); }
    constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }
    constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }

    inline ModInt fac() const {
        static vector<ModInt> facs;
        int l0 = facs.size();
        if (l0 > this->val) return facs[this->val];

        facs.resize(this->val + 1);
        for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));
        return facs[this->val];
    }

    ModInt doublefac() const {
        lint k = (this->val + 1) / 2;
        if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();
        else return ModInt(k).fac() * ModInt(2).power(k);
    }

    ModInt nCr(const ModInt &r) const {
        if (this->val < r.val) return ModInt(0);
        return this->fac() / ((*this - r).fac() * r.fac());
    }
};
using mint = ModInt<MOD>;

int main()
{
    int X, Y, Z;
    cin >> X >> Y >> Z;
    if (X + Y + Z == 0)
    {
        puts("1");
        return 0;
    }
    mint(2e6).fac();

    int N = X + Y + Z;
    vector<mint> f(N + 2);
    f[0] = -1;
    REP(i, N + 2)
    {
        f[i] += mint(2).power(N + 1) * mint(N + 1).nCr(i);
    }
    vector<mint> g(N + 1);
    IREP(i, N + 1)
    {
        g[i] = f[i + 1] / 2;
        f[i] -= g[i];
    }

    mint ret = 0;
    REP(i, N + 1)
    {
        ret += g[i] * mint(i).nCr(X) * mint(i).nCr(Y) * mint(i).nCr(Z) * mint(-1).power(i);
    }
    cout << ret * mint(-1).power(N) / 2 << endl;
}