#878137 (C++14) No.1629 Sorting Integers (SUM of M)

• 問題: No.1629 Sorting Integers (SUM of M)
• ユーザー: rokahikou1
• 提出日時: 2023-06-04 23:55:49
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 7 ms / 2,000 ms
• コード長: 12,905 bytes
• コンパイル時間: 1,948 ms
• コンパイル使用メモリ: 177,084 KB
• 実行使用メモリ: 7,936 KB
• 最終ジャッジ日時: 2024-06-09 04:13:51
• 合計ジャッジ時間: 2,390 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,812 KB
testcase_01	AC	2 ms; 6,940 KB
testcase_02	AC	2 ms; 6,944 KB
testcase_03	AC	2 ms; 6,940 KB
testcase_04	AC	4 ms; 6,948 KB
testcase_05	AC	2 ms; 6,944 KB
testcase_06	AC	2 ms; 6,940 KB
testcase_07	AC	5 ms; 6,944 KB
testcase_08	AC	4 ms; 6,940 KB
testcase_09	AC	4 ms; 6,940 KB
testcase_10	AC	4 ms; 6,940 KB
testcase_11	AC	3 ms; 6,940 KB
testcase_12	AC	3 ms; 6,944 KB
testcase_13	AC	4 ms; 6,944 KB
testcase_14	AC	3 ms; 6,940 KB
testcase_15	AC	4 ms; 6,940 KB
testcase_16	AC	4 ms; 6,944 KB
testcase_17	AC	7 ms; 7,936 KB

ソースコード

#pragma region Macros
#include <bits/stdc++.h>
#define rep(i, n) for(int(i) = 0; (i) < (n); (i)++)
#define rrep(i, n) for(int(i) = (n)-1; (i) >= 0; (i)--)
#define FOR(i, m, n) for(int(i) = (m); (i) < (n); (i)++)
#define ROF(i, m, n) for(int(i) = (n)-1; (i) >= (m); (i)--)
#define ALL(v) (v).begin(), (v).end()
#define LLA(v) (v).rbegin(), (v).rend()
#define SZ(v) (int)(v).size()
#define INT(...)     \
    int __VA_ARGS__; \
    read(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    read(__VA_ARGS__)
#define DOUBLE(...)     \
    double __VA_ARGS__; \
    read(__VA_ARGS__)
#define CHAR(...)     \
    char __VA_ARGS__; \
    read(__VA_ARGS__)
#define STRING(...)     \
    string __VA_ARGS__; \
    read(__VA_ARGS__)
#define VEC(type, name, size) \
    vector<type> name(size);  \
    read(name)
#define VEC2(type, name, height, width)                     \
    vector<vector<type>> name(height, vector<type>(width)); \
    read(name)
#define DVEC(type, name1, name2, size)     \
    vector<type> name1(size), name2(size); \
    read(name1, name2)
#define TVEC(type, name1, name2, name3, size)           \
    vector<type> name1(size), name2(size), name3(size); \
    read(name1, name2, name3)
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int INF = 1 << 30;
const ll LINF = 1LL << 60;
const int MOD = 1e9 + 7;
const char newl = '\n';
const int dx[] = {1, 0, -1, 0};
const int dy[] = {0, 1, 0, -1};
template <class T> inline bool between(T x, T l, T r) {
    return l <= x && x < r;
}
template <class T> inline vector<T> make_vec(size_t a, T val) {
    return vector<T>(a, val);
}
template <class... Ts> inline auto make_vec(size_t a, Ts... ts) {
    return vector<decltype(make_vec(ts...))>(a, make_vec(ts...));
}
void read() {}
template <class T> inline void read(T &a) { cin >> a; }
template <class T, class S> inline void read(pair<T, S> &p) {
    read(p.first), read(p.second);
}
template <class T> inline void read(vector<T> &v) {
    for(auto &&a : v)
        read(a);
}
template <class T, class U> inline void read(vector<T> &a, vector<U> &b) {
    for(int i = 0; i < a.size(); i++) {
        read(a[i]);
        read(b[i]);
    }
}
template <class T, class U, class V>
inline void read(vector<T> &a, vector<U> &b, vector<V> &c) {
    for(int i = 0; i < a.size(); i++) {
        read(a[i]);
        read(b[i]);
        read(c[i]);
    }
}
template <class Head, class... Tail>
inline void read(Head &head, Tail &...tail) {
    read(head), read(tail...);
}
template <class T> void _write(const T &a) { cout << a; }
template <class T, class U> void _write(const std::pair<T, U> &a) { cout << a.first << ' ' << a.second; }
template <class T> void write(const T &a) {
    _write(a);
    cout << newl;
}
template <class T> void write(const vector<T> &a) {
    for(int i = 0; i < a.size(); i++) {
        _write(a[i]);
        cout << (i + 1 == a.size() ? newl : ' ');
    }
}
template <class Head, class... Tail>
void write(const Head &head, const Tail &...tail) {
    _write(head);
    cout << ' ';
    write(tail...);
}
template <class T> void writel(const T &a) { cout << a << '\n'; }
template <class T> void writel(const vector<T> &a) {
    for(int i = 0; i < a.size(); i++) {
        _write(a[i]);
        cout << newl;
    }
}
template <class Head, class... Tail>
void writel(const Head &head, const Tail &...tail) {
    _write(head);
    cout << newl;
    write(tail...);
}
template <class T> void _debug(const T &a) { cerr << a; }
template <class T, class U> void _debug(const std::pair<T, U> &a) { cerr << a.first << ' ' << a.second; }
template <class T> void debug(const T &a) {
    _debug(a);
    cerr << newl;
}
template <class T> void debug(const vector<T> &a) {
    for(int i = 0; i < a.size(); i++) {
        _debug(a[i]);
        cerr << (i + 1 == a.size() ? newl : ' ');
    }
}
template <class Head, class... Tail>
void debug(const Head &head, const Tail &...tail) {
    _debug(head);
    cerr << ' ';
    debug(tail...);
}
template <class T> void debugl(const T &a) { cerr << a << '\n'; }
template <class T> void debugl(const vector<T> &a) {
    for(int i = 0; i < a.size(); i++) {
        _debug(a[i]);
        cerr << newl;
    }
}
template <class Head, class... Tail>
void debugl(const Head &head, const Tail &...tail) {
    _debug(head);
    cerr << newl;
    debug(tail...);
}
template <class T> auto sum(const vector<T> &a) {
    return accumulate(ALL(a), T(0));
}
template <class T> auto min(const vector<T> &a) { return *min_element(ALL(a)); }
template <class T> auto max(const vector<T> &a) { return *max_element(ALL(a)); }
template <class T, class U> void msort(vector<T> &a, vector<U> &b) {
    assert(a.size() == b.size());
    vector<pair<T, U>> ab(a.size());
    for(int i = 0; i < a.size(); i++)
        ab[i] = {a[i], b[i]};
    sort(ALL(ab));
    for(int i = 0; i < a.size(); i++) {
        a[i] = ab[i].first;
        b[i] = ab[i].second;
    }
}
template <class T, class U, class V>
void msort(vector<T> &a, vector<U> &b, vector<V> &c) {
    assert(a.size() == b.size() && b.size() == c.size());
    vector<tuple<T, U, V>> abc(a.size());
    for(int i = 0; i < a.size(); i++)
        abc[i] = {a[i], b[i], c[i]};
    sort(ALL(abc));
    for(int i = 0; i < a.size(); i++) {
        a[i] = get<0>(abc[i]);
        b[i] = get<1>(abc[i]);
        c[i] = get<2>(abc[i]);
    }
}
template <class T, class U> inline bool chmax(T &a, U b) {
    if(a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T, class U> inline bool chmin(T &a, U b) {
    if(a > b) {
        a = b;
        return 1;
    }
    return 0;
}
int digit(ll a) {
    ll ret = 0;
    while(a && ++ret)
        a /= 10;
    return ret;
}
int digit_sum(ll a) {
    ll ret = 0;
    while(a) {
        ret += a % 10;
        a /= 10;
    }
    return ret;
}
ll llpow(ll a, ll n) {
    ll ret = 1;
    rep(i, n) ret *= a;
    return ret;
}
inline int bsf(int v) { return __builtin_ctz(v); } // 最下位の1が下から何番目か
inline int bsf(ll v) { return __builtin_ctzll(v); }
inline int bsr(int v) {
    return 31 - __builtin_clz(v);
} // 最上位の1が下から何番目か
inline int bsr(ll v) { return 63 - __builtin_clzll(v); }
inline int lsb(int v) { return v & -v; }      // 最下位の1だけ残す
inline ll lsb(ll v) { return v & -v; }
inline int msb(int v) { return 1 << bsr(v); } // 最上位の1だけ残す
inline ll msb(ll v) { return 1LL << bsr(v); }
struct IO {
    IO() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout << fixed << setprecision(10);
    }
} io;
#pragma endregion

/* ModInt */
template <uint_fast64_t MOD> class ModInt {
    using u64 = uint_fast64_t;

  public:
    u64 val;

    ModInt(const u64 x = 0) : val((x + MOD) % MOD) {}
    constexpr u64 &value() { return val; }
    static const u64 get_mod() { return MOD; }
    constexpr ModInt operator-() { return val ? MOD - val : 0; }
    constexpr ModInt operator+(const ModInt &rhs) const {
        return ModInt(*this) += rhs;
    }
    constexpr ModInt operator-(const ModInt &rhs) const {
        return ModInt(*this) -= rhs;
    }
    constexpr ModInt operator*(const ModInt &rhs) const {
        return ModInt(*this) *= rhs;
    }
    constexpr ModInt operator/(const ModInt &rhs) const {
        return ModInt(*this) /= rhs;
    }
    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if(val >= MOD) {
            val -= MOD;
        }
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if(val < rhs.val) {
            val += MOD;
        }
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = val * rhs.val % MOD;
        return *this;
    }

    constexpr ModInt &operator/=(const ModInt &rhs) {
        *this *= rhs.inv();
        return *this;
    }

    constexpr bool operator==(const ModInt &rhs) const {
        return this->val == rhs.val;
    }
    constexpr bool operator!=(const ModInt &rhs) const {
        return this->val != rhs.val;
    }
    friend constexpr ostream &operator<<(ostream &os, const ModInt<MOD> &x) {
        return os << x.val;
    }
    friend constexpr istream &operator>>(istream &is, ModInt<MOD> &x) {
        return is >> x.val;
    }

    constexpr ModInt inv() const { return ModInt(*this).pow(MOD - 2); }

    constexpr ModInt pow(long long e) const {
        u64 x = 1, p = val;
        while(e > 0) {
            if(e % 2 == 0) {
                p = (p * p) % MOD;
                e /= 2;
            } else {
                x = (x * p) % MOD;
                e--;
            }
        }
        return ModInt(x);
    }
};

using mint = ModInt<1000000007UL>;
// using mint = ModInt<998244353UL>;

// 二項係数（nCk mod.p;1<=k<=n<=1e7,pは素数）for ModInt
template <class Mint> struct CombinationMint {
    int N;
    vector<Mint> fac, finv, inv;
    CombinationMint(const int n) : N(n + 1), fac(N), finv(N), inv(N) {
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        int mod = Mint::get_mod();
        for(int i = 2; i < N; i++) {
            fac[i] = fac[i - 1] * i;
            inv[i] = -inv[mod % i] * (mod / i);
            finv[i] = finv[i - 1] * inv[i];
        }
    }
    Mint comb(int n, int k) {
        assert(n < N);
        if(n < k)
            return 0;
        if(n < 0 || k < 0)
            return 0;
        return fac[n] * finv[k] * finv[n - k];
    }
};

// 長さn,1<=a[i]<=mで単調増加: comb(m, n)
// 長さn,1<=a[i]<=mで広義単調増加: (b[i]:=a[i]+iとおいて↑に帰着)
// 片方もしくは両端を固定するとき: comb(m + n - 1, (n - 1 or n - 2)), comb(m + n - 1, n);
// 足してS,長さn: comb(S + n - 1, n)
// 足してS以下,長さn: comb(S + n, n)

// 二項係数（nCk mod.p;1<=k<=n<=1e7,pは素数）for long long
struct CombinationLL {
    const int MOD = 1000000007;
    int N;
    vector<long long> fac, finv, inv;
    CombinationLL(const int n) : N(n + 1), fac(N), finv(N), inv(N) {
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        for(int i = 2; i < N; i++) {
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }
    long long comb(int n, int k) {
        if(n < k)
            return 0;
        if(n < 0 || k < 0)
            return 0;
        assert(n < N);
        return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
    }
};

// 二項係数（nCk mod.p;1<=k<=n<=2000,pは素数でなくともよい）
const int MAX_C = 1000;
long long Com[MAX_C][MAX_C];
void calc_com(int MOD) {
    memset(Com, 0, sizeof(Com));
    Com[0][0] = 1;
    for(int i = 1; i < MAX_C; ++i) {
        Com[i][0] = 1;
        for(int j = 1; j < MAX_C; ++j) {
            Com[i][j] = (Com[i - 1][j - 1] + Com[i - 1][j]) % MOD;
        }
    }
}

// 二項係数 (nCk mod.p; p is prime, Lucasの定理)
struct Lucas {
    vector<vector<long long>> com;
    long long p;
    Lucas(long long p) : p(p) { init(p); }

    void init(long long p) {
        com.assign(p, vector<long long>(p));
        com[0][0] = 1;
        for(int i = 1; i < p; i++) {
            com[i][0] = 1;
            for(int j = i; j > 0; j--) {
                com[i][j] = (com[i - 1][j - 1] + com[i - 1][j]) % p;
            }
        }
    }

    long long comb(long long n, long long k) {
        long long ret = 1;
        while(n > 0) {
            int ni = n % p;
            int ki = k % p;
            ret *= com[ni][ki];
            ret %= p;
            n /= p;
            k /= p;
        }
        return ret;
    }
};

// 二項係数 O(k)
//  nとkのどちらかが変化していくとき、O(変化量)ですべて求められる　多分
//  参考：https://perogram.hateblo.jp/entry/2020/07/08/120017
//  https://yukicoder.me/submissions/520882
template <class T> T nCk(long long n, long long k, map<pair<long long, long long>, T> &mp) {
    auto key = {n, k};
    if(mp.count(key))
        return mp[key];
    if(k == 0 || k == n) {
        T ret = 1;
        return ret;
    }
    if(k == 1 || k == n - 1) {
        T ret = n;
        return ret;
    }
    // return mp[key] = nCk(n, k - 1, mp) * (n - k + 1) / k;
    return mp[key] = nCk(n - 1, k, mp) * n / (n - k);
}

void solve() {
    INT(n);
    VEC(int, c, 9);
    CombinationMint<mint> C(n);
    mint power = (mint(10).pow(n) - 1) / 9;
    mint res = 0;
    rep(i, 9) {
        mint coef = 1;
        int m = n;
        rep(j, 9) {
            if(i == j) continue;
            coef *= C.comb(m, c[j]);
            m = m - c[j];
        }
        res += coef * power * mint(i + 1) * mint(c[i]) / n;
    }
    write(res);
}

int main() {
    int t = 1;
    // cin >> t;
    while(t--) {
        solve();
    }
}