verify/aoj-DPL_5_G.test.cpp

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• Last update: 2023-09-23 21:29:16+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_G

Depends on

• Combination(P, C, H, Stirling number, Bell number) (library/math/combination.cpp)
• library/mod/modint.cpp
• library/template/template.cpp

Code

#define PROBLEM \
    "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_G"
#include "library/template/template.cpp"
// library
#include "library/math/combination.cpp"
#include "library/mod/modint.cpp"
#define mod 1000000007ll
using mint = modint<mod>;
int main() {
    int n, k;
    cin >> n >> k;
    Combination<mint> comb(n);
    print(comb.Bell(n, k));
    return 0;
}

#line 1 "verify/aoj-DPL_5_G.test.cpp"
#define PROBLEM \
    "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_G"
#line 2 "library/template/template.cpp"
/* #region header */
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
// types
using ll = long long;
using ull = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<char> vc;
template <typename T>
using mat = vector<vector<T>>;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef vector<vector<char>> vvc;
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...) for (ll i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...) \
    for (ll i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define srep(i, a, b, c) for (ll i = (a), max_i = (b); i < max_i; i += c)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
//入出力
#define print(x) cout << x << endl
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v)
{
    for (auto &e : v)
        cout << e << " ";
    cout << endl;
    return os;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &a)
{
    for (auto &i : a)
        scan(i);
}
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
// gcd(0, x) fails.
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T>
T mypow(T x, ll n)
{
    T ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}
ll modpow(ll x, ll n, const ll mod)
{
    ll ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
        x %= mod;
        ret %= mod;
    }
    return ret;
}
ll safemod(ll x, ll mod) { return (x % mod + mod) % mod; }
int popcnt(ull x) { return __builtin_popcountll(x); }
template <typename T>
vector<int> IOTA(vector<T> a)
{
    int n = a.size();
    vector<int> id(n);
    iota(all(id), 0);
    sort(all(id), [&](int i, int j)
         { return a[i] < a[j]; });
    return id;
}
long long xor64(long long range) {
    static uint64_t x = 88172645463325252ULL;
    x ^= x << 13;
    x ^= x >> 7;
    return (x ^= x << 17) % range;
}
struct Timer
{
    clock_t start_time;
    void start() { start_time = clock(); }
    int lap()
    {
        // return x ms.
        return (clock() - start_time) * 1000 / CLOCKS_PER_SEC;
    }
};
template <typename T = int>
struct Edge
{
    int from, to;
    T cost;
    int idx;

    Edge() = default;

    Edge(int from, int to, T cost = 1, int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}

    operator int() const { return to; }
};

template <typename T = int>
struct Graph
{
    vector<vector<Edge<T>>> g;
    int es;

    Graph() = default;

    explicit Graph(int n) : g(n), es(0) {}

    size_t size() const { return g.size(); }

    void add_directed_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es++);
    }

    void add_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }

    void read(int M, int padding = -1, bool weighted = false,
              bool directed = false)
    {
        for (int i = 0; i < M; i++)
        {
            int a, b;
            cin >> a >> b;
            a += padding;
            b += padding;
            T c = T(1);
            if (weighted)
                cin >> c;
            if (directed)
                add_directed_edge(a, b, c);
            else
                add_edge(a, b, c);
        }
    }
};

/* #endregion*/
// constant
#define inf 1000000000ll
#define INF 4000000004000000000LL
#define endl '\n'
const long double eps = 0.000000000000001;
const long double PI = 3.141592653589793;
#line 4 "verify/aoj-DPL_5_G.test.cpp"
// library
#line 1 "library/math/combination.cpp"
/**
 * @brief Combination(P, C, H, Stirling number, Bell number)
 * @docs docs/Combination.md
 */
template <typename T>
struct Combination {
    vector<T> _fact, _rfact, _inv;

    Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
        _fact[0] = _rfact[sz] = _inv[0] = 1;
        for (int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
        _rfact[sz] /= _fact[sz];
        for (int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
        for (int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
    }

    inline T fact(int k) const { return _fact[k]; }

    inline T rfact(int k) const { return _rfact[k]; }

    inline T inv(int k) const { return _inv[k]; }

    T P(int n, int r) const {
        if (r < 0 || n < r) return 0;
        return fact(n) * rfact(n - r);
    }

    T C(int p, int q) const {
        if (q < 0 || p < q) return 0;
        return fact(p) * rfact(q) * rfact(p - q);
    }

    T H(int n, int r) const {
        if (n < 0 || r < 0) return (0);
        return r == 0 ? 1 : C(n + r - 1, r);
    }

    // O(klog(n))
    // n個の区別できる玉をk個のグループに分割する場合の数（グループのサイズは1以上）
    T Stirling(int n, int k) {
        T res = 0;
        rep(i, k + 1) {
            res += (T)((k - i) % 2 ? -1 : 1) * C(k, i) * mypow<T>(i, n);
        }
        return res / _fact[k];
    }

    // O(klog(n))
    // n個の区別できる玉をk個のグループに分割する場合の数（グループのサイズは0以上）
    // もしくは、k個以下の玉の一個以上入ったグループに分けると考えてもいい
    T Bell(int n, int k) {
        if (n < k) k = n;
        vector<T> sm(k + 1);
        sm[0] = 1;
        rep(j, 1, k + 1) { sm[j] = sm[j - 1] + (T)(j % 2 ? -1 : 1) / _fact[j]; }
        T res = 0;
        rep(i, k + 1) { res += mypow<T>(i, n) / _fact[i] * sm[k - i]; }
        return res;
    }
};
#line 2 "library/mod/modint.cpp"
template <int Mod>
struct modint
{
    int x;

    modint() : x(0) {}

    modint(long long y) : x(y >= 0 ? y % Mod : (Mod - (-y) % Mod) % Mod) {}

    modint &operator+=(const modint &p)
    {
        if ((x += p.x) >= Mod)
            x -= Mod;
        return *this;
    }

    modint &operator-=(const modint &p)
    {
        if ((x += Mod - p.x) >= Mod)
            x -= Mod;
        return *this;
    }

    modint &operator*=(const modint &p)
    {
        x = (int)(1LL * x * p.x % Mod);
        return *this;
    }

    modint &operator/=(const modint &p)
    {
        *this *= p.inverse();
        return *this;
    }

    modint operator-() const { return modint(-x); }

    modint operator+(const modint &p) const { return modint(*this) += p; }

    modint operator-(const modint &p) const { return modint(*this) -= p; }

    modint operator*(const modint &p) const { return modint(*this) *= p; }

    modint operator/(const modint &p) const { return modint(*this) /= p; }

    bool operator==(const modint &p) const { return x == p.x; }

    bool operator!=(const modint &p) const { return x != p.x; }

    modint inverse() const
    {
        int a = x, b = Mod, u = 1, v = 0, t;
        while (b > 0)
        {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return modint(u);
    }

    modint pow(int64_t n) const
    {
        modint ret(1), mul(x);
        while (n > 0)
        {
            if (n & 1)
                ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const modint &p)
    {
        return os << p.x;
    }

    friend istream &operator>>(istream &is, modint &a)
    {
        long long t;
        is >> t;
        a = modint<Mod>(t);
        return (is);
    }

    static int get_mod() { return Mod; }

    constexpr int get() const { return x; }
};
#line 7 "verify/aoj-DPL_5_G.test.cpp"
#define mod 1000000007ll
using mint = modint<mod>;
int main() {
    int n, k;
    cin >> n >> k;
    Combination<mint> comb(n);
    print(comb.Bell(n, k));
    return 0;
}

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