This documentation is automatically generated by online-judge-tools/verification-helper
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_G
#include "../../template/template.hpp"
#include "../../math/combinatorics/montgomery-mod-int.hpp"
#include "../../math/combinatorics/bell-number.hpp"
int main() {
int N, K;
cin >> N >> K;
cout << bell_number< modint1000000007 >(N, K) << endl;
}
#line 1 "test/verify/aoj-dpl-5-g.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_G
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (T &in : v) is >> in;
return is;
}
template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
for (auto &e : t) fill_v(e, v);
}
template <typename F>
struct FixPoint : F {
explicit FixPoint(F &&f) : F(forward<F>(f)) {}
template <typename... Args>
decltype(auto) operator()(Args &&...args) const {
return F::operator()(*this, forward<Args>(args)...);
}
};
template <typename F>
inline decltype(auto) MFP(F &&f) {
return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/aoj-dpl-5-g.test.cpp"
#line 2 "math/combinatorics/montgomery-mod-int.hpp"
template <uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
private:
using mint = MontgomeryModInt;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod_;
for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod_) % mod_;
static_assert(r * mod_ == 1, "invalid, r * mod != 1");
static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");
u32 x;
public:
MontgomeryModInt() : x{} {}
MontgomeryModInt(const i64 &a)
: x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}
static constexpr u32 reduce(const u64 &b) {
return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
}
mint &operator+=(const mint &p) {
if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
return *this;
}
mint &operator-=(const mint &p) {
if (i32(x -= p.x) < 0) x += 2 * mod();
return *this;
}
mint &operator*=(const mint &p) {
x = reduce(u64(x) * p.x);
return *this;
}
mint &operator/=(const mint &p) {
*this *= p.inv();
return *this;
}
mint operator-() const { return mint() - *this; }
mint operator+(const mint &p) const { return mint(*this) += p; }
mint operator-(const mint &p) const { return mint(*this) -= p; }
mint operator*(const mint &p) const { return mint(*this) *= p; }
mint operator/(const mint &p) const { return mint(*this) /= p; }
bool operator==(const mint &p) const {
return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
}
bool operator!=(const mint &p) const {
return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
}
u32 val() const {
u32 ret = reduce(x);
return ret >= mod() ? ret - mod() : ret;
}
mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
mint inv() const { return pow(mod() - 2); }
friend ostream &operator<<(ostream &os, const mint &p) {
return os << p.val();
}
friend istream &operator>>(istream &is, mint &a) {
i64 t;
is >> t;
a = mint(t);
return is;
}
static constexpr u32 mod() { return mod_; }
};
template <uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 6 "test/verify/aoj-dpl-5-g.test.cpp"
#line 1 "math/combinatorics/enumeration.hpp"
/**
* @brief Enumeration(組み合わせ)
*/
template <typename T>
struct Enumeration {
private:
static vector<T> _fact, _finv, _inv;
inline static void expand(size_t sz) {
if (_fact.size() < sz + 1) {
int pre_sz = max(1, (int)_fact.size());
_fact.resize(sz + 1, T(1));
_finv.resize(sz + 1, T(1));
_inv.resize(sz + 1, T(1));
for (int i = pre_sz; i <= (int)sz; i++) {
_fact[i] = _fact[i - 1] * T(i);
}
_finv[sz] = T(1) / _fact[sz];
for (int i = (int)sz - 1; i >= pre_sz; i--) {
_finv[i] = _finv[i + 1] * T(i + 1);
}
for (int i = pre_sz; i <= (int)sz; i++) {
_inv[i] = _finv[i] * _fact[i - 1];
}
}
}
public:
explicit Enumeration(size_t sz = 0) { expand(sz); }
static inline T fact(int k) {
expand(k);
return _fact[k];
}
static inline T finv(int k) {
expand(k);
return _finv[k];
}
static inline T inv(int k) {
expand(k);
return _inv[k];
}
static T P(int n, int r) {
if (r < 0 || n < r) return 0;
return fact(n) * finv(n - r);
}
static T C(int p, int q) {
if (q < 0 || p < q) return 0;
return fact(p) * finv(q) * finv(p - q);
}
static T H(int n, int r) {
if (n < 0 || r < 0) return 0;
return r == 0 ? 1 : C(n + r - 1, r);
}
};
template <typename T>
vector<T> Enumeration<T>::_fact = vector<T>();
template <typename T>
vector<T> Enumeration<T>::_finv = vector<T>();
template <typename T>
vector<T> Enumeration<T>::_inv = vector<T>();
#line 2 "math/combinatorics/bell-number.hpp"
/**
* @brief Bell Number(ベル数)
*
*/
template <typename T>
T bell_number(int n, int k) {
if (n == 0) return 1;
k = min(k, n);
Enumeration<T> uku(k);
T ret = 0;
vector<T> pref(k + 1);
pref[0] = 1;
for (int i = 1; i <= k; i++) {
if (i & 1)
pref[i] = pref[i - 1] - uku.finv(i);
else
pref[i] = pref[i - 1] + uku.finv(i);
}
for (int i = 1; i <= k; i++) {
ret += T(i).pow(n) * uku.finv(i) * pref[k - i];
}
return ret;
}
#line 8 "test/verify/aoj-dpl-5-g.test.cpp"
int main() {
int N, K;
cin >> N >> K;
cout << bell_number< modint1000000007 >(N, K) << endl;
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | 00_sample_01.in | AC | 6 ms | 4 MB |
g++ | 00_sample_02.in | AC | 6 ms | 4 MB |
g++ | 00_sample_03.in | AC | 6 ms | 4 MB |
g++ | 01_corner_00.in | AC | 6 ms | 4 MB |
g++ | 01_corner_01.in | AC | 6 ms | 4 MB |
g++ | 01_corner_02.in | AC | 6 ms | 4 MB |
g++ | 02_maximum_00.in | AC | 6 ms | 4 MB |
g++ | 02_maximum_01.in | AC | 6 ms | 4 MB |
g++ | 03_random_00.in | AC | 6 ms | 4 MB |
g++ | 03_random_01.in | AC | 6 ms | 4 MB |
g++ | 03_random_02.in | AC | 6 ms | 4 MB |
g++ | 03_random_03.in | AC | 6 ms | 4 MB |
g++ | 03_random_04.in | AC | 6 ms | 4 MB |
g++ | 03_random_05.in | AC | 6 ms | 4 MB |
g++ | 03_random_06.in | AC | 6 ms | 4 MB |
g++ | 03_random_07.in | AC | 6 ms | 4 MB |
g++ | 03_random_08.in | AC | 6 ms | 4 MB |
g++ | 03_random_09.in | AC | 6 ms | 4 MB |
g++ | 03_random_10.in | AC | 6 ms | 4 MB |
g++ | 03_random_11.in | AC | 6 ms | 4 MB |
g++ | 03_random_12.in | AC | 6 ms | 4 MB |
g++ | 03_random_13.in | AC | 6 ms | 4 MB |
g++ | 03_random_14.in | AC | 6 ms | 4 MB |
g++ | 03_random_15.in | AC | 6 ms | 4 MB |
g++ | 03_random_16.in | AC | 6 ms | 4 MB |
g++ | 03_random_17.in | AC | 6 ms | 4 MB |
g++ | 03_random_18.in | AC | 6 ms | 4 MB |
g++ | 03_random_19.in | AC | 6 ms | 4 MB |
clang++ | 00_sample_01.in | AC | 6 ms | 4 MB |
clang++ | 00_sample_02.in | AC | 6 ms | 4 MB |
clang++ | 00_sample_03.in | AC | 6 ms | 4 MB |
clang++ | 01_corner_00.in | AC | 6 ms | 4 MB |
clang++ | 01_corner_01.in | AC | 6 ms | 4 MB |
clang++ | 01_corner_02.in | AC | 6 ms | 4 MB |
clang++ | 02_maximum_00.in | AC | 6 ms | 4 MB |
clang++ | 02_maximum_01.in | AC | 6 ms | 4 MB |
clang++ | 03_random_00.in | AC | 6 ms | 4 MB |
clang++ | 03_random_01.in | AC | 6 ms | 4 MB |
clang++ | 03_random_02.in | AC | 6 ms | 4 MB |
clang++ | 03_random_03.in | AC | 6 ms | 4 MB |
clang++ | 03_random_04.in | AC | 6 ms | 4 MB |
clang++ | 03_random_05.in | AC | 6 ms | 4 MB |
clang++ | 03_random_06.in | AC | 6 ms | 4 MB |
clang++ | 03_random_07.in | AC | 6 ms | 4 MB |
clang++ | 03_random_08.in | AC | 6 ms | 4 MB |
clang++ | 03_random_09.in | AC | 6 ms | 4 MB |
clang++ | 03_random_10.in | AC | 6 ms | 4 MB |
clang++ | 03_random_11.in | AC | 6 ms | 4 MB |
clang++ | 03_random_12.in | AC | 6 ms | 4 MB |
clang++ | 03_random_13.in | AC | 6 ms | 4 MB |
clang++ | 03_random_14.in | AC | 6 ms | 4 MB |
clang++ | 03_random_15.in | AC | 6 ms | 4 MB |
clang++ | 03_random_16.in | AC | 6 ms | 4 MB |
clang++ | 03_random_17.in | AC | 6 ms | 4 MB |
clang++ | 03_random_18.in | AC | 6 ms | 4 MB |
clang++ | 03_random_19.in | AC | 6 ms | 4 MB |