結果
問題 | No.890 移調の限られた旋法 |
ユーザー |
|
提出日時 | 2020-12-02 12:04:54 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 83 ms / 2,000 ms |
コード長 | 16,987 bytes |
コンパイル時間 | 3,529 ms |
コンパイル使用メモリ | 320,780 KB |
最終ジャッジ日時 | 2025-01-16 13:07:02 |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 32 |
ソースコード
/*** date : 2020-12-02 12:04:49*/#define NDEBUG#include <immintrin.h>#include <bits/stdc++.h>using namespace std;template <uint32_t mod>struct LazyMontgomeryModInt {using mint = LazyMontgomeryModInt;using i32 = int32_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 a;constexpr LazyMontgomeryModInt() : a(0) {}constexpr LazyMontgomeryModInt(const int64_t &b): a(reduce(u64(b % mod + mod) * n2)){};static constexpr u32 reduce(const u64 &b) {return (b + u64(u32(b) * u32(-r)) * mod) >> 32;}constexpr mint &operator+=(const mint &b) {if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}constexpr mint &operator-=(const mint &b) {if (i32(a -= b.a) < 0) a += 2 * mod;return *this;}constexpr mint &operator*=(const mint &b) {a = reduce(u64(a) * b.a);return *this;}constexpr mint &operator/=(const mint &b) {*this *= b.inverse();return *this;}constexpr mint operator+(const mint &b) const { return mint(*this) += b; }constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }constexpr bool operator==(const mint &b) const {return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);}constexpr bool operator!=(const mint &b) const {return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);}constexpr mint operator-() const { return mint() - mint(*this); }constexpr mint pow(u64 n) const {mint ret(1), mul(*this);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}constexpr mint inverse() const { return pow(mod - 2); }friend ostream &operator<<(ostream &os, const mint &b) {return os << b.get();}friend istream &operator>>(istream &is, mint &b) {int64_t t;is >> t;b = LazyMontgomeryModInt<mod>(t);return (is);}constexpr u32 get() const {u32 ret = reduce(a);return ret >= mod ? ret - mod : ret;}static constexpr u32 get_mod() { return mod; }};using mint = LazyMontgomeryModInt<1000000007>;using vm = vector<mint>;using vvm = vector<vm>;using namespace std;template <typename T>struct Binomial {vector<T> fac_, finv_, inv_;Binomial(int MAX = 0) : fac_(MAX + 10), finv_(MAX + 10), inv_(MAX + 10) {assert(T::get_mod() != 0);MAX += 9;fac_[0] = finv_[0] = inv_[0] = 1;for (int i = 1; i <= MAX; i++) fac_[i] = fac_[i - 1] * i;finv_[MAX] = fac_[MAX].inverse();for (int i = MAX - 1; i > 0; i--) finv_[i] = finv_[i + 1] * (i + 1);for (int i = 1; i <= MAX; i++) inv_[i] = finv_[i] * fac_[i - 1];}void extend() {int n = fac_.size();T fac = fac_.back() * n;T inv = (-inv_[T::get_mod() % n]) * (T::get_mod() / n);T finv = finv_.back() * inv;fac_.push_back(fac);finv_.push_back(finv);inv_.push_back(inv);}T fac(int i) {while (i >= (int)fac_.size()) extend();return fac_[i];}T finv(int i) {while (i >= (int)finv_.size()) extend();return finv_[i];}T inv(int i) {while (i >= (int)inv_.size()) extend();return inv_[i];}T C(int n, int r) {if (n < r || r < 0) return T(0);return fac(n) * finv(n - r) * finv(r);}T C_naive(int n, int r) {if (n < r || r < 0) return T(0);T ret = T(1);r = min(r, n - r);for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);return ret;}T P(int n, int r) {if (n < r || r < 0) return T(0);return fac(n) * finv(n - r);}T H(int n, int r) {if (n < 0 || r < 0) return T(0);return r == 0 ? 1 : C(n + r - 1, r);}};Binomial<mint> C;using namespace std;using namespace std;// Prime Sieve {2, 3, 5, 7, 11, 13, 17, ...}vector<int> prime_enumerate(int N) {vector<bool> sieve(N / 3 + 1, 1);for (int p = 5, d = 4, i = 1, sqn = sqrt(N); p <= sqn; p += d = 6 - d, i++) {if (!sieve[i]) continue;for (int q = p * p / 3, r = d * p / 3 + (d * p % 3 == 2), s = 2 * p,qe = sieve.size();q < qe; q += r = s - r)sieve[q] = 0;}vector<int> ret{2, 3};for (int p = 5, d = 4, i = 1; p <= N; p += d = 6 - d, i++)if (sieve[i]) ret.push_back(p);while (!ret.empty() && ret.back() > N) ret.pop_back();return ret;}struct divisor_transform {template <typename T>static void zeta_transform(vector<T> &a) {int N = a.size() - 1;auto sieve = prime_enumerate(N);for (auto &p : sieve)for (int k = 1; k * p <= N; ++k) a[k * p] += a[k];}template <typename T>static void mobius_transform(T &a) {int N = a.size() - 1;auto sieve = prime_enumerate(N);for (auto &p : sieve)for (int k = N / p; k > 0; --k) a[k * p] -= a[k];}template <typename T>static void zeta_transform(map<long long, T> &a) {for (auto p = rbegin(a); p != rend(a); p++)for (auto &x : a) {if (p->first == x.first) break;if (p->first % x.first == 0) p->second += x.second;}}template <typename T>static void mobius_transform(map<long long, T> &a) {for (auto &x : a)for (auto p = rbegin(a); p != rend(a); p++) {if (x.first == p->first) break;if (p->first % x.first == 0) p->second -= x.second;}}};struct multiple_transform {template <typename T>static void zeta_transform(vector<T> &a) {int N = a.size() - 1;auto sieve = prime_enumerate(N);for (auto &p : sieve)for (int k = N / p; k > 0; --k) a[k] += a[k * p];}template <typename T>static void mobius_transform(vector<T> &a) {int N = a.size() - 1;auto sieve = prime_enumerate(N);for (auto &p : sieve)for (int k = 1; k * p <= N; ++k) a[k] -= a[k * p];}template <typename T>static void zeta_transform(map<long long, T> &a) {for (auto p1 = rbegin(a); p1 != rend(a); p1++)for (auto p2 = rbegin(a); p2 != p1; p2++)if (p2->first % p1->first == 0) p1->second += p2->second;}template <typename T>static void mobius_transform(map<long long, T> &a) {for (auto p1 = rbegin(a); p1 != rend(a); p1++)for (auto p2 = rbegin(a); p2 != p1; p2++)if (p2->first % p1->first == 0) p1->second -= p2->second;}};//using namespace std;// intrinstic// bits// utilitynamespace Nyaan {using ll = long long;using i64 = long long;using u64 = unsigned long long;using i128 = __int128_t;using u128 = __uint128_t;template <typename T>using V = vector<T>;template <typename T>using VV = vector<vector<T>>;using vi = vector<int>;using vl = vector<long long>;using vd = V<double>;using vs = V<string>;using vvi = vector<vector<int>>;using vvl = vector<vector<long long>>;template <typename T, typename U>struct P : pair<T, U> {template <typename... Args>P(Args... args) : pair<T, U>(args...) {}using pair<T, U>::first;using pair<T, U>::second;T &x() { return first; }const T &x() const { return first; }U &y() { return second; }const U &y() const { return second; }P &operator+=(const P &r) {first += r.first;second += r.second;return *this;}P &operator-=(const P &r) {first -= r.first;second -= r.second;return *this;}P &operator*=(const P &r) {first *= r.first;second *= r.second;return *this;}P operator+(const P &r) const { return P(*this) += r; }P operator-(const P &r) const { return P(*this) -= r; }P operator*(const P &r) const { return P(*this) *= r; }};using pl = P<ll, ll>;using pi = P<int, int>;using vp = V<pl>;constexpr int inf = 1001001001;constexpr long long infLL = 4004004004004004004LL;template <typename T>int sz(const T &t) {return t.size();}template <typename T, size_t N>void mem(T (&a)[N], int c) {memset(a, c, sizeof(T) * N);}template <typename T, typename U>inline bool amin(T &x, U y) {return (y < x) ? (x = y, true) : false;}template <typename T, typename U>inline bool amax(T &x, U y) {return (x < y) ? (x = y, true) : false;}template <typename T>int lb(const vector<T> &v, const T &a) {return lower_bound(begin(v), end(v), a) - begin(v);}template <typename T>int ub(const vector<T> &v, const T &a) {return upper_bound(begin(v), end(v), a) - begin(v);}constexpr long long TEN(int n) {long long ret = 1, x = 10;for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);return ret;}template <typename T, typename U>pair<T, U> mkp(const T &t, const U &u) {return make_pair(t, u);}template <typename T>vector<T> mkrui(const vector<T> &v, bool rev = false) {vector<T> ret(v.size() + 1);if (rev) {for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];} else {for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];}return ret;};template <typename T>vector<T> mkuni(const vector<T> &v) {vector<T> ret(v);sort(ret.begin(), ret.end());ret.erase(unique(ret.begin(), ret.end()), ret.end());return ret;}template <typename F>vector<int> mkord(int N, F f) {vector<int> ord(N);iota(begin(ord), end(ord), 0);sort(begin(ord), end(ord), f);return ord;}template <typename T>vector<T> reord(const vector<T> &v, const vector<T> &ord) {int N = v.size();vector<T> ret(N);for (int i = 0; i < N; i++) ret[i] = v[ord[i]];return ret;};template <typename T = int>vector<T> mkiota(int N) {vector<T> ret(N);iota(begin(ret), end(ret), 0);return ret;}template <typename T>vector<int> mkinv(vector<T> &v, int max_val = -1) {if (max_val < (int)v.size()) max_val = v.size() - 1;vector<int> inv(max_val + 1, -1);for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;return inv;}} // namespace Nyaan// bit operationnamespace Nyaan {__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {return _mm_popcnt_u64(a);}__attribute__((target("bmi"))) inline int botbit(const u64 &a) {return _tzcnt_u64(a);}__attribute__((target("bmi"))) inline int ctz(const u64 &a) {return _tzcnt_u64(a);}__attribute__((target("lzcnt"))) inline int topbit(const u64 &a) {return 63 - _lzcnt_u64(a);}__attribute__((target("lzcnt"))) inline int clz64(const u64 &a) {return _lzcnt_u64(a);}template <typename T>inline int gbit(const T &a, int i) {return (a >> i) & 1;}template <typename T>inline void sbit(T &a, int i, bool b) {a ^= (gbit(a, i) == b ? 0 : (T(b) << i));}constexpr long long PW(int n) { return 1LL << n; }constexpr long long MSK(int n) { return (1LL << n) - 1; }} // namespace Nyaan// inoutnamespace Nyaan {template <typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p) {os << p.first << " " << p.second;return os;}template <typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p) {is >> p.first >> p.second;return is;}template <typename T>ostream &operator<<(ostream &os, const vector<T> &v) {int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template <typename T>istream &operator>>(istream &is, vector<T> &v) {for (auto &x : v) is >> x;return is;}void in() {}template <typename T, class... U>void in(T &t, U &... u) {cin >> t;in(u...);}void out() { cout << "\n"; }template <typename T, class... U, char sep = ' '>void out(const T &t, const U &... u) {cout << t;if (sizeof...(u)) cout << sep;out(u...);}void outr() {}template <typename T, class... U, char sep = ' '>void outr(const T &t, const U &... u) {cout << t;outr(u...);}struct IoSetupNya {IoSetupNya() {cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetupnya;} // namespace Nyaan// debugnamespace DebugImpl {template <typename U, typename = void>struct is_specialize : false_type {};template <typename U>struct is_specialize<U, typename conditional<false, typename U::iterator, void>::type>: true_type {};template <typename U>struct is_specialize<U, typename conditional<false, decltype(U::first), void>::type>: true_type {};template <typename U>struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {};void dump(const char& t) { cerr << t; }void dump(const string& t) { cerr << t; }template <typename U,enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>void dump(const U& t) {cerr << t;}template <typename T>void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {string res;if (t == Nyaan::inf) res = "inf";if (is_signed<T>::value)if (t == -Nyaan::inf) res = "-inf";if (sizeof(T) == 8) {if (t == Nyaan::infLL) res = "inf";if (is_signed<T>::value)if (t == -Nyaan::infLL) res = "-inf";}if (res.empty()) res = to_string(t);cerr << res;}template <typename T, typename U>void dump(const pair<T, U>&);template <typename T>void dump(const pair<T*, int>&);template <typename T>void dump(const T& t,enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {cerr << "[ ";for (auto it = t.begin(); it != t.end();) {dump(*it);cerr << (++it == t.end() ? " ]" : ", ");}}template <typename T, typename U>void dump(const pair<T, U>& t) {cerr << "( ";dump(t.first);cerr << ", ";dump(t.second);cerr << " )";}template <typename T>void dump(const pair<T*, int>& t) {cerr << "[ ";for (int i = 0; i < t.second; i++) {dump(t.first[i]);cerr << (i == t.second - 1 ? " ]" : ", ");}}void trace() { cerr << endl; }template <typename Head, typename... Tail>void trace(Head&& head, Tail&&... tail) {cerr << " ";dump(head);if (sizeof...(tail) != 0) cerr << ",";trace(forward<Tail>(tail)...);}} // namespace DebugImplusing DebugImpl::trace;#ifdef NyaanDebug#define trc(...) \do { \cerr << "## " << #__VA_ARGS__ << " = "; \DebugImpl::trace(__VA_ARGS__); \} while (0)#else#define trc(...)#endif// macro#define each(x, v) for (auto&& x : v)#define all(v) (v).begin(), (v).end()#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)#define reg(i, a, b) for (long long i = (a); i < (b); i++)#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)#define repc(i, a, cond) for (long long i = (a); (cond); i++)#define ini(...) \int __VA_ARGS__; \in(__VA_ARGS__)#define inl(...) \long long __VA_ARGS__; \in(__VA_ARGS__)#define ins(...) \string __VA_ARGS__; \in(__VA_ARGS__)#define inc(...) \char __VA_ARGS__; \in(__VA_ARGS__)#define in2(s, t) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i]); \}#define in3(s, t, u) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i], u[i]); \}#define in4(s, t, u, v) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i], u[i], v[i]); \}#define die(...) \do { \Nyaan::out(__VA_ARGS__); \return; \} while (0)namespace Nyaan {void solve();}int main() { Nyaan::solve(); }using namespace Nyaan;void Nyaan::solve() {ini(N, K);vi ds;rep1(i, N) if (N % i == 0) ds.push_back(i);mint ans1, ans2;{vm a(N + 1);each(i, ds) {// i個周期 -> N/i個の区間が存在するif (K % (N / i) == 0)a[i] = C.C(i, K / (N / i));elsea[i] = 0;}auto ol = a;divisor_transform::mobius_transform(a);auto nw = a;divisor_transform::zeta_transform(nw);assert(ol == nw);ans1 = C.C(N, K) - a[N];}{map<ll, mint> a;each(i, ds) {if (K % (N / i) == 0)a[i] = C.C(i, K / (N / i));elsea[i] = 0;}auto ol = a;divisor_transform::mobius_transform(a);auto nw = a;divisor_transform::zeta_transform(nw);assert(ol == nw);ans2 = C.C(N, K) - a[N];}if (ans1 != ans2) exit(1);out(ans1);}