結果
問題 | No.963 門松列列(2) |
ユーザー |
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提出日時 | 2020-01-05 21:01:35 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 796 ms / 3,000 ms |
コード長 | 15,654 bytes |
コンパイル時間 | 2,467 ms |
コンパイル使用メモリ | 192,908 KB |
実行使用メモリ | 74,240 KB |
最終ジャッジ日時 | 2024-11-22 23:30:27 |
合計ジャッジ時間 | 6,090 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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ファイルパターン | 結果 |
---|---|
other | AC * 11 |
ソースコード
#include <bits/stdc++.h>using namespace std;#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define REP(i, n) FOR(i,0,n)template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;constexpr int MOD = 1012924417;template <int mod>struct ModInt{using lint = long long;static int get_mod() { return mod; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&](){std::set<int> fac;int v = mod - 1;for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < mod; g++) {bool ok = true;for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }if (ok) return g;}return -1;}();}return primitive_root;}int val;constexpr ModInt() : val(0) {}constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }constexpr ModInt(lint v) { _setval(v % mod + mod); }explicit operator bool() const { return val != 0; }constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }constexpr ModInt operator-() const { return ModInt()._setval(mod - 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()._setval(a % mod + x.val); }friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }constexpr bool operator==(const ModInt &x) const { return val == x.val; }constexpr bool operator!=(const ModInt &x) const { return val != x.val; }bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }friend std::ostream &operator<<(std::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 std::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());}ModInt sqrt() const {if (val == 0) return 0;if (mod == 2) return val;if (power((mod - 1) / 2) != 1) return 0;ModInt b = 1;while (b.power((mod - 1) / 2) == 1) b += 1;int e = 0, m = mod - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = power((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.power(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.power(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val, mod - x.val));}};using mint = ModInt<MOD>;struct cmplx{double x, y;cmplx() : x(0), y(0) {}cmplx(double x, double y) : x(x), y(y) {}inline cmplx operator+(const cmplx &r) const { return cmplx(x + r.x, y + r.y); }inline cmplx operator-(const cmplx &r) const { return cmplx(x - r.x, y - r.y); }inline cmplx operator*(const cmplx &r) const { return cmplx(x * r.x - y * r.y, x * r.y + y * r.x); }inline cmplx conj() const { return cmplx(x, -y); }};int fftbase = 1;vector<cmplx> fftrts = {{0, 0}, {1, 0}};vector<int> fftrev = {0, 1};void ensure_base(int nbase) {if (nbase <= fftbase) return;fftrev.resize(1 << nbase);fftrts.resize(1 << nbase);for (int i = 0; i < (1 << nbase); i++) {fftrev[i] = (fftrev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));}while (fftbase < nbase) {double angle = M_PI * 2.0 / (1 << (fftbase + 1));for (int i = 1 << (fftbase - 1); i < (1 << fftbase); i++) {fftrts[i << 1] = fftrts[i];double angle_i = angle * (2 * i + 1 - (1 << fftbase));fftrts[(i << 1) + 1] = {cos(angle_i), sin(angle_i)};}++fftbase;}}void fft(int n, vector<cmplx> &a) {assert((n & (n - 1)) == 0);int zeros = __builtin_ctz(n);ensure_base(zeros);int shift = fftbase - zeros;for (int i = 0; i < n; i++) {if (i < (fftrev[i] >> shift)) {swap(a[i], a[fftrev[i] >> shift]);}}for (int k = 1; k < n; k <<= 1) {for (int i = 0; i < n; i += 2 * k) {for (int j = 0; j < k; j++) {cmplx z = a[i + j + k] * fftrts[j + k];a[i + j + k] = a[i + j] - z;a[i + j] = a[i + j] + z;}}}}// Convolution for ModInt class// retval[i] = \sum_j a[j] b[i - j]template <typename MODINT>vector<MODINT> convolution_mod(vector<MODINT> a, vector<MODINT> b){int need = int(a.size() + b.size()) - 1;int nbase = 0;while ((1 << nbase) < need) nbase++;int sz = 1 << nbase;vector<cmplx> fa(sz);for (int i = 0; i < (int)a.size(); i++) fa[i] = {double(a[i].val & ((1 << 15) - 1)), double(a[i].val >> 15)};fft(sz, fa);vector<cmplx> fb(sz);if (a == b) fb = fa;else {for (int i = 0; i < (int)b.size(); i++) fb[i] = {double(b[i].val & ((1 << 15) - 1)), double(b[i].val >> 15)};fft(sz, fb);}double ratio = 0.25 / sz;cmplx r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);for (int i = 0; i <= (sz >> 1); i++) {int j = (sz - i) & (sz - 1);cmplx a1 = (fa[i] + fa[j].conj());cmplx a2 = (fa[i] - fa[j].conj()) * r2;cmplx b1 = (fb[i] + fb[j].conj()) * r3;cmplx b2 = (fb[i] - fb[j].conj()) * r4;if (i != j) {cmplx c1 = (fa[j] + fa[i].conj());cmplx c2 = (fa[j] - fa[i].conj()) * r2;cmplx d1 = (fb[j] + fb[i].conj()) * r3;cmplx d2 = (fb[j] - fb[i].conj()) * r4;fa[i] = c1 * d1 + c2 * d2 * r5;fb[i] = c1 * d2 + c2 * d1;}fa[j] = a1 * b1 + a2 * b2 * r5;fb[j] = a1 * b2 + a2 * b1;}fft(sz, fa);fft(sz, fb);vector<MODINT> ret(sz);for (int i = 0; i < need; i++) {int64_t aa = llround(fa[i].x);int64_t bb = llround(fb[i].x);int64_t cc = llround(fa[i].y);aa = MODINT(aa).val, bb = MODINT(bb).val, cc = MODINT(cc).val;ret[i] = aa + (bb << 15) + (cc << 30);}return ret;}template<typename T>struct FormalPowerSeries : vector<T>{using vector<T>::vector;using P = FormalPowerSeries;void shrink() { while (this->size() and this->back() == T(0)) this->pop_back(); }P operator+(const P &r) const { return P(*this) += r; }P operator+(const T &v) const { return P(*this) += v; }P operator-(const P &r) const { return P(*this) -= r; }P operator-(const T &v) const { return P(*this) -= v; }P operator*(const P &r) const { return P(*this) *= r; }P operator*(const T &v) const { return P(*this) *= v; }P operator/(const P &r) const { return P(*this) /= r; }P operator/(const T &v) const { return P(*this) /= v; }P operator%(const P &r) const { return P(*this) %= r; }P &operator+=(const P &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];shrink();return *this;}P &operator+=(const T &v) {if (this->empty()) this->resize(1);(*this)[0] += v;shrink();return *this;}P &operator-=(const P &r) {if(r.size() > this->size()) this->resize(r.size());for(int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];shrink();return *this;}P &operator-=(const T &v) {if(this->empty()) this->resize(1);(*this)[0] -= v;shrink();return *this;}P &operator*=(const T &v) {for (auto &x : (*this)) x *= v;shrink();return *this;}P &operator*=(const P &r) {if (this->empty() || r.empty()) this->clear();else {auto ret = convolution_mod(*this, r);*this = P(ret.begin(), ret.end());}return *this;}P &operator%=(const P &r) {*this -= *this / r * r;shrink();return *this;}P operator-() const {P ret = *this;for (auto &v : ret) v = -v;return ret;}P &operator/=(const T &v) {assert(v != T(0));for (auto &x : (*this)) x /= v;return *this;}P &operator/=(const P &r) {if (this->size() < r.size()) {this->clear();return *this;}int n = (int)this->size() - r.size() + 1;return *this = (reversed().pre(n) * r.reversed().inv(n)).pre(n).reversed(n);}P pre(int sz) const {P ret(this->begin(), this->begin() + min((int)this->size(), sz));ret.shrink();return ret;}P operator>>(int sz) const {if ((int)this->size() <= sz) return {};return P(this->begin() + sz, this->end());}P operator<<(int sz) const {if (this->empty()) return {};P ret(*this);ret.insert(ret.begin(), sz, T(0));return ret;}P reversed(int deg = -1) const {assert(deg >= -1);P ret(*this);if (deg != -1) ret.resize(deg, T(0));reverse(ret.begin(), ret.end());ret.shrink();return ret;}P differential() const { // formal derivative (differential) of f.p.s.const int n = (int)this->size();P ret(max(0, n - 1));for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);return ret;}P integral() const {const int n = (int)this->size();P ret(n + 1);ret[0] = T(0);for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);return ret;}P inv(int deg) const {assert(deg >= -1);assert(this->size() and ((*this)[0]) != T(0)); // Requirement: F(0) != 0const int n = this->size();if (deg == -1) deg = n;P ret({T(1) / (*this)[0]});for (int i = 1; i < deg; i <<= 1) {ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);}ret = ret.pre(deg);ret.shrink();return ret;}P log(int deg = -1) const {assert(deg >= -1);assert(this->size() and ((*this)[0]) == T(1)); // Requirement: F(0) = 1const int n = (int)this->size();if (deg == 0) return {};if (deg == -1) deg = n;return (this->differential() * this->inv(deg)).pre(deg - 1).integral();}P sqrt(int deg = -1) const {assert(deg >= -1);const int n = (int)this->size();if (deg == -1) deg = n;if (this->empty()) return {};if ((*this)[0] == T(0)) {for (int i = 1; i < n; i++) if ((*this)[i] != T(0)) {if ((i & 1) or deg - i / 2 <= 0) return {};return (*this >> i).sqrt(deg - i / 2) << (i / 2);}return {};}T sqrtf0 = (*this)[0].sqrt();if (sqrtf0 == T(0)) return {};P y = (*this) / (*this)[0], ret({T(1)});T inv2 = T(1) / T(2);for (int i = 1; i < deg; i <<= 1) {ret = (ret + y.pre(i << 1) * ret.inv(i << 1)) * inv2;}return ret.pre(deg) * sqrtf0;}P exp(int deg = -1) const {assert(deg >= -1);assert(this->empty() or ((*this)[0]) == T(0)); // Requirement: F(0) = 0const int n = (int)this->size();if (deg == -1) deg = n;P ret({T(1)});for (int i = 1; i < deg; i <<= 1) {ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);}return ret.pre(deg);}P pow(long long int k, int deg = -1) const {assert(deg >= -1);const int n = (int)this->size();if (deg == -1) deg = n;for (int i = 0; i < n; i++) {if ((*this)[i] != T(0)) {T rev = T(1) / (*this)[i];P C(*this * rev);P D(n - i);for (int j = i; j < n; j++) D[j - i] = C[j];D = (D.log(deg) * T(k)).exp(deg) * (*this)[i].power(k);P E(deg);if (k * (i > 0) > deg or k * i > deg) return {};long long int S = i * k;for (int j = 0; j + S < deg and j < (int)D.size(); j++) E[j + S] = D[j];E.shrink();return E;}}return *this;}T coeff(int i) const {if ((int)this->size() <= i) return T(0);return (*this)[i];}T eval(T x) const {T ret = 0, w = 1;for (auto &v : *this) ret += w * v, w *= x;return ret;}};int main(){int N;cin >> N;FormalPowerSeries<mint> cosx2(N * 2 + 1), sinx2(N * 2 + 1);REP(i, N) {cosx2.at(i * 2) = mint(1) / mint(i * 2).fac() / mint(2).power(i * 2) * (i % 2 ? -1 : 1);sinx2.at(i * 2 + 1) = mint(1) / mint(i * 2 + 1).fac() / mint(2).power(i * 2 + 1) * (i % 2 ? -1 : 1);}auto cos_plus_sin = cosx2 + sinx2;auto cos_minus_sin_inv = (cosx2 - sinx2).inv(N + 2);auto ret = cos_plus_sin * cos_minus_sin_inv;cout << ret.coeff(N) * 2 * mint(N).fac() << endl;}