結果

問題 No.963 門松列列(2)
ユーザー hitonanodehitonanode
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
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ソースコード

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プレゼンテーションモードにする

#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) != 0
const 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) = 1
const 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) = 0
const 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;
}
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