結果
| 問題 | No.1080 Strange Squared Score Sum |
| ユーザー |
 heno239
|
| 提出日時 | 2023-12-13 05:40:41 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3,658 ms / 5,000 ms |
| コード長 | 16,078 bytes |
| コンパイル時間 | 3,586 ms |
| コンパイル使用メモリ | 190,164 KB |
| 最終ジャッジ日時 | 2025-02-18 10:40:42 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 20 |
ソースコード
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;
//#define int long long
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
//ll mod = 1;
//constexpr ll mod = 998244353;
constexpr ll mod = 1000000009;
const int mod17 = 1000000007;
const ll INF = (ll)mod17 * mod17;
typedef pair<int, int>P;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
using ld = double;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);
template<typename T>
void chmin(T& a, T b) {
a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
a = max(a, b);
}
template<typename T>
vector<T> vmerge(vector<T>& a, vector<T>& b) {
vector<T> res;
int ida = 0, idb = 0;
while (ida < a.size() || idb < b.size()) {
if (idb == b.size()) {
res.push_back(a[ida]); ida++;
}
else if (ida == a.size()) {
res.push_back(b[idb]); idb++;
}
else {
if (a[ida] < b[idb]) {
res.push_back(a[ida]); ida++;
}
else {
res.push_back(b[idb]); idb++;
}
}
}
return res;
}
template<typename T>
void cinarray(vector<T>& v) {
rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
rep(i, v.size()) {
if (i > 0)cout << " "; cout << v[i];
}
cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
if (n < 0) {
ll res = mod_pow(x, -n, m);
return mod_pow(res, m - 2, m);
}
if (abs(x) >= m)x %= m;
if (x < 0)x += m;
//if (x == 0)return 0;
ll res = 1;
while (n) {
if (n & 1)res = res * x % m;
x = x * x % m; n >>= 1;
}
return res;
}
//mod should be <2^31
struct modint {
int n;
modint() :n(0) { ; }
modint(ll m) {
if (m < 0 || mod <= m) {
m %= mod; if (m < 0)m += mod;
}
n = m;
}
operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
if (n == 0)return modint(1);
modint res = (a * a) ^ (n / 2);
if (n % 2)res = res * a;
return res;
}
ll inv(ll a, ll p) {
return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
fact[0] = modint(1);
for (int i = 0; i < max_n - 1; i++) {
fact[i + 1] = fact[i] * modint(i + 1);
}
factinv[max_n - 1] = modint(1) / fact[max_n - 1];
for (int i = max_n - 2; i >= 0; i--) {
factinv[i] = factinv[i + 1] * modint(i + 1);
}
}
modint comb(int a, int b) {
if (a < 0 || b < 0 || a < b)return 0;
return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
if (a < 0 || b < 0 || a < b)return 0;
return fact[a] * factinv[a - b];
}
ll gcd(ll a, ll b) {
a = abs(a); b = abs(b);
if (a < b)swap(a, b);
while (b) {
ll r = a % b; a = b; b = r;
}
return a;
}
template<typename T>
void addv(vector<T>& v, int loc, T val) {
if (loc >= v.size())v.resize(loc + 1, 0);
v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
fill(isp + 2, isp + mn, true);
for (int i = 2; i < mn; i++) {
if (!isp[i])continue;
ps.push_back(i);
for (int j = 2 * i; j < mn; j += i) {
isp[j] = false;
}
}
}*/
//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
auto res = st.lower_bound(val);
if (res == st.begin())return st.end();
res--; return res;
}
//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
auto res = st.lower_bound(val);
return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
a = a + b; return a;
}
mP operator-(mP a, mP b) {
return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
a = a - b; return a;
}
LP operator+(LP a, LP b) {
return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
a = a + b; return a;
}
LP operator-(LP a, LP b) {
return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
a = a - b; return a;
}
mt19937 mt(time(0));
const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
//int dx[4] = { 1,0,-1,0 };
//int dy[4] = { 0,1,0,-1 };
//------------------------------------
modint r2 = 291087696;
modint ri = 430477711;
void expr() {
for (ll c = 1; c < mod; c++) {
if (c * c % mod == mod - 1) {
cout << "! -1 " << c << "\n";
}
if (c * c % mod == 2) {
cout << "! 2 " << c << "\n";
}
}
}
int bsf(int x) {
int res = 0;
while (!(x & 1)) {
res++; x >>= 1;
}
return res;
}
int ceil_pow2(int n) {
int x = 0;
while ((1 << x) < n) x++;
return x;
}
int get_premitive_root(const ll& p) {
int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
set<int> fac;
int v = p - 1;
for (ll 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 < p; g++) {
bool ok = true;
for (auto i : fac) if (mod_pow(g, (p - 1) / i, p) == 1) { ok = false; break; }
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
const array<ll, 3> ms = { 469762049,167772161,595591169 };
const array<ll, 3> proots = { get_premitive_root(469762049),get_premitive_root(167772161),get_premitive_root(595591169) };
using poly = vector<ll>;
using polys = array<poly, 3>;
void butterfly(polys& a) {
int n = int(a[0].size());
array<ll, 3> gs = proots;
int h = ceil_pow2(n);
static bool first = true;
static ll sum_e[3][30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
ll es[3][30], ies[3][30]; // es[i]^(2^(2+i)) == 1
int cnt2[3];
rep(i, 3)cnt2[i] = bsf(ms[i] - 1);
ll e[3];
rep(i, 3)e[i] = mod_pow(gs[i], (ms[i] - 1) >> cnt2[i], ms[i]);
ll ie[3];
rep(i, 3)ie[i] = mod_pow(e[i], ms[i] - 2, ms[i]);
rep(j, 3) {
for (int i = cnt2[j]; i >= 2; i--) {
// e^(2^i) == 1
es[j][i - 2] = e[j];
ies[j][i - 2] = ie[j];
e[j] *= e[j]; e[j] %= ms[j];
ie[j] *= ie[j]; ie[j] %= ms[j];
}
}
rep(j, 3) {
ll now = 1;
for (int i = 0; i < cnt2[j] - 2; i++) {
sum_e[j][i] = es[j][i] * now % ms[j];
now *= ies[j][i]; now %= ms[j];
}
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
ll now[3] = { 1,1,1 };
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
rep(j, 3) {
auto l = a[j][i + offset];
auto r = a[j][i + offset + p] * now[j] % ms[j];
a[j][i + offset] = l + r; if (a[j][i + offset] >= ms[j])a[j][i + offset] -= ms[j];
a[j][i + offset + p] = l - r; if (a[j][i + offset + p] < 0)a[j][i + offset + p] += ms[j];
}
}
rep(j, 3) {
now[j] *= sum_e[j][bsf(~(unsigned int)(s))];
now[j] %= ms[j];
}
}
}
}
void butterfly_inv(polys& a) {
int n = int(a[0].size());
array<ll, 3> gs = proots;
int h = ceil_pow2(n);
static bool first = true;
static ll sum_ie[3][30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
ll es[3][30], ies[3][30]; // es[i]^(2^(2+i)) == 1
int cnt2[3];
rep(i, 3)cnt2[i] = bsf(ms[i] - 1);
ll e[3];
rep(i, 3)e[i] = mod_pow(gs[i], (ms[i] - 1) >> cnt2[i], ms[i]);
ll ie[3];
rep(i, 3)ie[i] = mod_pow(e[i], ms[i] - 2, ms[i]);
rep(j, 3) {
for (int i = cnt2[j]; i >= 2; i--) {
// e^(2^i) == 1
es[j][i - 2] = e[j];
ies[j][i - 2] = ie[j];
e[j] *= e[j]; e[j] %= ms[j];
ie[j] *= ie[j]; ie[j] %= ms[j];
}
}
rep(j, 3) {
ll now = 1;
for (int i = 0; i < cnt2[j] - 2; i++) {
sum_ie[j][i] = ies[j][i] * now % ms[j];
now *= es[j][i]; now %= ms[j];
}
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
ll inow[3] = { 1,1,1 };
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
rep(j, 3) {
auto l = a[j][i + offset];
auto r = a[j][i + offset + p];
a[j][i + offset] = l + r; if (a[j][i + offset] >= ms[j])a[j][i + offset] -= ms[j];
a[j][i + offset + p] = (ms[j] + l - r) * inow[j] % ms[j];
}
}
rep(j, 3) {
inow[j] *= sum_ie[j][bsf(~(unsigned int)(s))];
inow[j] %= ms[j];
}
}
}
}
constexpr ll m0 = 469762049;
constexpr ll m1 = 167772161;
constexpr ll m2 = 595591169;
const ll inv01 = mod_pow(m0, m1 - 2, m1);
const ll inv012 = mod_pow(m0 * m1, m2 - 2, m2);
ll calc(ll& a, ll& b, ll& c, const ll& p) {
ll res = 0;
ll x1 = a;
ll x2 = (b - x1) * inv01;
x2 %= m1; if (x2 < 0)x2 += m1;
ll x3 = (c - x1 - x2 * m0) % m2 * inv012;
x3 %= m2; if (x3 < 0)x3 += m2;
res = x1 + x2 * m0 % p + x3 * m0 % p * m1;
return res % p;
}
using poly2 = vector<modint>;
vector<modint> multiply(poly2 _g, poly2 _h, const ll& p=mod) {
poly g(_g.size()), h(_h.size());
rep(i, g.size())g[i] = _g[i];
rep(i, h.size())h[i] = _h[i];
int n = g.size();
int m = h.size();
if (n == 0 || m == 0)return {};
if (min(g.size(), h.size()) < 60) {
vector<modint> res(g.size() + h.size() - 1);
rep(i, g.size())rep(j, h.size()) {
res[i + j] += g[i] * h[j];
}
return res;
}
int z = 1 << ceil_pow2(n + m - 1);
g.resize(z); h.resize(z);
polys gs, hs;
rep(j, 3) {
gs[j].resize(z);
hs[j].resize(z);
rep(i, z) {
gs[j][i] = g[i] % ms[j];
hs[j][i] = h[i] % ms[j];
}
}
butterfly(gs);
butterfly(hs);
rep(j, 3)rep(i, z) {
(gs[j][i] *= hs[j][i]) %= ms[j];
}
butterfly_inv(gs);
rep(j, 3) {
gs[j].resize(n + m - 1);
ll iz = mod_pow(z, ms[j] - 2, ms[j]);
rep(i, n + m - 1) {
(gs[j][i] *= iz) %= ms[j];
}
}
vector<modint> res(n + m - 1);
rep(i, n + m - 1) {
res[i] = calc(gs[0][i], gs[1][i], gs[2][i], p);
}
return res;
}
struct FormalPowerSeries :vector<modint> {
using vector<modint>::vector;
using fps = FormalPowerSeries;
void shrink() {
while (this->size() && this->back() == (modint)0)this->pop_back();
}
fps operator+(const fps& r)const { return fps(*this) += r; }
fps operator+(const modint& v)const { return fps(*this) += v; }
fps operator-(const fps& r)const { return fps(*this) -= r; }
fps operator-(const modint& v)const { return fps(*this) -= v; }
fps operator*(const fps& r)const { return fps(*this) *= r; }
fps operator*(const modint& v)const { return fps(*this) *= v; }
fps& operator+=(const fps& r) {
if (r.size() > this->size())this->resize(r.size());
rep(i, r.size())(*this)[i] += r[i];
shrink();
return *this;
}
fps& operator+=(const modint& v) {
if (this->empty())this->resize(1);
(*this)[0] += v;
shrink();
return *this;
}
fps& operator-=(const fps& r) {
if (r.size() > this->size())this->resize(r.size());
rep(i, r.size())(*this)[i] -= r[i];
shrink();
return *this;
}
fps& operator-=(const modint& v) {
if (this->empty())this->resize(1);
(*this)[0] -= v;
shrink();
return *this;
}
fps& operator*=(const fps& r) {
if (this->empty() || r.empty())this->clear();
else {
poly2 ret = multiply(*this, r);
*this = fps(all(ret));
}
shrink();
return *this;
}
fps& operator*=(const modint& v) {
for (auto& x : (*this))x *= v;
shrink();
return *this;
}
fps operator-()const {
fps ret = *this;
for (auto& v : ret)v = -v;
return ret;
}
modint sub(modint x) {
modint t = 1;
modint res = 0;
rep(i, (*this).size()) {
res += t * (*this)[i];
t *= x;
}
return res;
}
fps pre(int sz)const {
fps ret(this->begin(), this->begin() + min((int)this->size(), sz));
ret.shrink();
return ret;
}
fps integral() const {
const int n = (int)this->size();
fps ret(n + 1);
ret[0] = 0;
for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / (modint)(i + 1);
return ret;
}
fps inv(int deg = -1)const {
const int n = this->size();
if (deg == -1)deg = n;
fps ret({ (modint)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;
}
fps diff() const {
const int n = (int)this->size();
fps ret(max(0, n - 1));
for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * (modint)i;
return ret;
}
// F(0) must be 1
fps log(int deg = -1) const {
assert((*this)[0] == 1);
const int n = (int)this->size();
if (deg == -1) deg = n;
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
// F(0) must be 0
fps exp(int deg = -1)const {
assert((*this)[0] == 0);
const int n = (int)this->size();
if (deg == -1)deg = n;
fps ret = { 1 };
for (int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + 1 - ret.log(i << 1))).pre(i << 1);
}
//cout << "!!!! " << ret.size() << "\n";
return ret.pre(deg);
}
fps div(fps g) {
assert(g.size() && g.back() != (modint)0);
fps f = *this;
if (f.size() < g.size())return {};
int dif = f.size() - g.size();
reverse(all(f));
reverse(all(g));
g = g.inv(dif + 1);
fps fg = f * g;
fps ret(dif + 1);
rep(i, fg.size()) {
int id = i - dif;
if (-dif <= id && id <= 0) {
ret[-id] = fg[i];
}
}
return ret;
}
fps divr(fps g) {
fps ret = (*this) - g * (*this).div(g);
ret.shrink();
return ret;
}
};
using fps = FormalPowerSeries;
void solve() {
int n; cin >> n;
auto calc = [&](modint r,modint s) {
fps f(n + 1);
rep1(i, n) {
f[i] = (modint)(i + 1) * (modint)(i + 1) * r;
}
f = f.exp(n+1);
rep(i, f.size())f[i] *= s;
return f;
/*vector<modint> res(n + 1);
res[0] = s;
for (int i = 1; i <= n; i++) {
modint c = (modint)(i + 1) * (modint)(i + 1);
for (int j = n-i; j >= 0; j--) {
modint pro = res[j];
int t = 0;
for (int k = j + i; k <= n; k += i) {
pro *= r * c;
t++;
res[k] += pro * factinv[t];
}
}
}
return res;*/
};
modint t1 = ri;
modint s1 = (modint)1 / r2 - (modint)1 / r2 * ri;
modint t2 = -ri;
modint s2 = (modint)1 / r2 + (modint)1 / r2 * ri;
auto v1 = calc(t1,s1);
auto v2 = calc(t2,s2);
vector<modint> ans(n + 1);
modint cc = (modint)1 / r2;
rep(i, n + 1) {
ans[i] = v1[i] + v2[i];
ans[i] *= cc;
ans[i] *= fact[n];
}
rep1(i, n)cout << ans[i] << "\n";
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(0);
//cout << fixed<<setprecision(10);
init_f();
//init();
//while(true)
//expr();
//int t; cin >> t; rep(i, t)
solve();
return 0;
}