結果
| 問題 | No.1080 Strange Squared Score Sum |
| ユーザー |
 hitonanode
|
| 提出日時 | 2020-06-13 05:27:57 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2,801 ms / 5,000 ms |
| コード長 | 16,222 bytes |
| コンパイル時間 | 4,098 ms |
| コンパイル使用メモリ | 244,312 KB |
| 実行使用メモリ | 17,024 KB |
| 最終ジャッジ日時 | 2024-06-24 09:34:26 |
| 合計ジャッジ時間 | 38,471 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,376 KB |
| testcase_02 | AC | 1,232 ms
10,156 KB |
| testcase_03 | AC | 2,801 ms
15,120 KB |
| testcase_04 | AC | 537 ms
6,436 KB |
| testcase_05 | AC | 548 ms
6,448 KB |
| testcase_06 | AC | 104 ms
5,376 KB |
| testcase_07 | AC | 238 ms
5,376 KB |
| testcase_08 | AC | 1,211 ms
10,212 KB |
| testcase_09 | AC | 1,215 ms
9,104 KB |
| testcase_10 | AC | 106 ms
5,376 KB |
| testcase_11 | AC | 2,793 ms
15,108 KB |
| testcase_12 | AC | 1,220 ms
9,092 KB |
| testcase_13 | AC | 2,775 ms
14,960 KB |
| testcase_14 | AC | 1,220 ms
9,644 KB |
| testcase_15 | AC | 2 ms
5,376 KB |
| testcase_16 | AC | 2,796 ms
17,024 KB |
| testcase_17 | AC | 2,779 ms
15,224 KB |
| testcase_18 | AC | 2,760 ms
15,096 KB |
| testcase_19 | AC | 2,781 ms
15,220 KB |
| testcase_20 | AC | 2,762 ms
15,000 KB |
| testcase_21 | AC | 2,780 ms
15,092 KB |
ソースコード
#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
using namespace __gnu_pbds; // find_by_order(), order_of_key()
template<typename TK> using pbds_set = tree<TK, null_type, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename TK, typename TV> using pbds_map = tree<TK, TV, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
*/
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<1000000009>;
// Integer convolution for arbitrary mod
// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.
// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.
// input: a (size: n), b (size: m)
// return: vector (size: n + m - 1)
template <typename MODINT>
vector<MODINT> nttconv(vector<MODINT> a, vector<MODINT> b, bool skip_garner = false);
constexpr int nttprimes[3] = {998244353, 167772161, 469762049};
// Integer FFT (Fast Fourier Transform) for ModInt class
// (Also known as Number Theoretic Transform, NTT)
// is_inverse: inverse transform
// ** Input size must be 2^n **
template <typename MODINT>
void ntt(vector<MODINT> &a, bool is_inverse = false)
{
int n = a.size();
assert(__builtin_popcount(n) == 1);
MODINT h = MODINT(MODINT::get_primitive_root()).power((MODINT::get_mod() - 1) / n);
if (is_inverse) h = 1 / h;
int i = 0;
for (int j = 1; j < n - 1; j++) {
for (int k = n >> 1; k > (i ^= k); k >>= 1);
if (j < i) swap(a[i], a[j]);
}
for (int m = 1; m < n; m *= 2) {
int m2 = 2 * m;
MODINT base = h.power(n / m2), w = 1;
for (int x = 0; x < m; x++) {
for (int s = x; s < n; s += m2) {
MODINT u = a[s], d = a[s + m] * w;
a[s] = u + d, a[s + m] = u - d;
}
w *= base;
}
}
if (is_inverse) {
long long int n_inv = MODINT(n).inv();
for (auto &v : a) v *= n_inv;
}
}
// // from <https://yukicoder.me/submissions/496207>
// template <class T>
// void ntt(vector<T> &a, bool inverse) {
// int n = size(a);
// assert((n & (n - 1)) == 0);
// if(n < 2) return;
// assert((T::get_mod() - 1) % n == 0);
// static vector<T> w{1}, iw{1};
// for(int m = size(w); m < n / 2; m *= 2) {
// static T root = T::get_primitive_root();
// T dw = root.power((T::get_mod() - 1) / (4 * m)), idw = 1 / dw;
// w.resize(2 * m), iw.resize(2 * m);
// for(int i = 0; i < m; ++i)
// w[m + i] = w[i] * dw, iw[m + i] = iw[i] * idw;
// }
// if(not inverse) {
// for(int m = n; m >>= 1;) {
// for(int s = 0, k = 0; s < n; s += 2 * m, ++k) {
// for(int i = s, j = s + m; i < s + m; ++i, ++j) {
// T x = a[i], y = a[j] * w[k];
// a[i] = x + y, a[j] = x - y;
// }
// }
// }
// } else {
// for(int m = 1; m < n; m *= 2) {
// for(int s = 0, k = 0; s < n; s += 2 * m, ++k) {
// for(int i = s, j = s + m; i < s + m; ++i, ++j) {
// T x = a[i], y = a[j];
// a[i] = x + y, a[j] = (x - y) * iw[k];
// }
// }
// }
// auto inv = 1 / T(n);
// for(auto &&e : a) e *= inv;
// }
// }
template<int MOD>
vector<ModInt<MOD>> nttconv_(const vector<int> &a, const vector<int> &b) {
int sz = a.size();
assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
vector<ModInt<MOD>> ap(sz), bp(sz);
for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];
if (a == b) {
ntt(ap, false);
bp = ap;
}
else {
ntt(ap, false);
ntt(bp, false);
}
for (int i = 0; i < sz; i++) ap[i] *= bp[i];
ntt(ap, true);
return ap;
}
long long int extgcd_ntt_(long long int a, long long int b, long long int &x, long long int &y)
{
long long int d = a;
if (b != 0) d = extgcd_ntt_(b, a % b, y, x), y -= (a / b) * x;
else x = 1, y = 0;
return d;
}
long long int modinv_ntt_(long long int a, long long int m)
{
long long int x, y;
extgcd_ntt_(a, m, x, y);
return (m + x % m) % m;
}
long long int garner_ntt_(int r0, int r1, int r2, int mod)
{
array<long long int, 4> rs = {r0, r1, r2, 0};
vector<long long int> coffs(4, 1), constants(4, 0);
for (int i = 0; i < 3; i++) {
long long int v = (rs[i] - constants[i]) * modinv_ntt_(coffs[i], nttprimes[i]) % nttprimes[i];
if (v < 0) v += nttprimes[i];
for (int j = i + 1; j < 4; j++) {
(constants[j] += coffs[j] * v) %= (j < 3 ? nttprimes[j] : mod);
(coffs[j] *= nttprimes[i]) %= (j < 3 ? nttprimes[j] : mod);
}
}
return constants.back();
}
template <typename MODINT>
vector<MODINT> nttconv(vector<MODINT> a, vector<MODINT> b, bool skip_garner)
{
int sz = 1, n = a.size(), m = b.size();
while (sz < n + m) sz <<= 1;
if (sz <= 16) {
vector<MODINT> ret(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];
}
return ret;
}
int mod = MODINT::get_mod();
if (skip_garner or find(begin(nttprimes), end(nttprimes), mod) != end(nttprimes)) {
a.resize(sz), b.resize(sz);
if (a == b) { ntt(a, false); b = a; }
else ntt(a, false), ntt(b, false);
for (int i = 0; i < sz; i++) a[i] *= b[i];
ntt(a, true);
a.resize(n + m - 1);
}
else {
vector<int> ai(sz), bi(sz);
for (int i = 0; i < n; i++) ai[i] = a[i].val;
for (int i = 0; i < m; i++) bi[i] = b[i].val;
auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);
auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);
auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);
ModInt<nttprimes[1]> im0 = 1;
ModInt<nttprimes[2]> im1 = 1, im0m1;
im0 /= nttprimes[0];
im1 /= nttprimes[1];
im0m1 = im1 / nttprimes[0];
MODINT m0 = nttprimes[0], m0m1 = m0 * nttprimes[1];
a.resize(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
// a[i] = garner_ntt_(ntt0[i].val, ntt1[i].val, ntt2[i].val, mod);
int y0 = ntt0[i].val;
int y1 = (im0 * (ntt1[i] - y0)).val;
int y2 = (im0m1 * (ntt2[i] - y0) - im1 * y1).val;
a[i] = y0 + m0 * y1 + m0m1 * y2;
}
}
return a;
}
template <typename T>
std::vector<T> inv(const std::vector<T> &f)
{
assert(f.size() and f[0] != T(0)); // Requirement: F(0) != 0
std::vector<T> ret({T(1) / f[0]});
while (ret.size() < f.size())
{
std::vector<T> tmp(f.begin(), f.begin() + std::min(f.size(), ret.size() * 2));
tmp = nttconv(tmp, nttconv(ret, ret));
ret.resize(2 * ret.size());
for (int i = ret.size() / 2; i < ret.size(); i++) ret[i] = -tmp[i];
}
ret.resize(f.size());
return ret;
}
template <typename T>
std::vector<T> differential(std::vector<T> f)
{
for (int i = 0; i + 1 < f.size(); i++) f[i] = f[i + 1] * (i + 1);
if (f.size()) f.back() = 0;
return f;
}
template <typename T>
std::vector<T> integral(std::vector<T> f)
{
// f.emplace_back(0);
for (int i = f.size() - 1; i; i--) f[i] = f[i - 1] / i;
f[0] = 0;
return f;
}
template <typename T>
std::vector<T> log(const std::vector<T> &f)
{
assert(f.size() and f[0] == T(1)); // Requirement: F(0) = 1
auto g = nttconv(differential(f), inv(f));
g.resize(f.size());
return integral(g);
}
template <typename T>
std::vector<T> exp(const std::vector<T> &f)
{
assert(f.empty() or f[0] == T(0)); // Requirement: F(0) = 0
std::vector<T> ret({T(1)});
while (ret.size() < f.size())
{
int k = ret.size();
std::vector<T> g(f.begin(), f.begin() + min<int>(k * 2, f.size()));
g.resize(k * 2);
g[0] += 1;
auto rlog = ret;
rlog.resize(k * 2);
rlog = log(rlog);
for (int i = 0; i < min(rlog.size(), g.size()); i++) g[i] -= rlog[i];
ret = nttconv(ret, g);
ret.resize(k * 2);
}
ret.resize(f.size());
return ret;
}
int main()
{
mint j = mint(-1).sqrt();
int N;
cin >> N;
vector<mint> f0(N + 10);
FOR(i, 1, f0.size()) f0[i] = 1LL * (i + 1) * (i + 1);
auto f0a = f0, f0b = f0;
for (auto &x : f0a) x *= j;
for (auto &x : f0b) x *= -j;
f0a = exp(f0a);
f0b = exp(f0b);
mint ret = mint(N).fac();
FOR(K, 1, N + 1)
{
mint r = (f0a[K] - f0b[K]) / (2 * j) + (f0a[K] + f0b[K]) / 2;
cout << r * ret << '\n';
}
}