結果

問題 No.1080 Strange Squared Score Sum
ユーザー hitonanodehitonanode
提出日時 2020-06-13 13:49:47
言語 C++17(clang)
(17.0.6 + boost 1.83.0)
結果
AC  
実行時間 1,729 ms / 5,000 ms
コード長 15,173 bytes
コンパイル時間 3,827 ms
コンパイル使用メモリ 176,000 KB
実行使用メモリ 20,356 KB
最終ジャッジ日時 2024-11-30 18:36:11
合計ジャッジ時間 26,153 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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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
5,248 KB
testcase_02 AC 827 ms
11,916 KB
testcase_03 AC 1,723 ms
20,244 KB
testcase_04 AC 390 ms
7,396 KB
testcase_05 AC 394 ms
7,540 KB
testcase_06 AC 87 ms
5,248 KB
testcase_07 AC 186 ms
5,504 KB
testcase_08 AC 820 ms
11,628 KB
testcase_09 AC 819 ms
11,268 KB
testcase_10 AC 88 ms
5,248 KB
testcase_11 AC 1,720 ms
20,356 KB
testcase_12 AC 817 ms
11,396 KB
testcase_13 AC 1,721 ms
19,768 KB
testcase_14 AC 818 ms
11,832 KB
testcase_15 AC 2 ms
5,248 KB
testcase_16 AC 1,729 ms
19,968 KB
testcase_17 AC 1,723 ms
20,216 KB
testcase_18 AC 1,719 ms
20,220 KB
testcase_19 AC 1,720 ms
20,220 KB
testcase_20 AC 1,721 ms
20,220 KB
testcase_21 AC 1,721 ms
20,348 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::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(std::vector<MODINT> &a, bool is_inverse = false)
{
    int n = a.size();
    if (n == 1) return;
    static const int mod = MODINT::get_mod();
    static const MODINT root = MODINT::get_primitive_root();
    assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);

    static std::vector<MODINT> w{1}, iw{1};
    for (int m = w.size(); m < n / 2; m *= 2)
    {
        MODINT dw = root.power((mod - 1) / (4 * m)), dwinv = 1 / dw;
        w.resize(m * 2), iw.resize(m * 2);
        for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
    }

    if (!is_inverse) {
        for (int m = n; m >>= 1;) {
            for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
                for (int i = s; i < s + m; i++) {
#ifdef __clang__
                    a[i + m] *= w[k];
                    std::tie(a[i], a[i + m]) = std::make_pair(a[i] + a[i + m], a[i] - a[i + m]);
#else
                    MODINT x = a[i], y = a[i + m] * w[k];
                    a[i] = x + y, a[i + m] = x - y;
#endif
                }
            }
        }
    }
    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; i < s + m; i++) {
#ifdef __clang__
                    std::tie(a[i], a[i + m]) = std::make_pair(a[i] + a[i + m], a[i] - a[i + m]);
                    a[i + m] *= iw[k];
#else
                    MODINT x = a[i], y = a[i + m];
                    a[i] = x + y, a[i + m] = (x - y) * iw[k];
#endif
                }
            }
        }
        int n_inv = MODINT(n).inv();
        for (auto &v : a) v *= n_inv;
    }
}
template <int MOD>
std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {
    int sz = a.size();
    assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
    std::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 extgcd_ntt_(long long a, long long b, long long &x, long long &y)
{
    long long 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 modinv_ntt_(long long a, long long m)
{
    long long x, y;
    extgcd_ntt_(a, m, x, y);
    return (m + x % m) % m;
}
long long garner_ntt_(int r0, int r1, int r2, int mod)
{
    using mint2 = ModInt<nttprimes[2]>;
    static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
    static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv();
    static const long long m01_inv_m2 = mint2(m01).inv();

    int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
    auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;
    return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val) % mod;
}
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner)
{
    int sz = 1, n = a.size(), m = b.size();
    while (sz < n + m) sz <<= 1;
    if (sz <= 16) {
        std::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 std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::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 {
        std::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);
        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);
        }
    }
    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';
    }
}
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