#1139825 (C++23) No.3404 形式群法則

• 問題: No.3404 形式群法則
• ユーザー: tko919
• 提出日時: 2025-12-11 00:19:55
• 言語: C++23 (gcc 13.3.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 5 ms / 2,000 ms
• コード長: 18,537 bytes
• コンパイル時間: 4,092 ms
• コンパイル使用メモリ: 315,296 KB
• 実行使用メモリ: 7,848 KB
• 最終ジャッジ日時: 2025-12-11 00:20:01
• 合計ジャッジ時間: 5,227 ms
• ジャッジサーバーID （参考情報）: judge5 / judge4

ファイルパターン	結果
other	AC * 25

ソースコード

#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())

using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template <typename T, typename S = T> S SUM(const vector<T> &a) {
    return accumulate(ALL(a), S(0));
}
template <typename S, typename T = S> S POW(S a, T b) {
    S ret = 1, base = a;
    for (;;) {
        if (b & 1)
            ret *= base;
        b >>= 1;
        if (b == 0)
            break;
        base *= base;
    }
    return ret;
}
template <typename T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
    return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}

template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << "P(" << p.first << ", " << p.second << ")";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
    os << "{";
    for (int i = 0; i < vec.size(); i++) {
        os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
    }
    os << "}";
    return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
    os << "{";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")";
        itr++;
        if (itr != map_var.end())
            os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) {
    os << "{";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr;
        ++itr;
        if (itr != set_var.end())
            os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
    cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
    for (; a[i] != ',' && a[i] != '\0'; i++)
        cerr << a[i];
    cerr << ":" << b << " ";
    _show(i + 1, a, c...);
}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf

uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
    char num[10000][4];
    constexpr Pre() : num() {
        for (int i = 0; i < 10000; i++) {
            int n = i;
            for (int j = 3; j >= 0; j--) {
                num[i][j] = n % 10 | '0';
                n /= 10;
            }
        }
    }
} constexpr pre;

inline void load() {
    memmove(ibuf, ibuf + pil, pir - pil);
    pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
    pil = 0;
    if (pir < SZ)
        ibuf[pir++] = '\n';
}

inline void flush() {
    fwrite(obuf, 1, por, stdout);
    por = 0;
}

void rd(char &c) {
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
}

void rd(string &x) {
    x.clear();
    char c;
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
    do {
        x += c;
        if (pil == pir)
            load();
        c = ibuf[pil++];
    } while (!isspace(c));
}

template <typename T> void rd_real(T &x) {
    string s;
    rd(s);
    x = stod(s);
}

template <typename T> void rd_integer(T &x) {
    if (pil + 100 > pir)
        load();
    char c;
    do
        c = ibuf[pil++];
    while (c < '-');
    bool minus = 0;
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (c == '-') {
            minus = 1, c = ibuf[pil++];
        }
    }
    x = 0;
    while ('0' <= c) {
        x = x * 10 + (c & 15), c = ibuf[pil++];
    }
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (minus)
            x = -x;
    }
}

void rd(int &x) {
    rd_integer(x);
}
void rd(ll &x) {
    rd_integer(x);
}
void rd(i128 &x) {
    rd_integer(x);
}
void rd(uint &x) {
    rd_integer(x);
}
void rd(ull &x) {
    rd_integer(x);
}
void rd(u128 &x) {
    rd_integer(x);
}
void rd(double &x) {
    rd_real(x);
}
void rd(long double &x) {
    rd_real(x);
}

template <class T, class U> void rd(pair<T, U> &p) {
    return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
        auto &x = std::get<N>(t);
        rd(x);
        rd_tuple<N + 1>(t);
    }
}
template <class... T> void rd(tuple<T...> &tpl) {
    rd_tuple(tpl);
}

template <size_t N = 0, typename T> void rd(array<T, N> &x) {
    for (auto &d : x)
        rd(d);
}
template <class T> void rd(vector<T> &x) {
    for (auto &d : x)
        rd(d);
}

void read() {}
template <class H, class... T> void read(H &h, T &...t) {
    rd(h), read(t...);
}

void wt(const char c) {
    if (por == SZ)
        flush();
    obuf[por++] = c;
}
void wt(const string s) {
    for (char c : s)
        wt(c);
}
void wt(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++)
        wt(s[i]);
}

template <typename T> void wt_integer(T x) {
    if (por > SZ - 100)
        flush();
    if (x < 0) {
        obuf[por++] = '-', x = -x;
    }
    int outi;
    for (outi = 96; x >= 10000; outi -= 4) {
        memcpy(out + outi, pre.num[x % 10000], 4);
        x /= 10000;
    }
    if (x >= 1000) {
        memcpy(obuf + por, pre.num[x], 4);
        por += 4;
    } else if (x >= 100) {
        memcpy(obuf + por, pre.num[x] + 1, 3);
        por += 3;
    } else if (x >= 10) {
        int q = (x * 103) >> 10;
        obuf[por] = q | '0';
        obuf[por + 1] = (x - q * 10) | '0';
        por += 2;
    } else
        obuf[por++] = x | '0';
    memcpy(obuf + por, out + outi + 4, 96 - outi);
    por += 96 - outi;
}

template <typename T> void wt_real(T x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << double(x);
    string s = oss.str();
    wt(s);
}

void wt(int x) {
    wt_integer(x);
}
void wt(ll x) {
    wt_integer(x);
}
void wt(i128 x) {
    wt_integer(x);
}
void wt(uint x) {
    wt_integer(x);
}
void wt(ull x) {
    wt_integer(x);
}
void wt(u128 x) {
    wt_integer(x);
}
void wt(double x) {
    wt_real(x);
}
void wt(long double x) {
    wt_real(x);
}

template <class T, class U> void wt(const pair<T, U> val) {
    wt(val.first);
    wt(' ');
    wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
        if constexpr (N > 0) {
            wt(' ');
        }
        const auto x = std::get<N>(t);
        wt(x);
        wt_tuple<N + 1>(t);
    }
}
template <class... T> void wt(tuple<T...> tpl) {
    wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}
template <class T> void wt(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}

void print() {
    wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
    wt(head);
    if (sizeof...(Tail))
        wt(' ');
    print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
    flush();
}
} // namespace fastio

using fastio::flush;
using fastio::print;
using fastio::read;

inline void first(bool i = true) {
    print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
    print(i ? "Alice" : "Bob");
}
inline void Takahashi(bool i = true) {
    print(i ? "Takahashi" : "Aoki");
}
inline void yes(bool i = true) {
    print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
    print(i ? "Yes" : "No");
}
inline void No() {
    print("No");
}
inline void YES(bool i = true) {
    print(i ? "YES" : "NO");
}
inline void NO() {
    print("NO");
}
inline void Yay(bool i = true) {
    print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
    print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
    print(i ? "POSSIBLE" : "IMPOSSIBLE");
}

/**
 * @brief Fast IO
 */
#line 2 "library/Utility/random.hpp"

namespace Random {
mt19937_64 randgen(chrono::steady_clock::now().time_since_epoch().count());
using u64 = unsigned long long;
u64 get() {
    return randgen();
}
template <typename T> T get(T L) { // [0,L]
    return get() % (L + 1);
}
template <typename T> T get(T L, T R) { // [L,R]
    return get(R - L) + L;
}
double uniform() {
    return double(get(1000000000)) / 1000000000;
}
string str(int n) {
    string ret;
    rep(i, 0, n) ret += get('a', 'z');
    return ret;
}
template <typename Iter> void shuffle(Iter first, Iter last) {
    if (first == last)
        return;
    int len = 1;
    for (auto it = first + 1; it != last; it++) {
        len++;
        int j = get(0, len - 1);
        if (j != len - 1)
            iter_swap(it, first + j);
    }
}
template <typename T> vector<T> select(int n, T L, T R) { // [L,R]
    if (n * 2 >= R - L + 1) {
        vector<T> ret(R - L + 1);
        iota(ALL(ret), L);
        shuffle(ALL(ret));
        ret.resize(n);
        return ret;
    } else {
        unordered_set<T> used;
        vector<T> ret;
        while (SZ(used) < n) {
            T x = get(L, R);
            if (!used.count(x)) {
                used.insert(x);
                ret.push_back(x);
            }
        }
        return ret;
    }
}

void relabel(int n, vector<pair<int, int>> &es) {
    shuffle(ALL(es));
    vector<int> ord(n);
    iota(ALL(ord), 0);
    shuffle(ALL(ord));
    for (auto &[u, v] : es)
        u = ord[u], v = ord[v];
}
template <bool directed, bool multi, bool self>
vector<pair<int, int>> genGraph(int n, int m) {
    vector<pair<int, int>> cand, es;
    rep(u, 0, n) rep(v, 0, n) {
        if (!self and u == v)
            continue;
        if (!directed and u > v)
            continue;
        cand.push_back({u, v});
    }
    if (m == -1)
        m = get(SZ(cand));
    // chmin(m, SZ(cand));
    vector<int> ord;
    if (multi)
        rep(_, 0, m) ord.push_back(get(SZ(cand) - 1));
    else {
        ord = select(m, 0, SZ(cand) - 1);
    }
    for (auto &i : ord)
        es.push_back(cand[i]);
    relabel(n, es);
    return es;
}
vector<pair<int, int>> genTree(int n) {
    vector<pair<int, int>> es;
    rep(i, 1, n) es.push_back({get(i - 1), i});
    relabel(n, es);
    return es;
}
}; // namespace Random

/**
 * @brief Random
 */
#line 4 "sol.cpp"

#line 2 "library/Math/fastdiv.hpp"

struct FastDiv {
    using u64 = uint64_t;
    using u128 = __uint128_t;
    constexpr FastDiv() : m(), s(), x() {}
    constexpr FastDiv(int _m)
        : m(_m), s(__lg(m - 1)), x(((u128(1) << (s + 64)) + m - 1) / m) {}
    constexpr int get() {
        return m;
    }
    constexpr friend u64 operator/(u64 n, const FastDiv &d) {
        return (u128(n) * d.x >> d.s) >> 64;
    }
    constexpr friend int operator%(u64 n, const FastDiv &d) {
        return n - n / d * d.m;
    }
    constexpr pair<u64, int> divmod(u64 n) const {
        u64 q = n / (*this);
        return {q, n - q * m};
    }
    int m, s;
    u64 x;
};

struct FastDiv64 {
    using u64 = uint64_t;
    using u128 = __uint128_t;
    u128 mod, mh, ml;
    explicit FastDiv64(u64 mod = 1) : mod(mod) {
        u128 m = u128(-1) / mod;
        if (m * mod + mod == u128(0))
            ++m;
        mh = m >> 64;
        ml = m & u64(-1);
    }
    u64 umod() const {
        return mod;
    }
    u64 modulo(u128 x) {
        u128 z = (x & u64(-1)) * ml;
        z = (x & u64(-1)) * mh + (x >> 64) * ml + (z >> 64);
        z = (x >> 64) * mh + (z >> 64);
        x -= z * mod;
        return x < mod ? x : x - mod;
    }
    u64 mul(u64 a, u64 b) {
        return modulo(u128(a) * b);
    }
};

/**
 * @brief Fast Division
 */
#line 2 "library/Math/comb.hpp"

template <typename T> T Inv(ll n) {
    static int md;
    static vector<T> buf({0, 1});
    if (md != T::get_mod()) {
        md = T::get_mod();
        buf = vector<T>({0, 1});
    }
    assert(n > 0);
    n %= md;
    while (SZ(buf) <= n) {
        int k = SZ(buf), q = (md + k - 1) / k;
        buf.push_back(buf[k * q - md] * q);
    }
    return buf[n];
}

template <typename T> T Fact(ll n, bool inv = 0) {
    static int md;
    static vector<T> buf({1, 1}), ibuf({1, 1});
    if (md != T::get_mod()) {
        md = T::get_mod();
        buf = ibuf = vector<T>({1, 1});
    }
    assert(n >= 0 and n < md);
    while (SZ(buf) <= n) {
        buf.push_back(buf.back() * SZ(buf));
        ibuf.push_back(ibuf.back() * Inv<T>(SZ(ibuf)));
    }
    return inv ? ibuf[n] : buf[n];
}

template <typename T> T nPr(int n, int r, bool inv = 0) {
    if (n < 0 || n < r || r < 0)
        return 0;
    return Fact<T>(n, inv) * Fact<T>(n - r, inv ^ 1);
}
template <typename T> T nCr(int n, int r, bool inv = 0) {
    if (n < 0 || n < r || r < 0)
        return 0;
    return Fact<T>(n, inv) * Fact<T>(r, inv ^ 1) * Fact<T>(n - r, inv ^ 1);
}
// sum = n, r tuples
template <typename T> T nHr(int n, int r, bool inv = 0) {
    return nCr<T>(n + r - 1, r - 1, inv);
}
// [x^n]C(x)^k
template <typename T> T Catalan(int n, int k) {
    if (k == 0)
        return (n == 0 ? 1 : 0);
    return T(k) * Inv<T>(n * 2 + k) * nCr<T>(n * 2 + k, n);
}
// sum = n, a nonzero tuples and b tuples
template <typename T> T choose(int n, int a, int b) {
    if (n == 0)
        return !a;
    return nCr<T>(n + b - 1, a + b - 1);
}

/**
 * @brief Combination
 */
#line 4 "library/Math/dynamic.hpp"

struct Fp {
    using u64 = uint64_t;
    uint v;
    static uint get_mod() {
        return _getmod();
    }
    static void set_mod(uint _m) {
        bar = FastDiv(_m);
    }
    Fp inv() const {
        int tmp, a = v, b = get_mod(), x = 1, y = 0;
        while (b) {
            tmp = a / b, a -= tmp * b;
            swap(a, b);
            x -= tmp * y;
            swap(x, y);
        }
        if (x < 0) {
            x += get_mod();
        }
        return x;
    }
    Fp() : v(0) {}
    Fp(ll x) {
        v = (x % get_mod() + get_mod()) % get_mod();
    }
    Fp operator-() const {
        return Fp() - *this;
    }
    Fp pow(ll t) {
        assert(t >= 0);
        Fp res = 1, b = *this;
        while (t) {
            if (t & 1)
                res *= b;
            b *= b;
            t >>= 1;
        }
        return res;
    }
    Fp &operator+=(const Fp &x) {
        v += x.v;
        if (v >= get_mod())
            v -= get_mod();
        return *this;
    }
    Fp &operator-=(const Fp &x) {
        v += get_mod() - x.v;
        if (v >= get_mod())
            v -= get_mod();
        return *this;
    }
    Fp &operator*=(const Fp &x) {
        v = (u64(v) * x.v) % bar;
        return *this;
    }
    Fp &operator/=(const Fp &x) {
        (*this) *= x.inv();
        return *this;
    }
    Fp operator+(const Fp &x) const {
        return Fp(*this) += x;
    }
    Fp operator-(const Fp &x) const {
        return Fp(*this) -= x;
    }
    Fp operator*(const Fp &x) const {
        return Fp(*this) *= x;
    }
    Fp operator/(const Fp &x) const {
        return Fp(*this) /= x;
    }
    bool operator==(const Fp &x) const {
        return v == x.v;
    }
    bool operator!=(const Fp &x) const {
        return v != x.v;
    }
    friend istream &operator>>(istream &is, Fp &x) {
        return is >> x.v;
    }
    friend ostream &operator<<(ostream &os, const Fp &x) {
        return os << x.v;
    }

  private:
    static FastDiv bar;
    static uint _getmod() {
        return bar.get();
    }
};
FastDiv Fp::bar(998244353);

void rd(Fp &x) {
    fastio::rd(x.v);
}
void wt(Fp x) {
    fastio::wt(x.v);
}

/**
 * @brief Dynamic Modint
 */
#line 6 "sol.cpp"

int main() {
    int n, P;
    ll m;
    read(n, m, P);
    Fp::set_mod(P);
    vector<Fp> a(n + 1);
    rep(i, 1, n + 1) {
        ll x;
        read(x);
        a[i] = Fp(x);
    }

    // arctan
    vector<Fp> b(n + 1);
    {
        vector<Fp> num(n + 1), den(n + 1);
        rep(i, 0, n) num[i] = a[i + 1] * (i + 1);
        den[0] = 1;
        rep(i, 0, n + 1) {
            rep(j, 0, n + 1) {
                if (i + j > n)
                    break;
                den[i + j] += a[i] * a[j];
            }
        }
        vector<Fp> db(n + 1);
        rep(i, 0, n + 1) {
            db[i] = num[i];
            rep(j, 0, i) {
                db[i] -= db[j] * den[i - j];
            }
        }
        rep(i, 0, n) b[i + 1] = db[i] * Inv<Fp>(i + 1);
    }

    // *m
    rep(i, 0, n + 1) b[i] *= m;
    show(b);

    // tan
    vector<Fp> ret(n + 1);
    {
        vector<Fp> db(n);
        rep(i, 0, n) db[i] = b[i + 1] * (i + 1);
        vector<Fp> ret2(n + 1);
        ret2[0] = 1;
        rep(k, 1, n + 1) {
            rep(i, 0, k) {
                ret[k] += db[i] * ret2[k - 1 - i];
            }
            ret[k] *= Inv<Fp>(k);

            if (k * 2 <= n)
                ret2[k * 2] += ret[k] * ret[k];
            rep(i, 0, k) if (k + i <= n) ret2[k + i] += ret[k] * ret[i] * 2;
        }
    }
    ret.erase(ret.begin());
    print(ret);
    return 0;
}