#945201 (C++17) No.2613 Sum of Combination

提出ソース
結果

問題	No.2613 Sum of Combination
コンテスト
ユーザー	minato
提出日時	2024-01-19 22:56:38
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	205 ms / 4,500 ms
コード長	30,731 bytes
コンパイル時間	2,406 ms
コンパイル使用メモリ	161,236 KB
最終ジャッジ日時	2025-02-18 21:29:19
ジャッジサーバーID （参考情報）	judge2 / judge3
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 3
other	AC * 49
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ソースコード

raw source code
#line 1 "library-cpp/other/template.hpp"
// clang-format off
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using maxheap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vector<T>>;
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP0(n) for (auto minato = decay_t<decltype(n)>{}; minato < (n); ++minato)
#define REP1(i, n) for (auto i = decay_t<decltype(n)>{}; (i) < (n); (i)++)
#define REP2(i, l, r) for (auto i = (l); (i) < (r); (i)++)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, name, ...) name
#define RREP1(i, n) for (auto i = (n) - 1; (i) >= decay_t<decltype(n)>{}; (i)--)
#define RREP2(i, l, r) for (auto i = (r) - 1; (i) >= (l); (i)--)
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP2, RREP1)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
template <class Container> int SZ(const Container& v) { return int(v.size()); }
template <class T> void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template <class T> T MAX(const vector<T>& v) { return *max_element(v.begin(), v.end()); }
template <class T> T MIN(const vector<T>& v) { return *min_element(v.begin(), v.end()); }
template <class T> T SUM(const vector<T>& v) { return accumulate(v.begin(), v.end(), T(0)); }
template <class T> T ABS(T x) { return max(x, -x); }
long long floor_div(long long n, long long d) { return n / d - ((n ^ d) < 0 && n % d); }
template <class T1, class T2> bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }
template <class T1, class T2> bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }
int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
int popcount(ull x) { return __builtin_popcountll(x); }
int kthbit(ull x, int k) { return (x >> k) & 1; }
constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; }
template <typename S> void rearrange(const vector<S>& id) { (void)id; }
template <typename S, typename T> void rearrange_exec(const vector<S>& id, vector<T>& v) { vector<T> w(v.size()); for (size_t i = 0; i < id.size(); i++) { w[i] = v[id[i]]; } v.swap(w); }
template <typename S, typename Head, typename... Tail> void rearrange(const vector<S>& id, Head& a, Tail& ...tail) { rearrange_exec(id, a); rearrange(id, tail...); }
istream& operator>>(istream& is, __int128_t& x) {
    x = 0;
    string s;
    is >> s;
    int n = int(s.size()), it = 0;
    if (s[0] == '-') it++;
    for (; it < n; it++) x = (x * 10 + s[it] - '0');
    if (s[0] == '-') x = -x;
    return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
    if (x == 0) return os << 0;
    if (x < 0) os << '-', x = -x;
    deque<int> deq;
    while (x) deq.emplace_front(x % 10), x /= 10;
    for (int e : deq) os << e;
    return os;
}
template <class T> vector<T> &operator++(vector<T>& v) { for (auto& e : v) { e++; } return v;} 
template <class T> vector<T> operator++(vector<T>& v, int) { auto res = v; for (auto& e : v) { e++; } return res; }
template <class T> vector<T> &operator--(vector<T>& v) { for (auto& e : v) { e--; } return v; }
template <class T> vector<T> operator--(vector<T>& v, int) { auto res = v; for (auto& e : v) { e--; } return res; }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x) { return pair<T1, T2>(-x.first, -x.second); }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first - y.first, x.second - y.second); }
template <class T1, class T2> pair<T1, T2> operator+(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first + y.first, x.second + y.second); }
template <class T1, class T2> pair<T1, T2> operator+=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l + r; }
template <class T1, class T2> pair<T1, T2> operator-=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l - r; }
constexpr char ln = '\n';
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
void YES(bool t = true) { cout << YESNO[t] << "\n"; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = true) { cout << YesNo[t] << "\n"; }
void No(bool t = 1) { Yes(!t); }
template <class T> void drop(T x) { cout << x << "\n"; exit(0); }
#define INT(...)     \
    int __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    IN(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    IN(__VA_ARGS__)
#define CHR(...)      \
    char __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LDB(...)             \
    long double __VA_ARGS__; \
    IN(__VA_ARGS__)
#define VEC(type, name, size) \
    vector<type> name(size);  \
    IN(name)
#define VEC2(type, name1, name2, size)     \
    vector<type> name1(size), name2(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size)           \
    vector<type> name1(size), name2(size), name3(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size)                 \
    vector<type> name1(size), name2(size), name3(size), name4(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, N, M)                       \
    vector<vector<type>> name(N, vector<type>(M)); \
    IN(name)
template <class T> void scan(T& a) { cin >> a; }
template <class T> void scan(vector<T>& a) { for (auto& i : a) scan(i); }
void IN() {}
template <class Head, class... Tail> void IN(Head& head, Tail&... tail) { scan(head); IN(tail...); }
std::vector<std::vector<int>> read_graph(int N, int M) {
    std::vector<std::vector<int>> g(N);
    for (int i = 0; i < M; i++) {
        int a, b;
        cin >> a >> b;
        a--, b--;
        g[a].emplace_back(b);
        g[b].emplace_back(a);
    }
    return g;
}
std::vector<std::vector<int>> read_tree(int N) { return read_graph(N, N - 1); }
void print() { cout << "\n"; }
template <class T> void print(const vector<T>& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << *it; } print(); }
template <class T, class... Args> void print(const T& x, const Args& ... args) { cout << x; if (sizeof...(Args)) cout << " "; print(args...); }
#ifdef MINATO_LOCAL
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p);
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t);
template <class T> ostream& operator<<(ostream& os, vector<T> v);
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a);
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]);
template <class Key> ostream& operator<<(ostream& os, set<Key> s);
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp);
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s);
template <class T> ostream& operator<<(ostream& os, queue<T> q);
template <class T> ostream& operator<<(ostream& os, deque<T> q);
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q);
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q);
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <size_t N, class TUPLE> void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; }
template <size_t N, class TUPLE, class T, class ...Args> void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get<N>(t); debug_tuple<N + 1, TUPLE, Args...>(os, t); }
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t) { os << "("; debug_tuple<0, tuple<Args...>, Args...>(os, t); return os << ")"; }
string debug_delim(int& i) { return i++ == 0 ? "" : ", "; }
#define debug_embrace(x) { int i = 0; os << "{";  { x } return os << "}"; }
template <class T> ostream& operator<<(ostream& os, vector<T> v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class Key> ostream& operator<<(ostream& os, set<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) }
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class T> ostream& operator<<(ostream& os, queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) }
template <class T> ostream& operator<<(ostream& os, deque<T> q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
void debug_out() { cerr << endl; }
template <class T, class... Args> void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); }
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// clang-format on
#line 2 "library-cpp/mod/ModInt.hpp"

#line 2 "library-cpp/other/type_traits.hpp"

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal
#line 4 "library-cpp/mod/ModInt.hpp"

#line 6 "library-cpp/mod/ModInt.hpp"

template <int m> struct ModInt {
  public:
    static constexpr int mod() {
        return m;
    }
    static ModInt raw(int v) {
        ModInt x;
        x._v = v;
        return x;
    }

    ModInt() : _v(0) {
    }

    template <class T, internal::is_signed_int_t<T>* = nullptr> ModInt(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr> ModInt(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const {
        return _v;
    }

    ModInt& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    ModInt& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    ModInt operator++(int) {
        ModInt result = *this;
        ++*this;
        return result;
    }
    ModInt operator--(int) {
        ModInt result = *this;
        --*this;
        return result;
    }

    ModInt& operator+=(const ModInt& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    ModInt& operator-=(const ModInt& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    ModInt& operator*=(const ModInt& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    ModInt& operator^=(long long n) {
        ModInt x = *this;
        *this = 1;
        if (n < 0) x = x.inv(), n = -n;
        while (n) {
            if (n & 1) *this *= x;
            x *= x;
            n >>= 1;
        }
        return *this;
    }
    ModInt& operator/=(const ModInt& rhs) {
        return *this = *this * rhs.inv();
    }

    ModInt operator+() const {
        return *this;
    }
    ModInt operator-() const {
        return ModInt() - *this;
    }
    explicit operator bool() const {
        return _v != 0;
    }

    ModInt pow(long long n) const {
        ModInt r = *this;
        r ^= n;
        return r;
    }
    ModInt inv() const {
        int a = _v, b = umod(), y = 1, z = 0, t;
        for (;;) {
            t = a / b;
            a -= t * b;
            if (a == 0) {
                assert(b == 1 || b == -1);
                return ModInt(b * z);
            }
            y -= t * z;
            t = b / a;
            b -= t * a;
            if (b == 0) {
                assert(a == 1 || a == -1);
                return ModInt(a * y);
            }
            z -= t * y;
        }
    }

    friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) += rhs;
    }
    friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) -= rhs;
    }
    friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) *= rhs;
    }
    friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) /= rhs;
    }
    friend ModInt operator^(const ModInt& lhs, long long rhs) {
        return ModInt(lhs) ^= rhs;
    }
    friend bool operator==(const ModInt& lhs, const ModInt& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const ModInt& lhs, const ModInt& rhs) {
        return lhs._v != rhs._v;
    }
    friend ModInt operator+(long long lhs, const ModInt& rhs) {
        return (ModInt(lhs) += rhs);
    }
    friend ModInt operator-(long long lhs, const ModInt& rhs) {
        return (ModInt(lhs) -= rhs);
    }
    friend ModInt operator*(long long lhs, const ModInt& rhs) {
        return (ModInt(lhs) *= rhs);
    }
    friend ostream& operator<<(ostream& os, const ModInt& M) {
        return os << M._v;
    }
    friend istream& operator>>(istream& is, ModInt& M) {
        long long x;
        is >> x;
        M = x;
        return is;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() {
        return m;
    }
};
#line 2 "library-cpp/mod/ModCombination.hpp"

#line 5 "library-cpp/mod/ModCombination.hpp"

template <class M> struct ModCombination {
  public:
    ModCombination() {
    }
    ModCombination(int n) : n_(n), fac_(n + 1), facinv_(n + 1) {
        assert(1 <= n);
        fac_[0] = 1;
        for (int i = 1; i <= n; i++) fac_[i] = fac_[i - 1] * i;
        facinv_[n] = M(1) / fac_[n];
        for (int i = n; i >= 1; i--) facinv_[i - 1] = facinv_[i] * i;
    }

    M fac(int k) const {
        assert(0 <= k and k <= n_);
        return fac_[k];
    }
    M facinv(int k) const {
        assert(0 <= k and k <= n_);
        return facinv_[k];
    }
    M inv(int k) const {
        assert(1 <= k and k <= n_);
        return facinv_[k] * fac_[k - 1];
    }

    M P(int n, int k) const {
        if (k < 0 or k > n) return M(0);
        assert(n <= n_);
        return fac_[n] * facinv_[n - k];
    }
    M C(int n, int k) const {
        if (k < 0 or k > n) return M(0);
        assert(n <= n_);
        return fac_[n] * facinv_[n - k] * facinv_[k];
    }

    /**
     * @note H(n, k) = (n 個 のボールを k 個の箱に分ける方法の数)
     * @note H(n, k) = C(n + k - 1, n)
     */
    M H(int n, int k) const {
        if (n == 0 and k == 0) return M(1);
        return C(n + k - 1, n);
    }
    M catalan(int n) const {
        if (n == 0) return M(1);
        return C(2 * n, n) - C(2 * n, n - 1);
    }

  private:
    int n_;
    std::vector<M> fac_, facinv_;
};
#line 2 "library-cpp/mod/convolution998244353.hpp"

#line 5 "library-cpp/mod/convolution998244353.hpp"

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

template <class mint> struct fft_info {
    static constexpr int rank2 = 23;
    static constexpr int g = 3;
    std::array<mint, rank2 + 1> root;   // root[i]^(2^i) == 1
    std::array<mint, rank2 + 1> iroot;  // root[i] * iroot[i] == 1

    std::array<mint, rank2 - 1> rate2;
    std::array<mint, rank2 - 1> irate2;

    std::array<mint, rank2 - 2> rate3;
    std::array<mint, rank2 - 2> irate3;

    fft_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }

        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 2; i++) {
                rate2[i] = root[i + 2] * prod;
                irate2[i] = iroot[i + 2] * iprod;
                prod *= iroot[i + 2];
                iprod *= root[i + 2];
            }
        }
        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 3; i++) {
                rate3[i] = root[i + 3] * prod;
                irate3[i] = iroot[i + 3] * iprod;
                prod *= iroot[i + 3];
                iprod *= root[i + 3];
            }
        }
    }
};

template <class mint> void butterfly(std::vector<mint>& a) {
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static const fft_info<mint> info;

    int len = 0;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len < h) {
        if (h - len == 1) {
            int p = 1 << (h - len - 1);
            mint rot = 1;
            for (int s = 0; s < (1 << len); s++) {
                int offset = s << (h - len);
                for (int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p] * rot;
                    a[i + offset] = l + r;
                    a[i + offset + p] = l - r;
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate2[bsf(~(unsigned int)(s))];
            }
            len++;
        } else {
            // 4-base
            int p = 1 << (h - len - 2);
            mint rot = 1, imag = info.root[2];
            for (int s = 0; s < (1 << len); s++) {
                mint rot2 = rot * rot;
                mint rot3 = rot2 * rot;
                int offset = s << (h - len);
                for (int i = 0; i < p; i++) {
                    auto mod2 = 1ULL * mint::mod() * mint::mod();
                    auto a0 = 1ULL * a[i + offset].val();
                    auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
                    auto a1na3imag =
                        1ULL * mint(a1 + mod2 - a3).val() * imag.val();
                    auto na2 = mod2 - a2;
                    a[i + offset] = a0 + a2 + a1 + a3;
                    a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                    a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                    a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate3[bsf(~(unsigned int)(s))];
            }
            len += 2;
        }
    }
}

template <class mint> void butterfly_inv(std::vector<mint>& a) {
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static const fft_info<mint> info;

    int len = h;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len) {
        if (len == 1) {
            int p = 1 << (h - len);
            mint irot = 1;
            for (int s = 0; s < (1 << (len - 1)); s++) {
                int offset = s << (h - len + 1);
                for (int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p];
                    a[i + offset] = l + r;
                    a[i + offset + p] =
                        (unsigned long long)(mint::mod() + l.val() - r.val()) *
                        irot.val();
                    ;
                }
                if (s + 1 != (1 << (len - 1)))
                    irot *= info.irate2[bsf(~(unsigned int)(s))];
            }
            len--;
        } else {
            // 4-base
            int p = 1 << (h - len);
            mint irot = 1, iimag = info.iroot[2];
            for (int s = 0; s < (1 << (len - 2)); s++) {
                mint irot2 = irot * irot;
                mint irot3 = irot2 * irot;
                int offset = s << (h - len + 2);
                for (int i = 0; i < p; i++) {
                    auto a0 = 1ULL * a[i + offset + 0 * p].val();
                    auto a1 = 1ULL * a[i + offset + 1 * p].val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val();

                    auto a2na3iimag =
                        1ULL *
                        mint((mint::mod() + a2 - a3) * iimag.val()).val();

                    a[i + offset] = a0 + a1 + a2 + a3;
                    a[i + offset + 1 * p] =
                        (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
                    a[i + offset + 2 * p] =
                        (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
                        irot2.val();
                    a[i + offset + 3 * p] =
                        (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
                        irot3.val();
                }
                if (s + 1 != (1 << (len - 2)))
                    irot *= info.irate3[bsf(~(unsigned int)(s))];
            }
            len -= 2;
        }
    }
}

template <class mint>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}
}  // namespace internal

template <class mint>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
                                    const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    std::vector<mint> ans(n + m - 1);
    if (n < m) {
        for (int j = 0; j < m; j++) {
            for (int i = 0; i < n; i++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    } else {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    }
    return ans;
}

template <class mint>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}

template <class mint>
std::vector<mint> convolution(const std::vector<mint>& a,
                              const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}
#line 5 "G.cpp"
#include <atcoder/math>
using mint = ModInt<998244353>;
// using mint = ModInt<1000000007>;
void solve() {
    LL(N, P);
    vec<ll> fac(P, 1), facinv(P);
    rep(i, 1, P) fac[i] = fac[i - 1] * i % P;
    {
        ll k = P - 2;
        ll x = 1;
        while (k) {
            if (k & 1) x = x * fac[P - 1] % P;
            x = x * x % P;
            k >>= 1;
        }
        facinv[P - 1] = x;
    }
    rrep(i, 1, P) {
        facinv[i - 1] = facinv[i] * i % P;
    }
    auto nCk = [&](ll n, ll k) {
        if (n < k) return 0LL;
        return fac[n] * facinv[k] % P * facinv[n - k] % P;
    };
    vec<ll> A;
    {
        ll x = N;
        while (x) {
            A.push_back(x % P);
            x /= P;
        }
        reverse(ALL(A));
    }

    auto g = atcoder::internal::primitive_root_constexpr(P);
    // G[k] = g^k
    // Ginv[g^k] = k
    vec<ll> G(P - 1), Ginv(P, -1);
    G[0] = 1;
    rep(i, 1, P - 1) G[i] = G[i - 1] * g % P;
    rep(i, P - 1) Ginv[G[i]] = i;
    int S = SZ(A);
    vec<mint> dp(P - 1);
    dp[0] = 1;
    rep(i, S) {
        int a = A[i];
        vec<mint> ndp(P - 1);
        vec<mint> Y(P - 1);
        rep(b, a + 1) {
            int c = nCk(a, b);
            Y[Ginv[c]]++;
        }
        auto Z = convolution(dp, Y);
        rep(j, SZ(Z)) {
            int k = j;
            if (k >= P - 1) k -= P - 1;
            ndp[k] += Z[j];
        }
        swap(dp, ndp);
        // {
        //     vec<mint> Y(P);
        //     rep(j, a) {
        //         int c = nCk(a, j);
        //         Y[Ginv[c]]++;
        //     }
        //     auto Z = convolution(dp[0], Y);
        //     rep(j, SZ(Z)) {
        //         int k = j;
        //         if (k >= P) k -= P;
        //         ndp[1][j] += Z[j];
        //     }
        // }
        // {
        //     int b = Ginv[a];
        //     rep(j, P) {
        //         int k = j + b;
        //         if (k >= P) k -= P;
        //         ndp[0][k] += dp[0][j];
        //     }
        // }
        // {
        //     vec<mint> Y(P, 1);
        //     auto Z = convolution(dp[1], Y);
        //     rep(j, SZ(Z)) {
        //         int k = j;
        //         if (k >= P) k -= P;
        //         ndp[1][j] += Z[j];
        //     }
        // }
        // swap(dp, ndp);
    }
    mint ans = 0;
    debug(dp);
    rep(i, P - 1) {
        mint x = dp[i];
        ans += x * G[i];
    }
    print(ans);
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(7);

    int T = 1;
    // cin >> T;
    for (int test_case = 1; test_case <= T; test_case++) {
        // debug(test_case);
        solve();
    }
}
yukicoder

結果

ソースコード
