結果
問題 | No.1824 門\松\列 |
ユーザー | maspy |
提出日時 | 2022-09-11 04:04:06 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 105 ms / 2,000 ms |
コード長 | 41,192 bytes |
コンパイル時間 | 7,626 ms |
コンパイル使用メモリ | 348,836 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-05-05 13:48:46 |
合計ジャッジ時間 | 8,319 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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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 | 3 ms
5,248 KB |
testcase_01 | AC | 3 ms
5,376 KB |
testcase_02 | AC | 9 ms
5,376 KB |
testcase_03 | AC | 105 ms
5,376 KB |
testcase_04 | AC | 12 ms
5,376 KB |
コンパイルメッセージ
main.cpp: In function 'void solve()': main.cpp:34:23: warning: narrowing conversion of 'a.modint<1000000007>::val' from 'unsigned int' to 'int' [-Wnarrowing] 34 | #define vvv(type, name, h, w, ...) \ | ~~^~~ main.cpp:34:23: warning: narrowing conversion of 'a.modint<1000000007>::val' from 'unsigned int' to 'int' [-Wnarrowing] main.cpp:34:30: warning: narrowing conversion of 'b.modint<998244353>::val' from 'unsigned int' to 'int' [-Wnarrowing] 34 | #define vvv(type, name, h, w, ...) \ | ~~^~~ main.cpp:34:30: warning: narrowing conversion of 'b.modint<998244353>::val' from 'unsigned int' to 'int' [-Wnarrowing]
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp" #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include <bits/stdc++.h> using namespace std; using ll = long long; using pi = pair<ll, ll>; using vi = vector<ll>; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; template <class T> using vc = vector<T>; template <class T> using vvc = vector<vc<T>>; template <class T> using vvvc = vector<vvc<T>>; template <class T> using vvvvc = vector<vvvc<T>>; template <class T> using vvvvvc = vector<vvvvc<T>>; template <class T> using pq = priority_queue<T>; template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; #define vec(type, name, ...) vector<type> name(__VA_ARGS__) #define vv(type, name, h, ...) \ vector<vector<type>> name(h, vector<type>(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector<vector<vector<type>>> name( \ h, vector<vector<type>>(w, vector<type>(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector<vector<vector<vector<type>>>> name( \ a, vector<vector<vector<type>>>( \ b, vector<vector<type>>(c, vector<type>(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c)) #define overload4(a, b, c, d, e, ...) e #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) \ overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s)) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll ll SUM(vector<int> &A) { ll sum = 0; for (auto &&a: A) sum += a; return sum; } template <typename T> T SUM(vector<T> &A) { T sum = T(0); for (auto &&a: A) sum += a; return sum; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()) int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template <typename T> T pick(deque<T> &que) { assert(que.size()); T a = que.front(); que.pop_front(); return a; } template <typename T> T pick(pq<T> &que) { assert(que.size()); T a = que.top(); que.pop(); return a; } template <typename T> T pick(pqg<T> &que) { assert(que.size()); T a = que.top(); que.pop(); return a; } template <typename T> T pick(vc<T> &que) { assert(que.size()); T a = que.back(); que.pop_back(); return a; } template <typename T, typename U> T ceil(T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); } template <typename T, typename U> T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); } template <typename T, typename U> pair<T, T> divmod(T x, U y) { T q = floor(x, y); return {q, x - q * y}; } ll binary_search(function<bool(ll)> check, ll ok, ll ng) { assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; if (check(x)) ok = x; else ng = x; } return ok; } template <typename F> double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; if (check(x)) { ok = x; } else { ng = x; } } return (ok + ng) / 2; } template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } vi s_to_vi(const string &S, char first_char) { vi A(S.size()); FOR(i, S.size()) { A[i] = S[i] - first_char; } return A; } template <typename T> vector<T> cumsum(vector<T> &A, int off = 1) { int N = A.size(); vector<T> B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } template <typename CNT, typename T> vc<CNT> bincount(const vc<T> &A, int size) { vc<CNT> C(size); for (auto &&x: A) { ++C[x]; } return C; } template <typename T> vector<int> argsort(const vector<T> &A) { // stable vector<int> ids(A.size()); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); }); return ids; } // A[I[0]], A[I[1]], ... template <typename T> vc<T> rearrange(const vc<T> &A, const vc<int> &I) { int n = len(I); vc<T> B(n); FOR(i, n) B[i] = A[I[i]]; return B; } #line 1 "/home/maspy/compro/library/other/io.hpp" // based on yosupo's fastio #include <unistd.h> namespace detail { template <typename T, decltype(&T::is_modint) = &T::is_modint> std::true_type check_value(int); template <typename T> std::false_type check_value(long); } // namespace detail template <typename T> struct is_modint : decltype(detail::check_value<T>(0)) {}; template <typename T> using is_modint_t = enable_if_t<is_modint<T>::value>; template <typename T> using is_not_modint_t = enable_if_t<!is_modint<T>::value>; struct Scanner { FILE *fp; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += fread(line + ed, 1, (1 << 15) - ed, fp); line[ed] = '\0'; } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) { bool sep = false; for (size_t i = st; i < ed; i++) { if (isspace(line[i])) { sep = true; break; } } if (!sep) reread(); } return true; } template <class T, enable_if_t<is_same<T, string>::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; while (true) { size_t sz = 0; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (!sz || st != ed) break; reread(); } return true; } template <class T, enable_if_t<is_integral<T>::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); } if (neg) ref = -ref; return true; } template <class T, is_modint_t<T> * = nullptr> bool read_single(T &ref) { long long val = 0; bool f = read_single(val); ref = T(val); return f; } bool read_single(double &ref) { string s; if (!read_single(s)) return false; ref = std::stod(s); return true; } bool read_single(char &ref) { string s; if (!read_single(s) || s.size() != 1) return false; ref = s[0]; return true; } template <class T> bool read_single(vector<T> &ref) { for (auto &d: ref) { if (!read_single(d)) return false; } return true; } template <class T, class U> bool read_single(pair<T, U> &p) { return (read_single(p.first) && read_single(p.second)); } template <class A, class B, class C> bool read_single(tuple<A, B, C> &p) { return (read_single(get<0>(p)) && read_single(get<1>(p)) && read_single(get<2>(p))); } template <class A, class B, class C, class D> bool read_single(tuple<A, B, C, D> &p) { return (read_single(get<0>(p)) && read_single(get<1>(p)) && read_single(get<2>(p)) && read_single(get<3>(p))); } void read() {} template <class H, class... T> void read(H &h, T &... t) { bool f = read_single(h); assert(f); read(t...); } Scanner(FILE *fp) : fp(fp) {} }; struct Printer { Printer(FILE *_fp) : fp(_fp) {} ~Printer() { flush(); } static constexpr size_t SIZE = 1 << 15; FILE *fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write(const char &val) { if (pos == SIZE) flush(); line[pos++] = val; } template <class T, enable_if_t<is_integral<T>::value, int> = 0> void write(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write('0'); return; } if (val < 0) { write('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write(const string &s) { for (char c: s) write(c); } void write(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write(s[i]); } void write(const double &x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } void write(const long double &x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } template <class T, is_modint_t<T> * = nullptr> void write(T &ref) { write(ref.val); } template <class T> void write(const vector<T> &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } template <class T, class U> void write(const pair<T, U> &val) { write(val.first); write(' '); write(val.second); } template <class A, class B, class C> void write(const tuple<A, B, C> &val) { auto &[a, b, c] = val; write(a), write(' '), write(b), write(' '), write(c); } template <class A, class B, class C, class D> void write(const tuple<A, B, C, D> &val) { auto &[a, b, c, d] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d); } template <class A, class B, class C, class D, class E> void write(const tuple<A, B, C, D, E> &val) { auto &[a, b, c, d, e] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e); } template <class A, class B, class C, class D, class E, class F> void write(const tuple<A, B, C, D, E, F> &val) { auto &[a, b, c, d, e, f] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f); } template <class T, size_t S> void write(const array<T, S> &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } void write(i128 val) { string s; bool negative = 0; if(val < 0){ negative = 1; val = -val; } while (val) { s += '0' + int(val % 10); val /= 10; } if(negative) s += "-"; reverse(all(s)); if (len(s) == 0) s = "0"; write(s); } }; Scanner scanner = Scanner(stdin); Printer printer = Printer(stdout); void flush() { printer.flush(); } void print() { printer.write('\n'); } template <class Head, class... Tail> void print(Head &&head, Tail &&... tail) { printer.write(head); if (sizeof...(Tail)) printer.write(' '); print(forward<Tail>(tail)...); } void read() {} template <class Head, class... Tail> void read(Head &head, Tail &... tail) { scanner.read(head); read(tail...); } #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector<type> name(size); \ read(name) #define VV(type, name, h, w) \ vector<vector<type>> name(h, vector<type>(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 2 "/home/maspy/compro/library/seq/interpolate_linear_rec.hpp" #line 2 "/home/maspy/compro/library/seq/find_linear_rec.hpp" template <typename mint> vector<mint> find_linear_rec(vector<mint>& A) { int N = len(A); vc<mint> B = {1}, C = {1}; int l = 0, m = 1; mint p = 1; FOR(i, N) { mint d = A[i]; FOR3(j, 1, l + 1) { d += C[j] * A[i - j]; } if (d == 0) { ++m; continue; } auto tmp = C; mint q = d / p; if (len(C) < len(B) + m) C.insert(C.end(), len(B) + m - len(C), 0); FOR(j, len(B)) C[j + m] -= q * B[j]; if (l + l <= i) { B = tmp; l = i + 1 - l, m = 1; p = d; } else { ++m; } } return C; } #line 2 "/home/maspy/compro/library/mod/modint.hpp" template <unsigned int mod> struct modint { static constexpr bool is_modint = true; unsigned int val; constexpr modint(const long long val = 0) noexcept : val(val >= 0 ? val % mod : (mod - (-val) % mod) % mod) {} bool operator<(const modint &other) const { return val < other.val; } // To use std::map modint &operator+=(const modint &p) { if ((val += p.val) >= mod) val -= mod; return *this; } modint &operator-=(const modint &p) { if ((val += mod - p.val) >= mod) val -= mod; return *this; } modint &operator*=(const modint &p) { val = (unsigned int)(1LL * val * p.val % mod); return *this; } modint &operator/=(const modint &p) { *this *= p.inverse(); return *this; } modint operator-() const { return modint(get_mod() - val); } modint operator+(const modint &p) const { return modint(*this) += p; } modint operator-(const modint &p) const { return modint(*this) -= p; } modint operator*(const modint &p) const { return modint(*this) *= p; } modint operator/(const modint &p) const { return modint(*this) /= p; } bool operator==(const modint &p) const { return val == p.val; } bool operator!=(const modint &p) const { return val != p.val; } modint inverse() const { int a = val, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b), swap(u -= t * v, v); } return modint(u); } modint pow(int64_t n) const { modint ret(1), mul(val); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } static constexpr unsigned int get_mod() { return mod; } }; struct ArbitraryModInt { static constexpr bool is_modint = true; unsigned int val; ArbitraryModInt() : val(0) {} ArbitraryModInt(int64_t y) : val(y >= 0 ? y % get_mod() : (get_mod() - (-y) % get_mod()) % get_mod()) {} bool operator<(const ArbitraryModInt &other) const { return val < other.val; } // To use std::map<ArbitraryModInt, T> static unsigned int &get_mod() { static unsigned int mod = 0; return mod; } static void set_mod(int md) { get_mod() = md; } ArbitraryModInt &operator+=(const ArbitraryModInt &p) { if ((val += p.val) >= get_mod()) val -= get_mod(); return *this; } ArbitraryModInt &operator-=(const ArbitraryModInt &p) { if ((val += get_mod() - p.val) >= get_mod()) val -= get_mod(); return *this; } ArbitraryModInt &operator*=(const ArbitraryModInt &p) { unsigned long long a = (unsigned long long)val * p.val; unsigned xh = (unsigned)(a >> 32), xl = (unsigned)a, d, m; asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(get_mod())); val = m; return *this; } ArbitraryModInt &operator/=(const ArbitraryModInt &p) { *this *= p.inverse(); return *this; } ArbitraryModInt operator-() const { return ArbitraryModInt(get_mod() - val); } ArbitraryModInt operator+(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) += p; } ArbitraryModInt operator-(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) -= p; } ArbitraryModInt operator*(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) *= p; } ArbitraryModInt operator/(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) /= p; } bool operator==(const ArbitraryModInt &p) const { return val == p.val; } bool operator!=(const ArbitraryModInt &p) const { return val != p.val; } ArbitraryModInt inverse() const { int a = val, b = get_mod(), u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b), swap(u -= t * v, v); } return ArbitraryModInt(u); } ArbitraryModInt pow(int64_t n) const { ArbitraryModInt ret(1), mul(val); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } }; template <typename mint> mint inv(int n) { static const int mod = mint::get_mod(); static vector<mint> dat = {0, 1}; assert(0 <= n); if (n >= mod) n %= mod; while (int(dat.size()) <= n) { int k = dat.size(); auto q = (mod + k - 1) / k; int r = k * q - mod; dat.emplace_back(dat[r] * mint(q)); } return dat[n]; } template <typename mint> mint fact(int n) { static const int mod = mint::get_mod(); static vector<mint> dat = {1, 1}; assert(0 <= n); if (n >= mod) return 0; while (int(dat.size()) <= n) { int k = dat.size(); dat.emplace_back(dat[k - 1] * mint(k)); } return dat[n]; } template <typename mint> mint fact_inv(int n) { static const int mod = mint::get_mod(); static vector<mint> dat = {1, 1}; assert(0 <= n && n < mod); while (int(dat.size()) <= n) { int k = dat.size(); dat.emplace_back(dat[k - 1] * inv<mint>(k)); } return dat[n]; } template <typename mint> mint C_dense(int n, int k) { static vvc<mint> C; static int H = 0, W = 0; auto calc = [&](int i, int j) -> mint { if (i == 0) return (j == 0 ? mint(1) : mint(0)); return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0); }; if (W <= k) { FOR(i, H) { C[i].resize(k + 1); FOR(j, W, k + 1) { C[i][j] = calc(i, j); } } W = k + 1; } if (H <= n) { C.resize(n + 1); FOR(i, H, n + 1) { C[i].resize(W); FOR(j, W) { C[i][j] = calc(i, j); } } H = n + 1; } return C[n][k]; } template <typename mint, bool large = false, bool dense = false> mint C(ll n, ll k) { assert(n >= 0); if (k < 0 || n < k) return 0; if (dense) return C_dense<mint>(n, k); if (!large) return fact<mint>(n) * fact_inv<mint>(k) * fact_inv<mint>(n - k); k = min(k, n - k); mint x(1); FOR(i, k) { x *= mint(n - i); } x *= fact_inv<mint>(k); return x; } template <typename mint, bool large = false> mint C_inv(ll n, ll k) { assert(n >= 0); assert(0 <= k && k <= n); if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k); return mint(1) / C<mint, 1>(n, k); } // [x^d](1-x)^{-n} の計算 template <typename mint, bool large = false, bool dense = false> mint C_negative(ll n, ll d) { assert(n >= 0); if (d < 0) return mint(0); if (n == 0) { return (d == 0 ? mint(1) : mint(0)); } return C<mint, large, dense>(n + d - 1, d); } using modint107 = modint<1000000007>; using modint998 = modint<998244353>; using amint = ArbitraryModInt; #line 2 "/home/maspy/compro/library/mod/mod_inv.hpp" // long でも大丈夫 ll mod_inv(ll val, ll mod) { ll a = val, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b), swap(u -= t * v, v); } if(u < 0) u += mod; return u; } #line 1 "/home/maspy/compro/library/poly/convolution_naive.hpp" template <class T> vector<T> convolution_naive(const vector<T>& a, const vector<T>& b) { int n = int(a.size()), m = int(b.size()); vector<T> ans(n + m - 1); if (n < m) { FOR(j, m) FOR(i, n) ans[i + j] += a[i] * b[j]; } else { FOR(i, n) FOR(j, m) ans[i + j] += a[i] * b[j]; } return ans; } #line 2 "/home/maspy/compro/library/poly/ntt.hpp" template <class mint> struct ntt_info { static constexpr int bsf_constexpr(unsigned int n) { int x = 0; while (!(n & (1 << x))) x++; return x; } static constexpr int rank2 = bsf_constexpr(mint::get_mod() - 1); array<mint, rank2 + 1> root; array<mint, rank2 + 1> iroot; array<mint, max(0, rank2 - 1)> rate2; array<mint, max(0, rank2 - 1)> irate2; array<mint, max(0, rank2 - 2)> rate3; array<mint, max(0, rank2 - 2)> irate3; ntt_info() { int g = primitive_root(mint::get_mod()); root[rank2] = mint(g).pow((mint::get_mod() - 1) >> rank2); iroot[rank2] = mint(1) / root[rank2]; FOR_R(i, rank2) { 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]; } } } constexpr int primitive_root(int m) { if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 880803841) return 26; if (m == 998244353) return 3; return -1; } }; template <class mint> void ntt(vector<mint>& a, bool inverse) { int n = int(a.size()); int h = topbit(n); assert(n == 1 << h); static const ntt_info<mint> info; if (!inverse) { 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(s, 1 << len) { int offset = s << (h - len); FOR(i, p) { auto l = a[i + offset]; auto r = a[i + offset + p] * rot; a[i + offset] = l + r; a[i + offset + p] = l - r; } rot *= info.rate2[topbit(~s & -~s)]; } len++; } else { 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::get_mod() * mint::get_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); } rot *= info.rate3[topbit(~s & -~s)]; } len += 2; } } } else { mint coef = mint(1) / mint(len(a)); FOR(i, len(a)) a[i] *= coef; int len = h; while (len) { if (len == 1) { int p = 1 << (h - len); mint irot = 1; FOR(s, 1 << (len - 1)) { int offset = s << (h - len + 1); FOR(i, p) { auto l = a[i + offset]; auto r = a[i + offset + p]; a[i + offset] = l + r; a[i + offset + p] = (unsigned long long)(mint::get_mod() + l.val - r.val) * irot.val; ; } irot *= info.irate2[topbit(~s & -~s)]; } len--; } else { int p = 1 << (h - len); mint irot = 1, iimag = info.iroot[2]; FOR(s, (1 << (len - 2))) { 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::get_mod() + a2 - a3) * iimag.val).val; a[i + offset] = a0 + a1 + a2 + a3; a[i + offset + 1 * p] = (a0 + (mint::get_mod() - a1) + a2na3iimag) * irot.val; a[i + offset + 2 * p] = (a0 + a1 + (mint::get_mod() - a2) + (mint::get_mod() - a3)) * irot2.val; a[i + offset + 3 * p] = (a0 + (mint::get_mod() - a1) + (mint::get_mod() - a2na3iimag)) * irot3.val; } irot *= info.irate3[topbit(~s & -~s)]; } len -= 2; } } } } #line 1 "/home/maspy/compro/library/poly/fft.hpp" namespace CFFT { using real = double; struct C { real x, y; C() : x(0), y(0) {} C(real x, real y) : x(x), y(y) {} inline C operator+(const C& c) const { return C(x + c.x, y + c.y); } inline C operator-(const C& c) const { return C(x - c.x, y - c.y); } inline C operator*(const C& c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); } inline C conj() const { return C(x, -y); } }; const real PI = acosl(-1); int base = 1; vector<C> rts = {{0, 0}, {1, 0}}; vector<int> rev = {0, 1}; void ensure_base(int nbase) { if (nbase <= base) return; rev.resize(1 << nbase); rts.resize(1 << nbase); for (int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } while (base < nbase) { real angle = PI * 2.0 / (1 << (base + 1)); for (int i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; real angle_i = angle * (2 * i + 1 - (1 << base)); rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i)); } ++base; } } void fft(vector<C>& a, int n) { assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for (int i = 0; i < n; i++) { if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for (int k = 1; k < n; k <<= 1) { for (int i = 0; i < n; i += 2 * k) { for (int j = 0; j < k; j++) { C z = a[i + j + k] * rts[j + k]; a[i + j + k] = a[i + j] - z; a[i + j] = a[i + j] + z; } } } } } // namespace CFFT #line 7 "/home/maspy/compro/library/poly/convolution.hpp" template <class mint> vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) { int n = int(a.size()), m = int(b.size()); int sz = 1; while (sz < n + m - 1) sz *= 2; // sz = 2^k のときの高速化。分割統治的なやつで損しまくるので。 if ((n + m - 3) <= sz / 2) { auto a_last = a.back(), b_last = b.back(); a.pop_back(), b.pop_back(); auto c = convolution(a, b); c.resize(n + m - 1); c[n + m - 2] = a_last * b_last; FOR(i, len(a)) c[i + len(b)] += a[i] * b_last; FOR(i, len(b)) c[i + len(a)] += b[i] * a_last; return c; } a.resize(sz), b.resize(sz); bool same = a == b; ntt(a, 0); if (same) { b = a; } else { ntt(b, 0); } FOR(i, sz) a[i] *= b[i]; ntt(a, 1); a.resize(n + m - 1); return a; } template <typename mint> vector<mint> convolution_garner(const vector<mint>& a, const vector<mint>& b) { int n = len(a), m = len(b); if (!n || !m) return {}; static const long long nttprimes[] = {754974721, 167772161, 469762049}; using mint0 = modint<754974721>; using mint1 = modint<167772161>; using mint2 = modint<469762049>; vc<mint0> a0(n), b0(m); vc<mint1> a1(n), b1(m); vc<mint2> a2(n), b2(m); FOR(i, n) a0[i] = a[i].val, a1[i] = a[i].val, a2[i] = a[i].val; FOR(i, m) b0[i] = b[i].val, b1[i] = b[i].val, b2[i] = b[i].val; auto c0 = convolution_ntt<mint0>(a0, b0); auto c1 = convolution_ntt<mint1>(a1, b1); auto c2 = convolution_ntt<mint2>(a2, b2); static const long long m01 = 1LL * nttprimes[0] * nttprimes[1]; static const long long m0_inv_m1 = mint1(nttprimes[0]).inverse().val; static const long long m01_inv_m2 = mint2(m01).inverse().val; static const int mod = mint::get_mod(); auto garner = [&](mint0 x0, mint1 x1, mint2 x2) -> mint { int r0 = x0.val, r1 = x1.val, r2 = x2.val; int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1]; auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * mint2(m01_inv_m2); return mint(r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val); }; vc<mint> c(len(c0)); FOR(i, len(c)) c[i] = garner(c0[i], c1[i], c2[i]); return c; } template <typename R> vc<double> convolution_fft(const vc<R>& a, const vc<R>& b) { using C = CFFT::C; int need = (int)a.size() + (int)b.size() - 1; int nbase = 1; while ((1 << nbase) < need) nbase++; CFFT::ensure_base(nbase); int sz = 1 << nbase; vector<C> fa(sz); for (int i = 0; i < sz; i++) { int x = (i < (int)a.size() ? a[i] : 0); int y = (i < (int)b.size() ? b[i] : 0); fa[i] = C(x, y); } CFFT::fft(fa, sz); C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0); for (int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r; fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r; fa[i] = z; } for (int i = 0; i < (sz >> 1); i++) { C A0 = (fa[i] + fa[i + (sz >> 1)]) * t; C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * CFFT::rts[(sz >> 1) + i]; fa[i] = A0 + A1 * s; } CFFT::fft(fa, sz >> 1); vector<double> ret(need); for (int i = 0; i < need; i++) { ret[i] = (i & 1 ? fa[i >> 1].y : fa[i >> 1].x); } return ret; } vector<ll> convolution(const vector<ll>& a, const vector<ll>& b) { int n = len(a), m = len(b); if (!n || !m) return {}; if (min(n, m) <= 60) return convolution_naive(a, b); ll abs_sum_a = 0, abs_sum_b = 0; ll LIM = 1e15; FOR(i, n) abs_sum_a = min(LIM, abs_sum_a + abs(a[i])); FOR(i, n) abs_sum_b = min(LIM, abs_sum_b + abs(b[i])); if (i128(abs_sum_a) * abs_sum_b < 1e15) { vc<double> c = convolution_fft<ll>(a, b); vc<ll> res(len(c)); FOR(i, len(c)) res[i] = ll(floor(c[i] + .5)); return res; } static constexpr unsigned long long MOD1 = 754974721; // 2^24 static constexpr unsigned long long MOD2 = 167772161; // 2^25 static constexpr unsigned long long MOD3 = 469762049; // 2^26 static constexpr unsigned long long M2M3 = MOD2 * MOD3; static constexpr unsigned long long M1M3 = MOD1 * MOD3; static constexpr unsigned long long M1M2 = MOD1 * MOD2; static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3; static const unsigned long long i1 = mod_inv(MOD2 * MOD3, MOD1); static const unsigned long long i2 = mod_inv(MOD1 * MOD3, MOD2); static const unsigned long long i3 = mod_inv(MOD1 * MOD2, MOD3); using mint1 = modint<MOD1>; using mint2 = modint<MOD2>; using mint3 = modint<MOD3>; vc<mint1> a1(n), b1(m); vc<mint2> a2(n), b2(m); vc<mint3> a3(n), b3(m); FOR(i, n) a1[i] = a[i], a2[i] = a[i], a3[i] = a[i]; FOR(i, m) b1[i] = b[i], b2[i] = b[i], b3[i] = b[i]; auto c1 = convolution_ntt<mint1>(a1, b1); auto c2 = convolution_ntt<mint2>(a2, b2); auto c3 = convolution_ntt<mint3>(a3, b3); vc<ll> c(n + m - 1); FOR(i, n + m - 1) { u64 x = 0; x += (c1[i].val * i1) % MOD1 * M2M3; x += (c2[i].val * i2) % MOD2 * M1M3; x += (c3[i].val * i3) % MOD3 * M1M2; ll diff = c1[i].val - ((long long)(x) % (long long)(MOD1)); if (diff < 0) diff += MOD1; static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3}; x -= offset[diff % 5]; c[i] = x; } return c; } template <typename mint> enable_if_t<is_same<mint, modint998>::value, vc<mint>> convolution( const vc<mint>& a, const vc<mint>& b) { int n = len(a), m = len(b); if (!n || !m) return {}; if (min(n, m) <= 60) return convolution_naive(a, b); return convolution_ntt(a, b); } template <typename mint> enable_if_t<!is_same<mint, modint998>::value, vc<mint>> convolution( const vc<mint>& a, const vc<mint>& b) { int n = len(a), m = len(b); if (!n || !m) return {}; if (min(n, m) <= 60) return convolution_naive(a, b); return convolution_garner(a, b); } #line 2 "/home/maspy/compro/library/poly/coef_of_rational_fps.hpp" template <typename mint> mint coef_of_rational_fps(vector<mint> A, vector<mint> B, ll N) { if (len(A) == 0) return 0; assert(len(A) < len(B)); while (len(A) + 1 < len(B)) A.eb(0); assert(B[0] == mint(1)); assert(len(B) == len(A) + 1); while (N) { vc<mint> B1 = B; FOR(i, len(B1)) if (i & 1) B1[i] = -B1[i]; A = convolution(A, B1); B = convolution(B, B1); FOR(i, len(B1)) B[i] = B[2 * i]; if (N & 1) { FOR(i, len(B1) - 1) A[i] = A[2 * i | 1]; } else { FOR(i, len(B1) - 1) A[i] = A[2 * i]; } A.resize(len(B1) - 1); B.resize(len(B1)); N /= 2; } return A[0]; } #line 5 "/home/maspy/compro/library/seq/interpolate_linear_rec.hpp" template <typename mint> mint interpolate_linear_rec(vector<mint>& A, ll N, int off) { if(N < len(A)) return A[N]; A = {A.begin() + off, A.end()}; N -= off; auto G = find_linear_rec(A); auto F = convolution(A, G); F.resize(len(G) - 1); return coef_of_rational_fps(F, G, N); } #line 2 "/home/maspy/compro/library/mod/fast_div.hpp" struct fast_div { // Min25 https://judge.yosupo.jp/submission/46090 // 同じ定数で何度も除算するときの高速化に使える using i64 = long long; using u64 = unsigned long long; using u128 = __uint128_t; constexpr fast_div() : m(), s(), x() {} constexpr fast_div(int n) : m(n), s(std::__lg(n - 1)), x(((u128(1) << (s + 64)) + n - 1) / n) {} constexpr friend u64 operator/(u64 n, const fast_div& d) { return (u128(n) * d.x >> d.s) >> 64; } constexpr friend int operator%(u64 n, const fast_div& d) { return n - n / d * d.m; } constexpr std::pair<i64, int> divmod(u64 n) const { u64 q = n / *this; return {q, n - q * m}; } int m; int s; u64 x; }; #line 2 "/home/maspy/compro/library/nt/primetest.hpp" struct m64 { using i64 = int64_t; using u64 = uint64_t; using u128 = __uint128_t; inline static u64 m, r, n2; // r * m = -1 (mod 1<<64), n2 = 1<<128 (mod m) static void set_mod(u64 m) { assert(m < (1ull << 62)); assert((m & 1) == 1); m64::m = m; n2 = -u128(m) % m; r = m; FOR(_, 5) r *= 2 - m * r; r = -r; assert(r * m == -1ull); } static u64 reduce(u128 b) { return (b + u128(u64(b) * r) * m) >> 64; } u64 x; m64() : x(0) {} m64(u64 x) : x(reduce(u128(x) * n2)){}; u64 val() const { u64 y = reduce(x); return y >= m ? y - m : y; } m64 &operator+=(m64 y) { x += y.x - (m << 1); x = (i64(x) < 0 ? x + (m << 1) : x); return *this; } m64 &operator-=(m64 y) { x -= y.x; x = (i64(x) < 0 ? x + (m << 1) : x); return *this; } m64 &operator*=(m64 y) { x = reduce(u128(x) * y.x); return *this; } m64 operator+(m64 y) const { return m64(*this) += y; } m64 operator-(m64 y) const { return m64(*this) -= y; } m64 operator*(m64 y) const { return m64(*this) *= y; } bool operator==(m64 y) const { return (x >= m ? x - m : x) == (y.x >= m ? y.x - m : y.x); } bool operator!=(m64 y) const { return not operator==(y); } m64 pow(u64 n) const { m64 y = 1, z = *this; for (; n; n >>= 1, z *= z) if (n & 1) y *= z; return y; } }; bool primetest(const uint64_t x) { using u64 = uint64_t; if (x == 2 or x == 3 or x == 5 or x == 7) return true; if (x % 2 == 0 or x % 3 == 0 or x % 5 == 0 or x % 7 == 0) return false; if (x < 121) return x > 1; const u64 d = (x - 1) >> __builtin_ctzll(x - 1); m64::set_mod(x); const m64 one(1), minus_one(x - 1); auto ok = [&](u64 a) { auto y = m64(a).pow(d); u64 t = d; while (y != one and y != minus_one and t != x - 1) y *= y, t <<= 1; if (y != minus_one and t % 2 == 0) return false; return true; }; if (x < (1ull << 32)) { for (u64 a: {2, 7, 61}) if (not ok(a)) return false; } else { for (u64 a: {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) { if (x <= a) return true; if (not ok(a)) return false; } } return true; } #line 3 "/home/maspy/compro/library/nt/factor.hpp" mt19937_64 rng_mt{random_device{}()}; ll rnd(ll n) { return uniform_int_distribution<ll>(0, n - 1)(rng_mt); } ll rho(ll n, ll c) { m64::set_mod(n); assert(n > 1); const m64 cc(c); auto f = [&](m64 x) { return x * x + cc; }; m64 x = 1, y = 2, z = 1, q = 1; ll g = 1; const ll m = 1LL << (__lg(n) / 5); // ? for (ll r = 1; g == 1; r <<= 1) { x = y; FOR(_, r) y = f(y); for (ll k = 0; k < r and g == 1; k += m) { z = y; FOR(_, min(m, r - k)) y = f(y), q *= x - y; g = gcd(q.val(), n); } } if (g == n) do { z = f(z); g = gcd((x - z).val(), n); } while (g == 1); return g; } ll find_prime_factor(ll n) { assert(n > 1); if (primetest(n)) return n; FOR(_, 100) { ll m = rho(n, rnd(n)); if (primetest(m)) return m; n = m; } cerr << "failed" << endl; assert(false); return -1; } vc<pi> factor(ll n) { assert(n >= 1); vc<pi> pf; FOR3(p, 2, 100) { if (p * p > n) break; if (n % p == 0) { ll e = 0; do { n /= p, e += 1; } while (n % p == 0); pf.eb(p, e); } } while (n > 1) { ll p = find_prime_factor(n); ll e = 0; do { n /= p, e += 1; } while (n % p == 0); pf.eb(p, e); } sort(all(pf)); return pf; } vc<pi> factor_by_lpf(ll n, vc<int>& lpf) { vc<pi> res; while(n > 1){ int p = lpf[n]; int e = 0; while(n % p == 0){ n /= p; ++e; } res.eb(p, e); } return res; } #line 5 "/home/maspy/compro/library/nt/crt.hpp" // new_mod = -1 の場合:lcm が i128 範囲なら // 解なしなら -1 を返す i128 CRT(vc<int> vals, vc<int> mods, int new_mod = -1, bool coprime = false) { int n = len(vals); if (!coprime) { unordered_map<ll, vc<pi>> MP; FOR(i, n) { for (auto&& [p, e]: factor(mods[i])) { int mod = 1; FOR(e) mod *= p; MP[p].eb(vals[i] % mod, mod); } } vc<int> xx, mm; for (auto&& [p, dat]: MP) { int mod = 1; int val = 0; for (auto&& [x, m]: dat) if (chmax(mod, m)) val = x; for (auto&& [x, m]: dat) if ((val - x) % m != 0) return -1; xx.eb(val); mm.eb(mod); } swap(vals, xx); swap(mods, mm); n = len(vals); } vc<int> cfs(n); FOR(i, n) { auto mod = fast_div(mods[i]); ll a = vals[i]; ll prod = 1; FOR(j, i) { a = (a + cfs[j] * (mods[i] - prod)) % mod; prod = prod * mods[j] % mod; } cfs[i] = mod_inv(prod, mods[i]) * a % mod; } i128 ret = 0; ll prod = 1; FOR(i, n) { ret += prod * cfs[i]; prod *= mods[i]; if (new_mod != -1) { ret %= new_mod; prod %= new_mod; } } return ret; } #line 5 "main.cpp" void solve() { auto f = [&](ll n) -> ll { vi A; ll x = 0; FOR_R(i, 1, n + 1) A.eb(i); FOR_R(i, 1, n + 1) A.eb(i); FOR(k, len(A)) FOR(j, k) FOR(i, j) { if (A[i] == A[j] || A[i] == A[k] || A[j] == A[k]) continue; if (A[i] > A[j] && A[j] > A[k]) continue; if (A[i] < A[j] && A[j] < A[k]) continue; ++x; } return x; }; using M1 = modint107; using M2 = modint998; ll LIM = 30; vc<M1> A(LIM); vc<M2> B(LIM); FOR(n, LIM) A[n] = f(n); FOR(n, LIM) B[n] = f(n); LL(T); FOR(T) { LL(n); M1 a = interpolate_linear_rec<M1>(A, n, 0); M2 b = interpolate_linear_rec<M2>(B, n, 0); vc<int> vals = {a.val, b.val}; vc<int> mods = {M1::get_mod(), M2::get_mod()}; print(CRT(vals, mods, -1, 1)); } } signed main() { cout << fixed << setprecision(15); ll T = 1; // LL(T); FOR(T) solve(); return 0; }