#ifdef LOCAL #define _GLIBCXX_DEBUG #define __clock__ #else #pragma GCC optimize("Ofast") // #define NDEBUG #endif #define __buffer_check__ #define __precision__ 10 #define iostream_untie true #define debug_stream std::cerr #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define all(v) std::begin(v), std::end(v) #define rall(v) std::rbegin(v), std::rend(v) #define odd(n) ((n) & 1) #define even(n) (not __odd(n)) #define __popcount(n) __builtin_popcountll(n) #define __clz32(n) __builtin_clz(n) #define __clz64(n) __builtin_clzll(n) #define __ctz32(n) __builtin_ctz(n) #define __ctz64(n) __builtin_ctzll(n) using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t; using pii = std::pair; using pll = std::pair; template using heap = std::priority_queue; template using rheap = std::priority_queue, std::greater>; template using hashset = std::unordered_set; template using hashmap = std::unordered_map; namespace setting { using namespace std::chrono; system_clock::time_point start_time, end_time; long long get_elapsed_time() { end_time = system_clock::now(); return duration_cast(end_time - start_time).count(); } void print_elapsed_time() { debug_stream << "\n----- Exec time : " << get_elapsed_time() << " ms -----\n"; } void buffer_check() { char bufc; if(std::cin >> bufc) debug_stream << "\n\033[1;35mwarning\033[0m: buffer not empty.\n"; } struct setupper { setupper() { if(iostream_untie) std::ios::sync_with_stdio(false), std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(__precision__); #ifdef stderr_path if(freopen(stderr_path, "a", stderr)) { std::cerr << std::fixed << std::setprecision(__precision__); } #endif #ifdef stdout_path if(not freopen(stdout_path, "w", stdout)) { freopen("CON", "w", stdout); debug_stream << "\n\033[1;35mwarning\033[0m: failed to open stdout file.\n"; } std::cout << ""; #endif #ifdef stdin_path if(not freopen(stdin_path, "r", stdin)) { freopen("CON", "r", stdin); debug_stream << "\n\033[1;35mwarning\033[0m: failed to open stdin file.\n"; } #endif #ifdef LOCAL debug_stream << "\n----- stderr at LOCAL -----\n\n"; atexit(print_elapsed_time); #endif #ifdef __buffer_check__ atexit(buffer_check); #endif #if defined(__clock__) || defined(LOCAL) start_time = system_clock::now(); #endif } } __setupper; // struct setupper } // namespace setting #ifdef __clock__ class { std::chrono::system_clock::time_point built_pt, last_pt; int built_ln, last_ln; std::string built_func, last_func; bool is_built = false; public: void build(int crt_ln, const std::string &crt_func) { is_built = true, last_pt = built_pt = std::chrono::system_clock::now(), last_ln = built_ln = crt_ln, last_func = built_func = crt_func; } void set(int crt_ln, const std::string &crt_func) { if(is_built) last_pt = std::chrono::system_clock::now(), last_ln = crt_ln, last_func = crt_func; else debug_stream << "[ " << crt_ln << " : " << crt_func << " ] " << "myclock_t::set failed (yet to be built!)\n"; } void get(int crt_ln, const std::string &crt_func) { if(is_built) { std::chrono::system_clock::time_point crt_pt(std::chrono::system_clock::now()); long long diff = std::chrono::duration_cast(crt_pt - last_pt).count(); debug_stream << diff << " ms elapsed from" << " [ " << last_ln << " : " << last_func << " ]"; if(last_ln == built_ln) debug_stream << " (when built)"; debug_stream << " to" << " [ " << crt_ln << " : " << crt_func << " ]" << "\n"; last_pt = built_pt, last_ln = built_ln, last_func = built_func; } else { debug_stream << "[ " << crt_ln << " : " << crt_func << " ] " << "myclock_t::get failed (yet to be built!)\n"; } } } myclock; // unnamed class #define build_clock() myclock.build(__LINE__, __func__) #define set_clock() myclock.set(__LINE__, __func__) #define get_clock() myclock.get(__LINE__, __func__) #else #define build_clock() ((void)0) #define set_clock() ((void)0) #define get_clock() ((void)0) #endif namespace std { // hash template size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); } template struct hash> { size_t operator()(pair const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } }; template ::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc::apply(seed, t), get(t)); } }; template struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } }; template struct hash> { size_t operator()(tuple const &t) const { return tuple_hash_calc>::apply(0, t); } }; // iostream template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } template struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis::apply(is, t); return is >> get(t); } }; template struct tupleis { static istream &apply(istream &is, tuple_t &t) { return is; } }; template istream &operator>>(istream &is, tuple &t) { return tupleis, tuple_size>::value - 1>::apply(is, t); } template <> istream &operator>>(istream &is, tuple<> &t) { return is; } template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos::apply(os, t); return os << ' ' << get(t); } }; template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } }; template ostream &operator<<(ostream &os, const tuple &t) { return tupleos, tuple_size>::value - 1>::apply(os, t); } template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; } template , string>::value, nullptr_t> = nullptr> istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; } template , string>::value, nullptr_t> = nullptr> ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; } } // namespace std #ifdef LOCAL #define dump(...) \ debug_stream << "[ " << __LINE__ << " : " << __FUNCTION__ << " ]\n", \ dump_func(#__VA_ARGS__, __VA_ARGS__) template void dump_func(const char *ptr, const T &x) { debug_stream << '\t'; for(char c = *ptr; c != '\0'; c = *++ptr) if(c != ' ') debug_stream << c; debug_stream << " : " << x << '\n'; } template void dump_func(const char *ptr, const T &x, rest_t... rest) { debug_stream << '\t'; for(char c = *ptr; c != ','; c = *++ptr) if(c != ' ') debug_stream << c; debug_stream << " : " << x << ",\n"; dump_func(++ptr, rest...); } #else #define dump(...) ((void)0) #endif template T read() { T x; std::cin >> x; return x; } template void read(iterator __first, iterator __last) { for(iterator i = __first; i != __last; ++i) std::cin >> *i; } template void write(iterator __first, iterator __last) { for(iterator i = __first; i != __last; std::cout << (++i == __last ? "" : " ")) std::cout << *i; } // substitute y for x if x > y. template inline bool sbmin(T &x, const T &y) { return x > y ? x = y, true : false; } // substitute y for x if x < y. template inline bool sbmax(T &x, const T &y) { return x < y ? x = y, true : false; } // binary search on integers. long long bin(long long __ok, long long __ng, const std::function &pred) { while(std::abs(__ok - __ng) > 1) { long long mid{(__ok + __ng) / 2}; (pred(mid) ? __ok : __ng) = mid; } return __ok; } // binary search on real numbers. long double bin(long double __ok, long double __ng, const long double eps, const std::function &pred) { while(std::abs(__ok - __ng) > eps) { long double mid{(__ok + __ng) / 2}; (pred(mid) ? __ok : __ng) = mid; } return __ok; } // binary search on integers(with a class member function). template long long bin(long long __ok, long long __ng, bool (X::*const pred)(int_t), X *const x) { while(std::abs(__ok - __ng) > 1) { long long mid{(__ok + __ng) / 2}; ((x->*pred)(mid) ? __ok : __ng) = mid; } return __ok; } // binary search on real numbers(with a class member function). template long double bin(long double __ok, long double __ng, const long double eps, bool (X::*const pred)(real_t), X *const x) { while(std::abs(__ok - __ng) > eps) { long double mid{(__ok + __ng) / 2}; ((x->*pred)(mid) ? __ok : __ng) = mid; } return __ok; } // be careful that val is type-sensitive. template void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); } // reset all bits. template void reset(A &array) { memset(array, 0, sizeof(array)); } /* The main code follows. */ using namespace std; #ifndef FAST_FOURIER_TRANSFORM_HPP #define FAST_FOURIER_TRANSFORM_HPP #include namespace fast_Fourier_transform { using real_t = double; class cmplx_t { real_t re, im; friend constexpr cmplx_t conj(cmplx_t x) { return x.im = -x.im, x; } friend std::istream &operator>>(std::istream &s, cmplx_t &x) { return s >> x.re >> x.im; } friend std::ostream &operator<<(std::ostream &s, const cmplx_t &x) { return s << x.re << ' ' << x.im; } public: constexpr cmplx_t() : re{real_t{}}, im{real_t{}} {} constexpr cmplx_t(real_t _re) : re{_re}, im{real_t{}} {} constexpr cmplx_t(real_t _re, real_t _im) : re{_re}, im{_im} {} constexpr cmplx_t(std::complex x) : re{x.real()}, im{x.imag()} {} constexpr real_t real() const { return re; } constexpr void real(const real_t _re) { re = _re; } constexpr real_t imag() const { return im; } constexpr void imag(const real_t _im) { im = _im; } constexpr cmplx_t operator-() const { return cmplx_t(-re, -im); } constexpr cmplx_t &operator+=(const cmplx_t &x) { return re += x.re, im += x.im, *this; } constexpr cmplx_t &operator-=(const cmplx_t &x) { return *this += -x; } constexpr cmplx_t &operator*=(const cmplx_t &x) { real_t _re{re * x.re - im * x.im}; return im = im * x.re + x.im * re, re = _re, *this; } constexpr cmplx_t &operator*=(real_t x) { return re *= x, im *= x, *this; } constexpr cmplx_t &operator/=(const cmplx_t &x) { return conj(*this) /= re * re + im * im; } constexpr cmplx_t &operator/=(real_t x) { return re /= x, im /= x, *this; } constexpr cmplx_t operator+(const cmplx_t &x) const { return cmplx_t(*this) += x; } constexpr cmplx_t operator-(const cmplx_t &x) const { return cmplx_t(*this) -= x; } constexpr cmplx_t operator*(const cmplx_t &x) const { return cmplx_t(*this) *= x; } constexpr cmplx_t operator*(real_t x) const { return cmplx_t(*this) *= x; } constexpr cmplx_t operator/(const cmplx_t &x) const { return cmplx_t(*this) /= x; } constexpr cmplx_t operator/(real_t x) const { return cmplx_t(*this) /= x; } }; using poly_t = std::vector; void dft(poly_t &f) { const size_t n{f.size()}, mask{n - 1}; assert(__builtin_popcount(n) == 1); // degree of f must be a power of two. static poly_t g; g.resize(n); constexpr cmplx_t zeta[31] = { {1, 0}, {-1, 0}, {0, 1}, {0.70710678118654752438189403651, 0.70710678118654752443610414514}, {0.92387953251128675610142140795, 0.38268343236508977172325753068}, {0.98078528040323044911909938781, 0.19509032201612826785692544201}, {0.99518472667219688623102546998, 0.09801714032956060199569840382}, {0.99879545620517239270077028412, 0.04906767432741801425693899119}, {0.99969881869620422009748220149, 0.02454122852291228803212346128}, {0.99992470183914454093764001552, 0.01227153828571992607945510345}, {0.99998117528260114264494415325, 0.00613588464915447535972750246}, {0.99999529380957617150137498041, 0.00306795676296597627029751672}, {0.99999882345170190993313003025, 0.00153398018628476561237225788}, {0.99999970586288221914474799723, 0.00076699031874270452695124765}, {0.99999992646571785113833452651, 0.00038349518757139558906815188}, {0.99999998161642929381167504976, 0.00019174759731070330743679009}, {0.99999999540410731290905263501, 0.00009587379909597734587360460}, {0.99999999885102682753608427379, 0.00004793689960306688454884772}, {0.99999999971275670682981095982, 0.00002396844980841821872882467}, {0.99999999992818917670745273995, 0.00001198422490506970642183282}, {0.99999999998204729416331065783, 0.00000599211245264242784278378}, {0.99999999999551182356793271877, 0.00000299605622633466075058210}, {0.99999999999887795586487812538, 0.00000149802811316901122883643}, {0.99999999999971948897977205850, 0.00000074901405658471572113723}, {0.99999999999992987223139048746, 0.00000037450702829238412391495}, {0.99999999999998246807140014902, 0.00000018725351414619534486931}, {0.99999999999999561700429751010, 0.00000009362675707309808280024}, {0.99999999999999890425107437752, 0.00000004681337853654909269501}, {0.99999999999999972607632112153, 0.00000002340668926827455275977}, {0.99999999999999993153263280754, 0.00000001170334463413727718121}, {0.99999999999999998286960567472, 0.00000000585167231706863869077} }; for(size_t i{n >> 1}, ii{1}; i; i >>= 1, ++ii, swap(f, g)) { cmplx_t powzeta{1}; for(size_t j{}; j < n; powzeta *= zeta[ii]) { for(size_t k{}, x{mask & j << 1}, y{mask & (i + (j << 1))}; k < i; ++k, ++j, ++x, ++y) { g[j] = f[x] + powzeta * f[y]; } } } } void idft(poly_t &f) { dft(f), reverse(next(f.begin()), f.end()); for(cmplx_t &e : f) e /= f.size(); } poly_t convolute(poly_t f, poly_t g) { if(f.empty() || g.empty()) return poly_t(); const size_t deg_f{f.size() - 1}, deg_g{g.size() - 1}, deg_h{deg_f + deg_g}, n(1u << (32 - __builtin_clz(deg_h))); static poly_t h; f.resize(n, 0), g.resize(n, 0), h.resize(n); dft(f), dft(g); for(size_t i{}; i < n; ++i) h[i] = f[i] * g[i]; idft(h); h.resize(deg_h + 1); return h; } std::vector convolute(const std::vector &f, const std::vector &g) { if(f.empty() || g.empty()) return std::vector(); const size_t deg_f{f.size() - 1}, deg_g{g.size() - 1}, deg_h{deg_f + deg_g}, n(1u << (32 - __builtin_clz(deg_h))); static std::vector h; h.resize(deg_h + 1); static poly_t p; p.assign(n, 0); for(size_t i{}; i <= deg_f; ++i) p[i].real(f[i]); for(size_t i{}; i <= deg_g; ++i) p[i].imag(g[i]); dft(p); // perform discrete Fourier transformation on p = f + i*g. static poly_t q; q.resize(n); for(size_t i{}; i < n; ++i) { size_t j{i ? n - i : 0}; q[i] = (p[i] + conj(p[j])) * (p[i] - conj(p[j])); } idft(q); for(size_t i{}; i <= deg_h; ++i) h[i] = q[i].imag() / 4; return h; } std::vector convolute(const std::vector &f, const std::vector &g) { if(f.empty() || g.empty()) return std::vector(); const size_t deg_f{f.size() - 1}, deg_g{g.size() - 1}, deg_h{deg_f + deg_g}, n(1u << (32 - __builtin_clz(deg_h))); static std::vector h; h.resize(deg_h + 1); static poly_t p; p.assign(n, 0); for(size_t i{}; i <= deg_f; ++i) p[i].real(f[i]); for(size_t i{}; i <= deg_g; ++i) p[i].imag(g[i]); dft(p); // perform discrete Fourier transformation on p = f + i*g. static poly_t q; q.resize(n); for(size_t i{}; i < n; ++i) { size_t j{i ? n - i : 0}; q[i] = (p[i] + conj(p[j])) * (p[i] - conj(p[j])); } idft(q); for(size_t i{}; i <= deg_h; ++i) h[i] = round(q[i].imag() / 4); return h; } std::vector convolute(const std::vector &f, const std::vector &g) { if(f.empty() || g.empty()) return std::vector(); const size_t deg_f{f.size() - 1}, deg_g{g.size() - 1}, deg_h{deg_f + deg_g}, n(1u << (32 - __builtin_clz(deg_h))); static std::vector h; h.resize(deg_h + 1); static poly_t p; p.assign(n, 0); for(size_t i{}; i <= deg_f; ++i) p[i].real(f[i]); for(size_t i{}; i <= deg_g; ++i) p[i].imag(g[i]); dft(p); // perform discrete Fourier transformation on p = f + i*g. static poly_t q; q.resize(n); for(size_t i{}; i < n; ++i) { size_t j{i ? n - i : 0}; q[i] = (p[i] + conj(p[j])) * (p[i] - conj(p[j])); } idft(q); for(size_t i{}; i <= deg_h; ++i) h[i] = round(q[i].imag() / 4); return h; } } // namespace fast_Fourier_transform #endif using namespace fast_Fourier_transform; struct solver { solver() { int l,m,n; cin>>l>>m>>n; vector a(n),b(n); for(int i=0; i>x; a[n-x]=1; } for(int i=0; i>x; --x; b[x]=1; } int Q; cin>>Q; auto c=convolute(a,b); dump(c); for(int i=1; i<=Q; ++i) { cout << c[n-i] << "\n"; } } }; // struct solver int main(int argc, char *argv[]) { u32 t; // loop count #ifdef LOCAL t = 3; #else t = 1; // single test case #endif // t = -1; // infinite loop // cin >> t; // case number given while(t--) { solver(); } }