結果
問題 | No.1783 Remix Sum |
ユーザー | Pachicobue |
提出日時 | 2021-12-12 03:00:30 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 65,511 bytes |
コンパイル時間 | 4,258 ms |
コンパイル使用メモリ | 329,492 KB |
実行使用メモリ | 466,912 KB |
最終ジャッジ日時 | 2024-07-20 11:50:31 |
合計ジャッジ時間 | 96,404 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge2 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
5,248 KB |
testcase_01 | AC | 2 ms
5,376 KB |
testcase_02 | AC | 2 ms
5,376 KB |
testcase_03 | AC | 4 ms
5,376 KB |
testcase_04 | WA | - |
testcase_05 | WA | - |
testcase_06 | WA | - |
testcase_07 | AC | 510 ms
31,768 KB |
testcase_08 | WA | - |
testcase_09 | WA | - |
testcase_10 | WA | - |
testcase_11 | WA | - |
testcase_12 | AC | 729 ms
34,720 KB |
testcase_13 | AC | 180 ms
31,912 KB |
testcase_14 | WA | - |
testcase_15 | AC | 172 ms
18,428 KB |
testcase_16 | AC | 505 ms
33,936 KB |
testcase_17 | AC | 668 ms
33,808 KB |
testcase_18 | WA | - |
testcase_19 | WA | - |
testcase_20 | AC | 995 ms
60,464 KB |
testcase_21 | WA | - |
testcase_22 | WA | - |
testcase_23 | AC | 1,317 ms
61,504 KB |
testcase_24 | AC | 342 ms
57,920 KB |
testcase_25 | WA | - |
testcase_26 | AC | 684 ms
34,720 KB |
testcase_27 | AC | 5,625 ms
229,072 KB |
testcase_28 | WA | - |
testcase_29 | AC | 989 ms
62,112 KB |
testcase_30 | AC | 1,002 ms
60,552 KB |
testcase_31 | WA | - |
testcase_32 | AC | 333 ms
18,816 KB |
testcase_33 | AC | 979 ms
62,032 KB |
testcase_34 | AC | 392 ms
58,316 KB |
testcase_35 | AC | 232 ms
32,180 KB |
testcase_36 | AC | 141 ms
18,216 KB |
testcase_37 | AC | 128 ms
20,260 KB |
testcase_38 | AC | 197 ms
32,180 KB |
testcase_39 | AC | 374 ms
58,444 KB |
testcase_40 | WA | - |
testcase_41 | AC | 380 ms
58,316 KB |
testcase_42 | AC | 381 ms
58,448 KB |
testcase_43 | AC | 194 ms
32,180 KB |
testcase_44 | TLE | - |
testcase_45 | -- | - |
testcase_46 | -- | - |
testcase_47 | -- | - |
testcase_48 | -- | - |
testcase_49 | -- | - |
testcase_50 | -- | - |
testcase_51 | -- | - |
testcase_52 | -- | - |
testcase_53 | -- | - |
testcase_54 | -- | - |
testcase_55 | -- | - |
testcase_56 | -- | - |
testcase_57 | -- | - |
testcase_58 | -- | - |
testcase_59 | -- | - |
testcase_60 | -- | - |
testcase_61 | -- | - |
testcase_62 | -- | - |
testcase_63 | -- | - |
testcase_64 | -- | - |
testcase_65 | -- | - |
testcase_66 | -- | - |
testcase_67 | -- | - |
testcase_68 | -- | - |
testcase_69 | -- | - |
testcase_70 | -- | - |
testcase_71 | -- | - |
testcase_72 | -- | - |
testcase_73 | -- | - |
testcase_74 | -- | - |
testcase_75 | -- | - |
testcase_76 | -- | - |
testcase_77 | -- | - |
testcase_78 | -- | - |
testcase_79 | -- | - |
ソースコード
#include <immintrin.h> #include <bits/stdc++.h> #pragma region Header using i32 = int; using u32 = unsigned int; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; using f64 = double; using f80 = long double; using f128 = __float128; constexpr i32 operator"" _i32(u64 v) { return v; } constexpr i32 operator"" _u32(u64 v) { return v; } constexpr i64 operator"" _i64(u64 v) { return v; } constexpr u64 operator"" _u64(u64 v) { return v; } constexpr f64 operator"" _f64(f80 v) { return v; } constexpr f80 operator"" _f80(f80 v) { return v; } using Istream = std::istream; using Ostream = std::ostream; using Str = std::string; template<typename T> using Lt = std::less<T>; template<typename T> using Gt = std::greater<T>; template<typename T> using IList = std::initializer_list<T>; template<int n> using BSet = std::bitset<n>; template<typename T1, typename T2> using Pair = std::pair<T1, T2>; template<typename... Ts> using Tup = std::tuple<Ts...>; template<typename T, int N> using Arr = std::array<T, N>; template<typename... Ts> using Deq = std::deque<Ts...>; template<typename... Ts> using Set = std::set<Ts...>; template<typename... Ts> using MSet = std::multiset<Ts...>; template<typename... Ts> using USet = std::unordered_set<Ts...>; template<typename... Ts> using UMSet = std::unordered_multiset<Ts...>; template<typename... Ts> using Map = std::map<Ts...>; template<typename... Ts> using MMap = std::multimap<Ts...>; template<typename... Ts> using UMap = std::unordered_map<Ts...>; template<typename... Ts> using UMMap = std::unordered_multimap<Ts...>; template<typename... Ts> using Vec = std::vector<Ts...>; template<typename... Ts> using Stack = std::stack<Ts...>; template<typename... Ts> using Queue = std::queue<Ts...>; template<typename T> using MaxHeap = std::priority_queue<T>; template<typename T> using MinHeap = std::priority_queue<T, Vec<T>, Gt<T>>; using NSec = std::chrono::nanoseconds; using USec = std::chrono::microseconds; using MSec = std::chrono::milliseconds; using Sec = std::chrono::seconds; template<typename T> constexpr T LIMMIN = std::numeric_limits<T>::min(); template<typename T> constexpr T LIMMAX = std::numeric_limits<T>::max(); template<typename T> constexpr T INF = (LIMMAX<T> - 1) / 2; template<typename T> constexpr T PI = T{3.141592653589793238462643383279502884}; template<typename T = u64> constexpr T TEN(const int n) { return n == 0 ? T{1} : TEN<T>(n - 1) * T{10}; } Ostream& operator<<(Ostream& os, i128 v) { bool minus = false; if (v < 0) { minus = true, v = -v; } Str ans; if (v == 0) { ans = "0"; } while (v) { ans.push_back('0' + v % 10), v /= 10; } std::reverse(ans.begin(), ans.end()); return os << (minus ? "-" : "") << ans; } Ostream& operator<<(Ostream& os, u128 v) { Str ans; if (v == 0) { ans = "0"; } while (v) { ans.push_back('0' + v % 10), v /= 10; } std::reverse(ans.begin(), ans.end()); return os << ans; } template<typename T> bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } else { return false; } } template<typename T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else { return false; } } template<typename T> constexpr T floorDiv(T x, T y) { if (y < T{}) { x = -x, y = -y; } return x >= T{} ? x / y : (x - y + 1) / y; } template<typename T> constexpr T ceilDiv(T x, T y) { if (y < T{}) { x = -x, y = -y; } return x >= T{} ? (x + y - 1) / y : x / y; } template<typename T, typename I> constexpr T modPower(T v, I n, T mod) { T ans = 1 % mod; for (; n > 0; n >>= 1, (v *= v) %= mod) { if (n % 2 == 1) { (ans *= v) %= mod; } } return ans; } template<typename T, typename I> constexpr T power(T v, I n) { T ans = 1; for (; n > 0; n >>= 1, v *= v) { if (n % 2 == 1) { ans *= v; } } return ans; } template<typename T, typename I> constexpr T power(T v, I n, const T& e) { T ans = e; for (; n > 0; n >>= 1, v *= v) { if (n % 2 == 1) { ans *= v; } } return ans; } template<typename T> Vec<T> operator+=(Vec<T>& vs1, const Vec<T>& vs2) { vs1.insert(vs1.end(), vs2.begin(), vs2.end()); return vs1; } template<typename T> Vec<T> operator+(const Vec<T>& vs1, const Vec<T>& vs2) { auto vs = vs1; vs += vs2; return vs; } template<typename Vs, typename V> void fillAll(Vs& arr, const V& v) { if constexpr (std::is_convertible<V, Vs>::value) { arr = v; } else { for (auto& subarr : arr) { fillAll(subarr, v); } } } template<typename Vs> void sortAll(Vs& vs) { std::sort(std::begin(vs), std::end(vs)); } template<typename Vs, typename C> void sortAll(Vs& vs, C comp) { std::sort(std::begin(vs), std::end(vs), comp); } template<typename Vs> void reverseAll(Vs& vs) { std::reverse(std::begin(vs), std::end(vs)); } template<typename V, typename Vs> V sumAll(const Vs& vs) { if constexpr (std::is_convertible<Vs, V>::value) { return static_cast<V>(vs); } else { V ans = 0; for (const auto& v : vs) { ans += sumAll<V>(v); } return ans; } } template<typename Vs> int minInd(const Vs& vs) { return std::min_element(std::begin(vs), std::end(vs)) - std::begin(vs); } template<typename Vs> int maxInd(const Vs& vs) { return std::max_element(std::begin(vs), std::end(vs)) - std::begin(vs); } template<typename Vs, typename V> int lbInd(const Vs& vs, const V& v) { return std::lower_bound(std::begin(vs), std::end(vs), v) - std::begin(vs); } template<typename Vs, typename V> int ubInd(const Vs& vs, const V& v) { return std::upper_bound(std::begin(vs), std::end(vs), v) - std::begin(vs); } template<typename T, typename F> Vec<T> genVec(int n, F gen) { Vec<T> ans; std::generate_n(std::back_insert_iterator(ans), n, gen); return ans; } Vec<int> iotaVec(int n, int offset = 0) { Vec<int> ans(n); std::iota(ans.begin(), ans.end(), offset); return ans; } constexpr int popcount(const u64 v) { return v ? __builtin_popcountll(v) : 0; } constexpr int log2p1(const u64 v) { return v ? 64 - __builtin_clzll(v) : 0; } constexpr int lsbp1(const u64 v) { return __builtin_ffsll(v); } constexpr int clog(const u64 v) { return v ? log2p1(v - 1) : 0; } constexpr u64 ceil2(const u64 v) { const int l = clog(v); return (l == 64) ? 0_u64 : (1_u64 << l); } constexpr u64 floor2(const u64 v) { return v ? (1_u64 << (log2p1(v) - 1)) : 0_u64; } constexpr bool ispow2(const u64 v) { return (v > 0) and ((v & (v - 1)) == 0); } constexpr bool btest(const u64 mask, const int ind) { return (mask >> ind) & 1_u64; } template<typename F> struct Fix : F { Fix(F&& f) : F{std::forward<F>(f)} {} template<typename... Args> auto operator()(Args&&... args) const { return F::operator()(*this, std::forward<Args>(args)...); } }; class irange { private: struct itr { itr(i64 start = 0, i64 step = 1) : m_cnt{start}, m_step{step} {} bool operator!=(const itr& it) const { return m_cnt != it.m_cnt; } int operator*() { return m_cnt; } itr& operator++() { m_cnt += m_step; return *this; } i64 m_cnt, m_step; }; i64 m_start, m_end, m_step; public: irange(i64 start, i64 end, i64 step = 1) { assert(step != 0); const i64 d = std::abs(step); const i64 l = (step > 0 ? start : end); const i64 r = (step > 0 ? end : start); int n = (r - l) / d + ((r - l) % d ? 1 : 0); if (l >= r) { n = 0; } m_start = start; m_end = start + step * n; m_step = step; } itr begin() const { return itr{m_start, m_step}; } itr end() const { return itr{m_end, m_step}; } }; irange rep(int end) { return irange(0, end, 1); } irange per(int rend) { return irange(rend - 1, -1, -1); } #pragma COMMENT("[REFS] Xoshiro: https://prng.di.unimi.it") namespace xoshiro_impl { u64 x; u64 next() { uint64_t z = (x += 0x9e3779b97f4a7c15); z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9; z = (z ^ (z >> 27)) * 0x94d049bb133111eb; return z ^ (z >> 31); } } // namespace xoshiro_impl class Xoshiro32 { public: using result_type = u32; using T = result_type; Xoshiro32(T seed = 0) { xoshiro_impl::x = seed; s[0] = xoshiro_impl::next(); s[1] = xoshiro_impl::next(); s[2] = xoshiro_impl::next(); s[3] = xoshiro_impl::next(); } static constexpr T min() { return LIMMIN<T>; } static constexpr T max() { return LIMMAX<T>; } T operator()() { return next(); } private: static constexpr T rotl(const T x, int k) { return (x << k) | (x >> (32 - k)); } T next() { const T ans = rotl(s[1] * 5, 7) * 9; const T t = s[1] << 9; s[2] ^= s[0]; s[3] ^= s[1]; s[1] ^= s[2]; s[0] ^= s[3]; s[2] ^= t; s[3] = rotl(s[3], 11); return ans; } T s[4]; }; class Xoshiro64 { public: using result_type = u64; using T = result_type; Xoshiro64(T seed = 0) { xoshiro_impl::x = seed; s[0] = xoshiro_impl::next(); s[1] = xoshiro_impl::next(); s[2] = xoshiro_impl::next(); s[3] = xoshiro_impl::next(); } static constexpr T min() { return LIMMIN<T>; } static constexpr T max() { return LIMMAX<T>; } T operator()() { return next(); } private: static constexpr T rotl(const T x, int k) { return (x << k) | (x >> (64 - k)); } T next() { const T ans = rotl(s[1] * 5, 7) * 9; const T t = s[1] << 17; s[2] ^= s[0]; s[3] ^= s[1]; s[1] ^= s[2]; s[0] ^= s[3]; s[2] ^= t; s[3] = rotl(s[3], 45); return ans; } T s[4]; }; template<typename Rng> class RNG { public: using result_type = typename Rng::result_type; using T = result_type; static constexpr T min() { return Rng::min(); } static constexpr T max() { return Rng::max(); } RNG() : RNG(std::random_device{}()) {} RNG(T seed) : m_rng(seed) {} T operator()() { return m_rng(); } template<typename T> T val(T min, T max) { return std::uniform_int_distribution<T>(min, max)(m_rng); } template<typename T> Pair<T, T> pair(T min, T max) { return std::minmax({val<T>(min, max), val<T>(min, max)}); } template<typename T> Vec<T> vec(int n, T min, T max) { return genVec<T>(n, [&]() { return val<T>(min, max); }); } template<typename T> Vec<Vec<T>> vvec(int n, int m, T min, T max) { return genVec<Vec<T>>(n, [&]() { return vec(m, min, max); }); } private: Rng m_rng; }; RNG<std::mt19937> rng; RNG<std::mt19937_64> rng64; RNG<Xoshiro32> rng_xo; RNG<Xoshiro64> rng_xo64; class Scanner { public: Scanner(Istream& is = std::cin) : m_is{is} { m_is.tie(nullptr)->sync_with_stdio(false); } template<typename T> T val() { T v; return m_is >> v, v; } template<typename T> T val(T offset) { return val<T>() - offset; } template<typename T> Vec<T> vec(int n) { return genVec<T>(n, [&]() { return val<T>(); }); } template<typename T> Vec<T> vec(int n, T offset) { return genVec<T>(n, [&]() { return val<T>(offset); }); } template<typename T> Vec<Vec<T>> vvec(int n, int m) { return genVec<Vec<T>>(n, [&]() { return vec<T>(m); }); } template<typename T> Vec<Vec<T>> vvec(int n, int m, const T offset) { return genVec<Vec<T>>(n, [&]() { return vec<T>(m, offset); }); } template<typename... Args> auto tup() { return Tup<Args...>{val<Args>()...}; } template<typename... Args> auto tup(const Args&... offsets) { return Tup<Args...>{val<Args>(offsets)...}; } private: Istream& m_is; }; Scanner in; class Printer { public: Printer(Ostream& os = std::cout) : m_os{os} { m_os << std::fixed << std::setprecision(15); } template<typename... Args> int operator()(const Args&... args) { dump(args...); return 0; } template<typename... Args> int ln(const Args&... args) { dump(args...), m_os << '\n'; return 0; } template<typename... Args> int el(const Args&... args) { dump(args...), m_os << std::endl; return 0; } private: template<typename T> void dump(const T& v) { m_os << v; } template<typename T> void dump(const Vec<T>& vs) { for (const int i : rep(vs.size())) { m_os << (i ? " " : ""), dump(vs[i]); } } template<typename T> void dump(const Vec<Vec<T>>& vss) { for (const int i : rep(vss.size())) { m_os << (i ? "\n" : ""), dump(vss[i]); } } template<typename T, typename... Ts> int dump(const T& v, const Ts&... args) { dump(v), m_os << ' ', dump(args...); return 0; } Ostream& m_os; }; Printer out; #pragma endregion __attribute__((target("sse4.2"))) inline __m128i my128_mullo_epu32(const __m128i& a, const __m128i& b) { return _mm_mullo_epi32(a, b); } __attribute__((target("sse4.2"))) inline __m128i my128_mulhi_epu32(const __m128i& a, const __m128i& b) { __m128i a13 = _mm_shuffle_epi32(a, 0xF5); __m128i b13 = _mm_shuffle_epi32(b, 0xF5); __m128i prod02 = _mm_mul_epu32(a, b); __m128i prod13 = _mm_mul_epu32(a13, b13); __m128i prod = _mm_unpackhi_epi64(_mm_unpacklo_epi32(prod02, prod13), _mm_unpackhi_epi32(prod02, prod13)); return prod; } __attribute__((target("sse4.2"))) inline __m128i montgomery_mul_128(const __m128i& a, const __m128i& b, const __m128i& r, const __m128i& m1) { return _mm_sub_epi32( _mm_add_epi32(my128_mulhi_epu32(a, b), m1), my128_mulhi_epu32(my128_mullo_epu32(my128_mullo_epu32(a, b), r), m1)); } __attribute__((target("sse4.2"))) inline __m128i montgomery_add_128(const __m128i& a, const __m128i& b, const __m128i& m2, const __m128i& m0) { __m128i ret = _mm_sub_epi32(_mm_add_epi32(a, b), m2); return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret); } __attribute__((target("sse4.2"))) inline __m128i montgomery_sub_128(const __m128i& a, const __m128i& b, const __m128i& m2, const __m128i& m0) { __m128i ret = _mm_sub_epi32(a, b); return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret); } __attribute__((target("avx2"))) inline __m256i my256_mullo_epu32(const __m256i& a, const __m256i& b) { return _mm256_mullo_epi32(a, b); } __attribute__((target("avx2"))) inline __m256i my256_mulhi_epu32(const __m256i& a, const __m256i& b) { __m256i a13 = _mm256_shuffle_epi32(a, 0xF5); __m256i b13 = _mm256_shuffle_epi32(b, 0xF5); __m256i prod02 = _mm256_mul_epu32(a, b); __m256i prod13 = _mm256_mul_epu32(a13, b13); __m256i prod = _mm256_unpackhi_epi64(_mm256_unpacklo_epi32(prod02, prod13), _mm256_unpackhi_epi32(prod02, prod13)); return prod; } __attribute__((target("avx2"))) inline __m256i montgomery_mul_256(const __m256i& a, const __m256i& b, const __m256i& r, const __m256i& m1) { return _mm256_sub_epi32( _mm256_add_epi32(my256_mulhi_epu32(a, b), m1), my256_mulhi_epu32(my256_mullo_epu32(my256_mullo_epu32(a, b), r), m1)); } __attribute__((target("avx2"))) inline __m256i montgomery_add_256(const __m256i& a, const __m256i& b, const __m256i& m2, const __m256i& m0) { __m256i ret = _mm256_sub_epi32(_mm256_add_epi32(a, b), m2); return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2), ret); } __attribute__((target("avx2"))) inline __m256i montgomery_sub_256(const __m256i& a, const __m256i& b, const __m256i& m2, const __m256i& m0) { __m256i ret = _mm256_sub_epi32(a, b); return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2), ret); } namespace ntt_inner { using u64 = uint64_t; constexpr uint32_t get_pr(uint32_t mod) { if (mod == 2) return 1; u64 ds[32] = {}; int idx = 0; u64 m = mod - 1; for (u64 i = 2; i * i <= m; ++i) { if (m % i == 0) { ds[idx++] = i; while (m % i == 0) m /= i; } } if (m != 1) ds[idx++] = m; uint32_t pr = 2; while (1) { int flg = 1; for (int i = 0; i < idx; ++i) { u64 a = pr, b = (mod - 1) / ds[i], r = 1; while (b) { if (b & 1) r = r * a % mod; a = a * a % mod; b >>= 1; } if (r == 1) { flg = 0; break; } } if (flg == 1) break; ++pr; } return pr; } constexpr int SZ_FFT_BUF = 1 << 23; uint32_t _buf1[SZ_FFT_BUF] __attribute__((aligned(64))); uint32_t _buf2[SZ_FFT_BUF] __attribute__((aligned(64))); } // namespace ntt_inner template<typename mint> struct NTT { static constexpr uint32_t mod = mint::get_mod(); static constexpr uint32_t pr = ntt_inner::get_pr(mint::get_mod()); static constexpr int level = __builtin_ctzll(mod - 1); mint dw[level], dy[level]; mint *buf1, *buf2; constexpr NTT() { setwy(level); union raw_cast { mint dat; uint32_t _; }; buf1 = &(((raw_cast*)(ntt_inner::_buf1))->dat); buf2 = &(((raw_cast*)(ntt_inner::_buf2))->dat); } constexpr void setwy(int k) { mint w[level], y[level]; w[k - 1] = mint(pr).pow((mod - 1) / (1 << k)); y[k - 1] = w[k - 1].inverse(); for (int i = k - 2; i > 0; --i) w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1]; dw[0] = dy[0] = w[1] * w[1]; dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2]; for (int i = 3; i < k; ++i) { dw[i] = dw[i - 1] * y[i - 2] * w[i]; dy[i] = dy[i - 1] * w[i - 2] * y[i]; } } __attribute__((target("avx2"))) void ntt(mint* a, int n) { int k = n ? __builtin_ctz(n) : 0; if (k == 0) return; if (k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; return; } if (k & 1) { int v = 1 << (k - 1); if (v < 8) { for (int j = 0; j < v; ++j) { mint ajv = a[j + v]; a[j + v] = a[j] - ajv; a[j] += ajv; } } else { const __m256i m0 = _mm256_set1_epi32(0); const __m256i m2 = _mm256_set1_epi32(mod + mod); int j0 = 0; int j1 = v; for (; j0 < v; j0 += 8, j1 += 8) { __m256i T0 = _mm256_loadu_si256((__m256i*)(a + j0)); __m256i T1 = _mm256_loadu_si256((__m256i*)(a + j1)); __m256i naj = montgomery_add_256(T0, T1, m2, m0); __m256i najv = montgomery_sub_256(T0, T1, m2, m0); _mm256_storeu_si256((__m256i*)(a + j0), naj); _mm256_storeu_si256((__m256i*)(a + j1), najv); } } } int u = 1 << (2 + (k & 1)); int v = 1 << (k - 2 - (k & 1)); mint one = mint(1); mint imag = dw[1]; while (v) { if (v == 1) { mint ww = one, xx = one, wx = one; for (int jh = 0; jh < u;) { ww = xx * xx, wx = ww * xx; mint t0 = a[jh + 0], t1 = a[jh + 1] * xx; mint t2 = a[jh + 2] * ww, t3 = a[jh + 3] * wx; mint t0p2 = t0 + t2, t1p3 = t1 + t3; mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag; a[jh + 0] = t0p2 + t1p3, a[jh + 1] = t0p2 - t1p3; a[jh + 2] = t0m2 + t1m3, a[jh + 3] = t0m2 - t1m3; xx *= dw[__builtin_ctz((jh += 4))]; } } else if (v == 4) { const __m128i m0 = _mm_set1_epi32(0); const __m128i m1 = _mm_set1_epi32(mod); const __m128i m2 = _mm_set1_epi32(mod + mod); const __m128i r = _mm_set1_epi32(mint::r); const __m128i Imag = _mm_set1_epi32(imag.a); mint ww = one, xx = one, wx = one; for (int jh = 0; jh < u;) { if (jh == 0) { int j0 = 0; int j1 = v; int j2 = j1 + v; int j3 = j2 + v; int je = v; for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) { const __m128i T0 = _mm_loadu_si128((__m128i*)(a + j0)); const __m128i T1 = _mm_loadu_si128((__m128i*)(a + j1)); const __m128i T2 = _mm_loadu_si128((__m128i*)(a + j2)); const __m128i T3 = _mm_loadu_si128((__m128i*)(a + j3)); const __m128i T0P2 = montgomery_add_128(T0, T2, m2, m0); const __m128i T1P3 = montgomery_add_128(T1, T3, m2, m0); const __m128i T0M2 = montgomery_sub_128(T0, T2, m2, m0); const __m128i T1M3 = montgomery_mul_128( montgomery_sub_128(T1, T3, m2, m0), Imag, r, m1); _mm_storeu_si128( (__m128i*)(a + j0), montgomery_add_128(T0P2, T1P3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j1), montgomery_sub_128(T0P2, T1P3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j2), montgomery_add_128(T0M2, T1M3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j3), montgomery_sub_128(T0M2, T1M3, m2, m0)); } } else { ww = xx * xx, wx = ww * xx; const __m128i WW = _mm_set1_epi32(ww.a); const __m128i WX = _mm_set1_epi32(wx.a); const __m128i XX = _mm_set1_epi32(xx.a); int j0 = jh * v; int j1 = j0 + v; int j2 = j1 + v; int j3 = j2 + v; int je = j1; for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) { const __m128i T0 = _mm_loadu_si128((__m128i*)(a + j0)); const __m128i T1 = _mm_loadu_si128((__m128i*)(a + j1)); const __m128i T2 = _mm_loadu_si128((__m128i*)(a + j2)); const __m128i T3 = _mm_loadu_si128((__m128i*)(a + j3)); const __m128i MT1 = montgomery_mul_128(T1, XX, r, m1); const __m128i MT2 = montgomery_mul_128(T2, WW, r, m1); const __m128i MT3 = montgomery_mul_128(T3, WX, r, m1); const __m128i T0P2 = montgomery_add_128(T0, MT2, m2, m0); const __m128i T1P3 = montgomery_add_128(MT1, MT3, m2, m0); const __m128i T0M2 = montgomery_sub_128(T0, MT2, m2, m0); const __m128i T1M3 = montgomery_mul_128( montgomery_sub_128(MT1, MT3, m2, m0), Imag, r, m1); _mm_storeu_si128( (__m128i*)(a + j0), montgomery_add_128(T0P2, T1P3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j1), montgomery_sub_128(T0P2, T1P3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j2), montgomery_add_128(T0M2, T1M3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j3), montgomery_sub_128(T0M2, T1M3, m2, m0)); } } xx *= dw[__builtin_ctz((jh += 4))]; } } else { const __m256i m0 = _mm256_set1_epi32(0); const __m256i m1 = _mm256_set1_epi32(mod); const __m256i m2 = _mm256_set1_epi32(mod + mod); const __m256i r = _mm256_set1_epi32(mint::r); const __m256i Imag = _mm256_set1_epi32(imag.a); mint ww = one, xx = one, wx = one; for (int jh = 0; jh < u;) { if (jh == 0) { int j0 = 0; int j1 = v; int j2 = j1 + v; int j3 = j2 + v; int je = v; for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) { const __m256i T0 = _mm256_loadu_si256((__m256i*)(a + j0)); const __m256i T1 = _mm256_loadu_si256((__m256i*)(a + j1)); const __m256i T2 = _mm256_loadu_si256((__m256i*)(a + j2)); const __m256i T3 = _mm256_loadu_si256((__m256i*)(a + j3)); const __m256i T0P2 = montgomery_add_256(T0, T2, m2, m0); const __m256i T1P3 = montgomery_add_256(T1, T3, m2, m0); const __m256i T0M2 = montgomery_sub_256(T0, T2, m2, m0); const __m256i T1M3 = montgomery_mul_256( montgomery_sub_256(T1, T3, m2, m0), Imag, r, m1); _mm256_storeu_si256( (__m256i*)(a + j0), montgomery_add_256(T0P2, T1P3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j1), montgomery_sub_256(T0P2, T1P3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j2), montgomery_add_256(T0M2, T1M3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j3), montgomery_sub_256(T0M2, T1M3, m2, m0)); } } else { ww = xx * xx, wx = ww * xx; const __m256i WW = _mm256_set1_epi32(ww.a); const __m256i WX = _mm256_set1_epi32(wx.a); const __m256i XX = _mm256_set1_epi32(xx.a); int j0 = jh * v; int j1 = j0 + v; int j2 = j1 + v; int j3 = j2 + v; int je = j1; for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) { const __m256i T0 = _mm256_loadu_si256((__m256i*)(a + j0)); const __m256i T1 = _mm256_loadu_si256((__m256i*)(a + j1)); const __m256i T2 = _mm256_loadu_si256((__m256i*)(a + j2)); const __m256i T3 = _mm256_loadu_si256((__m256i*)(a + j3)); const __m256i MT1 = montgomery_mul_256(T1, XX, r, m1); const __m256i MT2 = montgomery_mul_256(T2, WW, r, m1); const __m256i MT3 = montgomery_mul_256(T3, WX, r, m1); const __m256i T0P2 = montgomery_add_256(T0, MT2, m2, m0); const __m256i T1P3 = montgomery_add_256(MT1, MT3, m2, m0); const __m256i T0M2 = montgomery_sub_256(T0, MT2, m2, m0); const __m256i T1M3 = montgomery_mul_256( montgomery_sub_256(MT1, MT3, m2, m0), Imag, r, m1); _mm256_storeu_si256( (__m256i*)(a + j0), montgomery_add_256(T0P2, T1P3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j1), montgomery_sub_256(T0P2, T1P3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j2), montgomery_add_256(T0M2, T1M3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j3), montgomery_sub_256(T0M2, T1M3, m2, m0)); } } xx *= dw[__builtin_ctz((jh += 4))]; } } u <<= 2; v >>= 2; } } __attribute__((target("avx2"))) void intt(mint* a, int n, int normalize = true) { int k = n ? __builtin_ctz(n) : 0; if (k == 0) return; if (k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; if (normalize) { a[0] *= mint(2).inverse(); a[1] *= mint(2).inverse(); } return; } int u = 1 << (k - 2); int v = 1; mint one = mint(1); mint imag = dy[1]; while (u) { if (v == 1) { mint ww = one, xx = one, yy = one; u <<= 2; for (int jh = 0; jh < u;) { ww = xx * xx, yy = xx * imag; mint t0 = a[jh + 0], t1 = a[jh + 1]; mint t2 = a[jh + 2], t3 = a[jh + 3]; mint t0p1 = t0 + t1, t2p3 = t2 + t3; mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy; a[jh + 0] = t0p1 + t2p3, a[jh + 2] = (t0p1 - t2p3) * ww; a[jh + 1] = t0m1 + t2m3, a[jh + 3] = (t0m1 - t2m3) * ww; xx *= dy[__builtin_ctz(jh += 4)]; } } else if (v == 4) { const __m128i m0 = _mm_set1_epi32(0); const __m128i m1 = _mm_set1_epi32(mod); const __m128i m2 = _mm_set1_epi32(mod + mod); const __m128i r = _mm_set1_epi32(mint::r); const __m128i Imag = _mm_set1_epi32(imag.a); mint ww = one, xx = one, yy = one; u <<= 2; for (int jh = 0; jh < u;) { if (jh == 0) { int j0 = 0; int j1 = v; int j2 = v + v; int j3 = j2 + v; for (; j0 < v; j0 += 4, j1 += 4, j2 += 4, j3 += 4) { const __m128i T0 = _mm_loadu_si128((__m128i*)(a + j0)); const __m128i T1 = _mm_loadu_si128((__m128i*)(a + j1)); const __m128i T2 = _mm_loadu_si128((__m128i*)(a + j2)); const __m128i T3 = _mm_loadu_si128((__m128i*)(a + j3)); const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0); const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0); const __m128i T0M1 = montgomery_sub_128(T0, T1, m2, m0); const __m128i T2M3 = montgomery_mul_128( montgomery_sub_128(T2, T3, m2, m0), Imag, r, m1); _mm_storeu_si128( (__m128i*)(a + j0), montgomery_add_128(T0P1, T2P3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j2), montgomery_sub_128(T0P1, T2P3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j1), montgomery_add_128(T0M1, T2M3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j3), montgomery_sub_128(T0M1, T2M3, m2, m0)); } } else { ww = xx * xx, yy = xx * imag; const __m128i WW = _mm_set1_epi32(ww.a); const __m128i XX = _mm_set1_epi32(xx.a); const __m128i YY = _mm_set1_epi32(yy.a); int j0 = jh * v; int j1 = j0 + v; int j2 = j1 + v; int j3 = j2 + v; int je = j1; for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) { const __m128i T0 = _mm_loadu_si128((__m128i*)(a + j0)); const __m128i T1 = _mm_loadu_si128((__m128i*)(a + j1)); const __m128i T2 = _mm_loadu_si128((__m128i*)(a + j2)); const __m128i T3 = _mm_loadu_si128((__m128i*)(a + j3)); const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0); const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0); const __m128i T0M1 = montgomery_mul_128( montgomery_sub_128(T0, T1, m2, m0), XX, r, m1); __m128i T2M3 = montgomery_mul_128( montgomery_sub_128(T2, T3, m2, m0), YY, r, m1); _mm_storeu_si128( (__m128i*)(a + j0), montgomery_add_128(T0P1, T2P3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j2), montgomery_mul_128( montgomery_sub_128(T0P1, T2P3, m2, m0), WW, r, m1)); _mm_storeu_si128( (__m128i*)(a + j1), montgomery_add_128(T0M1, T2M3, m2, m0)); _mm_storeu_si128( (__m128i*)(a + j3), montgomery_mul_128( montgomery_sub_128(T0M1, T2M3, m2, m0), WW, r, m1)); } } xx *= dy[__builtin_ctz(jh += 4)]; } } else { const __m256i m0 = _mm256_set1_epi32(0); const __m256i m1 = _mm256_set1_epi32(mod); const __m256i m2 = _mm256_set1_epi32(mod + mod); const __m256i r = _mm256_set1_epi32(mint::r); const __m256i Imag = _mm256_set1_epi32(imag.a); mint ww = one, xx = one, yy = one; u <<= 2; for (int jh = 0; jh < u;) { if (jh == 0) { int j0 = 0; int j1 = v; int j2 = v + v; int j3 = j2 + v; for (; j0 < v; j0 += 8, j1 += 8, j2 += 8, j3 += 8) { const __m256i T0 = _mm256_loadu_si256((__m256i*)(a + j0)); const __m256i T1 = _mm256_loadu_si256((__m256i*)(a + j1)); const __m256i T2 = _mm256_loadu_si256((__m256i*)(a + j2)); const __m256i T3 = _mm256_loadu_si256((__m256i*)(a + j3)); const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0); const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0); const __m256i T0M1 = montgomery_sub_256(T0, T1, m2, m0); const __m256i T2M3 = montgomery_mul_256( montgomery_sub_256(T2, T3, m2, m0), Imag, r, m1); _mm256_storeu_si256( (__m256i*)(a + j0), montgomery_add_256(T0P1, T2P3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j2), montgomery_sub_256(T0P1, T2P3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j1), montgomery_add_256(T0M1, T2M3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j3), montgomery_sub_256(T0M1, T2M3, m2, m0)); } } else { ww = xx * xx, yy = xx * imag; const __m256i WW = _mm256_set1_epi32(ww.a); const __m256i XX = _mm256_set1_epi32(xx.a); const __m256i YY = _mm256_set1_epi32(yy.a); int j0 = jh * v; int j1 = j0 + v; int j2 = j1 + v; int j3 = j2 + v; int je = j1; for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) { const __m256i T0 = _mm256_loadu_si256((__m256i*)(a + j0)); const __m256i T1 = _mm256_loadu_si256((__m256i*)(a + j1)); const __m256i T2 = _mm256_loadu_si256((__m256i*)(a + j2)); const __m256i T3 = _mm256_loadu_si256((__m256i*)(a + j3)); const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0); const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0); const __m256i T0M1 = montgomery_mul_256( montgomery_sub_256(T0, T1, m2, m0), XX, r, m1); const __m256i T2M3 = montgomery_mul_256( montgomery_sub_256(T2, T3, m2, m0), YY, r, m1); _mm256_storeu_si256( (__m256i*)(a + j0), montgomery_add_256(T0P1, T2P3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j2), montgomery_mul_256( montgomery_sub_256(T0P1, T2P3, m2, m0), WW, r, m1)); _mm256_storeu_si256( (__m256i*)(a + j1), montgomery_add_256(T0M1, T2M3, m2, m0)); _mm256_storeu_si256( (__m256i*)(a + j3), montgomery_mul_256( montgomery_sub_256(T0M1, T2M3, m2, m0), WW, r, m1)); } } xx *= dy[__builtin_ctz(jh += 4)]; } } u >>= 4; v <<= 2; } if (k & 1) { v = 1 << (k - 1); if (v < 8) { for (int j = 0; j < v; ++j) { mint ajv = a[j] - a[j + v]; a[j] += a[j + v]; a[j + v] = ajv; } } else { const __m256i m0 = _mm256_set1_epi32(0); const __m256i m2 = _mm256_set1_epi32(mod + mod); int j0 = 0; int j1 = v; for (; j0 < v; j0 += 8, j1 += 8) { const __m256i T0 = _mm256_loadu_si256((__m256i*)(a + j0)); const __m256i T1 = _mm256_loadu_si256((__m256i*)(a + j1)); __m256i naj = montgomery_add_256(T0, T1, m2, m0); __m256i najv = montgomery_sub_256(T0, T1, m2, m0); _mm256_storeu_si256((__m256i*)(a + j0), naj); _mm256_storeu_si256((__m256i*)(a + j1), najv); } } } if (normalize) { mint invn = mint(n).inverse(); for (int i = 0; i < n; i++) a[i] *= invn; } } __attribute__((target("avx2"))) void inplace_multiply(int l1, int l2, int zero_padding = true) { int l = l1 + l2 - 1; int M = 4; while (M < l) M <<= 1; if (zero_padding) { for (int i = l1; i < M; i++) ntt_inner::_buf1[i] = 0; for (int i = l2; i < M; i++) ntt_inner::_buf2[i] = 0; } const __m256i m0 = _mm256_set1_epi32(0); const __m256i m1 = _mm256_set1_epi32(mod); const __m256i r = _mm256_set1_epi32(mint::r); const __m256i N2 = _mm256_set1_epi32(mint::n2); for (int i = 0; i < l1; i += 8) { __m256i a = _mm256_loadu_si256((__m256i*)(ntt_inner::_buf1 + i)); __m256i b = montgomery_mul_256(a, N2, r, m1); _mm256_storeu_si256((__m256i*)(ntt_inner::_buf1 + i), b); } for (int i = 0; i < l2; i += 8) { __m256i a = _mm256_loadu_si256((__m256i*)(ntt_inner::_buf2 + i)); __m256i b = montgomery_mul_256(a, N2, r, m1); _mm256_storeu_si256((__m256i*)(ntt_inner::_buf2 + i), b); } ntt(buf1, M); ntt(buf2, M); for (int i = 0; i < M; i += 8) { __m256i a = _mm256_loadu_si256((__m256i*)(ntt_inner::_buf1 + i)); __m256i b = _mm256_loadu_si256((__m256i*)(ntt_inner::_buf2 + i)); __m256i c = montgomery_mul_256(a, b, r, m1); _mm256_storeu_si256((__m256i*)(ntt_inner::_buf1 + i), c); } intt(buf1, M, false); const __m256i INVM = _mm256_set1_epi32((mint(M).inverse()).a); for (int i = 0; i < l; i += 8) { __m256i a = _mm256_loadu_si256((__m256i*)(ntt_inner::_buf1 + i)); __m256i b = montgomery_mul_256(a, INVM, r, m1); __m256i c = my256_mulhi_epu32(my256_mullo_epu32(b, r), m1); __m256i d = _mm256_and_si256(_mm256_cmpgt_epi32(c, m0), m1); __m256i e = _mm256_sub_epi32(d, c); _mm256_storeu_si256((__m256i*)(ntt_inner::_buf1 + i), e); } } void ntt(Vec<mint>& a) { int M = (int)a.size(); for (int i = 0; i < M; i++) buf1[i].a = a[i].a; ntt(buf1, M); for (int i = 0; i < M; i++) a[i].a = buf1[i].a; } void intt(Vec<mint>& a) { int M = (int)a.size(); for (int i = 0; i < M; i++) buf1[i].a = a[i].a; intt(buf1, M, true); for (int i = 0; i < M; i++) a[i].a = buf1[i].a; } Vec<mint> multiply(const Vec<mint>& a, const Vec<mint>& b) { if (a.size() == 0 && b.size() == 0) return Vec<mint>{}; int l = a.size() + b.size() - 1; if (std::min<int>(a.size(), b.size()) <= 40) { Vec<mint> s(l); for (int i = 0; i < (int)a.size(); ++i) for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j]; return s; } assert(l <= ntt_inner::SZ_FFT_BUF); int M = 4; while (M < l) M <<= 1; for (int i = 0; i < (int)a.size(); ++i) buf1[i].a = a[i].a; for (int i = (int)a.size(); i < M; ++i) buf1[i].a = 0; for (int i = 0; i < (int)b.size(); ++i) buf2[i].a = b[i].a; for (int i = (int)b.size(); i < M; ++i) buf2[i].a = 0; ntt(buf1, M); ntt(buf2, M); for (int i = 0; i < M; ++i) buf1[i].a = mint::reduce(uint64_t(buf1[i].a) * buf2[i].a); intt(buf1, M, false); Vec<mint> s(l); mint invm = mint(M).inverse(); for (int i = 0; i < l; ++i) s[i] = buf1[i] * invm; return s; } void ntt_doubling(Vec<mint>& a) { int M = (int)a.size(); for (int i = 0; i < M; i++) buf1[i].a = a[i].a; intt(buf1, M); mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1)); for (int i = 0; i < M; i++) buf1[i] *= r, r *= zeta; ntt(buf1, M); a.resize(2 * M); for (int i = 0; i < M; i++) a[M + i].a = buf1[i].a; } }; template<typename mint> struct FormalPowerSeries : Vec<mint> { using Vec<mint>::Vec; using FPS = FormalPowerSeries; FPS& operator+=(const FPS& r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i]; return *this; } FPS& operator+=(const mint& r) { if (this->empty()) this->resize(1); (*this)[0] += r; return *this; } FPS& operator-=(const FPS& r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i]; return *this; } FPS& operator-=(const mint& r) { if (this->empty()) this->resize(1); (*this)[0] -= r; return *this; } FPS& operator*=(const mint& v) { for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v; return *this; } FPS& operator/=(const FPS& r) { if (this->size() < r.size()) { this->clear(); return *this; } int n = this->size() - r.size() + 1; if ((int)r.size() <= 64) { FPS f(*this), g(r); g.shrink(); mint coeff = g.back().inverse(); for (auto& x : g) x *= coeff; int deg = (int)f.size() - (int)g.size() + 1; int gs = g.size(); FPS quo(deg); for (int i = deg - 1; i >= 0; i--) { quo[i] = f[i + gs - 1]; for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j]; } *this = quo * coeff; this->resize(n, mint(0)); return *this; } return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev(); } FPS& operator%=(const FPS& r) { *this -= *this / r * r; shrink(); return *this; } FPS operator+(const FPS& r) const { return FPS(*this) += r; } FPS operator+(const mint& v) const { return FPS(*this) += v; } FPS operator-(const FPS& r) const { return FPS(*this) -= r; } FPS operator-(const mint& v) const { return FPS(*this) -= v; } FPS operator*(const FPS& r) const { return FPS(*this) *= r; } FPS operator*(const mint& v) const { return FPS(*this) *= v; } FPS operator/(const FPS& r) const { return FPS(*this) /= r; } FPS operator%(const FPS& r) const { return FPS(*this) %= r; } FPS operator-() const { FPS ret(this->size()); for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i]; return ret; } void shrink() { while (this->size() && this->back() == mint(0)) this->pop_back(); } FPS rev() const { FPS ret(*this); reverse(begin(ret), end(ret)); return ret; } FPS dot(FPS r) const { FPS ret(std::min(this->size(), r.size())); for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i]; return ret; } FPS pre(int sz) const { return FPS(begin(*this), begin(*this) + std::min((int)this->size(), sz)); } FPS operator>>(int sz) const { if ((int)this->size() <= sz) return {}; FPS ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } FPS operator<<(int sz) const { FPS ret(*this); ret.insert(ret.begin(), sz, mint(0)); return ret; } FPS diff() const { const int n = (int)this->size(); FPS ret(std::max(0, n - 1)); mint one(1), coeff(1); for (int i = 1; i < n; i++) { ret[i - 1] = (*this)[i] * coeff; coeff += one; } return ret; } FPS integral() const { const int n = (int)this->size(); FPS ret(n + 1); ret[0] = mint(0); if (n > 0) ret[1] = mint(1); auto mod = mint::get_mod(); for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i); for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i]; return ret; } mint eval(mint x) const { mint r = 0, w = 1; for (auto& v : *this) r += w * v, w *= x; return r; } FPS log(int deg = -1) const { assert((*this)[0] == mint(1)); if (deg == -1) deg = (int)this->size(); return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } FPS pow(int64_t k, int deg = -1) const { const int n = (int)this->size(); if (deg == -1) deg = n; for (int i = 0; i < n; i++) { if ((*this)[i] != mint(0)) { if (i * k > deg) return FPS(deg, mint(0)); mint rev = mint(1) / (*this)[i]; FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg) * ((*this)[i].pow(k)); ret = (ret << (i * k)).pre(deg); if ((int)ret.size() < deg) ret.resize(deg, mint(0)); return ret; } } return FPS(deg, mint(0)); } static void* ntt_ptr; static void set_fft(); FPS& operator*=(const FPS& r); void ntt(); void intt(); void ntt_doubling(); static int ntt_pr(); FPS inv(int deg = -1) const; FPS exp(int deg = -1) const; }; template<typename mint> void* FormalPowerSeries<mint>::ntt_ptr = nullptr; /** * @brief 多項式/形式的冪級数ライブラリ * @docs docs/fps/formal-power-series.md */ template<typename mint> void FormalPowerSeries<mint>::set_fft() { if (!ntt_ptr) ntt_ptr = new NTT<mint>; } template<typename mint> FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(const FormalPowerSeries<mint>& r) { if (this->empty() || r.empty()) { this->clear(); return *this; } set_fft(); auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r); return *this = FormalPowerSeries<mint>(ret.begin(), ret.end()); } template<typename mint> void FormalPowerSeries<mint>::ntt() { set_fft(); static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this); } template<typename mint> void FormalPowerSeries<mint>::intt() { set_fft(); static_cast<NTT<mint>*>(ntt_ptr)->intt(*this); } template<typename mint> void FormalPowerSeries<mint>::ntt_doubling() { set_fft(); static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this); } template<typename mint> int FormalPowerSeries<mint>::ntt_pr() { set_fft(); return static_cast<NTT<mint>*>(ntt_ptr)->pr; } template<typename mint> FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const { assert((*this)[0] != mint(0)); if (deg == -1) deg = (int)this->size(); FormalPowerSeries<mint> res(deg); res[0] = {mint(1) / (*this)[0]}; for (int d = 1; d < deg; d <<= 1) { FormalPowerSeries<mint> f(2 * d), g(2 * d); for (int j = 0; j < std::min((int)this->size(), 2 * d); j++) f[j] = (*this)[j]; for (int j = 0; j < d; j++) g[j] = res[j]; f.ntt(); g.ntt(); for (int j = 0; j < 2 * d; j++) f[j] *= g[j]; f.intt(); for (int j = 0; j < d; j++) f[j] = 0; f.ntt(); for (int j = 0; j < 2 * d; j++) f[j] *= g[j]; f.intt(); for (int j = d; j < std::min(2 * d, deg); j++) res[j] = -f[j]; } return res.pre(deg); } template<typename mint> FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const { using fps = FormalPowerSeries<mint>; assert((*this).size() == 0 || (*this)[0] == mint(0)); if (deg == -1) deg = this->size(); fps inv; inv.reserve(deg + 1); inv.push_back(mint(0)); inv.push_back(mint(1)); auto inplace_integral = [&](fps& F) -> void { const int n = (int)F.size(); auto mod = mint::get_mod(); while ((int)inv.size() <= n) { int i = inv.size(); inv.push_back((-inv[mod % i]) * (mod / i)); } F.insert(begin(F), mint(0)); for (int i = 1; i <= n; i++) F[i] *= inv[i]; }; auto inplace_diff = [](fps& F) -> void { if (F.empty()) return; F.erase(begin(F)); mint coeff = 1, one = 1; for (int i = 0; i < (int)F.size(); i++) { F[i] *= coeff; coeff += one; } }; fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1}; for (int m = 2; m < deg; m *= 2) { auto y = b; y.resize(2 * m); y.ntt(); z1 = z2; fps z(m); for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i]; z.intt(); fill(begin(z), begin(z) + m / 2, mint(0)); z.ntt(); for (int i = 0; i < m; ++i) z[i] *= -z1[i]; z.intt(); c.insert(end(c), begin(z) + m / 2, end(z)); z2 = c; z2.resize(2 * m); z2.ntt(); fps x(begin(*this), begin(*this) + std::min<int>(this->size(), m)); x.resize(m); inplace_diff(x); x.push_back(mint(0)); x.ntt(); for (int i = 0; i < m; ++i) x[i] *= y[i]; x.intt(); x -= b.diff(); x.resize(2 * m); for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0); x.ntt(); for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i]; x.intt(); x.pop_back(); inplace_integral(x); for (int i = m; i < std::min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i]; fill(begin(x), begin(x) + m, mint(0)); x.ntt(); for (int i = 0; i < 2 * m; ++i) x[i] *= y[i]; x.intt(); b.insert(end(b), begin(x) + m, end(x)); } return fps{begin(b), begin(b) + deg}; } /** * @brief NTT mod用FPSライブラリ * @docs docs/fps/ntt-friendly-fps.md */ template<typename fps> fps multivariate_multiplication(const fps& f, const fps& g, const Vec<int>& base) { int n = f.size(), s = base.size(), W = 1; if (s == 0) return fps{f[0] * g[0]}; while (W < 2 * n) W *= 2; Vec<int> chi(n); for (int i = 0; i < n; i++) { int x = i; for (int j = 0; j < s - 1; j++) chi[i] += (x /= base[j]); chi[i] %= s; } Vec<fps> F(s, fps(W)), G(s, fps(W)); for (int i = 0; i < n; i++) F[chi[i]][i] = f[i], G[chi[i]][i] = g[i]; for (auto& x : F) x.ntt(); for (auto& x : G) x.ntt(); fps a(s); for (int k = 0; k < W; k++) { fill(begin(a), end(a), typename fps::value_type()); for (int i = 0; i < s; i++) for (int j = 0; j < s; j++) { a[i + j - (i + j >= s ? s : 0)] += F[i][k] * G[j][k]; } for (int i = 0; i < s; i++) F[i][k] = a[i]; } for (auto& x : F) x.intt(); fps h(n); for (int i = 0; i < n; i++) h[i] = F[chi[i]][i]; return h; } /** * @brief Multivariate Multiplication * @docs docs/ntt/multivariate-multiplication.md */ template<uint32_t mod> struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(r * mod == 1, "invalid, r * mod != 1"); static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t& b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64& b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint& operator+=(const mint& b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint& operator-=(const mint& b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint& operator*=(const mint& b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint& operator/=(const mint& b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint& b) const { return mint(*this) += b; } constexpr mint operator-(const mint& b) const { return mint(*this) -= b; } constexpr mint operator*(const mint& b) const { return mint(*this) *= b; } constexpr mint operator/(const mint& b) const { return mint(*this) /= b; } constexpr bool operator==(const mint& b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint& b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { return pow(mod - 2); } friend Ostream& operator<<(Ostream& os, const mint& b) { return os << b.get(); } friend Istream& operator>>(Istream& is, mint& b) { int64_t t; is >> t; b = LazyMontgomeryModInt<mod>(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; constexpr u32 MOD = (1 << 20) * 115 + 1; // 120586241 using mint = LazyMontgomeryModInt<MOD>; using fps = FormalPowerSeries<mint>; int main() { const auto [N, K, M, T] = in.tup<int, int, i64, int>(); const auto as = in.vec<int>(N); Vec<int> ns(K); for (int i : rep(K)) { if (i < T) { ns[i] = 10; } else { ns[i] = 20; } } Vec<int> p10s(K + 1, 1); Vec<int> p20s(K + 1, 1); for (int i : rep(K)) { p10s[i + 1] = p10s[i] * 10; p20s[i + 1] = p20s[i] * 20; } const int B1 = p10s[T]; const int B2 = p20s[K - T]; auto d2x = [&, K = K, T = T]( int D) -> int { // dは10進数,xは(20,20,...,10,10,...)進数 int X = 0; int B = 1; for (int i : rep(K)) { const int dig = (i < T ? 10 : 20); X += (D % 10) * B; D /= 10; B *= dig; } return X; }; auto x2d = [&, K = K, T = T](int X) -> Pair<bool, int> { int D = 0; for (int i : rep(K)) { const int dig = (i < T ? 10 : 20); if (X % dig >= 10) { return {false, 0}; } D += p10s[i] * (X % dig); X /= dig; } return {true, D}; }; auto mul = [&, K = K, T = T](const fps& f, const fps& g) { auto h = multivariate_multiplication(f, g, ns); for (int n2 : rep(B2)) { int tmp = n2; int nn2 = 0; for (int i : rep(K - T)) { int d = tmp % 20; tmp /= 20; nn2 += (d % 10) * p20s[i]; } if (n2 == nn2) { continue; } for (int n1 : rep(B1)) { h[nn2 * B1 + n1] += h[n2 * B1 + n1]; h[n2 * B1 + n1] = 0; } } void(0); return h; }; auto power = Fix([&](auto dfs, const fps& f, const i64 M) -> fps { if (M == 1) { return f; } else if (M % 2 == 0) { return dfs(mul(f, f), M / 2); } else { return mul(dfs(f, M - 1), f); } }); fps f(B2 * B1, 0); for (int i : rep(N)) { f[d2x(as[i])] += 1; } Vec<mint> ans(p10s[K]); const auto dp = power(f, M); for (int i : rep(B1 * B2)) { const auto [b, j] = x2d(i); if (b) { ans[j] += dp[i]; } } for (int i : rep(p10s[K])) { out.ln(ans[i]); } return 0; }