結果
問題 | No.1783 Remix Sum |
ユーザー |
👑 ![]() |
提出日時 | 2021-12-13 02:12:58 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 7,517 ms / 10,000 ms |
コード長 | 51,863 bytes |
コンパイル時間 | 3,269 ms |
コンパイル使用メモリ | 284,084 KB |
最終ジャッジ日時 | 2025-01-26 09:36:21 |
ジャッジサーバーID (参考情報) |
judge4 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 76 |
ソースコード
using namespace std;// intrinstic#include <immintrin.h>#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <cctype>#include <cfenv>#include <cfloat>#include <chrono>#include <cinttypes>#include <climits>#include <cmath>#include <complex>#include <cstdarg>#include <cstddef>#include <cstdint>#include <cstdio>#include <cstdlib>#include <cstring>#include <deque>#include <fstream>#include <functional>#include <initializer_list>#include <iomanip>#include <ios>#include <iostream>#include <istream>#include <iterator>#include <limits>#include <list>#include <map>#include <memory>#include <new>#include <numeric>#include <ostream>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <streambuf>#include <string>#include <tuple>#include <type_traits>#include <typeinfo>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>// utilitynamespace Nyaan {using ll = long long;using i64 = long long;using u64 = unsigned long long;using i128 = __int128_t;using u128 = __uint128_t;template <typename T>using V = vector<T>;template <typename T>using VV = vector<vector<T>>;using vi = vector<int>;using vl = vector<long long>;using vd = V<double>;using vs = V<string>;using vvi = vector<vector<int>>;using vvl = vector<vector<long long>>;template <typename T, typename U>struct P : pair<T, U> {template <typename... Args>P(Args... args) : pair<T, U>(args...) {}using pair<T, U>::first;using pair<T, U>::second;T &x() { return first; }const T &x() const { return first; }U &y() { return second; }const U &y() const { return second; }P &operator+=(const P &r) {first += r.first;second += r.second;return *this;}P &operator-=(const P &r) {first -= r.first;second -= r.second;return *this;}P &operator*=(const P &r) {first *= r.first;second *= r.second;return *this;}P operator+(const P &r) const { return P(*this) += r; }P operator-(const P &r) const { return P(*this) -= r; }P operator*(const P &r) const { return P(*this) *= r; }};using pl = P<ll, ll>;using pi = P<int, int>;using vp = V<pl>;constexpr int inf = 1001001001;constexpr long long infLL = 4004004004004004004LL;template <typename T>int sz(const T &t) {return t.size();}template <typename T, typename U>inline bool amin(T &x, U y) {return (y < x) ? (x = y, true) : false;}template <typename T, typename U>inline bool amax(T &x, U y) {return (x < y) ? (x = y, true) : false;}template <typename T>inline T Max(const vector<T> &v) {return *max_element(begin(v), end(v));}template <typename T>inline T Min(const vector<T> &v) {return *min_element(begin(v), end(v));}template <typename T>inline long long Sum(const vector<T> &v) {return accumulate(begin(v), end(v), 0LL);}template <typename T>int lb(const vector<T> &v, const T &a) {return lower_bound(begin(v), end(v), a) - begin(v);}template <typename T>int ub(const vector<T> &v, const T &a) {return upper_bound(begin(v), end(v), a) - begin(v);}constexpr long long TEN(int n) {long long ret = 1, x = 10;for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);return ret;}template <typename T, typename U>pair<T, U> mkp(const T &t, const U &u) {return make_pair(t, u);}template <typename T>vector<T> mkrui(const vector<T> &v, bool rev = false) {vector<T> ret(v.size() + 1);if (rev) {for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];} else {for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];}return ret;};template <typename T>vector<T> mkuni(const vector<T> &v) {vector<T> ret(v);sort(ret.begin(), ret.end());ret.erase(unique(ret.begin(), ret.end()), ret.end());return ret;}template <typename F>vector<int> mkord(int N, F f) {vector<int> ord(N);iota(begin(ord), end(ord), 0);sort(begin(ord), end(ord), f);return ord;}template <typename T>vector<int> mkinv(vector<T> &v) {int max_val = *max_element(begin(v), end(v));vector<int> inv(max_val + 1, -1);for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;return inv;}} // namespace Nyaan// bit operationnamespace Nyaan {__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {return _mm_popcnt_u64(a);}inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }template <typename T>inline int gbit(const T &a, int i) {return (a >> i) & 1;}template <typename T>inline void sbit(T &a, int i, bool b) {if (gbit(a, i) != b) a ^= T(1) << i;}constexpr long long PW(int n) { return 1LL << n; }constexpr long long MSK(int n) { return (1LL << n) - 1; }} // namespace Nyaan// inoutnamespace Nyaan {template <typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p) {os << p.first << " " << p.second;return os;}template <typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p) {is >> p.first >> p.second;return is;}template <typename T>ostream &operator<<(ostream &os, const vector<T> &v) {int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template <typename T>istream &operator>>(istream &is, vector<T> &v) {for (auto &x : v) is >> x;return is;}void in() {}template <typename T, class... U>void in(T &t, U &... u) {cin >> t;in(u...);}void out() { cout << "\n"; }template <typename T, class... U, char sep = ' '>void out(const T &t, const U &... u) {cout << t;if (sizeof...(u)) cout << sep;out(u...);}void outr() {}template <typename T, class... U, char sep = ' '>void outr(const T &t, const U &... u) {cout << t;outr(u...);}struct IoSetupNya {IoSetupNya() {cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetupnya;} // namespace Nyaan// debugnamespace DebugImpl {template <typename U, typename = void>struct is_specialize : false_type {};template <typename U>struct is_specialize<U, typename conditional<false, typename U::iterator, void>::type>: true_type {};template <typename U>struct is_specialize<U, typename conditional<false, decltype(U::first), void>::type>: true_type {};template <typename U>struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {};void dump(const char& t) { cerr << t; }void dump(const string& t) { cerr << t; }void dump(const bool& t) { cerr << (t ? "true" : "false"); }template <typename U,enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>void dump(const U& t) {cerr << t;}template <typename T>void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {string res;if (t == Nyaan::inf) res = "inf";if constexpr (is_signed<T>::value) {if (t == -Nyaan::inf) res = "-inf";}if constexpr (sizeof(T) == 8) {if (t == Nyaan::infLL) res = "inf";if constexpr (is_signed<T>::value) {if (t == -Nyaan::infLL) res = "-inf";}}if (res.empty()) res = to_string(t);cerr << res;}template <typename T, typename U>void dump(const pair<T, U>&);template <typename T>void dump(const pair<T*, int>&);template <typename T>void dump(const T& t,enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {cerr << "[ ";for (auto it = t.begin(); it != t.end();) {dump(*it);cerr << (++it == t.end() ? "" : ", ");}cerr << " ]";}template <typename T, typename U>void dump(const pair<T, U>& t) {cerr << "( ";dump(t.first);cerr << ", ";dump(t.second);cerr << " )";}template <typename T>void dump(const pair<T*, int>& t) {cerr << "[ ";for (int i = 0; i < t.second; i++) {dump(t.first[i]);cerr << (i == t.second - 1 ? "" : ", ");}cerr << " ]";}void trace() { cerr << endl; }template <typename Head, typename... Tail>void trace(Head&& head, Tail&&... tail) {cerr << " ";dump(head);if (sizeof...(tail) != 0) cerr << ",";trace(forward<Tail>(tail)...);}} // namespace DebugImpl#ifdef NyaanDebug#define trc(...) \do { \cerr << "## " << #__VA_ARGS__ << " = "; \DebugImpl::trace(__VA_ARGS__); \} while (0)#else#define trc(...) (void(0))#endif// macro#define each(x, v) for (auto&& x : v)#define each2(x, y, v) for (auto&& [x, y] : v)#define all(v) (v).begin(), (v).end()#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)#define reg(i, a, b) for (long long i = (a); i < (b); i++)#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)#define fi first#define se second#define ini(...) \int __VA_ARGS__; \in(__VA_ARGS__)#define inl(...) \long long __VA_ARGS__; \in(__VA_ARGS__)#define ins(...) \string __VA_ARGS__; \in(__VA_ARGS__)#define in2(s, t) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i]); \}#define in3(s, t, u) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i], u[i]); \}#define in4(s, t, u, v) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i], u[i], v[i]); \}#define die(...) \do { \Nyaan::out(__VA_ARGS__); \return; \} while (0)namespace Nyaan {void solve();}int main() { Nyaan::solve(); }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; }};template <typename mint>struct FormalPowerSeries : vector<mint> {using vector<mint>::vector;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(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) + 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(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*/__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_innertemplate <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(vector<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(vector<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;}vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {if (a.size() == 0 && b.size() == 0) return vector<mint>{};int l = a.size() + b.size() - 1;if (min<int>(a.size(), b.size()) <= 40) {vector<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);vector<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(vector<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>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 < 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 < 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) + 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 < 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 vector<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;vector<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;}vector<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*/using i32 = int32_t;using u32 = uint32_t;using i64 = int64_t;using u64 = uint64_t;const u32 MOD = 120586241;using mint = LazyMontgomeryModInt<MOD>;using fps = FormalPowerSeries<mint>;mint NTTg = ntt_inner::get_pr(MOD);mint root10[100];mint inv10[6];void ntt_10(fps& F, int s, int d){mint tmp[10] = {};rep(i,10) rep(j,10) tmp[j] += F[s+d*i] * root10[i*j];rep(i,10) F[s+d*i] = tmp[i];}void intt_10(fps& F, int s, int d){mint tmp[10] = {};rep(i,10) rep(j,10) tmp[j] += F[s+d*i] * root10[90-i*j];rep(i,10) F[s+d*i] = tmp[i];}u64 N,K,M,T;int ten_to_K;int ten_to_T;void ntt_rotation(fps& f){for(int d=ten_to_T; d<ten_to_K; d*=10){for(int s=0; s<ten_to_K; s+=d*10){for(int ss=s; ss<s+d; ss++) ntt_10(f, ss, d);}}}void intt_rotation(fps& f){for(int d=ten_to_T; d<ten_to_K; d*=10){for(int s=0; s<ten_to_K; s+=d*10){for(int ss=s; ss<s+d; ss++) intt_10(f, ss, d);}}for(int i=0; i<ten_to_K; i++) f[i] *= inv10[K-T];}void pow_rotation(fps& f, u64 p){ntt_rotation(f);rep(i,ten_to_K) f[i] = f[i].pow(p);intt_rotation(f);}void mul_rotation(fps& f, fps& nttg){ntt_rotation(f);rep(i,ten_to_K) f[i] *= nttg[i];intt_rotation(f);}void mul_full(fps& f, fps& nttg){ntt_rotation(f);for(int s=0; s<ten_to_K; s+=ten_to_T){fps tmp(ten_to_T);fps tmpg(ten_to_T);rep(i,ten_to_T) tmp[i] = f[s+i];rep(i,ten_to_T) tmpg[i] = nttg[s+i];tmp = multivariate_multiplication(tmp, tmpg, vector<int>(T,10));rep(i,ten_to_T) f[s+i] = tmp[i];}intt_rotation(f);}void nttmul_full(fps& nttf, fps& nttg){fps tmp(ten_to_T);fps tmpg(ten_to_T);for(int s=0; s<ten_to_K; s+=ten_to_T){rep(i,ten_to_T) tmp[i] = nttf[s+i];rep(i,ten_to_T) tmpg[i] = nttg[s+i];tmp = multivariate_multiplication(tmp, tmpg, vector<int>(T,10));rep(i,ten_to_T) nttf[s+i] = tmp[i];}}mint mCi[51];namespace Nyaan {void solve(){rep(t,100) root10[t] = NTTg.pow((MOD-1)/10*(t%10));inv10[0] = 1; rep(t,5) inv10[t+1] = inv10[t] / 10;cin >> N >> K >> M >> T;ten_to_K = 1; rep(t,K) ten_to_K *= 10;ten_to_T = 1; rep(t,T) ten_to_T *= 10;fps A(ten_to_K);fps B(ten_to_K);rep(i,N){int a; cin >> a;if(a % ten_to_T == 0) A[a] += 1;else B[a] += 1;}int Z = min(K*10,M);ntt_rotation(B);vector<fps> powB(Z+1);powB[0] = fps(ten_to_K); powB[0][0] = 1;ntt_rotation(powB[0]);rep(i,Z){powB[i+1] = powB[i];nttmul_full(powB[i+1], B);}mCi[0] = 1;for(int i=1; i<=Z; i++) mCi[i] = mCi[i-1] * (M-i+1) / i;fps powA = A;pow_rotation(powA, M - Z);rep(i, ten_to_K) if(i % ten_to_T != 0) powA[i] = 0;fps nttA = A;ntt_rotation(nttA);fps ans(ten_to_K);pow_rotation(A, M - Z);for(int i=Z; i>=1; i--){fps tmp = powA;mul_full(tmp, powB[i]);mul_rotation(powA, nttA);ans += tmp * mCi[i];}ans += powA;rep(i,ten_to_K) out(ans[i]);}}