// #pragma GCC optimize("O3,unroll-loops") #pragma GCC optimize("Ofast") #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif template T rd_integer() { T ret = 0; bool minus = false; char c = getchar_unlocked(); while (!isdigit(c)) minus |= (c == '-'), c = getchar_unlocked(); while (isdigit(c)) ret = (ret << 1) + (ret << 3) + (c ^ 48), c = getchar_unlocked(); return minus ? -ret : ret; } int rdi() { return rd_integer(); } long long rdll() { return rd_integer(); } template void wt_integer(T x, char delim) { if (x == 0) { putchar('0'), putchar(delim); return; } if (x < 0) putchar('-'), x = -x; static char cache[20]; char *head = cache; while (x) *head = '0' + x % 10, head++, x /= 10; while (head != cache) putchar(*(--head)); putchar(delim); } constexpr int md = (115 << 20) + 1; #include using mint = atcoder::static_modint; #include // Multivariate convolution (Linear, overflow cutoff) // Complexity: (kN \log N + k^2 N)$ // Note that the vectors store the infomation in **column-major order** // Implementation idea: https://rushcheyo.blog.uoj.ac/blog/6547 // Details of my implementation: https://hitonanode.github.io/cplib-cpp/convolution/multivar_ntt.hpp template struct multivar_ntt { int K, N, fftlen; std::vector dim; std::vector chi; MODINT invfftlen; vector g; std::vector> gex, hex; vector> chi2i; private: void _initialize(const std::vector &dim_) { dim = dim_; K = dim_.size(); N = std::accumulate(dim_.begin(), dim_.end(), 1, [&](int l, int r) { return l * r; }); fftlen = 1; while (fftlen < N * 2) fftlen <<= 1; invfftlen = MODINT(fftlen).inv(); chi.resize(fftlen); int t = 1; for (auto d : dim_) { t *= d; for (int s = t; s < fftlen; s += t) chi[s] += 1; } for (int i = 0; i + 1 < fftlen; i++) { chi[i + 1] += chi[i]; if (chi[i + 1] >= K) chi[i + 1] -= K; } chi2i.assign(K, {}); if (K) { for (int i = 0; i < N; ++i) chi2i[chi[i]].push_back(i); } } public: void operator()(std::vector &f) { assert(int(f.size()) == N); assert(int(g.size()) == N); if (dim.empty()) { f[0] *= g[0]; return; } hex.assign(K, std::vector(fftlen)); vector fexdf(fftlen); for (int df = 0; df < K; ++df) { fexdf.assign(fftlen, 0); for (auto i : chi2i[df]) { fexdf[i] = f[i]; } atcoder::internal::butterfly(fexdf); for (int dg = 0; dg < K; dg++) { int dh = (df + dg < K) ? df + dg : df + dg - K; for (int i = 0; i < fftlen; i++) hex[dh][i] += fexdf[i] * gex[dg][i]; } } for (auto &vec : hex) atcoder::internal::butterfly_inv(vec); for (int i = 0; i < N; i++) f[i] = hex[chi[i]][i] * invfftlen; } multivar_ntt(const std::vector &dim_) { _initialize(dim_); } void set_g(const vector &g_) { g = g_; gex.assign(K, vector(fftlen)); if (dim.empty()) return; for (int i = 0; i < N; i++) gex[chi[i]][i] = g[i]; for (auto &vec : gex) atcoder::internal::butterfly(vec); } void double_g() { if (!K) { g[0] *= g[0]; return; } vector ftmp(K), gtmp(K * 2); for (int i = 0; i < fftlen; ++i) { gtmp.assign(K * 2, 0); for (int k = 0; k < K; ++k) ftmp[k] = gex[k][i], gtmp[k * 2] = ftmp[k] * ftmp[k]; for (int k = 0; k < K; ++k) { for (int l = 0; l < k; ++l) gtmp[k + l] += ftmp[k] * ftmp[l] * 2; } for (int k = 0; k < K; ++k) gex[k][i] = gtmp[k] + gtmp[k + K]; } for (auto &vec : gex) atcoder::internal::butterfly_inv(vec); for (int i = 0; i < N; ++i) g[i] = gex[chi[i]][i] * invfftlen; gex.assign(K, vector(fftlen)); for (int i = 0; i < N; i++) gex[chi[i]][i] = g[i]; for (auto &vec : gex) atcoder::internal::butterfly(vec); } }; void ntt(vector &vec, bool tf) { if (tf) { atcoder::internal::butterfly_inv(vec); mint szinv = mint(vec.size()).inv(); for (auto &x : vec) x *= szinv; } else { atcoder::internal::butterfly(vec); } } template std::vector inv_of_poly_mod_monomial(const std::vector &f, int l) { assert(l > 0); if (f.empty()) return {}; const ModInt ret0 = f[0].inv(); if (ret0 * f[0] != ModInt(1)) return {}; std::vector ret{ret0}; unsigned sz = 1; while (ret.size() < l) { std::vector h0(sz * 2), h1(sz * 2), a(sz * 2); std::copy(ret.begin(), ret.end(), a.begin()); std::copy(f.begin(), f.begin() + std::min(sz, f.size()), h0.begin()); if (int(f.size()) >= sz) std::copy(f.begin() + sz, f.begin() + std::min(sz * 2, f.size()), h1.begin()); ntt(a, false); ntt(h0, false); ntt(h1, false); for (unsigned i = 0; i < sz * 2; i++) h0[i] *= a[i]; for (unsigned i = 0; i < sz * 2; i++) h1[i] *= a[i]; ntt(h0, true); ntt(h1, true); for (unsigned i = 0; i < sz; i++) h1[i] += h0[i + sz]; std::fill(h1.begin() + sz, h1.end(), 0); ntt(h1, false); for (unsigned i = 0; i < sz * 2; i++) h1[i] *= a[i]; ntt(h1, true); ret.resize(std::min(sz * 2, l)); for (unsigned i = sz; i < ret.size(); i++) ret[i] = -h1[i - sz]; sz *= 2; } return ret; } // https://uoj.ac/submission/460059 using fps = vector; fps multi_inv(const fps &f, const vector &base) { assert(!f.empty() && f[0] != 0); int n = f.size(), s = base.size(), W = 1; while (W < 2 * n) W *= 2; vector chi(W); for (int i = 0; i < W; i++) { int x = i; for (int j = 0; j < s - 1; j++) chi[i] += (x /= base[j]); chi[i] %= s; } auto hadamard_prod = [&s](vector &F, vector &G, vector &H) { fps a(s); for (int k = 0; k < (int)F[0].size(); 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++) H[i][k] = a[i]; } }; fps g(W); g[0] = f[0].inv(); for (int d = 1; d < n; d *= 2) { vector F(s, fps(2 * d)), G(s, fps(2 * d)), H(s, fps(2 * d)); for (int j = 0; j < min((int)f.size(), 2 * d); j++) F[chi[j]][j] = f[j]; for (int j = 0; j < d; j++) G[chi[j]][j] = g[j]; for (auto &x : F) ntt(x, false); for (auto &x : G) ntt(x, false); hadamard_prod(F, G, H); for (auto &x : H) ntt(x, true); for (auto &x : F) fill(begin(x), end(x), typename fps::value_type()); for (int j = d; j < 2 * d; j++) F[chi[j]][j] = H[chi[j]][j]; for (auto &x : F) ntt(x, false); hadamard_prod(F, G, H); for (auto &x : H) ntt(x, true); for (int j = d; j < 2 * d; j++) g[j] = -H[chi[j]][j]; } return {begin(g), begin(g) + n}; } int main() { auto START = std::chrono::system_clock::now(); constexpr int E = 10; const mint r10 = 9142366; int N = rdi(), K = rdi(); lint M = rdll(); int T = rdi(); // M %= mint::mod() - 1; int K10 = 1; REP(t, K) K10 *= 10; vector diminfo(T, E); // T 桁切捨,K - T 桁周期 multivar_ntt mntt(diminfo); vector nttmat(E, vector(E)); REP(i, nttmat.size()) REP(j, nttmat[i].size()) nttmat[i][j] = r10.pow(i * j); auto inttmat = nttmat; for (auto &vec : inttmat) for (auto &x : vec) x = x.inv() / mint(10); auto ntt10 = [&](const array &v) { array ret; ret.fill(0); REP(i, E) REP(j, E) ret[i] += nttmat[i][j] * v[j]; return ret; }; auto intt10 = [&](const array &v) { array ret; ret.fill(0); REP(i, E) REP(j, E) ret[i] += inttmat[i][j] * v[j]; return ret; }; auto circular_ntt = [&](vector &f) { for (int di = mntt.N; di < K10; di *= 10) { for (int l = 0; l < K10; l += di * 10) { for (int i = l; i < l + di; ++i) { // [i, i + di, i + 2di, ..., i + 9di] を NTT auto impose_ntt = [&](vector &v) { static array ntttmp; ntttmp.fill(0); REP(k, E) ntttmp[k] = v[i + k * di]; ntttmp = ntt10(ntttmp); REP(k, E) v[i + k * di] = ntttmp[k]; }; impose_ntt(f); } } } }; auto circular_intt = [&](vector &g) { for (int di = mntt.N; di < K10; di *= 10) { for (int l = 0; l < K10; l += di * 10) { for (int i = l; i < l + di; ++i) { // [i, i + di, i + 2di, ..., i + 9di] を NTT auto impose_intt = [&](vector &v) { static array ntttmp; REP(k, E) ntttmp[k] = v[i + k * di]; ntttmp = intt10(ntttmp); REP(k, E) v[i + k * di] = ntttmp[k]; }; impose_intt(g); } } } }; vector dp(K10), trans(K10); dp[0] = 1; while (N--) trans[rdi()] += 1; circular_ntt(dp); circular_ntt(trans); // 寝たい for (int l = 0; l < K10; l += mntt.N) { vector fsub(dp.begin() + l, dp.begin() + l + mntt.N); vector gsub(trans.begin() + l, trans.begin() + l + mntt.N); lint p = M; if (gsub[0] == 0) chmin(p, 100000LL); else if (K > 0 and __builtin_popcountll(p) > __builtin_popcountll(p + 1) + 15) { // すみません... dbg("red"); p++; auto ginv = multi_inv(gsub, mntt.dim); mntt.set_g(ginv); mntt(fsub); } // Multivar pow なにもわからない...... mntt.set_g(gsub); while (p) { if (p & 1) mntt(fsub); p /= 2; if (!p) break; mntt.double_g(); } REP(i, fsub.size()) dp[i + l] = fsub[i]; } circular_intt(dp); // #ifndef HITONANODE_LOCAL for (auto x : dp) wt_integer(x.val(), '\n'); // #endif int64_t spent_ms = std::chrono::duration_cast(std::chrono::system_clock::now() - START).count(); dbg(spent_ms); }