#include //#include //#pragma GCC optimize("O2") using namespace std; #define reps(i,s,n) for(int i = s; i < n; i++) #define rep(i,n) reps(i,0,n) #define Rreps(i,n,e) for(int i = n - 1; i >= e; --i) #define Rrep(i,n) Rreps(i,n,0) #define ALL(a) a.begin(), a.end() using ll = long long; using vec = vector; using mat = vector; ll N,M,H,W,Q,K,A,B; string S; using P = pair; const ll INF = (1LL<<60); template bool chmin(T &a, const T &b){ if(a > b) {a = b; return true;} else return false; } template bool chmax(T &a, const T &b){ if(a < b) {a = b; return true;} else return false; } template void print_vector(std::vector v,bool endline = true){ if(!v.empty()){ for(std::size_t i{}; i class modint{ public: ll x; constexpr modint(){x = 0;} constexpr modint(ll _x) : x((_x < 0 ? ((_x += (LLONG_MAX / mod) * mod) < 0 ? _x + (LLONG_MAX / mod) * mod : _x) : _x)%mod){} constexpr modint set_raw(ll _x){ //_x in [0, mod) x = _x; return *this; } constexpr modint operator-(){ return x == 0 ? 0 : mod - x; } constexpr modint& operator+=(const modint& a){ if((x += a.x) >= mod) x -= mod; return *this; } constexpr modint operator+(const modint& a) const{ return modint(*this) += a; } constexpr modint& operator-=(const modint& a){ if((x -= a.x) < 0) x += mod; return *this; } constexpr modint operator-(const modint& a) const{ return modint(*this) -= a; } constexpr modint& operator*=(const modint& a){ (x *= a.x)%=mod; return *this; } constexpr modint operator*(const modint& a) const{ return modint(*this) *= a; } constexpr modint pow(unsigned long long pw) const{ modint res(1), comp(*this); while(pw){ if(pw&1) res *= comp; comp *= comp; pw >>= 1; } return res; } //以下、modが素数のときのみ constexpr modint inv() const{ if(x == 2) return (mod + 1) >> 1; return modint(*this).pow(mod - 2); } constexpr modint& operator/=(const modint &a){ (x *= a.inv().x)%=mod; return *this; } constexpr modint operator/(const modint &a) const{ return modint(*this) /= a; } }; #define mod1 998244353 using mint = modint; ostream& operator<<(ostream& os, const mint& a){ os << a.x; return os; } using vm = vector; class NTT{ static int root; static vector id; static void make_bit_reverse(int n){ if(n == (int)id.size()) return; if(n == (int)id.size() * 2){ int n2 = (int)id.size(); id.resize(n); rep(i, n2) { id[i] <<= 1; id[i | n2] = id[i] | 1; } }else { id.resize(n); iota(ALL(id), 0); for (int i = 1; (1 << i) <= n; ++i) { int l = 1 << (i - 1), r = 1 << i; int plus = n >> i; for (int j = l; j < r; ++j) { int temp = id[j - l] + plus; if (j < temp) swap(id[j], id[temp]); } } } } static void dft(int n, vm &f, bool inv){ make_bit_reverse(n); rep(i, n) if (i > id[i]) swap(f[i], f[id[i]]); int l{1}; for (int len = 1; len < n; ++l, len <<= 1) { mint root_diff = mint(root).pow(inv ? (mod1 - 1) - ((mod1 - 1)>>l) : ((mod1 - 1)>>l)); int len2 = len << 1; for (int i = 0; i < n; i += len2) { mint z = 1; reps(j, i, i + len) { mint z_f = z * f[j + len]; f[j + len] = f[j] - z_f; f[j] += z_f; z *= root_diff; } } } if(inv) { mint n_inv = mint(n).inv(); rep(i, n) f[i] *= n_inv; } } public: static void dft_2D(int n, int m, vector &a, bool inv){ //簡単に、書き換える形で //aがn×mサイズであることや、n,mが2冪であることは仮定 rep(i, n) dft(m, a[i], inv); rep(j, m){ vm temp(n); rep(i, n) temp[i] = a[i][j]; dft(n, temp, inv); rep(i, n) a[i][j] = temp[i]; } } static vm convolution(vm g, vm h){ int sz = g.size() + h.size() - 1, n = 1; while(sz > n) n *= 2; g.resize(n); h.resize(n); dft(n, g, false); dft(n, h, false); rep(i, n) g[i] *= h[i]; dft(n, g, true); g.resize(sz); return g; } static vm simple_pow(vm &a, ll pw){ int sz = a.size(), n = 1; while(sz > n) n <<= 1; n <<= 1; vm res(n, 0), cpy(n, 0); res[0] = 1; copy(ALL(a), cpy.begin()); while(pw){ dft(n, cpy, false); if(pw&1){ dft(n, res, false); rep(i, n) res[i] *= cpy[i]; dft(n, res, true); reps(i, n / 2, n) res[i] = 0; } rep(i, n) cpy[i] *= cpy[i]; dft(n, cpy, true); reps(i, n / 2, n) cpy[i] = 0; pw >>= 1; } res.resize(sz); return res; } static vm inversion(vm f){ assert(f[0].x != 0); int n = 1, sz = 1, first_sz = f.size(); while(first_sz > n) n <<= 1; f.resize(n); vm g(n), cpy_f(n<<1), cpy_g(n<<1); g[0] = f[0].inv(); while(sz < n){ sz <<= 1; copy(f.begin(), f.begin() + sz, cpy_f.begin()); copy(g.begin(), g.begin() + sz, cpy_g.begin()); dft(sz<<1, cpy_f, false); dft(sz<<1, cpy_g, false); rep(i, sz<<1) cpy_f[i] *= cpy_g[i] * cpy_g[i]; dft(sz<<1, cpy_f, true); rep(i, sz) (g[i] += g[i])-= cpy_f[i]; } g.resize(first_sz); return g; } static vm differential(vm f){ int n = f.size(); rep(i, n) f[i] = (i == n - 1 ? 0 : f[i + 1] * (i + 1)); return f; } static vm integral(vm f){ int n = f.size(); Rrep(i, n) f[i] = (i ? f[i - 1] : 0); mint fct(1); reps(i, 1, n){f[i] *= fct; fct*=i;} fct = fct.inv(); Rreps(i, n, 1){f[i] *= fct; fct*=i;} return f; } static vm log(vm f){ assert(f[0].x == 1); vm res = convolution(differential(f), inversion(f)); res.resize((int)f.size()); return integral(res); } static vm exp(vm f){ assert(f[0].x == 0); int n = 1, sz = 1, first_sz = f.size(); while(first_sz > n) n <<= 1; f.resize(n); vm g(1, 1), log_g; while(sz < n){ sz <<= 1; g.resize(sz); reps(i, sz>>1, sz) g[i] = 0; log_g = log(g); rep(i, sz) log_g[i] = f[i] - log_g[i]; log_g[0] += 1; g = convolution(g, log_g); } g.resize(first_sz); return g; } static vm pow(vm f, ll pw_int){ int n = f.size(), non_zero_id{0}; mint pw(pw_int); vm res(n, 0); if(pw_int == 0){ res[0] = 1; return res; } while(non_zero_id < n && f[non_zero_id].x == 0) ++non_zero_id; if((n + pw_int - 1) / pw_int <= non_zero_id) return res; mint d = f[non_zero_id], d_inv = d.inv(); rep(i, n - non_zero_id) f[i] = f[i + non_zero_id] * d.inv(); non_zero_id *= pw_int; d = d.pow(pw_int%(mod1 - 1)); f.resize(n - non_zero_id); res = log(f); for(auto &e : res) e *= pw; res = exp(res); res.resize(n); Rrep(i, n) res[i] = (i >= non_zero_id ? res[i - non_zero_id] * d : 0); return res; } }; int NTT::root = 3; vector NTT::id; int main(){ //cin.tie(nullptr); //ios::sync_with_stdio(false); cin>>N>>Q; vm a(N*2), q(N, 0); rep(i, N) { cin>>a[i].x; a[i+N] = a[i]; } rep(i, Q){cin>>A; q[A ? (N - A) : A] += 1;} vm res = NTT::convolution(a, q); reps(i, N, N * 2) cout<