#include #ifdef DEBUG #include #else #define dump(...) #endif /** * @title modint * @docs mint.md */ template class ModInt{ public: constexpr static uint32_t MOD = M; uint64_t val; constexpr ModInt(): val(0){} constexpr ModInt(int64_t n){ if(n >= M) val = n % M; else if(n < 0) val = n % M + M; else val = n; } inline constexpr auto operator+(const ModInt &a) const {return ModInt(val + a.val);} inline constexpr auto operator-(const ModInt &a) const {return ModInt(val - a.val);} inline constexpr auto operator*(const ModInt &a) const {return ModInt(val * a.val);} inline constexpr auto operator/(const ModInt &a) const {return ModInt(val * a.inv().val);} inline constexpr auto& operator=(const ModInt &a){val = a.val; return *this;} inline constexpr auto& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;} inline constexpr auto& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;} inline constexpr auto& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;} inline constexpr auto& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;} inline constexpr bool operator==(const ModInt &a) const {return val == a.val;} inline constexpr bool operator!=(const ModInt &a) const {return val != a.val;} inline constexpr auto& operator++(){*this += 1; return *this;} inline constexpr auto& operator--(){*this -= 1; return *this;} inline constexpr auto operator++(int){auto t = *this; *this += 1; return t;} inline constexpr auto operator--(int){auto t = *this; *this -= 1; return t;} inline constexpr static ModInt power(int64_t n, int64_t p){ if(p < 0) return power(n, -p).inv(); int64_t ret = 1, e = n % M; for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M; return ret; } inline constexpr static ModInt inv(int64_t a){ int64_t b = M, u = 1, v = 0; while(b){ int64_t t = a / b; a -= t * b; std::swap(a,b); u -= t * v; std::swap(u,v); } u %= M; if(u < 0) u += M; return u; } inline constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);} inline constexpr auto power(int64_t p) const {return power(val, p);} inline constexpr auto inv() const {return inv(val);} friend inline constexpr auto operator-(const ModInt &a){return ModInt(-a.val);} friend inline constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;} friend inline constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;} friend inline constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;} friend inline constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;} friend std::istream& operator>>(std::istream &s, ModInt &a){s >> a.val; return s;} friend std::ostream& operator<<(std::ostream &s, const ModInt &a){s << a.val; return s;} template inline static auto div(){ static auto value = inv(N); return value; } explicit operator int32_t() const noexcept {return val;} explicit operator int64_t() const noexcept {return val;} }; /** * @docs input_vector.md */ template std::vector input_vector(int N){ std::vector ret(N); for(int i = 0; i < N; ++i) std::cin >> ret[i]; return ret; } template std::vector> input_vector(int N, int M){ std::vector> ret(N); for(int i = 0; i < N; ++i) ret[i] = input_vector(M); return ret; } /** * @title NumberTheoreticTransform * @docs ntt_convolution.md */ template class NumberTheoreticTransform{ const int MAX_POWER; std::vector BASE, INV_BASE; public: NumberTheoreticTransform(): MAX_POWER(__builtin_ctz(MAX_SIZE)), BASE(MAX_POWER + 1), INV_BASE(MAX_POWER + 1) { static_assert((MAX_SIZE & (MAX_SIZE - 1)) == 0, "MAX_SIZE must be power of 2."); T t = T::power(PRIM_ROOT, (T::MOD-1) >> (MAX_POWER + 2)); T s = t.inv(); for(int i = MAX_POWER - 1; i >= 0; --i){ t *= t; s *= s; BASE[i] = -t; INV_BASE[i] = -s; } } void run_ntt(std::vector &f, bool INVERSE = false){ const int n = f.size(); assert((n & (n-1)) == 0 and n <= MAX_SIZE); // データ数は2の冪乗個 if(INVERSE){ for(int b = 1; b < n; b <<= 1){ T w = 1; for(int j = 0, k = 1; j < n; j += 2 * b, ++k){ for(int i = 0; i < b; ++i){ const auto s = f[i+j]; const auto t = f[i+j+b]; f[i+j] = s + t; f[i+j+b] = (s - t) * w; } w *= INV_BASE[__builtin_ctz(k)]; } } const T t = T::inv(n); for(auto &x : f) x *= t; }else{ for(int b = n >> 1; b; b >>= 1){ T w = 1; for(int j = 0, k = 1; j < n; j += 2 * b, ++k){ for(int i = 0; i < b; ++i){ const auto s = f[i+j]; const auto t = f[i+j+b] * w; f[i+j] = s + t; f[i+j+b] = s - t; } w *= BASE[__builtin_ctz(k)]; } } } } template std::vector run_convolution(std::vector f, std::vector g){ const int m = f.size() + g.size() - 1; int n = 1; while(n < m) n *= 2; std::vector f2(n), g2(n); for(int i = 0; i < (int)f.size(); ++i) f2[i] = f[i]; for(int i = 0; i < (int)g.size(); ++i) g2[i] = g[i]; run_ntt(f2); run_ntt(g2); for(int i = 0; i < n; ++i) f2[i] *= g2[i]; run_ntt(f2, true); return f2; } }; using mint = ModInt<998244353>; constexpr int PRIM_ROOT = 3; int main(){ int N, Q; while(std::cin >> N >> Q){ auto A = input_vector(N); auto B = input_vector(Q); std::vector f = {1}; for(auto x : A){ std::vector g(f.size() + 1); for(int i = 0; i < (int)f.size(); ++i) g[i+1] = f[i]; for(int i = 0; i < (int)f.size(); ++i) f[i] *= x - 1; f.push_back(0); for(int i = 0; i < (int)f.size(); ++i) f[i] += g[i]; if((int)f.size() > N+1) f.resize(N+1); } for(auto &x : B){ std::cout << f[x] << "\n"; } } return 0; }