// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; #define int ll #define double ld #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define rep1(i,n) for (int i = 1; i <= (int)(n); i++) #define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i,n) for (int i = (int)(n); i >= 1; i--) #define loop(i,a,B) for (int i = a; i B; i++) #define loopR(i,a,B) for (int i = a; i B; i--) #define all(x) (x).begin(), (x).end() #define allR(x) (x).rbegin(), (x).rend() #define pb push_back #define eb emplace_back #define mp make_pair #define fst first #define snd second #define INF (numeric_limits::max()/2-1) #ifdef LOCAL #include "debug.hpp" #define dump(...) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__) #define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl #define debug if (1) #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template using pque_max = priority_queue; template using pque_min = priority_queue, greater >; template ::value>::type> ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; } template ::value>::type> istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; } template constexpr bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(v.begin(), v.end(), x)-v.begin(); } template int ubd(C const& v, T const& x) { return upper_bound(v.begin(), v.end(), x)-v.begin(); } // <<< // >>> fast IO by yosupo template using V = vector; struct Scanner { FILE* fp = nullptr; char line[1 << 15]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += fread(line + ed, 1, (1 << 15) - ed, fp); } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) reread(); return true; } template ::value, int> = 0> bool read_single(T& ref) { if (!succ()) return false; while (true) { succ(); size_t sz = 1; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (st != ed) break; } return true; } template ::value, int> = 0> bool read_single(T& ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] - '0'); } if (neg) ref = -ref; return true; } template bool read_single(V& ref) { for (auto& d : ref) { if (!read_single(d)) return false; } return true; } void read() {} template void read(H& h, T&... t) { bool f = read_single(h); assert(f); read(t...); } Scanner(FILE* _fp) : fp(_fp) {} }; struct Printer { public: template void write() {} template void write(const H& h, const T&... t) { if (F) write_single(' '); write_single(h); write(t...); } template void writeln(const T&... t) { write(t...); write_single('\n'); } Printer(FILE* _fp) : fp(_fp) {} ~Printer() { flush(); } private: static constexpr size_t SIZE = 1 << 15; FILE* fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write_single(const char& val) { if (pos == SIZE) flush(); line[pos++] = val; } template ::value, int> = 0> void write_single(const T& val) { for (char c : val) write_single(c); } template ::value, int> = 0> void write_single(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write_single('0'); return; } if (val < 0) { write_single('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char('0' + (val % 10)); val /= 10; } reverse(small, small + len); memcpy(line + pos, small, len); pos += len; } template void write_single(const V& val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write_single(' '); write_single(val[i]); } } }; // <<< // >>> NTT template struct NTT { using modint = ModInt; static constexpr int64_t mod = ModInt::mod, gen = g, max_lg = __builtin_ctzll(mod-1); // mod:prime, g:primitive root static_assert(mod > 0 && g > 0 && max_lg > 0, ""); #define fast #ifdef fast using arr_t = array; static arr_t ws,iws; static void init() { for (int i = 0; i <= max_lg; i++) { ws[i] = -ModInt(g).pow((mod-1)>>(i+2)); iws[i] = ModInt(1)/ws[i]; } } static void ntt(ModInt a[], int lg) { for (int b = lg-1; b >= 0; b--) { ModInt w = 1; for (int i = 0, k = 0; i < (1<; static arr_t ws,iws; static void init() { for (int i = 0; i <= max_lg; i++) { ws[i] = ModInt(g).pow((mod-1)>>i); iws[i] = ModInt(1)/ws[i]; } } static void ntt(ModInt a[], int lg) { for (int b = lg-1; b >= 0; b--) { for (int i = 0; i < (1< conv(vector const& a, vector const& b) { vector aa(a.size()), bb(b.size()); rep (i,a.size()) aa[i] = a[i]; rep (i,b.size()) bb[i] = b[i]; auto cc = conv(move(aa), move(bb)); vector c(cc.size()); rep (i,c.size()) c[i] = cc[i].val(); return c; } static vector conv(vector a, vector b) { if (a.empty() || b.empty()) return {}; init(); const int s = a.size() + b.size() - 1, lg = __lg(2*s-1); assert(lg <= max_lg); a.resize(1< conv(vector const& a) { vector aa(a.size()); rep (i,a.size()) aa[i] = a[i]; auto cc = conv(move(aa)); vector c(cc.size()); rep (i,c.size()) c[i] = cc[i].val(); return c; } static vector conv(vector a) { if (a.empty()) return {}; init(); const int s = a.size() + a.size() - 1, lg = __lg(2*s-1); assert(lg <= max_lg); a.resize(1< typename NTT::arr_t NTT::ws; template typename NTT::arr_t NTT::iws; // <<< #define MONTGOMERY #ifdef MONTGOMERY // >>> montgomery modint template struct modint { using u32 = uint32_t; using u64 = uint64_t; using i64 = int64_t; using M = modint; static constexpr u32 mul_inv(u32 n, int e = 5, u32 x = 1) { return e == 0 ? x : mul_inv(n, e-1, x*(2-x*n)); } static constexpr u32 mod = MOD; static constexpr u32 nn = mul_inv(MOD); static constexpr u32 r2 = -u64(MOD) % MOD; u32 x; constexpr modint(i64 x = 0) : x(reduce(((x%=MOD)<0 ? x+MOD : x)*r2)) {} static constexpr u32 reduce(u64 w) { return u32(w >> 32) + MOD - i64((u64(u32(w) * nn) * MOD) >> 32); } constexpr bool operator==(M p) const { return val() == p.val(); } constexpr bool operator!=(M p) const { return val() != p.val(); } constexpr i64 val() const { i64 r = reduce(x); if (r >= MOD) r -= MOD; return r; } constexpr M operator+() const { return *this; } constexpr M operator-() const { M r; r.x = x ? i64(2*MOD)-x : 0; return r; } constexpr M &operator+=(M p) { i64 t = x; if (((t += p.x) -= 2*MOD) < 0) t += 2*MOD; x = t; return *this; } constexpr M &operator-=(M p) { return *this += -p; } constexpr M &operator*=(M p) { x = reduce(u64(x)*p.x); return *this; } constexpr M &operator/=(M p) { *this *= p.inv(); return *this; } constexpr M operator+(M p) const { return M(*this) += p; } constexpr M operator-(M p) const { return M(*this) -= p; } constexpr M operator*(M p) const { return M(*this) *= p; } constexpr M operator/(M p) const { return M(*this) /= p; } friend constexpr M operator+(i64 x, M y) { return M(x)+y; } friend constexpr M operator-(i64 x, M y) { return M(x)-y; } friend constexpr M operator*(i64 x, M y) { return M(x)*y; } friend constexpr M operator/(i64 x, M y) { return M(x)/y; } constexpr M inv() const { return pow(MOD - 2); } constexpr M pow(i64 n) const { if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } friend ostream &operator<<(ostream &os, M p) { return os << p.val(); } friend istream &operator>>(istream &is, M &a) { u32 t; is >> t; a = t; return is; } }; // <<< constexpr int64_t MOD = 1e9 + 7; using mint = modint; #else // >>> modint template class modint { static_assert(md > 0, ""); using M = modint; using ll = int64_t; int32_t x; public: static constexpr int32_t mod = md; constexpr modint(ll x = 0) : x((x%=mod) < 0 ? x+mod : x) { } constexpr ll val() const { return x; } constexpr bool operator==(M const& r) const { return x == r.x; } constexpr bool operator!=(M const& r) const { return x != r.x; } constexpr M operator+() const { return *this; } constexpr M operator-() const { return M()-*this; } constexpr M& operator+=(M const& r) { ll t = ll(x) + r.x; if (t >= mod) t -= mod; x = t; return *this; } constexpr M& operator-=(M const& r) { ll t = ll(x) + mod-r.x; if (t >= mod) t -= mod; x = t; return *this; } constexpr M& operator*=(M const& r) { return *this = *this * r; } constexpr M operator*(M const& r) const { M t; t.x = (ll(x)*r.x) % mod; return t; } constexpr M& operator/=(M const& r) { return *this *= r.inv(); } constexpr M operator+(M const& r) const { return M(*this) += r; } constexpr M operator-(M const& r) const { return M(*this) -= r; } constexpr M operator/(M const& r) const { return M(*this) /= r; } friend constexpr M operator+(ll x, M const& y) { return M(x)+y; } friend constexpr M operator-(ll x, M const& y) { return M(x)-y; } friend constexpr M operator*(ll x, M const& y) { return M(x)*y; } friend constexpr M operator/(ll x, M const& y) { return M(x)/y; } constexpr M pow(ll n) const { if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } constexpr M inv() const { assert(x > 0); ll t = 1, v = x, q = 0, r = 0; while (v != 1) { q = mod / v; r = mod % v; if (r * 2 < v) { t *= -q; t %= mod; v = r; } else { t *= q + 1; t %= mod; v -= r; } } if (t < 0) t += mod; M y; y.x = t; return y; } }; #ifdef LOCAL template string to_s(modint const& r) { return to_s(r.val(), MOD); } #endif template ostream& operator<<(ostream& os, modint const& r) { return os << r.val(); } template istream& operator>>(istream& is, modint &r) { int64_t x; is >> x; r = x; return is; } // <<< //constexpr int64_t MOD = 998244353; constexpr int64_t MOD = 1e9+7; using mint = modint<(int32_t)MOD>; #endif using ntt1 = NTT, 3>; // mod-1 = 5<<25 using ntt2 = NTT, 3>; // mod-1 = 7<<26 using ntt3 = NTT, 3>; // mod-1 = 73<<24 //using ntt3 = NTT, 3>; // mod-1 = 119<<23 // https://math314.hateblo.jp/entry/2015/05/07/014908 template constexpr ModInt garner(int64_t x, int64_t y, int64_t z) { constexpr int64_t m1 = ntt1::mod, m2 = ntt2::mod; constexpr auto m1_inv_m2 = ntt2::modint(m1).inv(); constexpr auto m12_inv_m3 = ntt3::modint(m1 * m2).inv(); constexpr auto m12_mod = ModInt(m1 * m2); auto v1 = (y - x) * m1_inv_m2; auto v2 = (z - (x + m1 * v1.val())) * m12_inv_m3; return x + m1 * v1.val() + m12_mod * v2.val(); } template vector conv(vector const& a, vector const& b) { vector aa(a.size()), bb(b.size()); rep (i,a.size()) aa[i] = a[i].val(); rep (i,b.size()) bb[i] = b[i].val(); auto x = ntt1::conv(aa, bb); auto y = ntt2::conv(aa, bb); auto z = ntt3::conv(aa, bb); vector ret(x.size()); rep (i,x.size()) ret[i] = garner(x[i],y[i],z[i]); return ret; } template vector conv(vector const& a) { vector aa(a.size()); rep (i,a.size()) aa[i] = a[i].val(); auto x = ntt1::conv(aa); auto y = ntt2::conv(aa); auto z = ntt3::conv(aa); vector ret(x.size()); rep (i,x.size()) ret[i] = garner(x[i],y[i],z[i]); return ret; } int32_t main() { Scanner sc(stdin); Printer pr(stdout); int p; sc.read(p); const int NN = 2e6 + 10; vector a(NN); a[0] = 0, a[1] = 1; rep (i,NN-2) a[i+2] = p*a[i+1] + a[i]; auto aa = conv(a); int Q; sc.read(Q); while (Q--) { int q; sc.read(q); pr.writeln(aa[q-2].val()); } }