#ifndef CLASS_FAST_MODINT #define CLASS_FAST_MODINT #include using singlebit = uint32_t; using doublebit = uint64_t; static constexpr int digit_level = 8 * sizeof(singlebit); static constexpr singlebit find_inv(singlebit n, int d = 6, singlebit x = 1) { return d == 0 ? x : find_inv(n, d - 1, x * (2 - x * n)); } template class fast_modint { // Fast Modulo Integer, Assertion: mod < 2^(bits of singlebit - 1) and mod is prime private: singlebit n; static constexpr singlebit r2 = (((doublebit(1) << digit_level) % mod) << digit_level) % mod; static constexpr singlebit ninv = singlebit(-1) * find_inv(mod); singlebit reduce(doublebit x) const { singlebit res = (x + doublebit(singlebit(x) * ninv) * mod) >> digit_level; return res < mod ? res : res - mod; } public: fast_modint() : n(0) {}; fast_modint(singlebit n_) { n = reduce(doublebit(n_ % mod) * r2); }; static constexpr singlebit get_mod() { return mod; } singlebit get() const { return reduce(n); } bool operator==(const fast_modint& x) const { return n == x.n; } bool operator!=(const fast_modint& x) const { return n != x.n; } fast_modint& operator+=(const fast_modint& x) { n += x.n; n -= (n < mod ? 0 : mod); return *this; } fast_modint& operator-=(const fast_modint& x) { n += mod - x.n; n -= (n < mod ? 0 : mod); return *this; } fast_modint& operator*=(const fast_modint& x) { n = reduce(doublebit(n) * x.n); return *this; } fast_modint operator+(const fast_modint& x) const { return fast_modint(*this) += x; } fast_modint operator-(const fast_modint& x) const { return fast_modint(*this) -= x; } fast_modint operator*(const fast_modint& x) const { return fast_modint(*this) *= x; } fast_modint inv() const { return binpow(mod - 2); } fast_modint binpow(singlebit b) const { fast_modint ans(1), cur(*this); while (b > 0) { if (b & 1) ans *= cur; cur *= cur; b >>= 1; } return ans; } }; #endif // CLASS_FAST_MODINT #ifndef CLASS_POLYNOMIAL_NTT #define CLASS_POLYNOMIAL_NTT #include #include template class polynomial_ntt { public: using modulo = fast_modint; static void fourier_transform(std::vector& v, bool inverse) { std::size_t s = v.size(); for (std::size_t i = 0, j = 1; j < s - 1; ++j) { for (std::size_t k = s >> 1; k > (i ^= k); k >>= 1); if (i < j) std::swap(v[i], v[j]); } std::size_t sc = 0, sz = 1; while (sz < s) sz *= 2, ++sc; modulo root = modulo(primroot).binpow((mod - 1) >> sc); std::vector pw(s + 1); pw[0] = 1; for (std::size_t i = 1; i <= s; i++) pw[i] = pw[i - 1] * root; std::size_t qs = s; for (std::size_t b = 1; b < s; b <<= 1) { qs >>= 1; for (std::size_t i = 0; i < s; i += b * 2) { for (std::size_t j = i; j < i + b; ++j) { modulo delta = pw[(inverse ? b * 2 - j + i : j - i) * qs] * v[j + b]; v[j + b] = v[j] - delta; v[j] += delta; } } } if (!inverse) return; modulo powinv = modulo((mod + 1) / 2).binpow(sc); for (std::size_t i = 0; i < s; ++i) { v[i] = v[i] * powinv; } } static std::vector convolve(std::vector v1, std::vector v2) { std::size_t s1 = v1.size(), s2 = v2.size(), s = 1; while (s < s1 || s < s2) s *= 2; v1.resize(s * 2); fourier_transform(v1, false); v2.resize(s * 2); fourier_transform(v2, false); for (singlebit i = 0; i < s * 2; ++i) v1[i] *= v2[i]; fourier_transform(v1, true); v1.resize(s1 + s2 - 1); return v1; } }; #endif // CLASS_POLYNOMIAL_NTT #include #include using namespace std; using ntt1 = polynomial_ntt<469762049, 26, 3>; using modulo1 = ntt1::modulo; using ntt2 = polynomial_ntt<167772161, 25, 3>; using modulo2 = ntt2::modulo; using ntt3 = polynomial_ntt<998244353, 23, 3>; using modulo3 = ntt3::modulo; using modulo = fast_modint<1000000007>; const modulo2 inv21 = modulo2(modulo1::get_mod()).inv(); const modulo3 inv31 = modulo3(modulo1::get_mod()).inv(); const modulo3 inv32 = modulo3(modulo2::get_mod()).inv(); const modulo1 inv1b = modulo1(modulo::get_mod()).inv(); const modulo2 inv2b = modulo2(modulo::get_mod()).inv(); const modulo3 inv3b = modulo3(modulo::get_mod()).inv(); template std::vector get_modvector(std::vector v) { std::vector ans(v.size()); for (std::size_t i = 0; i < v.size(); ++i) { ans[i] = modulox(v[i].get()); } return ans; } vector convolve(vector v1, vector v2) { vector res1 = ntt1::convolve(get_modvector(v1), get_modvector(v2)); vector res2 = ntt2::convolve(get_modvector(v1), get_modvector(v2)); vector res3 = ntt3::convolve(get_modvector(v1), get_modvector(v2)); vector res(v1.size() + v2.size() - 1); for (int i = 0; i < v1.size() + v2.size() - 1; ++i) { modulo1 m1 = res1[i]; modulo2 m2 = (res2[i] - m1.get()) * inv21; modulo3 m3 = ((res3[i] - m1.get()) * inv31 - m2.get()) * inv32; singlebit m4 = ((m1.get() + doublebit(m2.get()) * modulo1::get_mod()) % modulo::get_mod() + doublebit(m3.get()) * modulo1::get_mod() % modulo::get_mod() * modulo2::get_mod()) % modulo::get_mod(); res[i] = m4; } return res; } #include #include using namespace std; int main() { int N, P, Q; cin >> N >> P >> Q; vector seq(2000001); seq[0] = 0; if (N >= 2) seq[1] = 1; for (int i = 2; i < N; ++i) { seq[i] = seq[i - 1] * P + seq[i - 2]; } vector ans = convolve(seq, seq); for (int i = 0; i < Q; ++i) { int x; cin >> x; x -= 2; cout << ans[i].get() << '\n'; } return 0; }