#include using ll = long long; using uint = unsigned int; using ull = unsigned long long; using ld = long double; template using max_heap = std::priority_queue; template using min_heap = std::priority_queue, std::greater>; constexpr int popcount(const ull v) { return v ? __builtin_popcountll(v) : 0; } constexpr int log2p1(const ull v) { return v ? 64 - __builtin_clzll(v) : 0; } constexpr int lsbp1(const ull v) { return __builtin_ffsll(v); } constexpr int clog(const ull v) { return v ? log2p1(v - 1) : 0; } constexpr ull ceil2(const ull v) { return 1ULL << clog(v); } constexpr ull floor2(const ull v) { return v ? (1ULL << (log2p1(v) - 1)) : 0ULL; } constexpr bool btest(const ull mask, const int ind) { return (mask >> ind) & 1ULL; } template void bset(T& mask, const int ind) { mask |= ((T)1 << ind); } template void breset(T& mask, const int ind) { mask &= ~((T)1 << ind); } template void bflip(T& mask, const int ind) { mask ^= ((T)1 << ind); } template void bset(T& mask, const int ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); } template bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); } template bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); } template constexpr T inf_v = std::numeric_limits::max() / 4; template constexpr Real pi_v = Real{3.141592653589793238462643383279502884}; template constexpr T TEN(const int n) { return n == 0 ? T{1} : TEN(n - 1) * T{10}; } template struct fix : F { fix(F&& f) : F{std::forward(f)} {} template auto operator()(Args&&... args) const { return F::operator()(*this, std::forward(args)...); } }; template auto nd_array(int const (&szs)[n], const T x = T{}) { if constexpr (i == n) { return x; } else { return std::vector(szs[i], nd_array(szs, x)); } } class printer { public: printer(std::ostream& os_ = std::cout) : m_os{os_} { m_os << std::fixed << std::setprecision(15); } template int ln(const Args&... args) { return dump(args...), m_os << '\n', 0; } template int el(const Args&... args) { return dump(args...), m_os << std::endl, 0; } private: template void dump(const T& v) { m_os << v; } template void dump(const std::vector& vs) { for (int i = 0; i < (int)vs.size(); i++) { m_os << (i ? " " : ""), dump(vs[i]); } } template void dump(const std::vector>& vss) { for (int i = 0; i < (int)vss.size(); i++) { m_os << (0 <= i or i + 1 < (int)vss.size() ? "\n" : ""), dump(vss[i]); } } template int dump(const T& v, const Args&... args) { return dump(v), m_os << ' ', dump(args...), 0; } std::ostream& m_os; }; printer out; class scanner { public: scanner(std::istream& is_ = std::cin) : m_is{is_} { m_is.tie(nullptr), std::ios::sync_with_stdio(false); } template T val() { T v; return m_is >> v, v; } template T val(const T offset) { return val() - offset; } template std::vector vec(const int n) { return make_v(n, [this]() { return val(); }); } template std::vector vec(const int n, const T offset) { return make_v(n, [this, offset]() { return val(offset); }); } template std::vector> vvec(const int n0, const int n1) { return make_v>(n0, [this, n1]() { return vec(n1); }); } template std::vector> vvec(const int n0, const int n1, const T offset) { return make_v>(n0, [this, n1, offset]() { return vec(n1, offset); }); } template auto tup() { return std::tuple...>{val()...}; } template auto tup(const Args&... offsets) { return std::tuple...>{val(offsets)...}; } private: template std::vector make_v(const int n, F f) { std::vector ans; for (int i = 0; i < n; i++) { ans.push_back(f()); } return ans; } std::istream& m_is; }; scanner in; template struct complex { complex() : real{T{0}}, imag{T{0}} {} complex(const complex&) = default; complex(const T& r, const T& i) : real{r}, imag{i} {} friend complex operator+(const complex& c) { return c; } friend complex operator-(const complex& c) { return complex{-c.real, -c.imag}; } friend complex operator+(const complex& c1, const complex& c2) { return complex{c1.real + c2.real, c1.imag + c2.imag}; } friend complex operator-(const complex& c1, const complex& c2) { return complex{c1.real - c2.real, c1.imag - c2.imag}; } friend complex operator*(const complex& c1, const complex& c2) { return complex{c1.real * c2.real - c1.imag * c2.imag, c1.real * c2.imag + c1.imag * c2.real}; } friend complex operator/(complex& c1, complex& c2) { c1* c2.conj() / c2.norm(); } friend complex operator+(const complex& c, const T& v) { return complex{c.real + v, c.imag}; } friend complex operator-(const complex& c, const T& v) { return complex{c.real - v, c.imag}; } friend complex operator*(const complex& c, const T& v) { return complex{c.real * v, c.imag * v}; } friend complex operator/(const complex& c, const T& v) { return complex{c.real / v, c.imag / v}; } friend complex operator+(const T& v, const complex& c) { return complex{v + c.real, c.imag}; } friend complex operator-(const T& v, const complex& c) { return complex{v - c.real, -c.imag}; } friend complex operator*(const T& v, const complex& c) { return complex{v * c.real, v * c.imag}; } friend complex operator/(const T& v, const complex& c) { return v * c.conj() / c.norm(); } friend bool operator==(const complex& c1, const complex& c2) { return c1.real == c2.real and c1.imag == c2.imag; } friend bool operator!=(const complex& c1, const complex& c2) { return not(c1 == c2); } friend complex& operator+=(complex& c1, const complex& c2) { return c1.real += c2.real, c1.imag += c2.imag, c1; } friend complex& operator-=(complex& c1, const complex& c2) { return c1.real += c2.real, c1.imag += c2.imag, c1; } friend complex& operator*=(complex& c1, const complex& c2) { return c1 = c1 * c2; } friend complex& operator/=(complex& c1, const complex& c2) { return c1 = c1 / c2; } friend complex& operator+=(complex& c, const T& v) { return c = c + v; } friend complex& operator-=(complex& c, const T& v) { return c = c - v; } friend complex& operator*=(complex& c, const T& v) { return c = c * v; } complex conj() const { return complex{real, -imag}; } T norm() const { return real * real + imag * imag; } T abs() const { return std::sqrt(norm()); } T arg() const { return std::atan2(imag, real); } friend std::ostream& operator<<(std::ostream& os, const complex& c) { return os << c.real << "+" << c.imag << "i"; } T real, imag; }; template class modint { public: modint() : m_val{0} {} modint(const ll v) : m_val{normll(v)} {} modint(const modint& m) = default; modint& operator =(const modint& m) { return m_val = m(), (*this); } modint& operator =(const ll v) { return m_val = normll(v), (*this); } modint operator+() const { return *this; } modint operator-() const { return modint{0} - (*this); } modint& operator+=(const modint& m) { return m_val = norm(m_val + m()), *this; } modint& operator-=(const modint& m) { return m_val = norm(m_val + mod - m()), *this; } modint& operator*=(const modint& m) { return m_val = normll((ll)m_val * (ll)m() % (ll)mod), *this; } modint& operator/=(const modint& m) { return *this *= m.inv(); } modint& operator+=(const ll val) { return *this += modint{val}; } modint& operator-=(const ll val) { return *this -= modint{val}; } modint& operator*=(const ll val) { return *this *= modint{val}; } modint& operator/=(const ll val) { return *this /= modint{val}; } modint operator+(const modint& m) const { return modint{*this} += m; } modint operator-(const modint& m) const { return modint{*this} -= m; } modint operator*(const modint& m) const { return modint{*this} *= m; } modint operator/(const modint& m) const { return modint{*this} /= m; } modint operator+(const ll v) const { return *this + modint{v}; } modint operator-(const ll v) const { return *this - modint{v}; } modint operator*(const ll v) const { return *this * modint{v}; } modint operator/(const ll v) const { return *this / modint{v}; } bool operator==(const modint& m) const { return m_val == m(); } bool operator!=(const modint& m) const { return not(*this == m); } friend modint operator+(const ll v, const modint& m) { return modint{v} + m; } friend modint operator-(const ll v, const modint& m) { return modint{v} - m; } friend modint operator*(const ll v, const modint& m) { return modint{v} * m; } friend modint operator/(const ll v, const modint& m) { return modint{v} / m; } friend std::istream& operator>>(std::istream& is, modint& m) { ll v; return is >> v, m = v, is; } friend std::ostream& operator<<(std::ostream& os, const modint& m) { return os << m(); } uint operator()() const { return m_val; } modint pow(ull n) const { modint ans = 1; for (modint x = *this; n > 0; n >>= 1, x *= x) { if (n & 1ULL) { ans *= x; } } return ans; } modint inv() const { return m_val <= 2000000 ? sinv(m_val) : pow(mod - 2); } static modint fact(const uint n) { static std::vector fs{1, 1}; for (uint i = (uint)fs.size(); i <= n; i++) { fs.push_back(fs.back() * i); } return fs[n]; } static modint ifact(const uint n) { static std::vector ifs{1, 1}; for (uint i = (uint)ifs.size(); i <= n; i++) { ifs.push_back(ifs.back() * sinv(i)); } return ifs[n]; } static modint perm(const int n, const int k) { return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k); } static modint comb(const int n, const int k) { return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k) * ifact(k); } private: static constexpr uint norm(const uint x) { return x < mod ? x : x - mod; } static constexpr uint normll(const ll x) { return norm(uint(x % (ll)mod + (ll)mod)); } static modint sinv(const uint n) { static std::vector is{1, 1}; for (uint i = (uint)is.size(); i <= n; i++) { is.push_back(-is[mod % i] * (mod / i)); } return is[n]; } uint m_val; }; template class fft { private: static constexpr R pi = pi_v; static constexpr int D = 30; static constexpr int B = 14; public: static void trans(std::vector>& as, const int lg, const bool rev) { const int N = as.size(); static std::vector> root[D]; if (root[lg].empty()) { root[lg].resize(N); for (int i = 0; i < N; i++) { const R theta = pi * R(2 * i) / R(N); root[lg][i] = complex(std::cos(theta), std::sin(theta)); } } std::vector> tmp(N); for (int w = (N >> 1); w > 0; w >>= 1) { for (int y = 0; y < (N >> 1); y += w) { const complex r = rev ? root[lg][y].conj() : root[lg][y]; for (int x = 0; x < w; x++) { const auto u = as[y << 1 | x], v = as[y << 1 | x | w] * r; tmp[y | x] = u + v, tmp[y | x | (N >> 1)] = u - v; } } std::swap(tmp, as); } } fft() = delete; template static std::vector convolute_neg(const std::vector& as, const std::vector& bs) { const int need = as.size() + bs.size() - 1, lg = clog(need), sz = 1UL << lg; std::vector> xs(sz), ys(sz); for (int i = 0; i < as.size(); i++) { xs[i] = {(R)as[i], (R)0}; } for (int i = 0; i < bs.size(); i++) { ys[i] = {(R)bs[i], (R)0}; } trans(xs, lg, false), trans(ys, lg, false); for (int i = 0; i < sz; i++) { xs[i] *= ys[i]; } trans(xs, lg, true); std::vector ans(need); for (int i = 0; i < need; i++) { ans[i] = (T)std::round(xs[i].real / (R)sz); } return ans; } template static std::vector> conv_mod(const std::vector>& as, const std::vector>& bs, const int division = 2) { using T = modint; const int bitnum = (D + division - 1) / division; const int need = as.size() + bs.size() - 1, lg = clog(need), sz = 1UL << lg; std::vector>> xs(division, std::vector>(sz)), ys(division, std::vector>(sz)); std::vector> tmp(sz); for (int i = 0; i < division; i++) { std::fill(tmp.begin() + std::min(as.size(), bs.size()), tmp.end(), complex{}); for (int j = 0; j < (int)as.size(); j++) { tmp[j].real = R(((ll)as[j]() >> (bitnum * i)) & ((1 << bitnum) - 1)); } for (int j = 0; j < (int)bs.size(); j++) { tmp[j].imag = R(((ll)bs[j]() >> (bitnum * i)) & ((1 << bitnum) - 1)); } trans(tmp, lg, false); for (int j = 0; j < sz; j++) { tmp[j] *= R(0.5); } for (int j = 0; j < sz; j++) { const int k = j == 0 ? 0UL : sz - j; xs[i][j] = complex{tmp[j].real + tmp[k].real, tmp[j].imag - tmp[k].imag}, ys[i][j] = complex{tmp[j].imag + tmp[k].imag, -tmp[j].real + tmp[k].real}; } } std::vector>> zs(division, std::vector>(sz)); for (int a = 0; a < division; a++) { for (int b = 0; b < division; b++) { for (int i = 0; i < sz; i++) { if (a + b < division) { zs[a + b][i] += xs[a][i] * ys[b][i]; } else { zs[a + b - division][i] += xs[a][i] * ys[b][i] * complex(0, 1); } } } } for (int i = 0; i < division; i++) { trans(zs[i], lg, true); } std::vector ans(need); T base = 1; for (int k = 0; k < 2 * division - 1; k++, base *= (1LL << bitnum)) { for (int i = 0; i < need; i++) { if (k < division) { ans[i] += base * T((ll)std::round(zs[k][i].real / R(sz))); } else { ans[i] += base * T((ll)std::round(zs[k - division][i].imag / R(sz))); } } } return ans; } }; int main() { const auto [N, M] = in.tup(); auto dp = nd_array({2 * M + 1, 2 * N + 1}, 0); for (int a = 0; a <= M; a++) { for (int b = 0; b <= M; b++) { const int s = a * a + b * b; if (s > 2 * N) { break; } dp[a + b][s]++; } } std::vector ans(2 * N + 1, 0); for (int i = 0; i <= 2 * M; i++) { for (int j = 0; j <= 2 * M; j++) { if ((i + j) * (i + j) > 2 * N) { break; } const int s = (i + j) * (i + j); const auto conv = fft::convolute_neg(dp[i], dp[j]); for (int k = 0; k + s <= 2 * N; k++) { ans[k + s] += conv[k]; } } } for (int i = 0; i <= N; i++) { out.ln(ans[2 * i]); } return 0; }