// author: hotman78 // date: 2024/04/21-09:58:56 // --- begin raw code ----------------- // #include"cpplib/util/template.hpp" // // #include"cpplib/graph_tree/dijkstra.hpp" // #include"cpplib/math/ACL_modint998244353.hpp" // #include"cpplib/math/lagrange_interpolation.hpp" // #include // // void solve(){ // lint r,b; // cin>>r>>b; // lint k=0; // while(__int128_t(k)*(k+1)*(k*2+1)/6<=__int128_t(r+b))k++; // --k; // lint mn=min(r,b); // if(mn>1000){ // cout<v; // lint idx=1,su=0; // v[0]=1; // while(1){ // v|=v<<(idx*idx); // su+=idx*idx; // bool ok=0; // rep(i,mn+1){ // if(v[i]==0)continue; // if(0<=su-i&&su-i<=max(r,b)){ // ok=1; // break; // } // } // if(!ok){ // cout<>t;while(t--)solve(); // } // --- end raw code ----------------- #line 2 "cpplib/util/template.hpp" #ifdef LOCAL #define _GLIBCXX_DEBUG #endif #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") // #pragma GCC target("avx2") #include using namespace std; #line 1 "cpplib/util/ioutil.hpp" // template // std::ostream& output(std::ostream& out,const Head& head,const Args&... args){ // out>>head; // return output(head,args...); // } // template // std::ostream& output(std::ostream& out,const Head& head){ // out>>head; // return out; // } template std::ostream &operator<<(std::ostream &out, std::pair v) { out << "(" << v.first << "," << v.second << ")"; return out; } // template // ostream& operator<<(ostream& out,std::tuplev){ // std::apply(output,v); // return out; // } #line 11 "cpplib/util/template.hpp" struct __INIT__ { __INIT__() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } __INIT__; typedef long long lint; constexpr long long INF = 1LL << 60; constexpr int IINF = 1 << 30; constexpr double EPS = 1e-10; #ifndef REACTIVE #define endl '\n'; #endif typedef vector vec; typedef vector> mat; typedef vector>> mat3; typedef vector svec; typedef vector> smat; template using V = vector; template using VV = V>; #define output(t) \ { \ bool f = 0; \ for (auto val : (t)) { \ cout << (f ? " " : "") << val; \ f = 1; \ } \ cout << endl; \ } #define output2(t) \ { \ for (auto i : t) \ output(i); \ } #define debug(t) \ { \ bool f = 0; \ for (auto i : t) { \ cerr << (f ? " " : "") << i; \ f = 1; \ } \ cerr << endl; \ } #define debug2(t) \ { \ for (auto i : t) \ debug(i); \ } #define loop(n) for (long long _ = 0; _ < (long long)(n); ++_) #define _overload4(_1, _2, _3, _4, name, ...) name #define __rep(i, a) repi(i, 0, a, 1) #define _rep(i, a, b) repi(i, a, b, 1) #define repi(i, a, b, c) \ for (long long i = (long long)(a); i < (long long)(b); i += c) #define rep(...) _overload4(__VA_ARGS__, repi, _rep, __rep)(__VA_ARGS__) #define _overload3_rev(_1, _2, _3, name, ...) name #define _rep_rev(i, a) repi_rev(i, 0, a) #define repi_rev(i, a, b) \ for (long long i = (long long)(b)-1; i >= (long long)(a); --i) #define rrep(...) _overload3_rev(__VA_ARGS__, repi_rev, _rep_rev)(__VA_ARGS__) #define all(n) begin(n), end(n) template bool chmin(T &s, const E &t) { bool res = s > t; s = min(s, t); return res; } template bool chmax(T &s, const E &t) { bool res = s < t; s = max(s, t); return res; } const vector dx = {1, 0, -1, 0, 1, 1, -1, -1}; const vector dy = {0, 1, 0, -1, 1, -1, 1, -1}; #define SUM(v) accumulate(all(v), 0LL) #if __cplusplus >= 201703L template auto make_vector(T x, int arg, Args... args) { if constexpr (sizeof...(args) == 0) return vector(arg, x); else return vector(arg, make_vector(x, args...)); } #endif #define bit(n, a) ((n >> a) & 1) #define extrep(v, ...) for (auto v : make_mat_impl({__VA_ARGS__})) vector> make_mat_impl(vector v) { if (v.empty()) return vector>(1, vector()); long long n = v.back(); v.pop_back(); vector> ret; vector> tmp = make_mat_impl(v); for (auto e : tmp) for (long long i = 0; i < n; ++i) { ret.push_back(e); ret.back().push_back(i); } return ret; } using graph = vector>; template using graph_w = vector>>; #if __cplusplus >= 201703L constexpr inline long long powll(long long a, long long b) { long long res = 1; while (b--) res *= a; return res; } #endif template pair &operator+=(pair &s, const pair &t) { s.first += t.first; s.second += t.second; return s; } template pair &operator-=(pair &s, const pair &t) { s.first -= t.first; s.second -= t.second; return s; } template pair operator+(const pair &s, const pair &t) { auto res = s; return res += t; } template pair operator-(const pair &s, const pair &t) { auto res = s; return res -= t; } #define BEGIN_STACK_EXTEND(size) \ void *stack_extend_memory_ = malloc(size); \ void *stack_extend_origin_memory_; \ char *stack_extend_dummy_memory_ = (char *)alloca( \ (1 + (int)(((long long)stack_extend_memory_) & 127)) * 16); \ *stack_extend_dummy_memory_ = 0; \ asm volatile("mov %%rsp, %%rbx\nmov %%rax, %%rsp" \ : "=b"(stack_extend_origin_memory_) \ : "a"((char *)stack_extend_memory_ + (size)-1024)); #define END_STACK_EXTEND \ asm volatile("mov %%rax, %%rsp" ::"a"(stack_extend_origin_memory_)); \ free(stack_extend_memory_); int floor_pow(int n) { return n ? 31 - __builtin_clz(n) : 0; } #line 2 "main.cpp" // #include"cpplib/graph_tree/dijkstra.hpp" #line 2 "cpplib/math/ACL_modint998244353.hpp" #include #include #include #ifdef _MSC_VER #include #endif #include #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } struct barrett { unsigned int _m; unsigned long long im; explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} unsigned int umod() const { return _m; } unsigned int mul(unsigned int a, unsigned int b) const { unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder #include #include #include namespace atcoder { namespace internal { #ifndef _MSC_VER template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || is_signed_int128::value || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional< is_signed_int128::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; #else template using is_integral = typename std::is_integral; template using is_signed_int = typename std::conditional::value && std::is_signed::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional::value && std::is_unsigned::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, std::make_unsigned, std::common_type>::type; #endif template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace internal } // namespace atcoder namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template using is_modint = std::is_base_of; template using is_modint_t = std::enable_if_t::value>; } // namespace internal template * = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template * = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template * = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint &operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint &operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint &operator+=(const mint &rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint &operator-=(const mint &rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint &operator*=(const mint &rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime; }; template struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template * = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template * = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } unsigned int val() const { return _v; } mint &operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint &operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint &operator+=(const mint &rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint &operator-=(const mint &rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint &operator*=(const mint &rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template internal::barrett dynamic_modint::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template using is_static_modint = std::is_base_of; template using is_static_modint_t = std::enable_if_t::value>; template struct is_dynamic_modint : public std::false_type {}; template struct is_dynamic_modint> : public std::true_type {}; template using is_dynamic_modint_t = std::enable_if_t::value>; } // namespace internal } // namespace atcoder using mint = atcoder::modint998244353; #line 4 "cpplib/math/ACL_modint_base.hpp" std::ostream &operator<<(std::ostream &lhs, const mint &rhs) noexcept { lhs << rhs.val(); return lhs; } std::istream &operator>>(std::istream &lhs, mint &rhs) noexcept { long long x; lhs >> x; rhs = x; return lhs; } int MOD_NOW = -1; int FACT_TABLE_SIZE = 0; std::vector fact_table, fact_inv_table; void update(int x) { if (MOD_NOW != mint::mod() || FACT_TABLE_SIZE == 0) { fact_table.assign(1, 1); fact_inv_table.assign(1, 1); FACT_TABLE_SIZE = 1; MOD_NOW = mint::mod(); } while (FACT_TABLE_SIZE <= x) { fact_table.resize(FACT_TABLE_SIZE * 2); fact_inv_table.resize(FACT_TABLE_SIZE * 2); for (int i = FACT_TABLE_SIZE; i < FACT_TABLE_SIZE * 2; ++i) { fact_table[i] = fact_table[i - 1] * i; } fact_inv_table[FACT_TABLE_SIZE * 2 - 1] = fact_table[FACT_TABLE_SIZE * 2 - 1].inv(); for (int i = FACT_TABLE_SIZE * 2 - 2; i >= FACT_TABLE_SIZE; --i) { fact_inv_table[i] = fact_inv_table[i + 1] * (i + 1); } FACT_TABLE_SIZE *= 2; } } inline mint fact(int x) { assert(x >= 0); update(x); return fact_table[x]; } inline mint fact_inv(int x) { assert(x >= 0); update(x); return fact_inv_table[x]; } inline mint comb(int x, int y) { if (x < 0 || x < y || y < 0) return 0; return fact(x) * fact_inv(y) * fact_inv(x - y); } inline mint perm(int x, int y) { return fact(x) * fact_inv(x - y); } // x個のグループにy個のものを分ける場合の数 inline mint multi_comb(int x, int y) { if (y == 0 && x >= 0) return 1; if (y < 0 || x <= 0) return 0; return comb(x + y - 1, y); } #line 3 "cpplib/math/lagrange_interpolation.hpp" /** * @brief ラグランジュ補完(連続点->一点) */ template T lagrange_interpolation(std::vector v, long long n) { long long k = v.size(); if (n < k) return v[n]; std::vector tmp1(k + 1, 1), tmp2(k + 1, 1); T ans = 0; for (int i = 0; i < k; ++i) tmp1[i] = (i ? tmp1[i - 1] : T(1)) * (n - i); for (int i = k - 1; i >= 0; --i) tmp2[i] = (i < k - 1 ? tmp2[i + 1] : T(1)) * (n - i); for (int i = 0; i < k; ++i) { ans += v[i] * (i < k - 1 ? tmp2[i + 1] : 1) * (i ? tmp1[i - 1] : T(1)) / (fact(k - 1 - i) * fact(i) * T((k - 1 - i) % 2 ? -1 : 1)); } return ans; } #line 6 "main.cpp" void solve() { lint r, b; cin >> r >> b; lint k = 0; while (__int128_t(k) * (k + 1) * (k * 2 + 1) / 6 <= __int128_t(r + b)) k++; --k; lint mn = min(r, b); if (mn > 1000) { cout << k << endl; return; } bitset<1000> v; lint idx = 1, su = 0; v[0] = 1; while (1) { v |= v << (idx * idx); su += idx * idx; bool ok = 0; rep(i, mn + 1) { if (v[i] == 0) continue; if (0 <= su - i && su - i <= max(r, b)) { ok = 1; break; } } if (!ok) { cout << idx - 1 << endl; return; } ++idx; } } int main() { solve(); // lint t;cin>>t;while(t--)solve(); }