#ifdef NACHIA // #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #include #include #include #include #include #include #include #include #include using i64 = long long; using u64 = unsigned long long; #define rep(i,n) for(int i=0; i=0; i--) const i64 INF = 1001001001001001001; const char* yn(bool x){ return x ? "Yes" : "No"; } template void chmin(A& l, const A& r){ if(r < l) l = r; } template void chmax(A& l, const A& r){ if(l < r) l = r; } template using nega_queue = std::priority_queue,std::greater>; using Modint = atcoder::static_modint<998244353>; #include #include template struct vec; template struct seq_view{ using Ref = typename std::iterator_traits::reference; using Elem = typename std::iterator_traits::value_type; Iter a, b; Iter begin() const { return a; } Iter end() const { return b; } int size() const { return (int)(b-a); } seq_view(Iter first, Iter last) : a(first), b(last) {} seq_view sort() const { std::sort(a, b); return *this; } Ref& operator[](int x){ return *(a+x); } template, class ret = vec> ret sorti(F f = F()) const { ret x(size()); for(int i=0; i> ret col() const { return ret(begin(), end()); } template, class ret = vec>> ret rle(F eq = F()) const { auto x = ret(); for(auto& a : (*this)){ if(x.size() == 0 || !eq(x[x.size()-1].first, a)) x.emp(a, 1); else x[x.size()-1].second++; } return x; } template seq_view sort(F f) const { std::sort(a, b, f); return *this; } Iter uni() const { return std::unique(a, b); } Iter lb(const Elem& x) const { return std::lower_bound(a, b, x); } Iter ub(const Elem& x) const { return std::upper_bound(a, b, x); } int lbi(const Elem& x) const { return lb(x) - a; } int ubi(const Elem& x) const { return ub(x) - a; } seq_view bound(const Elem& l, const Elem& r) const { return { lb(l), lb(r) }; } template Iter lb(const Elem& x, F f) const { return std::lower_bound(a, b, x, f); } template Iter ub(const Elem& x, F f) const { return std::upper_bound(a, b, x, f); } template Iter when_true_to_false(F f) const { if(a == b) return a; return std::lower_bound(a, b, *a, [&](const Elem& x, const Elem&){ return f(x); }); } seq_view same(Elem x) const { return { lb(x), ub(x) }; } template auto map(F f) const { vec r; for(auto& x : *this) r.emp(f(x)); return r; } Iter max() const { return std::max_element(a, b); } Iter min() const { return std::min_element(a, b); } template> Iter min(F f) const { return std::min_element(a, b, f); } seq_view rev() const { std::reverse(a, b); return *this; } }; template struct vec { using Base = typename std::vector; using Iter = typename Base::iterator; using CIter = typename Base::const_iterator; using View = seq_view; using CView = seq_view; vec(){} explicit vec(int n, const Elem& value = Elem()) : a(0 vec(I2 first, I2 last) : a(first, last) {} vec(std::initializer_list il) : a(std::move(il)) {} vec(Base b) : a(std::move(b)) {} operator Base() const { return a; } Iter begin(){ return a.begin(); } CIter begin() const { return a.begin(); } Iter end(){ return a.end(); } CIter end() const { return a.end(); } int size() const { return a.size(); } bool empty() const { return a.empty(); } Elem& back(){ return a.back(); } const Elem& back() const { return a.back(); } vec sortunied(){ vec x = *this; x().sort(); x.a.erase(x().uni(), x.end()); return x; } Iter operator()(int x){ return a.begin() + x; } CIter operator()(int x) const { return a.begin() + x; } View operator()(int l, int r){ return { (*this)(l), (*this)(r) }; } CView operator()(int l, int r) const { return { (*this)(l), (*this)(r) }; } View operator()(){ return (*this)(0,size()); } CView operator()() const { return (*this)(0,size()); } Elem& operator[](int x){ return a[x]; } const Elem& operator[](int x) const { return a[x]; } Base& operator*(){ return a; } const Base& operator*() const { return a; } vec& push(Elem args){ a.push_back(std::move(args)); return *this; } template vec& emp(Args &&... args){ a.emplace_back(std::forward(args) ...); return *this; } template vec& app(Range& x){ for(auto& v : a) emp(v); } Elem pop(){ Elem x = std::move(a.back()); a.pop_back(); return x; } bool operator==(const vec& r) const { return a == r.a; } bool operator!=(const vec& r) const { return a != r.a; } bool operator<(const vec& r) const { return a < r.a; } bool operator<=(const vec& r) const { return a <= r.a; } bool operator>(const vec& r) const { return a > r.a; } bool operator>=(const vec& r) const { return a >= r.a; } vec> pile(int n) const { return vec>(n, *this); } template vec& filter(F f){ int p = 0; for(int q=0; q IStr& operator>>(IStr& is, vec>& v){ for(auto& x:v){ is >> x.first >> x.second; } return is; } template IStr& operator>>(IStr& is, vec& v){ for(auto& x:v){ is >> x; } return is; } template OStr& operator<<(OStr& os, const vec& v){ for(int i=0; i OStr& operator<<(OStr& os, const vec>& v){ for(int i=0; i namespace nachia{ int Popcount(unsigned long long c) noexcept { #ifdef __GNUC__ return __builtin_popcountll(c); #else c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3)); c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5)); c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17)); c = (c * (~0ull/257)) >> 56; return c; #endif } // please ensure x != 0 int MsbIndex(unsigned long long x) noexcept { #ifdef __GNUC__ return 63 - __builtin_clzll(x); #else using u64 = unsigned long long; int q = (x >> 32) ? 32 : 0; auto m = x >> q; constexpr u64 hi = 0x8888'8888; constexpr u64 mi = 0x1111'1111; m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35; m = (((m | ~(hi - (x & ~hi))) & hi) * mi) >> 31; q += (m & 0xf) << 2; q += 0x3333'3333'2222'1100 >> (((x >> q) & 0xf) << 2) & 0xf; return q; #endif } // please ensure x != 0 int LsbIndex(unsigned long long x) noexcept { #ifdef __GNUC__ return __builtin_ctzll(x); #else return MsbIndex(x & -x); #endif } } // need unit tests namespace nachia { struct Bitset { using u64 = unsigned long long; using i64 = long long; std::vector a; i64 n = 0; static u64 LowBits(i64 c){ return (c-64) ? (1ull << c) - 1 : ~0ull; } void safeOr64(i64 pos, u64 val){ if(0 <= pos && pos < i64(a.size())) a[pos] |= val; } void safeOr64_2(i64 pos, u64 val, int sh){ safeOr64(pos, val << sh); if(sh) safeOr64(pos+1, val >> (64 - sh)); } void resize(i64 sz){ a.resize((sz>>6)+1, 0); a[sz>>6] &= ~LowBits(sz&63); n = sz; } Bitset(i64 sz = 0){ resize(sz); } void set(i64 pos, bool x = true){ if(x) a[pos>>6] |= 1ull << (pos&63); else a[pos>>6] &= ~(1ull << (pos&63)); } u64 operator[](i64 pos) const { return (a[pos>>6] >> (pos&63)) & 1ull; } bool test(i64 pos) const { return operator[](pos); } i64 count(i64 l, i64 r) const { if(l > r) return -count(r, l); i64 ans = Popcount(a[r>>6] & LowBits(r&63)); r >>= 6; ans -= Popcount(a[l>>6] & LowBits(l&63)); l >>= 6; for(i64 i=l; i i64 noLess(i64 from) const { if(from >= n) return n; if(from < 0) from = 0; u64 t = (ToFind ? a[from>>6] : ~a[from>>6]) & ~LowBits(from&63); if(t) return ((from>>6)<<6) + LsbIndex(t); for(i64 p = (from>>6)+1; p < (i64)a.size(); p++){ u64 ap = ToFind ? a[p] : ~a[p]; if(ap) return (p<<6) + LsbIndex(ap); } return n; } template i64 noGreater(i64 from) const { if(from < 0) return -1; if(n <= from) from = n; u64 t = (ToFind ? a[from>>6] : ~a[from>>6]) & LowBits((from&63)+1); if(t) return ((from>>6)<<6) + MsbIndex(t); for(i64 p = (from>>6)-1; p >= 0; p--){ u64 ap = ToFind ? a[p] : ~a[p]; if(ap) return (p<<6) + MsbIndex(ap); } return -1; } i64 size() const { return n; } Bitset& operator|=(const Bitset& r){ i64 t = n < r.n ? n : r.n; i64 s = t >> 6; for(i64 i=0; i> 6; for(i64 i=0; i> 6; for(i64 i=0; i> 6; for(i64 i=0; i<=s; i++) res.a[i] = ~a[i]; res.a[s] &= LowBits(n&63); return res; } // buggy Bitset clip(i64 srcL = 0, i64 srcR = INT64_MIN, i64 destL = 0, i64 resSz = INT64_MIN) const { if(srcR == INT64_MIN) srcR = size(); if(resSz == INT64_MIN) resSz = destL + srcR - srcL; Bitset res(resSz); if(destL < 0){ srcL -= destL; destL = 0; } if(srcL < 0){ destL -= srcL; srcL = 0; } if(srcR > size()) srcR = size(); if(srcR - srcL > resSz - destL) srcR = srcL + resSz - destL; if(size() <= srcL || srcR <= 0 || resSz <= destL) return res; int q = (destL&63) - (srcL&63); i64 s = srcL >> 6; i64 d = destL >> 6; i64 e = (srcR >> 6) - s; if(q < 0){ q += 64; d--; } u64 m0 = ~LowBits(srcL&63); u64 m1 = LowBits(srcR&63); if((srcL >> 6) == (srcR >> 6)){ res.safeOr64_2(d, a[s] & m0 & m1, q); return res; } res.safeOr64_2(d, a[s] & m0, q); for(i64 t=1; t> q; if(q) res.a[d+t+1] |= a[s+t] << (64-q); } if(m1) res.safeOr64_2(d+e, a[s+e] & m1, q); return res; } std::string toString() const { std::string res; for(i64 i=0; i A){ using i64 = long long; Bitset res(1); res.set(0); for(auto a : A){ Bitset nx = res.clip(-a); nx |= res; std::swap(res, nx); } return res; } } // namespace nachia #include using namespace std; void testcase(){ i64 R, B; cin >> R >> B; if(R > B) swap(R, B); i64 C = R + B; using Set = bitset<50000>; if(C <= 30000){ Set ssp; ssp.set(0); i64 ans = 0; i64 acnt = 0; for(i64 N=1; N<=50; N++){ acnt += N*N; ssp |= ssp << (N*N); rep(i,acnt+1) if(ssp[i]){ if(i <= R && acnt-i <= B) chmax(ans, N); } } cout << ans << endl; return; } auto useBlockCount = [&](i64 k) -> i64 { return k * (k+1) / 2 * (2*k+1) / 3; }; auto maxHeight = [&](i64 n) -> i64 { i64 x = 0; while(n >= (x+1) * (x+1)){ x++; n -= x*x; } return x; }; if(150 <= R){ cout << maxHeight(C) << endl; return; } { Set ssp; ssp.set(0); i64 minDiff = INF; i64 acnt = 0; for(i64 N=1; N<=20; N++) ssp |= ssp << (N*N); rep(i,R+1) if(ssp[i]) chmin(minDiff, R-i); cout << maxHeight(C - minDiff) << endl; } } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); #ifdef NACHIA int T; cin >> T; for(int t=0; t