#include #define VARNAME(x) #x #define show(x) cerr << #x << " = " << x << endl using namespace std; using ll = long long; using ld = long double; template ostream& operator<<(ostream& os, const vector& v) { os << "sz:" << v.size() << "\n["; for (const auto& p : v) { os << p << ","; } os << "]\n"; return os; } template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } constexpr ll MOD = (ll)1e9 + 7LL; constexpr ld PI = static_cast(3.1415926535898); template constexpr T INF = numeric_limits::max() / 10; constexpr ll W_MAX = 30000000; constexpr ll NW_MAX = 80000000; constexpr ll N_MAX = 1000; constexpr ll NVV_MAX = 30000000; constexpr ll T = 100000000; inline uint32_t rnd(void) { static uint32_t y = 2463534242; y = y ^ (y << 13); y = y ^ (y >> 17); return y = y ^ (y << 5); } bool next(long long b, int t) { if (b > 0) { return true; } return exp(b / 10000.0 / pow(0.99999, t)) > double(rnd()) / numeric_limits::max(); } int main() { cin.tie(0); ios::sync_with_stdio(false); int N; ll W; cin >> N >> W; using P = pair; vector

p; ll wsum = 0; ll vsum = 0; for (int i = 0; i < N; i++) { ll w, v; cin >> v >> w; if (w <= W) { wsum += w; vsum += v; p.push_back(make_pair(v, w)); } } if (wsum <= W) { cout << vsum << endl; return 0; } if (N == 0) { cout << 0 << endl; return 0; } auto comp = [](const P& p1, const P& p2) { return __int128_t(p1.first) * __int128_t(p2.second) > __int128_t(p1.second) * __int128_t(p2.first); }; sort(p.begin(), p.end(), comp); N = p.size(); if (W * N < NW_MAX and W < W_MAX) { vector dp(W + 1, 0); dp[0] = 0; for (int i = 0; i < N; i++) { vector tmp(W + 1, 0); for (int j = 0; j <= W; j++) { tmp[j] = max(tmp[j], dp[j]); if (j + p[i].second <= W) { tmp[j + p[i].second] = max(tmp[j + p[i].second], dp[j] + p[i].first); } } dp = tmp; } cout << *max_element(dp.begin(), dp.end()) << endl; } else { ll cap = W; ll ans = 0; ll rest = N; ll used = 0; vector

res; for (used = 0; used < N and rest > N_MAX and rest * cap > NW_MAX; used++) { if (cap >= p[used].second) { rest--; cap -= p[used].second; ans += p[used].first; } else { res.push_back(p[used]); } } for (int i = used; i < N; i++) { res.push_back(p[i]); } if (rest * cap <= NW_MAX) { p.clear(); p.shrink_to_fit(); vector dp(cap + 1, 0); dp[0] = 0; for (int i = 0; i < rest; i++) { vector tmp(cap + 1, 0); for (int j = 0; j <= cap; j++) { tmp[j] = max(tmp[j], dp[j]); if (j + res[i].second <= W) { tmp[j + res[i].second] = max(tmp[j + res[i].second], dp[j] + res[i].first); } } dp = tmp; } cout << ans + *max_element(dp.begin(), dp.end()) << endl; return 0; } if (rest <= N_MAX) { p.clear(); p.shrink_to_fit(); ll VMAX = 0; for (const auto& e : res) { VMAX = max(VMAX, e.first); } const ll V_SMALL = (ll)sqrt(NVV_MAX / rest); const ll K = VMAX / V_SMALL; auto rescop = res; for (auto& e : rescop) { e.first = e.first / K; } ll vsum = 0; for (const auto& e : rescop) { vsum += e.first; } vector> dp(rest + 1, vector(vsum + 1, INF)); dp[0][0] = 0; for (int i = 0; i < rest; i++) { for (ll j = 0; j <= vsum; j++) { if (dp[i][j] != INF) { dp[i + 1][j] = min(dp[i + 1][j], dp[i][j]); dp[i + 1][j + rescop[i].first] = min(dp[i + 1][j + rescop[i].first], dp[i][j] + rescop[i].second); } } } ll maxind = vsum; for (ll i = vsum; i >= 0; i--) { if (dp[rest][i] <= cap) { maxind = i; break; } } ll pos = maxind; for (int i = rest; i >= 1; i--) { if (dp[i][pos] != dp[i - 1][pos]) { ans += res[i - 1].first; pos -= rescop[i - 1].first; } } cout << ans << endl; return 0; } ans = 0; res.clear(); res.shrink_to_fit(); // cap = W; // used = 0; // vector use; // vector unuse; // for (used = 0; used < N; used++) { // if (cap >= p[used].second) { // cap -= p[used].second; // ans += p[used].first; // use.push_back(used); // } else { // unuse.push_back(used); // } // } vector use; vector unuse(N); iota(unuse.begin(), unuse.end(), 0); for (int t = 0; t < T; t++) { int k = rnd() % unuse.size(); int ss = 0; long long tt = 0; vector del; while (tt < p[k].first and ans + p[unuse[k]].second - ss > W) { int kk = rnd() % use.size(); if (find(del.begin(), del.end(), kk) != del.end()) { continue; } ss += p[use[kk]].second; tt += p[use[kk]].first; del.emplace_back(kk); } if (next(p[k].first - tt, t) and ans + p[unuse[k]].second - ss <= W) { ans += p[k].second - ss; t += p[k].first - tt; unuse[k] = unuse.back(); unuse.pop_back(); use.emplace_back(k); sort(del.rbegin(), del.rend()); for (int kk : del) { use[kk] = use.back(); use.pop_back(); unuse.emplace_back(kk); } } } cout << ans << endl; } return 0; }