#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #if __has_include() #include namespace atcoder { ostream& operator<<(ostream& os, modint x) { return os << x.val(); } template ostream& operator<<(ostream& os, static_modint x) { return os << x.val(); } istream& operator>>(istream& is, modint x) { long long a; is >> a; x = a; return is; } template istream& operator>>(istream& is, static_modint x) { long long a; is >> a; x = a; return is; } } // namespace atcoder #endif #define GET_MACRO(_1, _2, _3, NAME, ...) NAME #define _rep(i, n) _rep2(i, 0, n) #define _rep2(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define rep(...) GET_MACRO(__VA_ARGS__, _rep2, _rep)(__VA_ARGS__) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define UNIQUE(x) \ std::sort((x).begin(), (x).end()); \ (x).erase(std::unique((x).begin(), (x).end()), (x).end()) using i64 = long long; using u64 = unsigned long long; using u32 = unsigned int; using i32 = int; using ld = long double; using f64 = double; template bool chmin(T& a, const U& b) { return (b < a) ? (a = b, true) : false; } template bool chmax(T& a, const U& b) { return (b > a) ? (a = b, true) : false; } template inline void YesNo(bool f = 0, const T yes = "Yes", const U no = "No") { if (f) std::cout << yes << "\n"; else std::cout << no << "\n"; } namespace io { template istream& operator>>(istream& i, pair& p) { i >> p.first >> p.second; return i; } template ostream& operator<<(ostream& o, pair& p) { o << p.first << " " << p.second; return o; } template istream& operator>>(istream& i, vector& v) { rep(j, v.size()) i >> v[j]; return i; } template string join(vector& v) { stringstream s; rep(i, v.size()) s << ' ' << v[i]; return s.str().substr(1); } template ostream& operator<<(ostream& o, vector& v) { if (v.size()) o << join(v); return o; } template string join(vector>& vv) { string s = "\n"; rep(i, vv.size()) s += join(vv[i]) + "\n"; return s; } template ostream& operator<<(ostream& o, vector>& vv) { if (vv.size()) o << join(vv); return o; } void OUT() { std::cout << "\n"; } template void OUT(Head&& head, Tail&&... tail) { std::cout << head; if (sizeof...(tail)) std::cout << ' '; OUT(std::forward(tail)...); } void OUTL() { std::cout << std::endl; } template void OUTL(Head&& head, Tail&&... tail) { std::cout << head; if (sizeof...(tail)) std::cout << ' '; OUTL(std::forward(tail)...); } void IN() {} template void IN(Head&& head, Tail&&... tail) { cin >> head; IN(std::forward(tail)...); } } // namespace io using namespace io; namespace useful { long long modpow(long long a, long long b, long long mod) { long long res = 1; while (b) { if (b & 1) res *= a, res %= mod; a *= a; a %= mod; b >>= 1; } return res; } bool is_pow2(long long x) { return x > 0 && (x & (x - 1)) == 0; } template void rearrange(vector& a, vector& p) { vector b = a; for (int i = 0; i < int(a.size()); i++) { a[i] = b[p[i]]; } return; } template std::vector::value_type, int>> run_length_encoding(I s, I t) { if (s == t) return {}; std::vector::value_type, int>> res; res.emplace_back(*s, 1); for (auto it = ++s; it != t; it++) { if (*it == res.back().first) res.back().second++; else res.emplace_back(*it, 1); } return res; } vector linear_sieve(int n) { vector primes; vector res(n + 1); iota(all(res), 0); for (int i = 2; i <= n; i++) { if (res[i] == i) primes.emplace_back(i); for (auto j : primes) { if (j * i > n) break; res[j * i] = j; } } return res; // return primes; } template vector dijkstra(vector>>& graph, int start) { int n = graph.size(); vector res(n, 2e18); res[start] = 0; priority_queue, vector>, greater>> que; que.push({0, start}); while (!que.empty()) { auto [c, v] = que.top(); que.pop(); if (res[v] < c) continue; for (auto [nxt, cost] : graph[v]) { auto x = c + cost; if (x < res[nxt]) { res[nxt] = x; que.push({x, nxt}); } } } return res; } } // namespace useful using namespace useful; template struct RandomIntGenerator { std::random_device seed; std::mt19937_64 engine; std::uniform_int_distribution uid; RandomIntGenerator() { engine = std::mt19937_64(seed()); uid = std::uniform_int_distribution(l, r); } T gen() { return uid(engine); } }; // https://ei1333.github.io/luzhiled/snippets/dp/knapsack-limitations.html template > vector knapsack_limitations(const vector& w, const vector& m, const vector& v, const int& W, const T& NG, const Compare& comp = Compare()) { const int N = (int)w.size(); vector dp(W + 1, NG), deqv(W + 1); dp[0] = T(); vector deq(W + 1); for (int i = 0; i < N; i++) { for (int a = 0; a < w[i]; a++) { int s = 0, t = 0; for (int j = 0; w[i] * j + a <= W; j++) { if (dp[w[i] * j + a] != NG) { auto val = dp[w[i] * j + a] - j * v[i]; while (s < t && comp(val, deqv[t - 1])) --t; deq[t] = j; deqv[t++] = val; } if (s < t) { dp[j * w[i] + a] = deqv[s] + j * v[i]; if (deq[s] == j - m[i]) ++s; } } } } return dp; } template T knapsack_limitations(const vector& w, const vector& m, const vector& v, const T& W) { const int N = (int)w.size(); auto v_max = *max_element(begin(v), end(v)); if (v_max == 0) return 0; vector ma(N); vector mb(N); for (int i = 0; i < N; i++) { ma[i] = min(m[i], v_max - 1); mb[i] = m[i] - ma[i]; } T sum = 0; for (int i = 0; i < N; i++) sum += ma[i] * v[i]; auto dp = knapsack_limitations(v, ma, w, sum, T(-1), less<>()); vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), [&](int a, int b) { return v[a] * w[b] > v[b] * w[a]; }); T ret = T(); for (int i = 0; i < dp.size(); i++) { if (dp[i] > W || dp[i] == -1) continue; T rest = W - dp[i], cost = i; for (auto& p : ord) { auto get = min(mb[p], rest / w[p]); if (get == 0) break; cost += get * v[p]; rest -= get * w[p]; } ret = max(ret, cost); } return ret; } int main() { std::cout << fixed << setprecision(15); cin.tie(nullptr); ios::sync_with_stdio(false); i64 n, W; IN(n, W); vector w(n), m(n, W); vector v(n); rep(i, n) { IN(v[i], w[i]); } OUT(knapsack_limitations(w, m, v, W)); }