#include using namespace std; #ifdef LOCAL #include #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast(0)) #endif // #pragma GCC target("avx,avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; using pii = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vul = vector; using vpii = vector; using vvpii = vector; using vpll = vector; using vs = vector; template using pq = priority_queue, greater>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++i) #define rep3(i, a, b) for (ll i = (a); i < (b); ++i) #define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;i >= 0;i--) #define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--) #define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--) #define rrep4(i,a,b,c) for(ll i = (a) + (((b)-(a)-1) / (c) - (((b)-(a)-1) % (c) && (((b)-(a)-1) ^ c) < 0)) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i) , end(i) #define all2(i,a) begin(i) , begin(i) + a #define all3(i,a,b) begin(i) + a , begin(i) + b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template auto min(const T& a){return *min_element(all(a));} template auto max(const T& a){return *max_element(all(a));} template void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector name(size); in(name) #define VV(type, name, h, w) vector> name(h, vector(w)); in(name) ll intpow(ll a, ll b){ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } bool is_clamp(ll val,ll low,ll high) {return low <= val && val < high;} void Yes() {cout << "Yes\n";return;} void No() {cout << "No\n";return;} void YES() {cout << "YES\n";return;} void NO() {cout << "NO\n";return;} template U floor(U a, T b) {return a / b - (a % b && (a ^ b) < 0);} template U ceil(U x, T y) {return floor(x + y - 1, y);} template T bmod(U x, T y) {return x - y * floor(x, y);} template pair divmod(U x, T y) {U q = floor(x, y);return {q, x - q * y};} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(15);}} setting; template struct P : P{}; template<> struct P<0>{}; template void i(T& t){ i(t, P<3>{}); } void i(vector::reference t, P<3>){ int a; i(a); t = a; } template auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template void ituple(T& t, index_sequence){in(get(t)...);} template auto i(T& t, P<0>) -> VOID(tuple_size{}){ituple(t, make_index_sequence::value>{});} #undef VOID } #define unpack(a) (void)initializer_list{(a, 0)...} template void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack constexpr long double PI = 3.141592653589793238462643383279L; template struct REC { F f; REC(F &&f_) : f(forward(f_)) {} template auto operator()(Args &&...args) const { return f(*this, forward(args)...); }}; constexpr int mod = 998244353; //constexpr int mod = 1000000007; using i64 = long long; struct Item { i64 W, V, M; }; i64 knapsack_8(i64 Z, vector items) { for (auto &a : items) { Item &t = items.back(); __int128 lhs = (__int128)a.V * t.W; __int128 rhs = (__int128)t.V * a.W; if (lhs > rhs) swap(a, t); } Item top = items.back(); items.pop_back(); i64 Wp = top.W; i64 Vp = top.V; i64 q = Z / Wp; i64 R = Z % Wp; const i64 NEG = (i64)-4e18; vector dp(Wp, NEG); dp[0] = 0; for (auto &it : items) { i64 Wi = it.W; i64 Vi = it.V; vector gain(Wp); for (i64 r = 0; r < Wp; ++r) { i64 delta = (r + Wi) / Wp; gain[r] = Vi - delta * Vp; } vector used(Wp, 0); for (i64 start = 0; start < Wp; ++start) { if (used[start]) continue; vector cyc; i64 r = start; while (!used[r]) { used[r] = 1; cyc.push_back(r); r = (r + Wi) % Wp; } int L = (int)cyc.size(); vector best(L); for (int j = 0; j < L; ++j) { best[j] = dp[cyc[j]]; } for (int t = 0; t < 2 * L; ++t) { int j = t % L; int prev = (j - 1 + L) % L; i64 prevRem = cyc[prev]; if (best[prev] <= NEG / 2) continue; i64 cand = best[prev] + gain[prevRem]; if (cand > best[j]) best[j] = cand; } for (int j = 0; j < L; ++j) { dp[cyc[j]] = best[j]; } } } i64 bestOffset = NEG; for (i64 r = 0; r < Wp; ++r) { if (dp[r] <= NEG / 2) continue; int delta_z = (r <= R ? 0 : 1); i64 val = dp[r] - (i64)delta_z * Vp; if (val > bestOffset) bestOffset = val; } if (bestOffset < NEG / 2) bestOffset = 0; i64 ans = q * Vp + bestOffset; return ans; } void solve() { INT(n,W); vi v(n),w(n); rep(i,n) cin >> v[i] >> w[i]; vector V(n); rep(i,n) V[i] = {w[i],v[i],(ll)1e18}; if(W > 1000 * 1000) { cout << knapsack_8(W,V) << '\n'; } else { vl dp(W+1); rep(i,n) { rep(j,W+1-w[i]) { chmax(dp[j+w[i]],dp[j]+v[i]); } } cout << dp[W] << '\n'; } } int main() { //INT(TT); int TT = 1; rep(i,TT) solve(); }