#include #include #include using namespace std; const int N = 5000; int n; long long C; long long V[N]; long long W[N]; int p[N]; long long sumV[N + 1]; long long sumW[N + 1]; long long ans; long double estimate(long long A, int k) { int ok = k; int ng = n + 1; while (ng - ok > 1) { int mid = (ok + ng) / 2; if (sumW[mid] - sumW[k] <= A) { ok = mid; } else { ng = mid; } } long double ret = sumV[ok] - sumV[k]; A -= sumW[ok] - sumW[k]; if (ok < n) { ret += A * (long double)V[ p[ok] ] / W[ p[ok] ]; } return ret; } // ***************************........ // [--------greedy-----------] // // **********************.*...*.**.... // [--------core--------] void dfs(long long w, long long v, int k) { if (w > C) return; ans = max(ans, v); for (int i = k; i < n; i++) { // You can estimate the upper bound by Rational Knapsack problem. if (v + estimate(C - w, i) < ans - 1e-8) break; dfs(w + W[ p[i] ], v + V[ p[i] ], i + 1); } } int main() { cin >> n >> C; for (int i = 0; i < n; i++) { cin >> V[i] >> W[i]; p[i] = i; } sort(p, p + n, [&](int i, int j) { return (long double)V[i] / W[i] > (long double)V[j] / W[j]; }); for (int i = 0; i < n; i++) { sumV[i + 1] = sumV[i] + V[ p[i] ]; sumW[i + 1] = sumW[i] + W[ p[i] ]; } long long v = 0; long long w = 0; int k = 0; while (k < n) { v += V[ p[k] ]; w += W[ p[k] ]; k++; if (w > C) break; } for (int i = k - 1; i >= 0; i--) { w -= W[ p[i] ]; v -= V[ p[i] ]; if (v + estimate(C - w, i + 1) < ans - 1e-8) continue; dfs(w, v, i + 1); } cout << ans << endl; }