Pipeline Throughput Maximization Under Budget (Binary Search)

Problem: Maximize Serial Pipeline Throughput Under Budget You have a serial pipeline consisting of n services. Service i has base throughput t[i]. Because the pipeline is serial, overall throughput is the minimum throughput across services: throughput = min_i throughput_i You may scale each service. If you scale service i by x times (x is a non-negative integer), its throughput becomes: throughput_i = t[i] * (1 + x) The cost of scaling service i by x is: cost_i(x) = x * c[i] Given a total budget B, compute the maximum achievable overall pipeline throughput (output an integer). Input Format Line 1: integer n Line 2: n integers t[i] Line 3: n integers c[i] Line 4: integer B Output One line: the maximum achievable overall throughput (integer). Constraints 1 <= n <= 2e5 1 <= t[i], c[i] <= 1e9 0 <= B <= 1e18 Example Input: 3 5 2 4 3 10 2 20 Output: 6 (Example for illustration; exact value depends on feasibility check.) Example Input 3 5 2 4 3 10 2 0 Output 2