Maximum Throughput After Scaling - Atlassian Intern Online Assessment IIT BHU

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"There are `N` servers connected in series. For each server: * Initial throughput is `throughput[i]`. * One upgrade increases its throughput by `1`. * One upgrade costs `cost[i]`. You are given a total budget `B`. Since the servers are connected in series, the overall throughput of the system equals the **minimum throughput among all servers**. Determine the maximum overall throughput that can be achieved without exceeding the budget. --- ## Input Format * First line contains integer `N`. * Second line contains `N` integers `throughput[i]`. * Third line contains `N` integers `cost[i]`. * Fourth line contains integer `B`. --- ## Output Format Print one integer — the maximum achievable overall throughput. --- ## Constraints * `1 ≤ N ≤ 2 × 10^5` * `1 ≤ throughput[i] ≤ 10^9` * `1 ≤ cost[i] ≤ 10^9` * `1 ≤ B ≤ 10^18` --- ## Example ### Input ``` 3 3 5 2 2 1 3 10 ``` ### Output ``` 5 ``` ### Explanation To make every server have throughput at least `5`: * Server 1: already `5` * Server 2: upgrade `3` times → cost `3 × 3 = 9` * Server 0: upgrade `2` times → cost `2 × 2 = 4` Target `5` is feasible only if total cost is within budget. Binary searching on the answer gives the maximum feasible throughput. ---"