Days needed to finish recurring tasks

You run n recurring tasks. Task i runs for the first time on day 1 and then again every intervals[i] days, so it runs on days 1, 1 + intervals[i], 1 + 2 * intervals[i], .... Any number of task runs can happen on the same day.

Given intervals and a target goal, return the smallest day d such that the total number of task runs on days 1 through d is at least goal.

def min_days(intervals: list[int], goal: int) -> int: ...

Constraints

• 1 <= len(intervals) <= 10^5
• 1 <= intervals[i] <= 10^5
• 1 <= goal <= 10^9

Example 1

intervals = [3, 5], goal = 5  ->  7

The 3-day task runs on days 1, 4, 7. The 5-day task runs on days 1, 6. By day 6 there are 4 runs; day 7 brings the total to 5.

Example 2

intervals = [2, 2, 2], goal = 7  ->  5

All three tasks run on days 1, 3, 5. That is 3 runs by day 1, 6 by day 3, and 9 by day 5, so day 5 is the first day with at least 7.

Reconstructed from the reported question; details may differ from what interviewers ask.