Minimize Points Used Across Multiple Reward Programs

## Problem A customer has several reward programs. Program `i` has at most `balance[i]` points, and each point is worth `value[i]` integer microdollars. Given a target in microdollars, return the minimum total number of points whose combined value is at least the target, or `-1` if the available points cannot cover it. ### Constraints & Assumptions - There are between 1 and 100 reward programs. - Balances are nonnegative integers and values are positive integers. - All inputs and intermediate products stay within 2^53. - Points are indivisible and each program's balance is a hard upper bound. ### Clarifications - Overpaying the target is allowed; the primary objective is fewest points. - Any combination with the minimum point count is acceptable, so return only that count. - Exchange values are already fixed for the transaction date. ### Examples ```text target = 168_000_000 balance = [36_000, 12_000, 25_000] value = [12_000, 9_000, 8_500] output = 14_000 explanation: 14,000 points at 12,000 microdollars each reach the target. ``` ### Hints ```hint Compare point values Every point has the same objective cost of one, so consider whether using higher-value points first can ever hurt the minimum count. ``` ```hint Respect finite balances Consume the most valuable available points in bounded groups and detect any remaining uncovered target. ```