In the coupon collectors problem, there are $n$ unique coupons and each cereal box has 1 coupon only. I would like to modify the problem such that there are $m$ boxes of cereal in total and each box has $c_i (1 \le c_i \le n)$ number of coupons.
Then how many boxes of cereal do I need to buy to have $n$ unique coupons?