Ball Distribution

Chef has $N$ empty boxes. There are $M$ different colours numbered from $1$ to $M$ such that Chef has $A_i$ balls of the $i^{th}$ colour. A distribution of these balls into boxes is said to be *valid* if: - Each ball is placed in a box; - All the balls in a box are of different colour. Over all *valid* distributions, find the **minimum** number of boxes having $M$ balls. Under the given constra