Supply Warehouse Cleanup

The supply warehouse has $N$ supply boxes numbered from $1$ to $N$, lined up in numerical order. Box $i$ holds $a_i$ supplies. The unit in charge of cleanup has $M$ squads numbered from $1$ to $M$, and squad $j$ has $b_j$ soldiers.

The commander told the deputy to use the following method. Split the $N$ boxes into at most $M$ groups of consecutive boxes. Pick as many squads as there are groups, and assign each group to one squad. The soldiers of that squad clean up all supplies in the group. Each group must contain at least one box.

To keep the work from being pushed onto others, the deputy assigns each soldier a fixed number of supplies to clean up. To make the split as fair as possible, the deputy wants to minimize the number of supplies handled by the soldier with the largest share, while still following the commander's method.

When every soldier is assigned according to the deputy's plan, find the number of supplies handled by the soldier who cleans up the most.

The first line contains the number of boxes $N$ and the number of squads $M$, separated by a space. ($1 \leq N \leq 500\,000$; $1 \leq M \leq \min(N, 7)$)

The second line contains the supply counts $a_1, a_2, \cdots, a_N$ in each box, separated by spaces. ($1 \leq a_i \leq 1\,000\,000$)

The third line contains the number of soldiers $b_1, b_2, \cdots, b_M$ in each squad, separated by spaces. ($1 \leq b_j \leq 1\,000\,000$)

Print the number of supplies handled by the soldier who cleans up the most.