Maximum stability of a server group

A cloud provider offers n servers. Server i has two positive integer scores: reliability[i] and availability[i].

A client deploys on any non-empty group of servers. A group is only as available as its weakest member, and its reliabilities add up. So the stability of a group is:

stability = min(availability of servers in the group) * sum(reliability of servers in the group)

Implement get_max_stability(reliability, availability) that returns the largest stability any group can reach. The value can be very large, so return it modulo 10^9 + 7. Pick the group by its true stability, not by the reduced value.

Constraints

• 1 <= n <= 10^5
• len(reliability) == len(availability) == n
• 1 <= reliability[i], availability[i] <= 10^6

Example 1

reliability  = [2, 3, 1]
availability = [5, 1, 4]
output: 12

Choose servers 0 and 2. The minimum availability is 4 and the reliabilities sum to 3, so the stability is 12. Server 0 alone scores 10, and all three servers score only 6.

Example 2

reliability  = [10, 1]
availability = [1, 100]
output: 100

Server 1 alone scores 100 * 1 = 100. Adding server 0 drops the minimum availability to 1, for a score of 11.