Problem Brief

Maximum Stability

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AWS provides a range of servers to meet the deployment needs of its clients. A client wants to choose a set of servers to deploy their application. Each server is associated with an availability factor and a reliability factor.

The client defines the stability of a set of servers as the minimum availability amongst the servers multiplied by the sum of reliabilities of all the servers. Given two arrays of integers, availability, and reliability, where the availability[i] and reliability[i] represent the availability and reliability factors of the i^th server, find the maximum possible stability of any subset of servers.

Since the answer can be large, report the answer modulo (10^9 + 7).

Function Description

Complete the function maximumStability in the editor.

maximumStability has the following parameters:

1. int reliability[n]: an array of integers
2. int availability[n]: an array of integers

Returns

int: the maximum stability above among all possible non-empty subsets, modulo (10^9+7)

1Example 1

Input

reliability = [1, 2, 2], availability = [1, 1, 3]

Output

Explanation

The possible subsets of servers are: So the answer is maximum stability for the set of index [2], answer = 6 % 1000000007 = 6.

Constraints

Limits and guarantees your solution can rely on.

1 ≤ n ≤ 10^5
1 ≤ reliability[i], availability[i] ≤ 10^6
It is guaranteed that lengths of reliability and availability are the same.