Given a table product_history including records of products status & stock changes from May October 2018.

You have one sample dataset attached to this test:

Dimension	Definition
Date	Log Date (FROM 5/1/2018 TO 10/30/2018)
Product ID	Unique ID for each product
Product Status	Status of a product: + ON: Available for Sales + OFF: Unavailable for Sales
Stock	Total stock of a product at specific log date

a. Write a SQL query to find the number of product that were available for sales at the end of each month.

b. Average stock is calculated as: Total stock in a month/ total date in a month. Write a SQL query to find Product ID with the most average stock by month.