What's his last name? Of the Southern aisles

Logic Level 4

You are given a list of the first one trillion positive integers and you must perform the following steps:

Step 1) Pick any two numbers at random from this list.
Step 2) Find the sum and the product of these numbers.
Step 3) Find the sum of the numbers found in step 2.
Step 4) Remove the two chosen numbers in step one from the list.
Step 5) Add the new number found in step 3 into the list.
Step 6) Repeat steps 1 to 5 until there is only one number left.

What is the last 9 (rightmost) digits of the one remaining number?


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