# Throwing Number

Consider the sequence of positive integers $$1,2,3,4,5,6, \ldots$$. An operation throw consists of taking the first number $$k$$ and move it to the back of the $$(k+1)^\text{th}$$ number. For example,

 1 2 3 4 5 6 seq 1 : 1 2 3 4 5 seq 2 : 2 1 3 4 5 seq 3 : 1 3 2 4 5 seq 4 : 3 1 2 4 5 seq 5 : 1 2 4 3 5 seq 6 : 2 1 4 3 5 

Let $$S$$ be the first sequence that has number 1000 as its leading number. What is the last 3 digit of $$S$$?

Bonus: How about the second sequence that has number 1000 as its leading number?

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