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 

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?