LogicalAndReasoning TrialAndError Intermediate

Problem - 3935
Take a list of positive integers $1$, $2$, $3$, $\cdots$, $2017$. At each step, pick up two of the numbers on the list, say $a$ and $b$, cross them out and replace them by the single number $(ab+a+b)$. Keep doing this until only a single number is left. What is (are) the possible value(s) of this last number?

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