Matt has somewhere between $1000$ and $2000$ pieces of paper that he is trying to divide into piles of the same size. He attempts to divide them into $2$, $3$, $4$, $5$, $6$, $7$, and $8$ piles, but each time he ends up with one sheet left over. How many piles does he need?

Let's think step by step and output the final answer within \boxed{}.
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