DE-BUNDESWETTBEWERB 2004 Problem 1

At the beginning of a game, I write the numbers $1$ , $2$ , ..., $2004$ onto a desk. A move consists of

• selecting some numbers standing on the desk;
• calculating the rest of the sum of these numbers under division by $11$ and writing this rest onto the desk;
• deleting the selected numbers.

In such a game, after a number of moves, only two numbers remained on the desk. One of them was $1000$ . What was the other one?