OMM 2002 Problem 1

The numbers $1$ to $1024$ are written one per square on a $32 \times 32$ board, so that the first row is $1, 2, ... , 32$ , the second row is $33, 34, ... , 64$ and so on. Then the board is divided into four $16 \times 16$ boards and the position of these boards is moved round clockwise, so that $AB$ goes to $DA$ $DC \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, CB$ then each of the $16 \times 16$ boards is divided into four equal $8 \times 8$ parts and each of these is moved around in the same way (within the $16 \times 16$ board). Then each of the $8 \times 8$ boards is divided into four $4 \times 4$ parts and these are moved around, then each $4 \times 4$ board is divided into $2 \times 2$ parts which are moved around, and finally the squares of each $2 \times 2$ part are moved around. What numbers end up on the main diagonal (from the top left to bottom right)?