Memory Pool

Simulate a memory allocator that hands out contiguous blocks from a fixed pool using the first-fit rule.

The pool has size cells with addresses 0 to size - 1, all free at the start. Each block has a positive integer id, a start address, and a length, and occupies cells start to start + length - 1. Blocks never overlap. A gap is a maximal run of consecutive free cells (including the run at the very end of the pool). Process commands in order; each command returns one integer. A command that cannot be carried out returns -1 and changes nothing.

• ["alloc", id, n]: allocate a block of n cells for id in the first-fit position: the lowest address at which n free cells in a row begin (equivalently, the first gap, scanning from address 0, with at least n cells; the block goes at the start of that gap). Return its start address. Return -1 if id is already allocated, if n < 1, or if no gap is large enough.
• ["free", id]: release the block. Return its length, or -1 if id is not allocated.
• ["realloc", id, n]: resize the block to n cells. Return -1 if id is not allocated or n < 1. Otherwise:

1. If n is at most the current length, shrink in place (the first n cells are kept) and return the unchanged start address. (n equal to the current length changes nothing.)
2. Otherwise, if the cells directly after the block are free for long enough (the block can reach n cells before it runs into the next block or the end of the pool), grow in place and return the unchanged start address.
3. Otherwise try to move the block: imagine the block lifted out of the pool (its old cells now count as free, and merge with neighbouring free cells), and look for the first-fit position for n cells as in alloc. If one exists, move the block there and return the new start address (which may overlap its old cells or be lower than its old address). If none exists, return -1 and the block stays exactly as it was.

• ["compact"]: slide every block toward address 0, keeping their relative order, with no gaps between them. Return the number of blocks whose start address changed.
• ["owner", a]: return the id of the block that occupies cell a, or -1 if the cell is free or a is outside 0..size-1.
• Any other command (an unknown name, or the wrong number of items) returns -1.

The pool can be very large (up to 10^9 cells), so do not model it cell by cell.

Input: size, an integer, and commands, a list of commands as described.

Output: a list of integers, one per command.