On Storing Clothes

In a laundry, clothes are hung on coat hangers placed on hooks that are fixed to a circular rail rotated electrically by a computer. The hooks are numbered so that any garment is easy to find, and the rail turns to bring a chosen hook in front of a fixed mark.

Model the rail as a circular array of $N$ hooks whose indices are taken modulo $N$. To store a batch of $n$ garments, the operator types $n$. Starting from the hook currently in front of the mark and scanning to the right (increasing indices, modulo $N$), the computer finds the first block of $n+2$ usable hooks $k, k+1, \dots, k+n+1$. Hook $k$ and hook $k+n+1$ become separators and are not used for garments; the $n$ garments are hung on hooks $k+1, \dots, k+n$. The rail then turns so that hook $k+n+1$ comes in front of the mark, and the operator hands the customer ticket number $k$. Hooks holding a customer's garments stay assigned to that customer, even while the garments are being cleaned.

A separator may be shared: the block's two end hooks may reuse hooks that are already separators. The $n$ middle hooks, however, must be empty.

When the customer returns with ticket $k$, the operator types $k$; the rail turns so that separator hook $k$ of that batch is in front of the mark (the rail does not move while the batch is handed back). Every hook that held one of that batch's garments becomes free. A separator hook of the removed batch also becomes free if both of its neighbors are free. (As the note goes: once both neighbors of a separator are empty, that separator may be reused for any purpose.)

At the start the rail is empty and hook $0$ is in front of the mark. Only garments that have been deposited can be withdrawn.

The first line contains the number of hooks $N$ ($1 \le N \le 300$). The second line contains the number $l$ of command lines that follow. Each of the next $l$ lines has one of the two forms:

D n

deposit a batch of $n$ garments, or

W k

withdraw the batch with ticket $k$ ($0 \le k < N$).

For each command, print the corresponding messages.

On a deposit, if no block of $n+2$ suitable hooks exists, print

No space left, please come back later.

otherwise, when ticket $k$ is issued, print

The launderer gives ticket k.

On a withdrawal of ticket $k$, print

The launderer gives back batch k.

and free every hook of that batch. Whenever hooks $h, \dots, h+q$ become free (a contiguous block, indices modulo $N$), print

i is freed.

for each $i$ from $h$ to $h+q$ in order.