Hexagonal Pasture Network

Farmer John recently acquired some new land to expand his farm. His cows have taken a liking to the hexagonal structure of bee honeycombs, so Farmer John has laid out a new system of pastures and cowpaths in that shape.

The whole plot of pastures and cowpaths forms a hexagon with side length $K$ ($2 \le K \le 50$). The pastures are numbered $1 \ldots 3K(K-1)+1$.

Think of the hexagon as a set of vertical columns. From left to right the columns contain $K, K+1, \ldots, 2K-1, \ldots, K+1, K$ pastures (the middle column is the tallest, with $2K-1$ pastures). Pastures are numbered consecutively starting from $1$: column by column from left to right, and within each column from bottom to top. So pasture $1$ sits at the bottom of the leftmost column, and the last pasture $3K(K-1)+1$ sits at the top of the rightmost column.

Each pasture is connected by a cowpath to every one of its immediate neighbors. A pasture in the interior of the hexagon is adjacent to exactly six others; for example, when $K = 3$, pasture $10$ is adjacent to pastures $5$, $6$, $9$, $11$, $14$, and $15$. A pasture on an edge (but not a corner) is adjacent to exactly four others (e.g. pasture $4$ is adjacent to $1$, $5$, $8$, and $9$), and a pasture at a corner is adjacent to only three (e.g. pasture $1$ is adjacent to $2$, $4$, and $5$). Every cowpath has length $1$, and the distance between two pastures is the length of the shortest route between them.

Farmer John's Holstein cows have been grazing in pasture $H$ ($1 \le H \le 3K(K-1)+1$) for several days and have grown fat and lazy. To make them exercise, Farmer John places tasty treats in every pasture that is exactly at distance $L$ ($1 \le L \le 2K-2$) from the cows. He promises that at least one treat has been placed, but he does not reveal which pastures hold them.

Help the cows avoid unnecessary walking: determine how many pastures could hold a treat, and list them in ascending order.

The first line contains three space-separated integers $K$, $H$, and $L$.

On the first line, print a single integer: the number of pastures that are exactly at distance $L$ from pasture $H$.

On each of the following lines, print one such pasture number, in ascending order.