Post Office 3

A circular road with circumference L runs past V villages. The road is a circle of integer positions from 0 to L-1, and each village is placed at an integer coordinate on it. Several villages may share the same position. The distance between villages at coordinates x and y is $\min(|x-y|, L-|x-y|)$.

You want to build P post offices at village locations. Not every village gets one. Choose P of the V villages and build a post office at each chosen position. Each village is served by the nearest post office. Minimize the sum of distances from every village to its nearest post office.

The first line contains three integers V, P, and L. ($1 \le P \le V \le 250$, $1 \le L \le 10^{12}$)

The second line contains V integers, the coordinates of the villages. The coordinates are sorted in non-decreasing order, and each lies between 0 and L-1, inclusive.

On the first line, print S, the minimum possible sum of distances from each village to its nearest post office.

On the second line, print P integers, the positions of the villages where the post offices are built, in non-decreasing order.