Post Office 2

A circular main road runs around a loop, and V villages are located along it. The circumference of the road is the integer L. In this problem, the road is a circle of integers from 0 to L-1, and each village position is an integer coordinate on the road. Several villages may share the same position. The distance between two villages at coordinates x and y is $\min(|x - y|, L - |x - y|)$.

You want to build P post offices where the villages are. Not every village gets one. Choose P of the V villages and build a post office at each chosen position. The goal is to minimize the sum of distances between each village and its nearest post office.

Write a program that reads the village positions and the number P, computes the minimum possible sum of distances from each village to its nearest post office, and prints the positions where the post offices should be built so that this sum is achieved.

The first line contains three integers V, P, and L. ($1 \le P \le V \le 100$, $1 \le L \le 10^{12}$)

The next line contains V integer coordinates giving the position of each village. The coordinates are sorted in non-decreasing order. Each coordinate is between 0 and L-1, inclusive.

On the first line, print the integer S, the minimum possible sum of distances between each village and its nearest post office.

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