Bridging the Gap

A group of walkers arrives at a river in the night. They want to cross a bridge, which can hold a limited number of walkers at a time. The walkers have just one torch, which needs to be used when crossing the bridge. Each walker takes a certain time to cross; a group crossing together must walk at the slowest walker’s pace. What is the shortest time it takes for all walkers to cross the bridge?

For example, Sample Input 1 assumes the bridge can hold $2$ walkers at a time and there are $4$ walkers with crossing times $1$ minute, $2$ minutes, $5$ minutes and $10$ minutes, respectively. The shortest time of $17$ minutes can be achieved by the following sequence of crossings. First, the two fastest walkers cross in $2$ minutes. Second, the fastest walker crosses back in $1$ minute. Third, the two slowest walkers cross in $10$ minutes. Fourth, the second-fastest walker crosses back in $2$ minutes. Fifth, the two fastest walkers cross in $2$ minutes.

The first line of input contains two integers $n$ and $c$, where $n$ ($2≤n≤10^4$) is the number of walkers, and $c$ ($2≤c≤10^4$) is the number of walkers the bridge can hold at a time.

Then follows a line containing $n$ integers $t\_1,\dots ,t\_n$ ($1≤t\_i≤10^9$ for all $i$). The $i$th walker takes time $t\_i$ to cross.

Output the minimum total time it takes for the entire group to cross the bridge.