New Game Plus!
Description
Wabbit is playing a game with $n$ bosses numbered from $1$ to $n$. The bosses can be fought in any order. Each boss needs to be defeated exactly once. There is a parameter called boss bonus which is initially $0$.
When the $i$-th boss is defeated, the current boss bonus is added to Wabbit's score, and then the value of the boss bonus increases by the point increment $c_i$. Note that $c_i$ can be negative, which means that other bosses now give fewer points.
However, Wabbit has found a glitch in the game. At any point in time, he can reset the playthrough and start a New Game Plus playthrough. This will set the current boss bonus to $0$, while all defeated bosses remain defeated. The current score is also saved and does not reset to zero after this operation. This glitch can be used at most $k$ times. He can reset after defeating any number of bosses (including before or after defeating all of them), and he also can reset the game several times in a row without defeating any boss.
Help Wabbit determine the maximum score he can obtain if he has to defeat all $n$ bosses.
The first line of input contains two spaced integers $n$ and $k$ ($1 \leq n \leq 5 \cdot 10^5$, $0 \leq k \leq 5 \cdot 10^5$), representing the number of bosses and the number of resets allowed.
The next line of input contains $n$ spaced integers $c_1,c_2,\ldots,c_n$ ($-10^6 \leq c_i \leq 10^6$), the point increments of the $n$ bosses.
Output a single integer, the maximum score Wabbit can obtain by defeating all $n$ bosses (this value may be negative).
Input
The first line of input contains two spaced integers $n$ and $k$ ($1 \leq n \leq 5 \cdot 10^5$, $0 \leq k \leq 5 \cdot 10^5$), representing the number of bosses and the number of resets allowed.
The next line of input contains $n$ spaced integers $c_1,c_2,\ldots,c_n$ ($-10^6 \leq c_i \leq 10^6$), the point increments of the $n$ bosses.
Output
Output a single integer, the maximum score Wabbit can obtain by defeating all $n$ bosses (this value may be negative).
Samples
3 0
1 1 1
3
5 1
-1 -2 -3 -4 5
11
13 2
3 1 4 1 5 -9 -2 -6 -5 -3 -5 -8 -9
71
Note
In the first test case, no resets are allowed. An optimal sequence of fights would be
- Fight the first boss $(+0)$. Boss bonus becomes equal to $1$.
- Fight the second boss $(+1)$. Boss bonus becomes equal to $2$.
- Fight the third boss $(+2)$. Boss bonus becomes equal to $3$.
Thus the answer for the first test case is $0+1+2=3$.
In the second test case, it can be shown that one possible optimal sequence of fights is
- Fight the fifth boss $(+0)$. Boss bonus becomes equal to $5$.
- Fight the first boss $(+5)$. Boss bonus becomes equal to $4$.
- Fight the second boss $(+4)$. Boss bonus becomes equal to $2$.
- Fight the third boss $(+2)$. Boss bonus becomes equal to $-1$.
- Reset. Boss bonus becomes equal to $0$.
- Fight the fourth boss $(+0)$. Boss bonus becomes equal to $-4$.
Hence the answer for the second test case is $0+5+4+2+0=11$.