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.

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).

见题面 Input 部分

见题面 Output 部分

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 $0+5+4+2+0=11$.