{"raw_statement":[{"iden":"problem statement","content":"Takahashi has come to a party as a special guest. There are $N$ ordinary guests at the party. The $i$\\-th ordinary guest has a _power_ of $A_i$.\nTakahashi has decided to perform $M$ _handshakes_ to increase the _happiness_ of the party (let the current happiness be $0$). A handshake will be performed as follows:\n\n*   Takahashi chooses one (ordinary) guest $x$ for his left hand and another guest $y$ for his right hand ($x$ and $y$ can be the same).\n*   Then, he shakes the left hand of Guest $x$ and the right hand of Guest $y$ simultaneously to increase the happiness by $A_x+A_y$.\n\nHowever, Takahashi should not perform the same handshake more than once. Formally, the following condition must hold:\n\n*   Assume that, in the $k$\\-th handshake, Takahashi shakes the left hand of Guest $x_k$ and the right hand of Guest $y_k$. Then, there is no pair $p, q$ $(1 \\leq p < q \\leq M)$ such that $(x_p,y_p)=(x_q,y_q)$.\n\nWhat is the maximum possible happiness after $M$ handshakes?"},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq M \\leq N^2$\n*   $1 \\leq A_i \\leq 10^5$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$\n$A_1$ $A_2$ $...$ $A_N$"},{"iden":"sample input 1","content":"5 3\n10 14 19 34 33"},{"iden":"sample output 1","content":"202\n\nLet us say that Takahashi performs the following handshakes:\n\n*   In the first handshake, Takahashi shakes the left hand of Guest $4$ and the right hand of Guest $4$.\n*   In the second handshake, Takahashi shakes the left hand of Guest $4$ and the right hand of Guest $5$.\n*   In the third handshake, Takahashi shakes the left hand of Guest $5$ and the right hand of Guest $4$.\n\nThen, we will have the happiness of $(34+34)+(34+33)+(33+34)=202$.\nWe cannot achieve the happiness of $203$ or greater, so the answer is $202$."},{"iden":"sample input 2","content":"9 14\n1 3 5 110 24 21 34 5 3"},{"iden":"sample output 2","content":"1837"},{"iden":"sample input 3","content":"9 73\n67597 52981 5828 66249 75177 64141 40773 79105 16076"},{"iden":"sample output 3","content":"8128170"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}