{"problem":{"name":"Handshake","description":{"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 $A_i$. Takahashi has decided to perform $M$ _handshakes_ to in","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc149_e"},"statements":[{"statement_type":"Markdown","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?\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq M \\leq N^2$\n*   $1 \\leq A_i \\leq 10^5$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n$A_1$ $A_2$ $...$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc149_e","tags":[],"sample_group":[["5 3\n10 14 19 34 33","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 $202$."],["9 14\n1 3 5 110 24 21 34 5 3","1837"],["9 73\n67597 52981 5828 66249 75177 64141 40773 79105 16076","8128170"]],"created_at":"2026-03-03 11:01:14"}}