Pairs

AtCoder

IDabc155_d

Time2000ms

Memory256MB

Difficulty—

We have $N$ integers $A_1, A_2, ..., A_N$. There are $\frac{N(N-1)}{2}$ ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the $K$\-th number in that list? ## Constraints * All values in input are integers. * $2 \leq N \leq 2 \times 10^5$ * $1 \leq K \leq \frac{N(N-1)}{2}$ * $-10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

4 3
3 3 -4 -2

Output #1

\-6

There are six ways to form a pair. The products of those pairs are $9$, $-12$, $-6$, $-12$, $-6$, $8$.
Sorting those numbers in ascending order, we have $-12$, $-12$, $-6$, $-6$, $8$, $9$. The third number in this list is $-6$.

Input #2

10 40
5 4 3 2 -1 0 0 0 0 0

Output #2

Input #3

30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0

Output #3

448283280358331064

API Response (JSON)

{
  "problem": {
    "name": "Pairs",
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      "content": "We have $N$ integers $A_1, A_2, ..., A_N$. There are $\\frac{N(N-1)}{2}$ ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending o",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc155_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ integers $A_1, A_2, ..., A_N$.\nThere are $\\frac{N(N-1)}{2}$ ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending o...",
      "is_translate": false,
      "language": "English"
    }
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}

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