Kth Takoyaki Set

AtCoder

IDabc297_e

Time3000ms

Memory256MB

Difficulty—

In AtCoder Kingdom, $N$ kinds of _takoyaki_s (ball-shaped Japanese food) are sold. A takoyaki of the $i$\-th kind is sold for $A_i$ yen. Takahashi will buy at least one takoyaki in total. He is allowed to buy multiple takoyakis of the same kind. Find the $K$\-th lowest price that Takahashi may pay. Here, if there are multiple sets of takoyakis that cost the same price, the price is counted only once. ## Constraints * $1 \le N \le 10$ * $1 \le K \le 2 \times 10^5$ * $1 \le A_i \le 10^9$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

4 6
20 25 30 100

Output #1

50

The four kinds of takoyakis sold in AtCoder Kingdom cost $20$ yen, $25$ yen, $30$ yen, and $100$ yen.
The six lowest prices that Takahashi may pay are $20$ yen, $25$ yen, $30$ yen, $40$ yen, $45$ yen, and $50$ yen. Thus, the answer is $50$.
Note that at least one takoyaki must be bought.

Input #2

2 10
2 1

Output #2

10

Note that a price is not counted more than once even if there are multiple sets of takoyakis costing that price.

Input #3

10 200000
955277671 764071525 871653439 819642859 703677532 515827892 127889502 881462887 330802980 503797872

Output #3

5705443819

API Response (JSON)

{
  "problem": {
    "name": "Kth Takoyaki Set",
    "description": {
      "content": "In AtCoder Kingdom, $N$ kinds of _takoyaki_s (ball-shaped Japanese food) are sold. A takoyaki of the $i$\\-th kind is sold for $A_i$ yen. Takahashi will buy at least one takoyaki in total. He is allowe",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc297_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In AtCoder Kingdom, $N$ kinds of _takoyaki_s (ball-shaped Japanese food) are sold. A takoyaki of the $i$\\-th kind is sold for $A_i$ yen.\nTakahashi will buy at least one takoyaki in total. He is allowe...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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