Contest Duration: - (local time) (100 minutes) Back to Home
E - Kth Takoyaki Set /

Time Limit: 3 sec / Memory Limit: 1024 MB

### 問題文

AtCoder 王国では、N 種類のたこ焼きが売られています。i 種類目のたこ焼きの値段は A_i 円です。

### 制約

• 1 \le N \le 10
• 1 \le K \le 2 \times 10^5
• 1 \le A_i \le 10^9
• 入力はすべて整数

### 入力

N K
A_1 A_2 \dots A_N


### 入力例 1

4 6
20 25 30 100


### 出力例 1

50


AtCoder 王国で売られている 4 種類のたこ焼きは、それぞれ 20 円、25 円、30 円、100 円です。

### 入力例 2

2 10
2 1


### 出力例 2

10


### 入力例 3

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


### 出力例 3

5705443819


Score : 500 points

### Problem Statement

In AtCoder Kingdom, N kinds of takoyakis (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


### Output

Print the answer as an integer.

### Sample Input 1

4 6
20 25 30 100


### Sample 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.

### Sample Input 2

2 10
2 1


### Sample Output 2

10


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

### Sample Input 3

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


### Sample Output 3

5705443819