You are given n integer numbers. If you compute all the (

n |

2 |

) sums of any two of those numbers, and you sort them all, which is the k-th of those sums?

For instance, if n = 3 and you are given the numbers 6, 6, and 4, you can make three sums: 6 + 6 = 12, 6 + 4 = 10, and 6 + 4 = 10. Therefore, the first of those sums is 10, the second is 10, and the third is 12.

Input

Input consists of several cases,
each with k and n, followed by the n numbers,
all between 1 and 10^{8}.
Assume 2 ≤ n ≤ 4 · 10^{4}
and 1 ≤ k ≤ (

n |

2 |

).

Output

For every case, print the k-th sum of all the pairs of numbers.

Public test cases

**Input**

1 3 6 6 4 2 3 6 6 4 3 3 6 6 4 1 2 1 100000000 1 4 10 10 10 10 6 4 10 10 10 10

**Output**

10 10 12 100000001 20 20

Information

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++