Ranking sums P21654

You are given $n$ integer numbers. If you compute all the $\binom{n}{2}$ 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 $2 \le n \le 4 \cdot 10^4$ and $1 \le k \le \binom{n}{2}$.

Output

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