Ranking sums

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.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T10:12:33.233Z