long min = n;
            for (int i = 0; i < k; i++)
                for (int j = i + 1; j < k; j++) {
                    long diff = (data[i] + data[j] - n);
                    if (diff < min)
                        min = diff;
                }
            Console.WriteLine(min < 0 ? 0 : min);

Sorry, it's my fault. This case find Max, not Min.

Does you algorithm work (with your last changes)?

It probably shouldn't (if I am correct)

Consider the following
3 3
2 2 2
The answer, program will give you in this case is 1

But i can easily prove it is wrong:

First man speaks dialects 1 and 2
Second one speaks dialects 2 and 3
The third speaks dialects 3 and 1

Therefore there is nobody, who can speak all three dialects

you help a lot,thank you