How to save CPU cycles when searching for a value in a sorted list?

Question

In CodinGame learning platform, one of the questions used as an example in a C# tutorial is this one:

The aim of this exercise is to check the presence of

Answer 1

 public static bool Exists(int[] ints, int k)
        {
            var d = 0;
            var f = ints.Length - 1;
            if (d > f) return false;
            if (k > ints[f] || k < ints[d]) return false;
            if (k == ints[f] || k == ints[d]) return true;
            return (BinarySearch(ints, k, d, f) > 0);
        }

 public static int BinarySearch(int[] V, int Key, int begin, int end)
        {
            if (begin > end)
                return -1;
            var MidellIndex = (begin + end) / 2;

            if (Key == V[MidellIndex])
                return MidellIndex;
            else
            {
                if (Key > V[MidellIndex])
                {
                    begin = MidellIndex + 1;
                    return BinarySearch(V, Key, begin, end);
                }
                else
                {
                    end = MidellIndex - 1;
                    return BinarySearch(V, Key, begin, end);
                }
            }

        }