Find Two Repeating Elements

Assume the usual contract: an array of size n contains numbers 1 through n-2, with exactly two values repeated once. XOR every array value and every number in the expected range. Non-repeated values cancel, leaving x ^ y for the two repeated numbers. Since x and y differ, isolate any set bit, commonly xor & -xor. XOR values and expected-range numbers into two buckets based on that bit; each bucket cancels all ordinary values and leaves one of x or y. If the output requires a specific order, scan the input or compare according to the stated rule to identify it. This avoids overflow and does not mutate input. A frequency array is easier but costs O(n) space; sum/product equations can overflow. Clarify the range and repetition assumptions because without them XOR cannot distinguish arbitrary corruption. Time is O(n), extra space O(1).