Shortest palindrome by prepending

You may only PREPEND characters to the front of s. Return the shortest palindrome obtainable this way. For example "aacecaaa" becomes "aaacecaaa" and "abcd" becomes "dcbabcd". An already-palindromic string is returned unchanged, and the empty string returns the empty string. Strings can be up to 10^5 characters, so an O(n) approach using the KMP failure function on s + sentinel + reverse(s) is intended.