Precision Permissioning

In a security system, a 'Master Key' (a 32-bit integer) defines required permission bits. A 'Subordinate Key' is 'Aligned' if it has all the bits set that the Master Key has set. Among a list of N Subordinate Keys, find the Aligned key that has the minimum number of 'Extra Bits' (bits set where the Master Key has none). If there's a tie in the number of Extra Bits, choose the Subordinate Key with the smallest numerical value. If no keys are Aligned, output -1. Example: Input: 10 3 11 14 31 Output: 11 Explanation: Master Key 10 (1010). 11 (1011): Aligned (has bits at 8 and 2). Extra bits: bit 0 (1 bit). 14 (1110): Aligned (has bits at 8 and 2). Extra bits: bit 4 (1 bit). 31 (11111): Aligned. Extra bits: bits 0, 4, 16 (3 bits). Tie between 11 and 14 (both 1 extra bit). Smallest value is 11.