Maximum XOR Product

Problem: Maximum XOR Product Given three non-negative integers a, b, and n, choose an integer x satisfying: 0 <= x < 2^n such that the following product is maximized: (a XOR x) * (b XOR x) Return the maximum product modulo 1_000_000_007. Here, XOR denotes the bitwise exclusive-or operation. Input Format One line containing three integers: a b n. Output Format Print the maximum possible product modulo 1000000007. Example Input: 12 5 4 Output: 98 One optimal choice is x = 2: (12 XOR 2) * (5 XOR 2) = 14 * 7 = 98 Constraints 0 <= a, b < 2^50 0 <= n <= 50 Return the result modulo 1_000_000_007. Example Input 12 5 4 Output 98