Yet Another XOR Task

You are given integers $N, M, K$ and $N$ integers $A_1, A_2, \ldots, A_N$. You can perform the following operation at most $K$ times: * Choose any integer $x$ such that $0 \le x < 2^M$. Then, for each $1 \le i \le N$, you can replace $A_i$ with $A_i \oplus x$, or leave it unchanged. What is the maximum value of $A_1 + A_2 + \ldots + A_N$ that you can achieve after this process? ### Input The f