Need help in solving this problem : Modified Hamming Distance

How to solve the following problem ?↵
↵
For any 3 bit strings (consisting only of 1s and 0s) A, B and C, f(A,B,C) is defined as:↵
↵
f(A,B,C)=(no. of 1s in ((A XOR B) AND C))/(no. of 1s in C).↵
↵
We are given N bit strings initially. Then we are given Q queries. Each query contains 2 bit strings B and C. For each query output a single bit string A from the initial set of N bit strings, such that f(A,B,C) is minimum.↵
↵
It is given that the size of all the bit strings given in the input = 2048 (constant).↵
↵
↵
~~~~~↵
Input:↵
   First line contains 2 integers N and Q.↵
   Then N lines follow, each containing a single bit string of length = 2048.↵
   Then Q lines follow,↵
   each containing 2 bit strings B and C each of length = 2048. B and C are space separated.↵
~~~~~↵
↵
~~~~~↵
Output:↵
   For each query output one line containing the string A and f(A,B,C) (space separated).↵
~~~~~↵
↵
~~~~~↵
Constraints:↵
   1<=N<=10000↵
   1<=Q<=10000↵
   |A|=|B|=|C|=2048 (fixed for all strings)↵
~~~~~↵
↵
↵
Example:↵
↵
~~~~~↵
   Input:↵
     2 1\n↵
     1001\n↵
     1011\n↵
     1\n↵
     1111 1111\n↵
   Output:↵
     1011 0.25↵
~~~~~↵
↵
↵
Eagerly waiting for your replies. Thanks in advance.↵