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
     1001
     1011
     1
     1111 1111
   Output:
     1011 0.25

Eagerly waiting for your replies. Thanks in advance.