In the first line of the standard input, there are two integers, N and K (1<=N<=60,0<=K<=1000000,k<=2^N-1, N*k<=5000000) separated by a single space. These are the length of town names in bits and the the number of N -bit sequences that do not correspond to any town, respectively. In the second line, there are two strings, separated by a single space, each consisting of characters 0 and/or 1. These are the names of the towns x and y. In the K lines that follow, all the sequences of N bits that do not correspond to any town are given, one sequence per line. Each such sequence is a string of characters 0 and/or1. You may assume that x and y are not among those K sequences.