[POI2013] SPA-Walk

The names of towns in Byteotia are unique sequences of exactly $n$ bits. There are $2^n-k$ towns in Byteotia, and thus,only $k$ sequences of $n$ bits do not correspond to any town. Some pairs of towns are connected with roads. Specifically, two towns are directly linked by a road if and only if their names differ in a single bit. The roads do not cross outside of towns. Byteasar intends to take a stroll - he intends to walk from the town $x$ to the town $y$, taking the existing roads. Your task is to write a program that will determine if such a walk is possible. 有2^n个长度为n的01串，两个01串之间有边当且仅当这两个01串只有一位不同，现在从这2n个串中拿掉k个，问指定两个串之间能否到达

In the first line of the standard input, there are two integers,$n$ and $k$($1\le n\le 60$, $0\le k\le 1\ 000\ 000$, $k\le 2^n-1$, $n\times k\le 5\ 000\ 000$), 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 $n$ 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.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 $n$ characters 0 and/or 1.You may assume that $x$ and $y$ are not among those $k$ sequences.

Your program should print to the standard output the word TAK (Polish for yes) if walking from the town x to the town y is possible, and the word NIE (Polish for no) otherwise.

4 6
0000 1011
0110
0111
0011
1101
1010
1001

TAK

有2^n个长度为n的01串，两个01串之间有边当且仅当这两个01串只有一位不同，现在从这2n个串中拿掉k个，问指定两个串之间能否到达