# P3552 [POI2013]SPA-Walk

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• 11提交
• 题目提供者 洛谷
• 评测方式 云端评测
• 标签 哈希,HASH 数论,数学 POI 2013 高性能
• 难度 省选/NOI-
• 时空限制 1000ms / 128MB
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## 题目描述

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

## 输入输出格式

输入格式：

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.

输出格式：

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.

## 输入输出样例

输入样例#1： 复制
4 6
0000 1011
0110
0111
0011
1101
1010
1001

输出样例#1： 复制
TAK


## 说明

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

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