P3552 [POI 2013] 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

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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