Description

Given $n,b,d$, find $n$ binary codewords consisting of 0 and 1, each with $b$ bits, such that the Hamming distance between every pair of codewords is at least $d$.

The Hamming distance is the number of differing bit positions between two binary codewords. For example, the Hamming distance between 0101 0101 0100 and 0010 0011 0100 is $5$:

0101 0101 0100
0010 0011 0100
 ^^^  ^^       

Input Format

One line containing three integers $n,b,d$.

Output Format

Output the lexicographically smallest solution (the $n$ codewords must also be printed in ascending order). Print a newline after every $10$ codewords.

You should first treat each codeword as a binary number, then convert it to a decimal number for output.

16 7 3

0 7 25 30 42 45 51 52 75 76
82 85 97 102 120 127

Hint

Constraints: For $100\%$ of the testdata, $1\le n \le 64$, $1\le b \le 8$, $1\le d \le 7$.

Please note: the problem only requires the Hamming distance to be at least $\bm d$, so it may also be greater than $\bm d$.

USACO 2.1

Translation from NOCOW

Translated by ChatGPT 5