Ternary Strings

AtCoder

IDarc127_b

Time2000ms

Memory256MB

Difficulty—

Given are integers $N$ and $L$. Find a tuple of $3N$ strings $(S_1,S_2,\cdots,S_{3N})$ that satisfies all of the following conditions. * $S_i$ is a string of length $L$ consisting of `0`, `1`, `2`. * All $S_i$ are pairwise distinct. * For every $j$ ($1 \leq j \leq L$) and every $c=$`0`, `1`, `2`, the following holds. * For exactly $N$ of the strings $S_i$, the $j$\-th character is $c$. * Let $t$ be the lexicographically largest string among $S_1,S_2,\cdots,S_{3N}$. $t$ for this tuple is the lexicographically smallest among all strings that $t$ can be. ## Constraints * $1 \leq N \leq 5 \times 10^4$ * $1 \leq L \leq 15$ * $3N \leq 3^L$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $L$ [samples]

Samples

Input #1

2 2

Output #1

00
02
11
12
20
21

This Sample Output satisfies all conditions.
For example, there are two strings whose second character is `0`.
Also, we have $t=$`21` in this sample, and $t$ is never lexicographically smaller than this.

API Response (JSON)

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    "name": "Ternary Strings",
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      "content": "Given are integers $N$ and $L$. Find a tuple of $3N$ strings $(S_1,S_2,\\cdots,S_{3N})$ that satisfies all of the following conditions. *   $S_i$ is a string of length $L$ consisting of `0`, `1`, `2`.",
      "description_type": "Markdown"
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      "statement_type": "Markdown",
      "content": "Given are integers $N$ and $L$. Find a tuple of $3N$ strings $(S_1,S_2,\\cdots,S_{3N})$ that satisfies all of the following conditions.\n\n*   $S_i$ is a string of length $L$ consisting of `0`, `1`, `2`....",
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