{"raw_statement":[{"iden":"problem statement","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`.\n    \n*   All $S_i$ are pairwise distinct.\n    \n*   For every $j$ ($1 \\leq j \\leq L$) and every $c=$`0`, `1`, `2`, the following holds.\n    *   For exactly $N$ of the strings $S_i$, the $j$\\-th character is $c$.\n*   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."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 5 \\times 10^4$\n*   $1 \\leq L \\leq 15$\n*   $3N \\leq 3^L$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $L$"},{"iden":"sample input 1","content":"2 2"},{"iden":"sample output 1","content":"00\n02\n11\n12\n20\n21\n\nThis Sample Output satisfies all conditions.\nFor example, there are two strings whose second character is `0`.\nAlso, we have $t=$`21` in this sample, and $t$ is never lexicographically smaller than this."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}