{"trustable":true,"prependHtml":"\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eProfessor Zhang would like to solve the multiple pattern matching problem, but he only has only one pattern string $p\u003dp_{1}p_{2}...p_{m}$. So, he wants to generate as many as possible pattern strings from $p$ using the following method:\u003cbr\u003e\u003cbr\u003e1. select some indices $i_1,i_2,...,i_k$ such that $1 \\le i_1 \u0026lt; i_2 \u0026lt; ... \u0026lt; i_k \u0026lt;|p|$ and $|i_j-i_{j+1}| \u0026gt; 1$ for all $1 \\le j \u0026lt; k$.\u003cbr\u003e2. swap $p_{i_j}$ and $p_{i_j+1}$ for all $1 \\le j \\le k$.\u003cbr\u003e\u003cbr\u003eNow, for a given a string $s\u003ds_{1}s_{2}...s_{n}$, Professor Zhang wants to find all occurrences of all the generated patterns in $s$.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"There are multiple test cases. The first line of input contains an integer $T$, indicating the number of test cases. For each test case:\u003cbr\u003e\u003cbr\u003eThe first line contains two integers $n$ and $m$ $(1 \\le n \\le 10^5, 1 \\le m \\le \\min\\{5000, n\\})$ -- the length of $s$ and $p$.\u003cbr\u003e\u003cbr\u003eThe second line contains the string $s$ and the third line contains the string $p$. Both the strings consist of only lowercase English letters."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output a binary string of length $n$. The $i$-th character is \"1\" if and only if the substring $s_{i}s_{i+1}...s_{i+m-1}$ is one of the generated patterns."}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n4 1\r\nabac\r\na\r\n4 2\r\naaaa\r\naa\r\n9 3\r\nabcbacacb\r\nabc\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1010\r\n1110\r\n100100100\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}