{"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\"\u003e$n$ soldiers are dispatched to somewhere in Byteland. These soldiers are going to set off now, but the target location is not so clear.\u003cbr\u003e\u003cbr\u003eAssume the target location is at $(x_e,y_e)$, it is clear that $x_e,y_e$ are both non-negative integers within $[0,m]$. For the $i$-th soldier, the only thing he knows is that $(|x_i-x_e|+|y_i-y_e|)\\bmod k_i\u003dt_i$.\u003cbr\u003e\u003cbr\u003eTo find the correct target location, these soldiers are working on the information they have now. Please write a program to figure out the number of possible target locations.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains an integer $T(1\\leq T\\leq 10)$, denoting the number of test cases.\u003cbr\u003e\u003cbr\u003eIn each test case, there are two integers $n,m(1\\leq n\\leq 10,1\\leq m\\leq 10^9)$ in the first line, denoting the number of soldiers and the upper bound of $x_e,y_e$.\u003cbr\u003e\u003cbr\u003eFor the next $n$ lines, each line contains four integers $x_i,y_i,k_i,t_i(0\\leq x_i,y_i\\leq m,2\\leq k_i\\leq 5,0\\leq t_i\u0026lt;k_i)$, denoting what each soldier knows."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print a single line containing an integer, denoting the number of possible target locations."}},{"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\u003e2\r\n2 5\r\n1 2 4 2\r\n3 1 2 1\r\n2 5\r\n1 2 4 2\r\n1 2 4 3\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e10\r\n0\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}