{"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\"\u003eThere is a positive integer sequence $a_1,a_2,...,a_n$ with some unknown positions, denoted by 0. Little Q will replace each 0 by a random integer within the range $[1,m]$ equiprobably. After that, he will calculate the value of this sequence using the following formula :\u003cbr\u003e\\begin{eqnarray*}\u003cbr\u003e\\prod_{i\u003d1}^{n-3} v[\\gcd(a_i,a_{i+1},a_{i+2},a_{i+3})]\u003cbr\u003e\\end{eqnarray*}\u003cbr\u003eLittle Q is wondering what is the expected value of this sequence. Please write a program to calculate the expected value.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains an integer $T(1\\leq T\\leq10)$, denoting the number of test cases.\u003cbr\u003eIn each test case, there are $2$ integers $n,m(4\\leq n\\leq 100,1\\leq m\\leq 100)$ in the first line, denoting the length of the sequence and the bound of each number.\u003cbr\u003eIn the second line, there are $n$ integers $a_1,a_2,...,a_n(0\\leq a_i\\leq m)$, denoting the sequence.\u003cbr\u003eIn the third line, there are $m$ integers $v_1,v_2,...v_m(1\\leq v_i\\leq 10^9)$, denoting the array $v$.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print a single line containing an integer, denoting the expected value. If the answer is $\\frac{A}{B}$, please print $C(0\\leq C\u0026lt;10^9+7)$ where $A\\equiv C\\times B\\pmod{10^9+7}$.\u003cbr\u003e"}},{"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\t\t\t\t\t\r\n6 8\t\t\t\t\t\r\n4 8 8 4 6 5\t\t\t\t\r\n10 20 30 40 50 60 70 80\r\n4 3\t\t\t\t\t\r\n0 0 0 0\t\t\t\t\r\n3 2 4\t\t\t\t\t\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e8000\r\n3\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}