{"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\"\u003eNeko has a tree with $n$ nodes. \u003cbr\u003eThere are $m$ key nodes on tree. Neko want to you to selecte some key nodes satisfying the distance between any two selected nodes less than or equal to $k$. \u003cbr\u003eNeko thinks this work is too easy,so Neko want to know how many different way for selecting nodes. \u003cbr\u003eCalculate the answer after mod $10^9+7$.\u003cbr\u003eNote that you have to select at least one key node. \u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains three integers $n, m, k(1 \\leq n,m,k \\leq 5000)$. \u003cbr\u003eThe next $n-1$ line, each line contains two integers $u, v$,indicating there is an edge connecting node $u$ and node $v$. \u003cbr\u003eThe last line contains $m$ integers, indicating key node. "}},{"title":"Output","value":{"format":"HTML","content":"Output the number of way for selecting nodes. "}},{"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\u003e4 3 2\r\n1 2\r\n1 3\r\n2 4\r\n2 3 1\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e7\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}