{"trustable":false,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\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 type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e\nSabiha and Fabiha wants to surprise their mother with a brand new smartphone.\nThus they broke their piggybanks and found that Sabiha has \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e coins and Fabiha has \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eM\u003c/i\u003e\u003c/span\u003e coins. \nThe smartphone costs \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e\u003c/span\u003e taka. \n\nFind the number of ways in which they can pay exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e\u003c/span\u003e taka such that the difference \nbetween what each of them paid doesn\u0027t exceed \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eK\u003c/i\u003e\u003c/span\u003e.\n\u003c/p\u003e\n\n\u003cp\u003e\nIn other words, find the number of ways in which Sabiha can choose \na subset of sum \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eS\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e\u003c/span\u003e and Fabiha can choose a subset of sum \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eS\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e\nsuch that \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eS\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e + \u003ci\u003eS\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e \u003d \u003ci\u003eW\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e|\u003ci\u003eS\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e - \u003ci\u003eS\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e| ≤ \u003ci\u003eK\u003c/i\u003e\u003c/span\u003e.\n\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of input contains a single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eT\u003c/i\u003e\u003c/span\u003e, the number of test cases.\u003c/p\u003e\n\u003cp\u003eThe first line of each test case contains four integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eM\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eK\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003eN\u003c/i\u003e, \u003ci\u003eM\u003c/i\u003e ≤ 150)\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(0 ≤ \u003ci\u003eK\u003c/i\u003e ≤ \u003ci\u003eW\u003c/i\u003e)\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003eW\u003c/i\u003e ≤ 15000)\u003c/span\u003e, the number of coins Sabiha has, the number of coins Fabiha has, the maximum difference between what each of them will pay, and the cost of the smartphone, respectively.\u003c/p\u003e\n\u003cp\u003eThe second line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e space-separated integers, each integer represents the value of one of Sabiha’s coins.\u003c/p\u003e\n\u003cp\u003eThe third line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eM\u003c/i\u003e\u003c/span\u003e space-separated integers, representing the values of Fabiha’s coins.\u003c/p\u003e\n\u003cp\u003eThe values of the coins are between \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e100\u003c/span\u003e (inclusive).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, print the number of ways modulo \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e on a single line.\u003c/p\u003e"}},{"title":"Example","value":{"format":"HTML","content":"\u003cdiv class\u003d\"sample-test\"\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e2\u003cbr\u003e4 3 5 18\u003cbr\u003e2 3 4 1\u003cbr\u003e10 5 5\u003cbr\u003e2 1 20 20\u003cbr\u003e10 30\u003cbr\u003e50\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003e2\u003cbr\u003e0\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n\u003c/div\u003e"}}]}