{"trustable":true,"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\u003eHasan and Bahosain want to buy a new video game, they want to share the expenses. Hasan has a set of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e coins and Bahosain has a set of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eM\u003c/i\u003e\u003c/span\u003e coins. The video game costs \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e\u003c/span\u003e JDs. Find the number of ways in which they can pay exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e\u003c/span\u003e JDs such that the difference between what each of them payed doesn’t exceed \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eK\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eIn other words, find the number of ways in which Hasan can choose a 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 Bahosain 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\u003c/span\u003e such 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.\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\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 Hasan has, the number of coins Bahosain has, the maximum difference between what each of them will pay, and the cost of the video game, respectively.\u003c/p\u003e\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 Hasan’s coins.\u003c/p\u003e\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 Bahosain’s coins.\u003c/p\u003e\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":"Examples","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\n4 3 5 18\n2 3 4 1\n10 5 5\n2 1 20 20\n10 30\n50\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2\n0\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}