{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003ch1 id\u003d\"rectangle\"\u003eRectangle\u003c/h1\u003e\n\u003cp\u003efrog has a piece of paper divided into \u003cspan class\u003d\"math\"\u003e\\(n\\)\u003c/span\u003e rows and \u003cspan class\u003d\"math\"\u003e\\(m\\)\u003c/span\u003e columns. Today, she would like to draw a rectangle whose perimeter is not greater than \u003cspan class\u003d\"math\"\u003e\\(k\\)\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class\u003d\"figure\"\u003e\u003cimg src\u003d\"CDN_BASE_URL/5697275a9b7230433e5774788fa3e897?v\u003d1672684727\" alt\u003d\"There are 8 (out of 9) ways when n \u003d m \u003d 2, k \u003d 6\"\u003e\n \u003cp class\u003d\"caption\"\u003eThere are \u003cspan class\u003d\"math\"\u003e\\(8\\)\u003c/span\u003e (out of \u003cspan class\u003d\"math\"\u003e\\(9\\)\u003c/span\u003e) ways when \u003cspan class\u003d\"math\"\u003e\\(n \u003d m \u003d 2, k \u003d 6\\)\u003c/span\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eFind the number of ways of drawing.\u003c/p\u003e\n\u003ch2 id\u003d\"input\"\u003eInput\u003c/h2\u003e\n\u003cp\u003eThe input consists of multiple tests. For each test:\u003c/p\u003e\n\u003cp\u003eThe first line contains \u003cspan class\u003d\"math\"\u003e\\(3\\)\u003c/span\u003e integer \u003cspan class\u003d\"math\"\u003e\\(n, m, k\\)\u003c/span\u003e (\u003cspan class\u003d\"math\"\u003e\\(1 \\leq n, m \\leq 5 \\cdot 10^4, 0 \\leq k \\leq 10^9\\)\u003c/span\u003e).\u003c/p\u003e\n\u003ch2 id\u003d\"output\"\u003eOutput\u003c/h2\u003e\n\u003cp\u003eFor each test, write \u003cspan class\u003d\"math\"\u003e\\(1\\)\u003c/span\u003e integer which denotes the number of ways of drawing.\u003c/p\u003e\n\u003ch2 id\u003d\"sample-input\"\u003eSample Input\u003c/h2\u003e\n\u003cpre\u003e\u003ccode\u003e 2 2 6\n 1 1 0\n 50000 50000 1000000000\u003c/code\u003e\u003c/pre\u003e\n\u003ch2 id\u003d\"sample-output\"\u003eSample Output\u003c/h2\u003e\n\u003cpre\u003e\u003ccode\u003e 8\n 0\n 1562562500625000000\u003c/code\u003e\u003c/pre\u003e"}}]}