{"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\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e\u003c/p\u003e\u003cp\u003eThere\u0027s a table of $$$n \\times m$$$ cells ($$$n$$$ rows and $$$m$$$ columns). The value of $$$n \\cdot m$$$ is even.\u003c/p\u003e\u003cp\u003eA domino is a figure that consists of two cells having a common side. It may be horizontal (one of the cells is to the right of the other) or vertical (one of the cells is above the other).\u003c/p\u003e\u003cp\u003eYou need to find out whether it is possible to place $$$\\frac{nm}{2}$$$ dominoes on the table so that exactly $$$k$$$ of them are horizontal and all the other dominoes are vertical. The dominoes cannot overlap and must fill the whole table.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains one integer $$$t$$$ ($$$1 \\le t \\le 10$$$) — the number of test cases. Then $$$t$$$ test cases follow.\u003c/p\u003e\u003cp\u003eEach test case consists of a single line. The line contains three integers $$$n$$$, $$$m$$$, $$$k$$$ ($$$1 \\le n,m \\le 100$$$, $$$0 \\le k \\le \\frac{nm}{2}$$$, $$$n \\cdot m$$$ is even) — the number of rows, columns and horizontal dominoes, respectively.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case output \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eYES\u003c/span\u003e\", if it is possible to place dominoes in the desired way, or \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eNO\u003c/span\u003e\" otherwise.\u003c/p\u003e\u003cp\u003eYou may print each letter in any case (\u003cspan class\u003d\"tex-font-style-tt\"\u003eYES\u003c/span\u003e, \u003cspan class\u003d\"tex-font-style-tt\"\u003eyes\u003c/span\u003e, \u003cspan class\u003d\"tex-font-style-tt\"\u003eYes\u003c/span\u003e will all be recognized as positive answer, \u003cspan class\u003d\"tex-font-style-tt\"\u003eNO\u003c/span\u003e, \u003cspan class\u003d\"tex-font-style-tt\"\u003eno\u003c/span\u003e and \u003cspan class\u003d\"tex-font-style-tt\"\u003enO\u003c/span\u003e will all be recognized as negative answer).\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\u003e8\n4 4 2\n2 3 0\n3 2 3\n1 2 0\n2 4 2\n5 2 2\n2 17 16\n2 1 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eYES\nYES\nYES\nNO\nYES\nNO\nYES\nNO\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}