{"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\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$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e\u003cspan class\u003d\"tex-font-style-it\"\u003eThe only difference between this problem and D2 is that you don\u0027t have to provide the way to construct the answer in this problem, but you have to do it in D2.\u003c/span\u003e\u003c/p\u003e\u003cp\u003eThere\u0027s a table of $$$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"}}]}