description: The only difference between this problem and D2 is that you don't have to provide the way to construct the answer in this problem, but you have to do it in D2.
  
  There's a table of n × m cells (n rows and m columns). The value of n ⋅ m is even.
  
  A 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).
  
  You need to find out whether it is possible to place 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.
  
  Input
  
  The first line contains one integer t (1 ≤ t ≤ 10) — the number of test cases. Then t test cases follow.
  
  Each test case consists of a single line. The line contains three integers n, m, k (1 ≤ n,m ≤ 100, 0 ≤ k ≤ nm/2, n ⋅ m is even) — the number of rows, columns and horizontal dominoes, respectively.
  
  Output
  
  For each test case output "YES", if it is possible to place dominoes in the desired way, or "NO" otherwise.
  
  You may print each letter in any case (YES, yes, Yes will all be recognized as positive answer, NO, no and nO will all be recognized as negative answer).
  
  Example
  
  Input
  
  
  8
  4 4 2
  2 3 0
  3 2 3
  1 2 0
  2 4 2
  5 2 2
  2 17 16
  2 1 1
  
  
  Output
  
  
  YES
  YES
  YES
  NO
  YES
  NO
  YES
  NO
solution: import java.io.ByteArrayInputStream;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.PrintWriter;
  import java.util.Arrays;
  import java.util.InputMismatchException;
  
  public class Main {
  
  	private static final String NO = "No";
  	private static final String YES = "Yes";
  	InputStream is;
  	PrintWriter out;
  	String INPUT = "";
  
  	private static final long MOD = (long) (1e9 + 7);
  
  	void solve() {
  		int T = ni();
  		for (int i = 0; i < T; i++)
  			solve(i);
  	}
  
  	void solve(int nth) {
  		int n = ni();
  		int m = ni();
  		int h = ni();
  		int total = n * m / 2;
  		int v = total - h;
  		boolean yes = false;
  		if (n % 2 == 1) {
  			int h0 = m / 2;
  			yes = (h >= h0 && (h - h0) % 2 == 0);
  		} else if (m % 2 == 1) {
  			int v0 = n / 2;
  			yes = (v >= v0 && (v - v0) % 2 == 0);
  		} else
  			yes = h % 2 == 0;
  
  		out.println(yes ? YES : NO);
  
  	}
  
  	void run() throws Exception {
  		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
  		out = new PrintWriter(System.out);
  
  		long s = System.currentTimeMillis();
  		solve();
  		out.flush();
  		if (!INPUT.isEmpty())
  			tr(System.currentTimeMillis() - s + "ms");
  	}
  
  	public static void main(String[] args) throws Exception {
  		new Main().run();
  	}
  
  	private byte[] inbuf = new byte[1024];
  	public int lenbuf = 0, ptrbuf = 0;
  
  	private int readByte() {
  		if (lenbuf == -1)
  			throw new InputMismatchException();
  		if (ptrbuf >= lenbuf) {
  			ptrbuf = 0;
  			try {
  				lenbuf = is.read(inbuf);
  			} catch (IOException e) {
  				throw new InputMismatchException();
  			}
  			if (lenbuf <= 0)
  				return -1;
  		}
  		return inbuf[ptrbuf++];
  	}
  
  	private boolean isSpaceChar(int c) {
  		return !(c >= 33 && c <= 126);
  	}
  
  	private int skip() {
  		int b;
  		while ((b = readByte()) != -1 && isSpaceChar(b))
  			;
  		return b;
  	}
  
  	private double nd() {
  		return Double.parseDouble(ns());
  	}
  
  	private char nc() {
  		return (char) skip();
  	}
  
  	private char[] nc(int n) {
  		char[] ret = new char[n];
  		for (int i = 0; i < n; i++)
  			ret[i] = nc();
  		return ret;
  	}
  
  	private String ns() {
  		int b = skip();
  		StringBuilder sb = new StringBuilder();
  		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
  									// ')
  			sb.appendCodePoint(b);
  			b = readByte();
  		}
  		return sb.toString();
  	}
  
  	private char[] ns(int n) {
  		char[] buf = new char[n];
  		int b = skip(), p = 0;
  		while (p < n) {
  			if (!(isSpaceChar(b)))
  				buf[p++] = (char) b;
  			b = readByte();
  		}
  		return n == p ? buf : Arrays.copyOf(buf, p);
  	}
  
  	private char[][] nm(int n, int m) {
  		char[][] map = new char[n][];
  		for (int i = 0; i < n; i++)
  			map[i] = ns(m);
  		return map;
  	}
  
  	private int[] na(int n) {
  		int[] a = new int[n];
  		for (int i = 0; i < n; i++)
  			a[i] = ni();
  		return a;
  	}
  
  	private Integer[] na2(int n) {
  		Integer[] a = new Integer[n];
  		for (int i = 0; i < n; i++)
  			a[i] = ni();
  		return a;
  	}
  
  	private int[][] na(int n, int m) {
  		int[][] a = new int[n][];
  		for (int i = 0; i < n; i++)
  			a[i] = na(m);
  		return a;
  	}
  
  	private int ni() {
  		int num = 0, b;
  		boolean minus = false;
  		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
  			;
  		if (b == '-') {
  			minus = true;
  			b = readByte();
  		}
  
  		while (true) {
  			if (b >= '0' && b <= '9') {
  				num = num * 10 + (b - '0');
  			} else {
  				return minus ? -num : num;
  			}
  			b = readByte();
  		}
  	}
  
  	private Long[] nl2(int n) {
  		Long[] a = new Long[n];
  		for (int i = 0; i < n; i++)
  			a[i] = nl();
  		return a;
  	}
  
  	private long[] nl(int n) {
  		long[] a = new long[n];
  		for (int i = 0; i < n; i++)
  			a[i] = nl();
  		return a;
  	}
  
  	private long[][] nl(int n, int m) {
  		long[][] a = new long[n][];
  		for (int i = 0; i < n; i++)
  			a[i] = nl(m);
  		return a;
  	}
  
  	private long nl() {
  		long num = 0;
  		int b;
  		boolean minus = false;
  		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
  			;
  		if (b == '-') {
  			minus = true;
  			b = readByte();
  		}
  
  		while (true) {
  			if (b >= '0' && b <= '9') {
  				num = num * 10 + (b - '0');
  			} else {
  				return minus ? -num : num;
  			}
  			b = readByte();
  		}
  	}
  
  	private static void tr(Object... o) {
  		System.out.println(Arrays.deepToString(o));
  	}
  
  }
  