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.*;
  import java.util.*;
  import java.math.BigInteger;
  import java.util.InputMismatchException;
  
  public class Main {
  	static PrintWriter out;
  	static Reader in;
  	public static void main(String[] args) throws IOException {
  		input_output();
  		Main solver = new Main();
  		solver.solve();
  		out.close();
  
  		out.flush();
  	} 
  
  	static long INF = (long)1e18;
  	static int MAXN = (int)1e5 + 5;
  	static int MOD = (int)1e9 + 7;
  	static int q, t, n, m, k;
  	static double pi = Math.PI;
  
  	void solve() throws IOException {
  		t = in.nextInt();
  		
  
  		while (t --> 0) {
  			n = in.nextInt();
  			m = in.nextInt();
  			k = in.nextInt();
  			int vert = (n*m)/2 - k;
  			
  			if (m%2 == 1) {
  				if (vert < n/2) {
  					out.println("NO");
  					continue;
  				}
  				vert -= n/2;
  				m--;
  			}
  
  			for (int i = 0; i < n-(n%2 == 0 ? 0: 1); i+=2) {
  				int	rem = Math.min(m, vert-(vert%2 == 0 ? 0 : 1));
  				vert -= rem;
  				if (vert == 0) break;
  			}
  
  			if (vert == 0) out.println("YES");
  			else out.println("NO");
  		}	
  	}
  
  
  	static class Reader {
  		private InputStream mIs;
  		private byte[] buf = new byte[1024];
  		private int curChar;
  		private int numChars;
  
  		public Reader() {
  			this(System.in);
  		}
  
  		public Reader(InputStream is) {
  			mIs = is;
  		}
  
  		public int read() {
  			if (numChars == -1) {
  				throw new InputMismatchException();
  
  			}
  			if (curChar >= numChars) {
  				curChar = 0;
  				try {
  					numChars = mIs.read(buf);
  				} catch (IOException e) {
  					throw new InputMismatchException();
  				}
  				if (numChars <= 0) {
  					return -1;
  				}
  			}
  			return buf[curChar++];
  		}
  
  		public String nextLine() {
  			int c = read();
  			while (isSpaceChar(c)) {
  				c = read();
  			}
  			StringBuilder res = new StringBuilder();
  			do {
  				res.appendCodePoint(c);
  				c = read();
  			} while (!isEndOfLine(c));
  			return res.toString();
  		}
  
  		public String next() {
  			int c = read();
  			while (isSpaceChar(c)) {
  				c = read();
  			}
  			StringBuilder res = new StringBuilder();
  			do {
  				res.appendCodePoint(c);
  				c = read();
  			} while (!isSpaceChar(c));
  			return res.toString();
  		}
  
  		double nextDouble() {
  			return Double.parseDouble(next());
  		}
  
  		public long nextLong() {
  			int c = read();
  			while (isSpaceChar(c)) {
  				c = read();
  			}
  			int sgn = 1;
  			if (c == '-') {
  				sgn = -1;
  				c = read();
  			}
  			long res = 0;
  			do {
  				if (c < '0' || c > '9') {
  					throw new InputMismatchException();
  				}
  				res *= 10;
  				res += c - '0';
  				c = read();
  			} while (!isSpaceChar(c));
  			return res * sgn;
  		}
  
  		public int nextInt() {
  			int c = read();
  			while (isSpaceChar(c)) {
  				c = read();
  			}
  			int sgn = 1;
  			if (c == '-') {
  				sgn = -1;
  				c = read();
  			}
  			int res = 0;
  			do {
  				if (c < '0' || c > '9') {
  					throw new InputMismatchException();
  				}
  				res *= 10;
  				res += c - '0';
  				c = read();
  			} while (!isSpaceChar(c));
  			return res * sgn;
  		}
  
  		public boolean isSpaceChar(int c) {
  			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
  		}
  
  		public boolean isEndOfLine(int c) {
  			return c == '\n' || c == '\r' || c == -1;
  		}
  
  	}
  	static void input_output() throws IOException {
  		File f = new File("in.txt");
  		if (f.exists() && !f.isDirectory()) {
  			in = new Reader(new FileInputStream("in.txt"));
  		} else in = new Reader();
  		f = new File("out.txt");
  		if (f.exists() && !f.isDirectory()) {
  			out = new PrintWriter(new File("out.txt"));
  		} else out = new PrintWriter(System.out);
  	}
  }