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.DataInputStream;
  import java.io.FileInputStream;
  import java.io.IOException;
  import java.util.AbstractMap;
  import java.util.Comparator;
  import java.util.HashMap;
  import java.util.Map;
  import java.util.Map.Entry;
  import java.util.PriorityQueue;
  import java.util.*;
  import java.io.*;
  
  // Java Template Pramod Hosahalli...
  @SuppressWarnings("unused")
  public class Solution {
  
  	static FastReader in = new FastReader();
  	//static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
  	static int mod = 1000000007;
  
  	private static boolean solve(int n,int m,int k)
  	{
  		if(n == 0 || m == 0) return k == 0;
  		if(k == 0)return n % 2 == 0;
  		
  		if(n % 2 != 0 && m % 2 != 0)return false; // we cant place dominos
  		if(2 * k > (n * m)) return false; // table is not enough
  		
  		if(n % 2 == 0){
  			if(m == 1)return k == 0; // only possible if k==0			
  			if(k >= n) return solve(n, m - 2, k - n); //place all as horizontal
  			return solve(n, m - 2, (n - k) % 2);
  		}
  		
  		//means m is even and n is odd
  		if(k >= m/2)return solve(n-1, m, k-(m/2));
  		if(n == 1)return false;
  		return solve(n,m-2,k-1);
  	} 
  
  	private static void go() throws Exception{
  		int n = in.ni();
  		int m = in.ni();
  		int k = in.ni();
  		
  		boolean res = solve(n,m,k);
  		print(1, res ? "YES" : "NO");
  	}
  
  	public static void main(String[] args) throws Exception {
  		int t = in.ni();
          //int t = pi(in.readLine());
  		for(int _i = 1; _i <= t; _i++){
  			go();
  		}
  		in.close();
  	}
  
  	static int mul(int a, int  b) {
  		return ((a % mod) * (b % mod)) % mod;
  	}
  	
  
  	static class FastReader {
  		final private int BUFFER_SIZE = 1 << 16;
  		private DataInputStream din;
  		private byte[] buffer;
  		private int bufferPointer, bytesRead;
  
  		public FastReader() {
  			din = new DataInputStream(System.in);
  			buffer = new byte[BUFFER_SIZE];
  			bufferPointer = bytesRead = 0;
  		}
  
  		public FastReader(String file_name) throws IOException {
  			din = new DataInputStream(new FileInputStream(file_name));
  			buffer = new byte[BUFFER_SIZE];
  			bufferPointer = bytesRead = 0;
  		}
  
  		public String readLine() throws IOException {
  			byte[] buf = new byte[64]; // line length
  			int cnt = 0, c;
  			while ((c = read()) != -1) {
  				if (c == '\n') {
  					if (cnt != 0) {
  						break;
  					} else {
  						continue;
  					}
  				}
  				buf[cnt++] = (byte) c;
  			}
  			return new String(buf, 0, cnt);
  		}
  
  		public int ni() throws IOException {
  			int ret = 0;
  			byte c = read();
  			while (c <= ' ') {
  				c = read();
  			}
  			boolean neg = (c == '-');
  			if (neg)
  				c = read();
  			do {
  				ret = ret * 10 + c - '0';
  			} while ((c = read()) >= '0' && c <= '9');
  
  			if (neg)
  				return -ret;
  			return ret;
  		}
  
  		public long nl() throws IOException {
  			long ret = 0;
  			byte c = read();
  			while (c <= ' ')
  				c = read();
  			boolean neg = (c == '-');
  			if (neg)
  				c = read();
  			do {
  				ret = ret * 10 + c - '0';
  			} while ((c = read()) >= '0' && c <= '9');
  			if (neg)
  				return -ret;
  			return ret;
  		}
  
  		public double nd() throws IOException {
  			double ret = 0, div = 1;
  			byte c = read();
  			while (c <= ' ')
  				c = read();
  			boolean neg = (c == '-');
  			if (neg)
  				c = read();
  
  			do {
  				ret = ret * 10 + c - '0';
  			} while ((c = read()) >= '0' && c <= '9');
  
  			if (c == '.') {
  				while ((c = read()) >= '0' && c <= '9') {
  					ret += (c - '0') / (div *= 10);
  				}
  			}
  
  			if (neg)
  				return -ret;
  			return ret;
  		}
  
  		private void fillBuffer() throws IOException {
  			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
  			if (bytesRead == -1)
  				buffer[0] = -1;
  		}
  
  		private byte read() throws IOException {
  			if (bufferPointer == bytesRead)
  				fillBuffer();
  			return buffer[bufferPointer++];
  		}
  
  		public void close() throws IOException {
  			if (din == null)
  				return;
  			din.close();
  		}
  	}
  
  	static String rl() throws Exception{
  		return in.readLine();
  	}
  
  	static int pi(String s) {
  		return Integer.parseInt(s);
  	}
  
  	static long pl(String s) {
  		return Long.parseLong(s);
  	}
  
  	static void print(int newline, String s) {
  		System.out.print(s);
  		if (newline != 0)
  			System.out.println();
  		// System.out.flush();
  	}
  
  	static void cprint(int x) {
  		print(0, "Case #" + x + ": ");
  	}
  }
  