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: //Utilities
  import java.io.*;
  import java.util.*;
  
  public class A {
  	static int t;
  	static int n, m, k;
  	
  	public static void main(String[] args) throws IOException {
  		t = in.iscan();
  		while (t-- > 0) {
  			n = in.iscan(); m = in.iscan(); k = in.iscan();
  			if (n % 2 == 1 && m % 2 == 0) { // -> n is odd, m is even
  				int needPerRow = m / 2;
  				if (k < needPerRow) {
  					out.println("NO");
  				}
  				else {
  					k -= needPerRow;
  					n--;
  					if (k % 2 == 0) {
  						out.println("YES");
  					}
  					else {
  						out.println("NO");
  					}
  				}
  			}
  			else if (n % 2 == 0 && m % 2 == 1) { // n is even, m is odd
  				if (k % 2 == 1) {
  					out.println("NO");
  				}
  				else {
  					int max = m / 2 * n;
  					if (k > max) {
  						out.println("NO");
  					}
  					else {
  						out.println("YES");
  					}
  				}
  			}
  			else { // n is even and m is even
  				if (k % 2 == 1) {
  					out.println("NO");
  				}
  				else {
  					out.println("YES");
  				}
  			}
  		}
  		out.close();
  	} 
  	
  	static INPUT in = new INPUT(System.in);
  	static PrintWriter out = new PrintWriter(System.out);
  	private static class INPUT {
  
  		private InputStream stream;
  		private byte[] buf = new byte[1024];
  		private int curChar, numChars;
  
  		public INPUT (InputStream stream) {
  			this.stream = stream;
  		}
  
  		public INPUT (String file) throws IOException {
  			this.stream = new FileInputStream (file);
  		}
  
  		public int cscan () throws IOException {
  			if (curChar >= numChars) {
  				curChar = 0;
  				numChars = stream.read (buf);
  			}
  			
  			if (numChars == -1)
  				return numChars;
  
  			return buf[curChar++];
  		}
  
  		public int iscan () throws IOException {
  			int c = cscan (), sgn = 1;
  			
  			while (space (c))
  				c = cscan ();
  
  			if (c == '-') {
  				sgn = -1;
  				c = cscan ();
  			}
  
  			int res = 0;
  
  			do {
  				res = (res << 1) + (res << 3);
  				res += c - '0';
  				c = cscan ();
  			}
  			while (!space (c));
  
  			return res * sgn;
  		}
  
  		public String sscan () throws IOException {
  			int c = cscan ();
  			
  			while (space (c))
  				c = cscan ();
  
  			StringBuilder res = new StringBuilder ();
  
  			do {
  				res.appendCodePoint (c);
  				c = cscan ();
  			}
  			while (!space (c));
  
  			return res.toString ();
  		}
  
  		public double dscan () throws IOException {
  			int c = cscan (), sgn = 1;
  			
  			while (space (c))
  				c = cscan ();
  
  			if (c == '-') {
  				sgn = -1;
  				c = cscan ();
  			}
  
  			double res = 0;
  
  			while (!space (c) && c != '.') {
  				if (c == 'e' || c == 'E')
  					return res * UTILITIES.fast_pow (10, iscan ());
  				
  				res *= 10;
  				res += c - '0';
  				c = cscan ();
  			}
  
  			if (c == '.') {
  				c = cscan ();
  				double m = 1;
  
  				while (!space (c)) {
  					if (c == 'e' || c == 'E')
  						return res * UTILITIES.fast_pow (10, iscan ());
  
  					m /= 10;
  					res += (c - '0') * m;
  					c = cscan ();
  				}
  			}
  
  			return res * sgn;
  		}
  
  		public long lscan () throws IOException {
  			int c = cscan (), sgn = 1;
  			
  			while (space (c))
  				c = cscan ();
  
  			if (c == '-') {
  				sgn = -1;
  				c = cscan ();
  			}
  
  			long res = 0;
  
  			do {
  				res = (res << 1) + (res << 3);
  				res += c - '0';
  				c = cscan ();
  			}
  			while (!space (c));
  
  			return res * sgn;
  		}
  
  		public boolean space (int c) {
  			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
  		}
  	}
  
  	public static class UTILITIES {
  
  		static final double EPS = 10e-6;
  
  		public static int lower_bound (int[] arr, int x) {
  			int low = 0, high = arr.length, mid = -1;
  
  			while (low < high) {
  				mid = (low + high) / 2;
  
  				if (arr[mid] >= x)
  					high = mid;
  				else
  					low = mid + 1;
  			}
  
  			return low;
  		}
  
  		public static int upper_bound (int[] arr, int x) {
  			int low = 0, high = arr.length, mid = -1;
  
  			while (low < high) {
  				mid = (low + high) / 2;
  
  				if (arr[mid] > x)
  					high = mid;
  				else
  					low = mid + 1;
  			}
  
  			return low;
  		}
  
  		public static int gcd (int a, int b) {
  			return b == 0 ? a : gcd (b, a % b);
  		}
  
  		public static int lcm (int a, int b) {
  			return a * b / gcd (a, b);
  		}
  
  		public static long fast_pow_mod (long b, long x, int mod) {
  			if (x == 0) return 1;
  			if (x == 1) return b;
  			if (x % 2 == 0) return fast_pow_mod (b * b % mod, x / 2, mod) % mod;
  
  			return b * fast_pow_mod (b * b % mod, x / 2, mod) % mod;
  		}
  
  		public static int fast_pow (int b, int x) {
  			if (x == 0) return 1;
  			if (x == 1) return b;
  			if (x % 2 == 0) return fast_pow (b * b, x / 2);
  
  			return b * fast_pow (b * b, x / 2);
  		}
  
  		public static long choose (long n, long k) {
  			k = Math.min (k, n - k);
  			long val = 1;
  
  			for (int i = 0; i < k; ++i)
  				val = val * (n - i) / (i + 1);
  
  			return val;
  		}
  
  		public static long permute (int n, int k) {
  			if (n < k) return 0;
  			long val = 1;
  
  			for (int i = 0; i < k; ++i)
  				val = (val * (n - i));
  
  			return val;
  		}
  		
  		// start of permutation and lower/upper bound template
  		public static void nextPermutation(int[] nums) {
  		    //find first decreasing digit
  		    int mark = -1;
  		    for (int i = nums.length - 1; i > 0; i--) {
  		        if (nums[i] > nums[i - 1]) {
  		            mark = i - 1;
  		            break;
  		        }
  		    }
  		 
  		    if (mark == -1) {
  		        reverse(nums, 0, nums.length - 1);
  		        return;
  		    }
  		 
  		    int idx = nums.length-1;
  		    for (int i = nums.length-1; i >= mark+1; i--) {
  		        if (nums[i] > nums[mark]) {
  		            idx = i;
  		            break;
  		        }
  		    }
  		 
  		    swap(nums, mark, idx);
  		 
  		    reverse(nums, mark + 1, nums.length - 1);
  		}
  		 
  		public static void swap(int[] nums, int i, int j) {
  		    int t = nums[i];
  		    nums[i] = nums[j];
  		    nums[j] = t;
  		}
  		 
  		public static void reverse(int[] nums, int i, int j) {
  		    while (i < j) {
  		        swap(nums, i, j);
  		        i++;
  		        j--;
  		    }
  		}
  		
  		static int lower_bound (int[] arr, int hi, int cmp) {
  			int low = 0, high = hi, mid = -1;
  			while (low < high) {
  				mid = (low + high) / 2;
  				if (arr[mid] >= cmp) high = mid;
  				else low = mid + 1;
  			}
  			return low;
  		}
  	 
  		static int upper_bound (int[] arr, int hi, int cmp) {
  			int low = 0, high = hi, mid = -1;
  			while (low < high) {
  				mid = (low + high) / 2;
  				if (arr[mid] > cmp) high = mid;
  				else low = mid + 1;
  			}
  			return low;
  		}
  		// end of permutation and lower/upper bound template
  	}
  }
  