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.sql.Array;
  import java.text.DateFormat;
  import java.text.ParseException;
  import java.text.SimpleDateFormat;
  import java.time.Instant;
  import java.util.*;
  import java.util.regex.Matcher;
  import java.util.regex.Pattern;
  
  
  public class Main {
      public static class Node implements Comparable<Node> {
          int my;
          int oth;
          Node(int my,int oth) {
              this.my = my;
              this.oth = oth;
          }
  
          @Override
          public int compareTo(Node o) {
              return ((o.oth - o.my) - (this.oth - this.my));
          }
      }
  
      public static class Point implements Comparable<Point>{
          int i;
          int j;
          Point(int i, int j) {
              this.i = i;
              this.j = j;
          }
  
          @Override
          public int compareTo(Point o) {
              return this.i - o.i;
          }
      }
  
      static long inverse(int n,int MD) {
          return n == 1 ? 1 : inverse(n - MD % n, MD) * (MD / n + 1) % MD;
      }
  
      static long choose(int n, int k, int MD) {
          return k == 0 ? 1 : choose(n - 1, k - 1, MD) * n % MD * inverse(k, MD) % MD;
      }
  
      /************************ SOLUTION STARTS HERE ************************/
      private static void solve() {
          int t = nextInt();
  
          while(t-- > 0) {
              long n = nextLong();
              long m = nextLong();
              long k = nextLong();
  
              long allowed = (m/2) * n;
              if(k > allowed) println("NO");
              else if(n%2 == 0 && m%2 == 0){
                  println(k%2 == 0 ? "YES" : "NO");
              } else if(n%2 == 0) {
                  println(k%2 == 0 ? "YES" : "NO");
              } else {
                  if(k == 0)
                      println("NO");
                  else if(k < m/2)
                      println("NO");
                  else if((k - m/2)%2 != 0)
                      println("NO");
                  else
                      println("YES");
              }
          }
      }
  
  
      /************************ SOLUTION ENDS HERE ************************/
  
  
  
      /************************ TEMPLATE STARTS HERE **********************/
  
      public static void main(String[] args) throws IOException, ParseException {
          reader = new BufferedReader(new InputStreamReader(System.in));
          writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), false);
          st = null;
          solve();
          reader.close();
          writer.close();
      }
  
      static BufferedReader  reader;
      static PrintWriter     writer;
      static StringTokenizer st;
  
      static String next() {
          while (st == null || !st.hasMoreTokens()) {
              try {
                  String line = reader.readLine();
                  if (line == null) {
                      return null;
                  }
                  st = new StringTokenizer(line);
              } catch (Exception e) {
                  throw new RuntimeException();
              }
          }
          return st.nextToken();
      }
  
      static String nextLine() {
          String s = null;
          try {
              s = reader.readLine();
          } catch (IOException e) {
              e.printStackTrace();
          }
          return s;
      }
  
      static int nextInt() {
          return Integer.parseInt(next());
      }
  
      static long nextLong() {
          return Long.parseLong(next());
      }
  
      static double nextDouble() {
          return Double.parseDouble(next());
      }
  
      static char nextChar() {
          return next().charAt(0);
      }
  
      static int[] nextIntArray(int n) {
          int[] a = new int[n];
          int i = 0;
          while (i < n) {
              a[i++] = nextInt();
          }
          return a;
      }
  
      static long[] nextLongArray(int n) {
          long[] a = new long[n];
          int i = 0;
          while (i < n) {
              a[i++] = nextLong();
          }
          return a;
      }
  
      static int[] nextIntArrayOneBased(int n) {
          int[] a = new int[n + 1];
          int i = 1;
          while (i <= n) {
              a[i++] = nextInt();
          }
          return a;
      }
  
      static long[] nextLongArrayOneBased(int n) {
          long[] a = new long[n + 1];
          int i = 1;
          while (i <= n) {
              a[i++] = nextLong();
          }
          return a;
      }
  
      static void print(Object o) {
          writer.print(o);
      }
  
      static void println(Object o) {
          writer.println(o);
      }
  
      static void printArr(int[] arr) {
          for(int i = 0 ; i < arr.length; i++)
              System.out.print(arr[i] + " ");
          System.out.println();
      }
  
      public static void exchange(int[] arr, int i, int j) {
          int temp = arr[i];
          arr[i] = arr[j];
          arr[j] = temp;
      }
  
      public static void shuffle(int arr[], int n) {
          for (int i = 0; i < n; i++) {
              int r = (int)Math.floor(Math.random() * (i+1));
              exchange(arr, i, r);
          }
      }
  
      /************************ TEMPLATE ENDS HERE ************************/
  }
  