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.util.*;
  import java.io.*;
  import java.lang.*;
  
  public class Main {
      //input
      static out op = new out();
      static inp ip = new inp();
      static FastReader sc = new FastReader();
      static BufferedWriter output = new BufferedWriter( 
          new OutputStreamWriter(System.out));
      static long inf = (long)1e9+7;
     
     static long mod = (long)1e18+7;
     static long z = 0;
  
     static void sol() throws Exception{
        int n = ip.in();
        int m = ip.in();
        int k = ip.in();
  
        m = m - m%2;
        
        if(k>n*m/2){
           op.no();
           return;
        }
        
        k = k - (m*(n%2))/2;
        
        if(k<0){
           op.no();
           return;
        }
        
        if(k%2 == 0)op.yes();
        else op.no();
        
     }
     
     static long gcd(long a,long b){
       if(b==0)
       return a;
       return gcd(b,a%b);
     }
     
     public static void main(String[] args) throws Exception { 
         
        int t = ip.in();
        while(t-- > 0){
           sol();
        }
        op.output.flush();
      }
     //  static class Node implements Comparable<Node>{
     //     int data;
     //     int ind;
     //    //  Node left,right;
     //    //  Node(){
     //    //       left = null;
     //    //       right = null;
     //    //  }
     //     Node(int ind,int data){
     //          this.data = data;
     //          this.ind = ind;
     //     }
      
     //       @Override
     //       public int compareTo(Node o) {
     //           if(this.data == o.data)
     //           return this.ind - o.ind;
     //           // TODO Auto-generated method stub
     //           return this.data - o.data;
     //       }
     //  }
  }
  
  
  class FastReader 
  { 
      BufferedReader br; 
      StringTokenizer st; 
  
      public FastReader() 
      { 
          br = new BufferedReader(new
                   InputStreamReader(System.in)); 
      } 
  
      String next() 
      { 
          while (st == null || !st.hasMoreElements()) 
          { 
              try
              { 
                  st = new StringTokenizer(br.readLine()); 
              } 
              catch (IOException  e) 
              { 
                  e.printStackTrace(); 
              } 
          } 
          return st.nextToken(); 
      } 
  
      int nextInt() 
      { 
          return Integer.parseInt(next()); 
      } 
  
      long nextLong() 
      { 
          return Long.parseLong(next()); 
      } 
  
      double nextDouble() 
      { 
          return Double.parseDouble(next()); 
      } 
  
      String nextLine() 
      { 
          String str = ""; 
          try
          { 
              str = br.readLine(); 
          } 
          catch (IOException e) 
          { 
              e.printStackTrace(); 
          } 
          return str; 
      }
  
  }
  class inp{
      FastReader sc = new FastReader();
      int in(){
          int a = sc.nextInt();
          return a;
      }
      long lin(){
          long a = sc.nextLong();
          return a;
      }
      char cin(){
          char c = sc.next().charAt(0);
          return c;
      }
      char[] cain(){
          char[] a = sc.nextLine().toCharArray();
          return a;
      }
      int[] arrin(int n){
          int [] arr = new int[n];
          for(int i=0;i<n;i++)
              arr[i] = in();
  
          return arr;
      }
      int[] mm_arr(int[] arr){
          int max = Integer.MIN_VALUE;
          int min = Integer.MAX_VALUE;
          for(int i=0;i<arr.length;i++){
              max = Math.max(max,arr[i]);
              min = Math.min(min,arr[i]);
          }
          int ans[] = {max,min};
          return ans;
      }
      int[] srt(int[] arr){
          Arrays.sort(arr);
          return arr;
      }
      long pow(long a,long b){
          if(b == 0)return 1;
          long res = pow(a,b/2);
          //System.out.println(res + " " + b + " " + (b&1));
          if((b&1) == 0)return res*res;
          return a*res*res; 
      }
  
     //  boolean[] prime(){
     //     boolean prime[] = new boolean[100000001];
     //     Arrays.fill(prime,true);
     //     for (int p = 2; p * p <= 10000000; p++)
     //     {
     //          // If prime[p] is not changed,
     //          // then it is a prime
     //          if (prime[p] == true)
     //          {
     //              // Update all multiples
     //              // of p greater than or
     //              // equal to the square of it
     //              // numbers which are multiple
     //              // of p and are less than p^2
     //              // are already been marked.
     //              for (int i = p * p; i <= 10000000; i += p)
     //                 prime[i] = false;
     //          }
     //     }
     //     return prime;
     //  }
  }
  class out{
      BufferedWriter output = new BufferedWriter( 
          new OutputStreamWriter(System.out)); 
  
      void sb(String s) throws IOException {
          output.write(s);
      }
      void sbln(Object s) throws IOException {
          output.write(s+"\n");
      }
      void yes() throws IOException{
          output.write("YES\n");
      }
      void no() throws IOException{
          output.write("NO\n");
      }
  }