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: /*
   
      /$$$$$  /$$$$$$  /$$    /$$  /$$$$$$                                                                  
     |__  $$ /$$__  $$ |$$    |$$ /$$__  $$                                                                 
            | $$| $$  \ $$|    $$|$$| $$  \ $$                                                                 
            | $$| $$$$$$$$|  $$ / $$/| $$$$$$$$                                                                 
  / $$  | $$| $$__  $$ \  $$ $$/ | $$__  $$                                                                 
  | $$  | $$| $$  | $$  \  $$$/  | $$  | $$                                                                 
  |  $$$$$$/| $$  | $$   \  $/   | $$  | $$                                                                 
   \______/ |__/  |__/    \_/    |__/  |__/    
   
  /$$$$$$$  /$$$$$$$   /$$$$$$   /$$$$$$  /$$$$$$$   /$$$$$$  /$$      /$$ /$$      /$$ /$$$$$$$$ /$$$$$$$ 
  | $$__  $$| $$__  $$ /$$__  $$ /$$__  $$| $$__  $$ /$$__  $$| $$$    /$$$| $$$    /$$$| $$_____/| $$__  $$
  | $$  \ $$| $$  \ $$| $$  \ $$| $$  \__/| $$  \ $$| $$  \ $$| $$$$  /$$$$| $$$$  /$$$$| $$      | $$  \ $$
  | $$$$$$$/| $$$$$$$/| $$  | $$| $$ /$$$$| $$$$$$$/| $$$$$$$$| $$ $$/$$ $$| $$ $$/$$ $$| $$$$$   | $$$$$$$/
  | $$____/ | $$__  $$| $$  | $$| $$|_  $$| $$__  $$| $$__  $$| $$  $$$| $$| $$  $$$| $$| $$__/   | $$__  $$
  | $$      | $$  \ $$| $$  | $$| $$  \ $$| $$  \ $$| $$  | $$| $$\  $ | $$| $$\  $ | $$| $$      | $$  \ $$
  | $$      | $$  | $$|  $$$$$$/|  $$$$$$/| $$  | $$| $$  | $$| $$ \/  | $$| $$ \/  | $$| $$$$$$$$| $$  | $$
  |__/      |__/  |__/ \______/  \______/ |__/  |__/|__/  |__/|__/     |__/|__/     |__/|________/|__/  |__/
                                                                                                             
                                                                                                                                                                                                                   
                                                                                                                                                                                                                  
   
  */
  ////solution at bottom 
  import java.util.*;
  import java.lang.*;
  import java.io.*;
  import java.math.*;
  
   
  /* Name of the class has to be "Main" only if the class is public. */
           public class test
  {
  
      
      
  public static void main (String[] args) throws java.lang.Exception
      {
          // your code goes here
           
          int t=1;
          br=new FastReader();
                                    t=br.ni();
  
          
    
       in1 :   for(int TC = 1; TC <= t ; TC++)
          {
              
                  solve();
   
   
       
          }
            
              //          System.out.println("OUTPUT:::");
      
            System.out.print(sb);
      }
      ///end main
      static StringBuilder sb = new StringBuilder();
      
      static void solve() throws Exception{
                            int m  = br.ni() , n = br.ni() , k = br.ni();
                            int tot = m * n;
                            tot /= 2;
  
                            if(m%2 == 0 && n%2 == 0){
                               if(k%2 == 0){
                                  sb.append("YES\n");
                                  return;
                               }
                               else {
                                  sb.append("NO\n");
                                  return;
                               }
  
                            }
                            if(m%2 == 0){
                              tot -= (m/2);
                              if(k<=tot && k%2 == 0){
                                  sb.append("YES\n");
                                  return;
                              }
                              else {
                                  sb.append("NO\n");
                                  return;
                              }
                            }
                            int y = tot;
                            while(y >= n/2){
                              if(y == k){
                                  sb.append("YES\n");
                                  return;
                              }
                              y -= 2;
                            }
                            sb.append("NO\n");
  
             }
                  
      //end solve
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
      static void shuffle( int arr[])
      {
          int n = arr.length;
          Random r = new Random();
           
         for (int i = n-1; i > 0; i--) {
             int j = r.nextInt(i+1);
               
              int temp = arr[i];
              arr[i] = arr[j];
              arr[j] = temp;
          }
      }
      static void shuffle( long arr[])
      {
          int n = arr.length;
          Random r = new Random();
           
         for (int i = n-1; i > 0; i--) {
             int j = r.nextInt(i+1);
               
              long temp = arr[i];
              arr[i] = arr[j];
              arr[j] = temp;
          }
      }
      static void shuffle( int arr[][])
      {
          int n = arr.length;
          Random r = new Random();
           
         for (int i = n-1; i > 0; i--) {
             int j = r.nextInt(i+1);
               
              int[] temp = arr[i];
              arr[i] = arr[j];
              arr[j] = temp;
          }
      }
      
      static 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[][] tdiarr(int m , int n){
              int[][] a = new int[m][n];
              for(int i=0;i<m;i++){
                  for(int j=0;j<n;j++){
                      a[i][j]=Integer.parseInt(next());
                  }
              }
              return a;
          }
          long[][] tdlarr(int m , int n){
              long[][] a = new long[m][n];
              for(int i=0;i<m;i++){
                  for(int j=0;j<n;j++){
                      a[i][j]=Long.parseLong(next());
                  }
              }
              return a;
          }
   
          int[] niarr(int n)
          {
              int[] a = new int[n];
              for(int i=0;i<n;i++)a[i]=Integer.parseInt(next());
              return a;
          }
          long[] nlarr(int n)
          {
              long[] a = new long[n];
              for(int i=0;i<n;i++)a[i]=Long.parseLong(next());
              return a;
          }
          char[] ncarr(){
              return next().trim().toCharArray();
              
              
          }
          
    
          int ni() 
          { 
              return Integer.parseInt(next()); 
          } 
    
          long nl() 
          { 
              return Long.parseLong(next()); 
          } 
    
          double nd() 
          { 
              return Double.parseDouble(next()); 
          } 
    
          String nstr() 
          { 
              String str = ""; 
              try
              { 
                  str = br.readLine(); 
              } 
              catch (IOException e) 
              { 
                  e.printStackTrace(); 
              } 
              return str; 
          } 
      }
      
       
      static boolean checkbound(int x , int y , int m , int n){
          if(x<0 || x>=m || y<0 || y>=n)return false;
          return true;
      }
      static void printarr(int[][] a){
          int m = a.length , n = a[0].length;
          for(int i=0;i<m;i++){
              for(int j=0;j<n;j++){
                  System.out.print(a[i][j]+" ");
              }
              System.out.println();
          }
      }
      static void printarr(char[][] a){
          int m = a.length , n = a[0].length;
          for(int i=0;i<m;i++){
              for(int j=0;j<n;j++){
                  System.out.print(a[i][j]+" ");
              }
              System.out.println();
          }
      }
      static void printarr(int[] a){
          int n = a.length;
          StringBuilder sb = new StringBuilder();
              for(int j=0;j<n;j++){
                  sb.append(a[j]+" "); 
              }
              System.out.println(sb);
   
          
      }
      static void printarr(long[] a){
          int n = a.length;
          StringBuilder sb = new StringBuilder();
              for(int j=0;j<n;j++){
                  sb.append(a[j]+" "); 
              }
              System.out.println(sb);
   
          
      }
   
      static void revarr(int[] a ){
          int i=0,j=a.length-1;
          while(i<j){
              int tem = a[i];
              a[i]=a[j];
              a[j]=tem;
              i++;j--;
          }
           
      }
     
      
   
       static boolean[] sieveOfEratosthenes(int n)
      {
           
          boolean prime[] = new boolean[n + 1];
          for (int i = 0; i <= n; i++)
              prime[i] = true;
   
          for (int p = 2; p * p <= n; p++)
          {
               if (prime[p] == true)
              {
                   for (int i = p * p; i <= n; i += p)
                      prime[i] = false;
              }
          }
          prime[1]=false;
   
          return prime;
      }
   
      static int gcd(int a, int b)
      {
          if (a == 0)
              return b;
           
          return gcd(b%a, a);
      }
   
      static int lcm(int a, int b)
      {
          return (a / gcd(a, b)) * b;
      }
   
      static long gcd(long a, long b)
      {
          if (a == 0L)
              return b;
           
          return gcd(b%a, a);
      }
   
      static long lcm(long a, long b)
      {
          return (a / gcd(a, b)) * b;
      }
   
      public static class Pair{
          int x;
          int y;
   
          public Pair(int x, int y){
              this.x = x;
              this.y = y;
          }
   
           
      }
      
      
      static FastReader br=new FastReader();
  /*
   
  */
  ///////////////////////////////////////////////////////////
   
   
   
   
   
  
              
   
      }
      //end class  
   
      /* stuff you should look for
      * int overflow, array bounds
      * special cases (n=1?)
      * do smth instead of nothing and stay organized
      * WRITE STUFF DOWN
      * DON'T GET STUCK ON ONE APPROACH
    
   TC:
     
   
   
        */          
             
  