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 javax.swing.*;
  import java.io.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.lang.reflect.Array;
  import java.math.BigInteger;
  import java.security.cert.CollectionCertStoreParameters;
  import java.util.*;
  
  
  
  import static javax.swing.UIManager.get;
  import static javax.swing.UIManager.getString;
  
  
  public class Main {
  
  
      static class Pair implements Comparable<Pair>{
          int x=0;
          int y=0;
          public Pair(int x1,int y1)
          { x=x1;
              y=y1;
          }
  
  
          @Override
          public int compareTo(Pair o) {
              return this.x-o.x;
          }
      }
  
      static boolean checkPallindrome(int n)
      {    ArrayList<Integer> list = new ArrayList<>();
          while(n>0)
          { list.add(n%10);
              n/=10;
          }
          int low=0,high=list.size()-1;
          while(low<=high)
          {     if(list.get(low)!=list.get(high))
              return false;
              low++;
              high--;
          }
          return true;
      }
  
  
      static boolean check(String s)
      {
  
          int low=0,high=s.length()-1;
          while(low<=high)
          {     if(s.charAt(low)!=s.charAt(high))
              return false;
              low++;
              high--;
          }
          return true;
      }
  
      static  int min=Integer.MAX_VALUE;
      public static void main(String[] args) throws IOException {
          FastReader sc = new FastReader();
  //(1)very very important**(never take the first problem for granted, always check the test cases) take 5 minutes more and check the edge cases
          // 5 minutes will not decreases rating as much as a wrong submission does it is easy u just think with an open mind and u will surely get the answer
          //(2)let ur brain consume the problem don't just jump to the solution. after reading the problem take a pause 1 minute
          //(3)go through the example test cases and also at least two of ur own test cases.Think of testcases which are difficult(edge cases).dry run ur concept
  
          int t = sc.nextInt();
          while (t-- > 0) {
            int n = sc.nextInt(),m=sc.nextInt(),k=sc.nextInt();
  
             if(n%2==1) {
                 if (k < m / 2) {
                     System.out.println("NO");
           continue;
                 } else {
                     n--;
                     k -= m / 2;
  
                 }
  
             }
             if(n%2==0)
             {       if(m%2==1&&n/2*(m-1)<k)
                 System.out.println("NO");
                 else if(k%2==1)
                     System.out.println("NO");
                 else System.out.println("YES");
  
             }
          }
      }
  
  
  
  
  
  
  
  
  //Things to check when u r getting wrong answer
  // syntax of conditional operator y=(x==1)?1:0;
  // 1-  check the flow of the code
  //2- If ur stuck read the problem once again
  //3- before submitting always check the output format of ur code
  //4- don't check standings until problem B is done
  //5- if u r thinking ur concept is correct but still u r getting wrong answer try to implement it in another way
  //6- By default, java interpret all numeral literals as 32-bit integer values.
  // If you want to explicitely specify that this is something bigger then 32-bit integer you should use suffix L for long values.    example   long a = 600851475143L
  
  //All the functions
  
  
  
      static void debug(String s)
      { System.out.println(s);
  
      }
  
      //collections.sort use merge sort instead of quick sort but arrays.sort use quicksort whose worst time complexity is O(n^2)
      static int[] sort(int[] a)
      {         ArrayList<Integer> list = new ArrayList<>();
          for(int i=0;i<a.length;i++)
              list.add(a[i]);
  
          Collections.sort(list);
          int ind=0;
          for(int x:list)
              a[ind++]=x;
          return a;
  
      }
  
      //function to print an array for debugging
      static void print(int[] a) {
          for (int i = 0; i < a.length; i++)
              System.out.print(a[i] + " ");
          System.out.println();
      }
  
      static void printc(char[] a) {
          for (int i = 0; i < a.length; i++)
              System.out.print(a[i] + " ");
          System.out.println();
      }
  
  
      //normal gcd function, always put the greater number as a and the smaller number as b
      static int gcd(int a, int b) {
          if (b == 0)
              return a;
          return gcd(b, a % b);
  
      }
  
      static int lcm(int a,int b)
      {
          return (a*b)/gcd(a,b);
      }
  
  
      //to find gcd and lcm for numbers of long data type
      static long gcdl(long a, long b) {
          if (b == 0)
              return a;
          return gcdl(b, a % b);
  
      }
  
      static long lcml(long a,long b)
      {
          return (a*b)/gcdl(a,b);
      }
  
  
      //Input Reader to read faster input
      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 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;
          }
  
  
          int[] readArray(int n)
          {  int[] a = new int[n];
              for(int i=0;i<n;i++)
                  a[i]=nextInt();
  
              return a;
          }
      }
  
  
  
  }
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  