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: // package Div3_734;
  
  import java.io.DataInputStream;
  import java.io.FileInputStream;
  import java.io.IOException;
  
  public class ProblemD {
      static class Reader
      {
          final private int BUFFER_SIZE = 1 << 16;
          private DataInputStream din;
          private byte[] buffer;
          private int bufferPointer, bytesRead;
  
          public Reader()
          {
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public Reader(String file_name) throws IOException
          {
              din = new DataInputStream(new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public String readLine() throws IOException
          {
              byte[] buf = new byte[64]; // line length
              int cnt = 0, c;
              while ((c = read()) != -1)
              {
                  if (c == '\n')
                      break;
                  buf[cnt++] = (byte) c;
              }
              return new String(buf, 0, cnt);
          }
  
          public int nextInt() throws IOException
          {
              int ret = 0;
              byte c = read();
              while (c <= ' ')
                  c = read();
              boolean neg = (c == '-');
              if (neg)
                  c = read();
              do
              {
                  ret = ret * 10 + c - '0';
              }  while ((c = read()) >= '0' && c <= '9');
  
              if (neg)
                  return -ret;
              return ret;
          }
  
          public long nextLong() throws IOException
          {
              long ret = 0;
              byte c = read();
              while (c <= ' ')
                  c = read();
              boolean neg = (c == '-');
              if (neg)
                  c = read();
              do {
                  ret = ret * 10 + c - '0';
              }
              while ((c = read()) >= '0' && c <= '9');
              if (neg)
                  return -ret;
              return ret;
          }
  
          public double nextDouble() throws IOException
          {
              double ret = 0, div = 1;
              byte c = read();
              while (c <= ' ')
                  c = read();
              boolean neg = (c == '-');
              if (neg)
                  c = read();
  
              do {
                  ret = ret * 10 + c - '0';
              }
              while ((c = read()) >= '0' && c <= '9');
  
              if (c == '.')
              {
                  while ((c = read()) >= '0' && c <= '9')
                  {
                      ret += (c - '0') / (div *= 10);
                  }
              }
  
              if (neg)
                  return -ret;
              return ret;
          }
  
          private void fillBuffer() throws IOException
          {
              bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
              if (bytesRead == -1)
                  buffer[0] = -1;
          }
  
          private byte read() throws IOException
          {
              if (bufferPointer == bytesRead)
                  fillBuffer();
              return buffer[bufferPointer++];
          }
  
          public void close() throws IOException
          {
              if (din == null)
                  return;
              din.close();
          }
      }
      public static void main(String[] args)throws IOException {
          Reader s=new Reader();
          int test=s.nextInt();
          StringBuilder print=new StringBuilder();
          while(test--!=0){
              int m=s.nextInt();
              int n=s.nextInt();
              int k=s.nextInt();
              if(m%2==0){
                  int max_in_row=n/2;
                  int max_row_poss=m;
                  if(k%2==0&&k<=max_in_row*max_row_poss){
                      print.append("YES\n");
                  }
                  else{
                      print.append("NO\n");
                  }
              }
              else{
                  if(k<n/2){
                      print.append("NO\n");
                      continue;
                  }
                  k-=n/2;
                  int max_in_row=n/2;
                  int max_row_poss=m-1;
                  if(k%2==0&&k<=max_in_row*max_row_poss){
                      print.append("YES\n");
                  }
                  else{
                      print.append("NO\n");
                  }
              }
          }
          System.out.print(print.toString());
      }
  }
  