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.*;
  
  public class Main {
    static StringBuilder sb;
    static dsu dsu;
    static long fact[];
    static int mod = (int) (1e9 + 7);
  
    static void solve() {
  int n=i();
  int m=i();
  int k=i();
  
  
  
  
  
  
  
  if(n%2==0&&m%2==0){
      if(k%2==0) {
          sb.append("YES\n");
          return;
      }
      else{
          sb.append("NO\n");}
  }
  
  else if(n%2==1){
      if(k>=m/2&&(k-(m/2))%2==0) {
          sb.append("YES\n");
          return;
      }
      else{
          sb.append("NO\n");}
  }
  
  else{
      if(k%2==0&&k<=((n)*(m-1))/2) {
          sb.append("YES\n");
          return;
      }
      else{
          sb.append("NO\n");}
  }
    }
  
    public static void main(String[] args) {
      sb = new StringBuilder();
      int test = i();
      while (test-- > 0) {
        solve();
      }
      System.out.println(sb);
  
    }
  
    /*
     * fact=new long[(int)1e6+10]; fact[0]=fact[1]=1; for(int i=2;i<fact.length;i++)
     * { fact[i]=((long)(i%mod)1L(long)(fact[i-1]%mod))%mod; }
     */
  //**************NCR%P******************
    static long ncr(int n, int r) {
      if (r > n)
        return (long) 0;
  
      long res = fact[n] % mod;
      // System.out.println(res);
      res = ((long) (res % mod) * (long) (p(fact[r], mod - 2) % mod)) % mod;
      res = ((long) (res % mod) * (long) (p(fact[n - r], mod - 2) % mod)) % mod;
      // System.out.println(res);
      return res;
  
    }
  
    static long p(long x, long y)// POWER FXN //
    {
      if (y == 0)
        return 1;
  
      long res = 1;
      while (y > 0) {
        if (y % 2 == 1) {
          res = (res * x) % mod;
          y--;
        }
  
        x = (x * x) % mod;
        y = y / 2;
  
      }
      return res;
    }
  
  //**************END******************
  
    // *************Disjoint set
    // union*********//
    static class dsu {
      int parent[];
  
      dsu(int n) {
        parent = new int[n];
        for (int i = 0; i < n; i++)
          parent[i] = -1;
      }
  
      int find(int a) {
        if (parent[a] < 0)
          return a;
        else {
          int x = find(parent[a]);
          parent[a] = x;
          return x;
        }
      }
  
      void merge(int a, int b) {
        a = find(a);
        b = find(b);
        if (a == b)
          return;
        parent[b] = a;
      }
    }
  
  //**************PRIME FACTORIZE **********************************//
    static TreeMap<Integer, Integer> prime(long n) {
      TreeMap<Integer, Integer> h = new TreeMap<>();
      long num = n;
      for (int i = 2; i <= Math.sqrt(num); i++) {
        if (n % i == 0) {
          int nt = 0;
          while (n % i == 0) {
            n = n / i;
            nt++;
          }
          h.put(i, nt);
        }
      }
      if (n != 1)
        h.put((int) n, 1);
      return h;
  
    }
  
  //****CLASS PAIR ************************************************
    static class Pair implements Comparable<Pair> {
      int x;
      long y;
  
      Pair(int x, long y) {
        this.x = x;
        this.y = y;
      }
  
      public int compareTo(Pair o) {
        return (int) (this.y - o.y);
  
      }
  
    }
  //****CLASS PAIR **************************************************
  
    static class InputReader {
      private InputStream stream;
      private byte[] buf = new byte[1024];
      private int curChar;
      private int numChars;
      private SpaceCharFilter filter;
  
      public InputReader(InputStream stream) {
        this.stream = stream;
      }
  
      public int read() {
        if (numChars == -1)
          throw new InputMismatchException();
        if (curChar >= numChars) {
          curChar = 0;
          try {
            numChars = stream.read(buf);
          } catch (IOException e) {
            throw new InputMismatchException();
          }
          if (numChars <= 0)
            return -1;
        }
        return buf[curChar++];
      }
  
      public int Int() {
        int c = read();
        while (isSpaceChar(c))
          c = read();
        int sgn = 1;
        if (c == '-') {
          sgn = -1;
          c = read();
        }
        int res = 0;
        do {
          if (c < '0' || c > '9')
            throw new InputMismatchException();
          res *= 10;
          res += c - '0';
          c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
      }
  
      public String String() {
        int c = read();
        while (isSpaceChar(c))
          c = read();
        StringBuilder res = new StringBuilder();
        do {
          res.appendCodePoint(c);
          c = read();
        } while (!isSpaceChar(c));
        return res.toString();
      }
  
      public boolean isSpaceChar(int c) {
        if (filter != null)
          return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
      }
  
      public String next() {
        return String();
      }
  
      public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
      }
    }
  
    static class OutputWriter {
      private final PrintWriter writer;
  
      public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
      }
  
      public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
      }
  
      public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
          if (i != 0)
            writer.print(' ');
          writer.print(objects[i]);
        }
      }
  
      public void printLine(Object... objects) {
        print(objects);
        writer.println();
      }
  
      public void close() {
        writer.close();
      }
  
      public void flush() {
        writer.flush();
      }
    }
  
    static InputReader in = new InputReader(System.in);
    static OutputWriter out = new OutputWriter(System.out);
  
    public static long[] sort(long[] a2) {
      int n = a2.length;
      ArrayList<Long> l = new ArrayList<>();
      for (long i : a2)
        l.add(i);
      Collections.sort(l);
      for (int i = 0; i < l.size(); i++)
        a2[i] = l.get(i);
      return a2;
    }
  
    public static char[] sort(char[] a2) {
      int n = a2.length;
      ArrayList<Character> l = new ArrayList<>();
      for (char i : a2)
        l.add(i);
      Collections.sort(l);
      for (int i = 0; i < l.size(); i++)
        a2[i] = l.get(i);
      return a2;
    }
  
    public static long pow(long x, long y) {
      long res = 1;
      while (y > 0) {
        if (y % 2 != 0) {
          res = (res * x);// % modulus;
          y--;
  
        }
        x = (x * x);// % modulus;
        y = y / 2;
      }
      return res;
    }
  
  //GCD___+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    public static long gcd(long x, long y) {
      if (x == 0)
        return y;
      else
        return gcd(y % x, x);
    }
    // ******LOWEST COMMON MULTIPLE
    // *********************************************
  
    public static long lcm(long x, long y) {
      return (x * (y / gcd(x, y)));
    }
  
  //INPUT PATTERN********************************************************
    public static int i() {
      return in.Int();
    }
  
    public static long l() {
      String s = in.String();
      return Long.parseLong(s);
    }
  
    public static String s() {
      return in.String();
    }
  
    public static int[] readArrayi(int n) {
      int A[] = new int[n];
      for (int i = 0; i < n; i++) {
        A[i] = i();
      }
      return A;
    }
  
    public static long[] readArray(long n) {
      long A[] = new long[(int) n];
      for (int i = 0; i < n; i++) {
        A[i] = l();
      }
      return A;
    }
  
  }