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 long startTime = System.currentTimeMillis();
  
      // for global initializations and methods starts here
  
      // global initialisations and methods end here
  
      static void run() {
          boolean tc = true;
          AdityaFastIO r = new AdityaFastIO();
          //FastReader r = new FastReader();
  
          try (OutputStream out = new BufferedOutputStream(System.out)) {
  
              //long startTime = System.currentTimeMillis();
  
              int testcases = tc ? r.ni() : 1;
              int tcCounter = 1;
              // Hold Here Sparky------------------->>>
              // Solution Starts Here
  
              start:
              while (testcases-- > 0) {
  
                  int n = r.ni();
                  int m = r.ni();
                  int k = r.ni();
  
                  int c1 = 0;
                  int c2 = 0;
                  int sum = (n * m) >> 1;
  
                  if ((n & 1) == 1) c1 = m >> 1;
                  if ((m & 1) == 1) c2 = n >> 1;
  
                  if (((c1 - k) & 1) == 1 || c1 > k || k > sum - c2) out.write(("NO" + " ").getBytes());
                  else out.write(("YES" + " ").getBytes());
  
                  out.write(("\n").getBytes());
              }
              // Solution Ends Here
          } catch (IOException e) {
              e.printStackTrace();
          }
      }
  
      static class AdityaFastIO {
          final private int BUFFER_SIZE = 1 << 16;
          private final DataInputStream din;
          private final byte[] buffer;
          private int bufferPointer, bytesRead;
          public BufferedReader br;
          public StringTokenizer st;
  
          public AdityaFastIO() {
              br = new BufferedReader(new InputStreamReader(System.in));
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public AdityaFastIO(String file_name) throws IOException {
              din = new DataInputStream(new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public String word() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          public String line() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
  
          public String readLine() throws IOException {
              byte[] buf = new byte[100000001]; // 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 ni() 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 nl() 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 nd() 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 Exception {
          run();
      }
  
      static long mod = 998244353;
  
      static long modInv(long base, long e) {
          long result = 1;
          base %= mod;
          while (e > 0) {
              if ((e & 1) > 0) result = result * base % mod;
              base = base * base % mod;
              e >>= 1;
          }
          return result;
      }
  
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
  
          public FastReader() {
              br = new BufferedReader(new InputStreamReader(System.in));
          }
  
          String word() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          String line() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
  
          int ni() {
              return Integer.parseInt(word());
          }
  
          long nl() {
              return Long.parseLong(word());
          }
  
          double nd() {
              return Double.parseDouble(word());
          }
      }
  
      static int MOD = (int) (1e9 + 7);
  
      static long powerLL(long x, long n) {
          long result = 1;
          while (n > 0) {
              if (n % 2 == 1) result = result * x % MOD;
              n = n / 2;
              x = x * x % MOD;
          }
          return result;
      }
  
      static long powerStrings(int i1, int i2) {
          String sa = String.valueOf(i1);
          String sb = String.valueOf(i2);
          long a = 0, b = 0;
          for (int i = 0; i < sa.length(); i++) a = (a * 10 + (sa.charAt(i) - '0')) % MOD;
          for (int i = 0; i < sb.length(); i++) b = (b * 10 + (sb.charAt(i) - '0')) % (MOD - 1);
          return powerLL(a, b);
      }
  
      static long gcd(long a, long b) {
          if (a == 0) return b;
          else return gcd(b % a, a);
      }
  
      static long lcm(long a, long b) {
          return (a * b) / gcd(a, b);
      }
  
      static long lower_bound(List<Long> list, long k) {
          int s = 0;
          int e = list.size();
          while (s != e) {
              int mid = (s + e) >> 1;
              if (list.get(mid) < k) s = mid + 1;
              else e = mid;
          }
          if (s == list.size()) return -1;
          return s;
      }
  
      static int upper_bound(List<Long> list, long k) {
          int s = 0;
          int e = list.size();
          while (s != e) {
              int mid = (s + e) >> 1;
              if (list.get(mid) <= k) s = mid + 1;
              else e = mid;
          }
          if (s == list.size()) return -1;
          return s;
      }
  
      static void addEdge(ArrayList<ArrayList<Integer>> graph, int edge1, int edge2) {
          graph.get(edge1).add(edge2);
          graph.get(edge2).add(edge1);
      }
  
      public static class Pair implements Comparable<Pair> {
          int first;
          int second;
  
          public Pair(int first, int second) {
              this.first = first;
              this.second = second;
          }
  
          public String toString() {
              return "(" + first + "," + second + ")";
          }
  
          public int compareTo(Pair o) {
              // TODO Auto-generated method stub
              if (this.first != o.first)
                  return (int) (this.first - o.first);
              else return (int) (this.second - o.second);
          }
      }
  
      public static class PairC<X, Y> implements Comparable<PairC> {
          X first;
          Y second;
  
          public PairC(X first, Y second) {
              this.first = first;
              this.second = second;
          }
  
          public String toString() {
              return "(" + first + "," + second + ")";
          }
  
          public int compareTo(PairC o) {
              // TODO Auto-generated method stub
              return o.compareTo((PairC) first);
          }
      }
  
      static boolean isCollectionsSorted(List<Long> list) {
          if (list.size() == 0 || list.size() == 1) return true;
          for (int i = 1; i < list.size(); i++) if (list.get(i) <= list.get(i - 1)) return false;
          return true;
      }
  
      static boolean isCollectionsSortedReverseOrder(List<Long> list) {
          if (list.size() == 0 || list.size() == 1) return true;
          for (int i = 1; i < list.size(); i++) if (list.get(i) >= list.get(i - 1)) return false;
          return true;
      }
  
  }