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.text.html.parser.Entity;
  import java.io.*;
  import java.util.*;
  import java.math.BigInteger;
  
  /**
   _                  _
   ( _)                ( _)
   / / \\              / /\_\_
   / /   \\            / / | \ \
   / /     \\          / /  |\ \ \
   /  /   ,  \ ,       / /   /|  \ \
   /  /    |\_ /|      / /   / \   \_\
   /  /  |\/ _ '_| \   / /   /   \    \\
   |  /   |/  0 \0\    / |    |    \    \\
   |    |\|      \_\_ /  /    |     \    \\
   |  | |/    \.\ o\o)  /      \     |    \\
   \    |     /\\`v-v  /        |    |     \\
   | \/    /_| \\_|  /         |    | \    \\
   | |    /__/_ - /   ___  |    |  \    \\
   \|    [__]  \_/  |_________  \   |   \    ()
   /    [___] (    \         \  |\ |   |   //
   |    [___]                  |\| \|   /  |/
   /|    [____]                  \  |/\ / / ||
   (  \   [____ /     ) _\      \  \    \| | ||
   \  \  [_____|    / /     __/    \   / / //
   |   \ [_____/   / /        \    |   \/ //
   |   /  '----|   /=\____   _/    |   / //
   __ /  /        |  /   ___/  _/\    \  | ||
   (/-(/-\)       /   \  (/\/\)/  |    /  | /
   (/\/\)           /   /   //
   _________/   /    /
   \____________/    (
  
  
   @author NTUDragons-Reborn
   */
  
  public class Main{
      public static void main(String[] args) {
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader in = new InputReader(inputStream);
          PrintWriter out = new PrintWriter(outputStream);
          Task solver = new Task();
          solver.solve(in, out);
          out.close();
      }
      // main solver
      static class Task{
  
          double eps= 0.00000001;
          static final int MAXN = 1010;
          static final int MOD= 1000000007;
  
          // stores smallest prime factor for every number
          static int spf[] = new int[MAXN];
  
          static boolean[] prime;
  
          // Calculating SPF (Smallest Prime Factor) for every
          // number till MAXN.
          // Time Complexity : O(nloglogn)
          public void sieve()
          {
              spf[1] = 1;
              for (int i=2; i<MAXN; i++)
  
                  // marking smallest prime factor for every
                  // number to be itself.
                  spf[i] = i;
  
              // separately marking spf for every even
              // number as 2
              for (int i=4; i<MAXN; i+=2)
                  spf[i] = 2;
  
              for (int i=3; i*i<MAXN; i++)
              {
                  // checking if i is prime
                  if (spf[i] == i)
                  {
                      // marking SPF for all numbers divisible by i
                      for (int j=i*i; j<MAXN; j+=i)
  
                          // marking spf[j] if it is not
                          // previously marked
                          if (spf[j]==j)
                              spf[j] = i;
                  }
              }
          }
  
          void sieveOfEratosthenes(int n)
          {
              // Create a boolean array
              // "prime[0..n]" and
              // initialize all entries
              // it as true. A value in
              // prime[i] will finally be
              // false if i is Not a
              // prime, else true.
              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] is not changed, then it is a
                  // prime
                  if (prime[p] == true)
                  {
                      // Update all multiples of p
                      for (int i = p * p; i <= n; i += p)
                          prime[i] = false;
                  }
              }
          }
  
          // function to find first index >= x
          public int lowerIndex(List<Integer> arr, int n, int x)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr.get(mid) >= x)
                      h = mid - 1;
                  else
                      l = mid + 1;
              }
              return l;
          }
          public int lowerIndex(int[] arr, int n, int x)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr[mid] >= x)
                      h = mid - 1;
                  else
                      l = mid + 1;
              }
              return l;
          }
  
          // function to find last index <= y
          public int upperIndex(List<Integer> arr, int n, int y)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr.get(mid) <= y)
                      l = mid + 1;
                  else
                      h = mid - 1;
              }
              return h;
          }
          public int upperIndex(int[] arr, int n, int y)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr[mid] <= y)
                      l = mid + 1;
                  else
                      h = mid - 1;
              }
              return h;
          }
  
          // function to count elements within given range
          public int countInRange(List<Integer> arr, int n, int x, int y)
          {
              // initialize result
              int count = 0;
              count = upperIndex(arr, n, y) -
                      lowerIndex(arr, n, x) + 1;
              return count;
          }
  
          public int _gcd(int a,  int  b)
          {
  
              if(b == 0) {
                  return a;
              }
              else {
                  return _gcd(b, a % b);
              }
          }
  
          public int add(int a, int b){
              a+=b;
              if(a>=MOD) a-=MOD;
              else if(a<0) a+=MOD;
              return a;
          }
  
          public int mul(int a, int b){
              long res= (long)a*(long)b;
              return (int)(res%MOD);
          }
  
          public int power(int a, int b) {
              int ans=1;
              while(b>0){
                  if((b&1)!=0) ans= mul(ans,a);
                  b>>=1;
                  a= mul(a,a);
              }
              return ans;
          }
  
          int[] fact= new int[MAXN];
          int[] inv= new int[MAXN];
  
          public int Ckn(int n, int k){
              if(k<0 || n<0) return 0;
              return mul(mul(fact[n],inv[k]),inv[n-k]);
          }
  
          public int inverse(int a){
              return power(a,MOD-2);
          }
  
          public void preprocess() {
              fact[0]=1;
              for(int i=1;i<MAXN;i++) fact[i]= mul(fact[i-1],i);
              inv[MAXN-1]= inverse(fact[MAXN-1]);
              for(int i=MAXN-2;i>=0;i--){
                  inv[i]= mul(inv[i+1],i+1);
              }
          }
  
          /**
           * return VALUE of lower bound for unsorted array
           */
          public int lowerBoundNormalArray(int[] arr, int x){
              TreeSet<Integer> set= new TreeSet<>();
              for(int num: arr) set.add(num);
              return set.lower(x);
          }
          /**
           * return VALUE of upper bound for unsorted array
           */
          public int upperBoundNormalArray(int[] arr, int x){
              TreeSet<Integer> set= new TreeSet<>();
              for(int num: arr) set.add(num);
              return set.higher(x);
          }
  
          public void debugArr(int[] arr){
              for(int i: arr) out.print(i+" ");
              out.println();
          }
  
          public int rand(){
              int min=0, max= MAXN;
              int random_int = (int)Math.floor(Math.random()*(max-min+1)+min);
              return random_int;
          }
  
          InputReader in; PrintWriter out;
          static int INF = (int)1e9;
          int A[] = new int[2001];
          int dp[][] = new int[2001][2001]; // dp[i][j]: consider the array A[1:i:] -> delete at most j elements -> no of max elements on the right position (i.e. A[i] == i);
          public void solve(InputReader in, PrintWriter out) {
              int t = in.nextInt();
              while (t-->0){
                  int n = in.nextInt();
                  int m = in.nextInt();
                  int k = in.nextInt();
                  if (n%2==0){
                      if (k%2==0&&m%2==0){
                          out.println("Yes");
                      }
                      else if (k%2==0&&m%2==1&&k<=(m-1)*(n/2)){
                          out.println("Yes");
                      }
                      else{
                          out.println("No");
                      }
                  }
                  else{
                      if ((m*n/2-k)%2==0&&k>=m/2){
                          out.println("Yes");
                      }
                      else{
                          out.println("No");
                      }
                  }
              }
          }
  
          class SEG {
              int n;
              int[] segs;
              public SEG (int[] a){
                  this.n= a.length;
                  segs= new int[4*this.n];
                  build(a,0,0,this.n-1);
              }
              public void build(int[] a, int root, int l, int r){
                  if(l==r){
                      segs[root]=a[l];
                      return;
                  }
                  int m= (l+r)/2;
                  build(a,2*root+1,l,m);
                  build(a,2*root+2,m+1,r);
                  segs[root]= _gcd(segs[2*root+1], segs[2*root+2]);
              }
              public int query(int root, int l, int r, int lq, int rq){
                  if(lq<=l && rq>=r) return segs[root];
                  if(lq>r || rq<l) return 0;
                  int m= (l+r)/2;
                  int left= query(2*root+1, l, m, lq, rq);
                  int right= query(2*root+2, m+1, r, lq, rq);
                  return _gcd(left,right);
              }
  
          }
  
      }
  
      static class Venice{
          public Map<Long,Long> m= new HashMap<>();
          public long base=0;
          public long totalValue=0;
          private int M= 1000000007;
  
          private long addMod(long a, long b){
              a+=b;
              if(a>=M) a-=M;
              return a;
          }
  
          public void reset(){
              m= new HashMap<>();
              base=0;
              totalValue=0;
          }
          public void update(long add){
              base= base+ add;
          }
          public void add(long key, long val){
              long newKey= key-base;
              m.put(newKey, addMod(m.getOrDefault(newKey,(long)0),val));
          }
      }
  
  
  
      static class Tuple implements Comparable<Tuple>{
          int x, y, z;
          public Tuple(int x, int y, int z){
              this.x= x;
              this.y= y;
              this.z=z;
          }
          @Override
          public int compareTo(Tuple o){
              return this.x-o.x;
          }
      }
  
      static class Pair implements Comparable<Pair>{
          public int x;
          public int y;
          public Pair(int x, int y){
              this.x= x;
              this.y= y;
          }
  
          @Override
          public int compareTo(Pair o) {
              return this.x-o.x;
          }
      }
  
      // public static class compareL implements Comparator<Tuple>{
      //     @Override
      //     public int compare(Tuple t1, Tuple t2) {
      //         return t2.l - t1.l;
      //     }
      // }
  
      // fast input reader class;
      static class InputReader {
          public BufferedReader br;
          public StringTokenizer st;
  
          public InputReader(InputStream stream) {
              br = new BufferedReader(new InputStreamReader(stream));
          }
  
          public String nextToken() {
              while (st == null || !st.hasMoreTokens()) {
                  String line = null;
                  try {
                      line = br.readLine();
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
                  if (line == null) {
                      return null;
                  }
                  st = new StringTokenizer(line);
              }
              return st.nextToken();
          }
  
          public int nextInt() {
              return Integer.parseInt(nextToken());
          }
          public double nextDouble(){
              return Double.parseDouble(nextToken());
          }
          public long nextLong(){
              return Long.parseLong(nextToken());
          }
          public int[] nextIntArr(int n){
              int[] arr= new int[n];
              for(int i=0;i<n;i++) arr[i]= nextInt();
              return arr;
          }
          public long[] nextLongArr(int n){
              long[] arr= new long[n];
              for(int i=0;i<n;i++) arr[i]= nextLong();
              return arr;
          }
          public List<Integer> nextIntList(int n){
              List<Integer> arr= new ArrayList<>();
              for(int i=0;i<n;i++) arr.add(nextInt());
              return arr;
          }
          public int[][] nextIntMatArr(int n, int m){
              int[][] mat= new int[n][m];
              for(int i=0;i<n;i++) for(int j=0;j<m;j++) mat[i][j]= nextInt();
              return mat;
          }
          public List<List<Integer>> nextIntMatList(int n, int m){
              List<List<Integer>> mat= new ArrayList<>();
              for(int i=0;i<n;i++){
                  List<Integer> temp= new ArrayList<>();
                  for(int j=0;j<m;j++) temp.add(nextInt());
                  mat.add(temp);
              }
              return mat;
          }
          public char[] nextStringCharArr(){
              return nextToken().toCharArray();
          }
      }
  }