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.*;
  import java.math.*;
  
  /**
   * @author Naitik
   * 
   */
  public class B
  
  { 
  	 static FastReader sc=new FastReader();
  	 static long dp[][];
  	 static int mod=1000000007;
  	 static int max;
  	 static long bit[];
  	 static int in[];
  	 static int ot[];
  	 static int timer=1;
  	 static long seg[];
  	 static long A[];
  	 static HashMap<Integer,Integer> map;
  		  public static void main(String[] args) 
      {
  			//CHECK FOR N=1
  		       	//CHECK FOR N=1
  		  PrintWriter out=new PrintWriter(System.out);
  		 // StringBuffer sb=new StringBuffer("");
  		  int ttt=1;
  		    ttt =i(); 
  	        while (ttt-- > 0) 
  			{
  	        	int n=i();
  	        	int m=i();
  	        	int k=i();
  	        	if(n%2==0) {
  	        		if(m%2==0) {
  	        		if(k%2==0) {
  	        			System.out.println("YES");
  	        		}
  	        		else {
  	        			System.out.println("NO");
  	        		}
  	        		}
  	        		else {
  	        			int y=n/2;
  	        			int tot=(m*n)/2;
  	        			int min=tot-y;
  	        			if(k>min) {
  	        				System.out.println("NO");
  	        				continue;
  	        			}
  	        			if(k%2==0) {
  		        			System.out.println("YES");
  		        		}
  		        		else {
  		        			System.out.println("NO");
  		        		}
  	        			
  	        		}
  	        		continue;
  	        	}
  	        	int min=m/2;
  	        	if(k<min) {
  	        		System.out.println("NO");
  	        		continue;
  	        	}
  	        	k-=min;
  	        	if(k%2==0) {
          			System.out.println("YES");
          		}
          		else {
          			System.out.println("NO");
          		}
  	        	
  	        	
  	        	
  	        	
  	        	
  
  	   		 
  	        	
  			}
  		  out.close();
  	        	//System.out.println(sb.toString());
  		    
  		    //CHECK FOR N=1                    //CHECK FOR M=0
  	        //CHECK FOR N=1                    //CHECK FOR M=0
  	       	
      }
  		  static void build(int si , int ss , int se)
  		  {
  		  	if(ss == se)
  		  	{
  		  		seg[si] = A[ss];
  		  		return ;
  		  	}
  		   
  		  	int mid = (ss + se) / 2;
  		  	build(2*si , ss , mid);
  		  	build(2*si+1 ,mid+1 , se);
  		   
  		  	seg[si] = max(seg[2*si] , seg[2*si+1]);
  		  }
  		  static void update(int si,int ss,int se,int qi) {
  			  if(ss == se)
  			  	{
  			  		seg[si] = A[ss];
  			  		return ;
  			  	}
  			   
  			  	int mid = (ss + se) / 2;
  			  	if(qi<=mid) {
  			  	update(2*si , ss , mid,qi);
  			  	}
  			  	else {
  			  	update(2*si+1 ,mid+1 , se,qi);
  			  	}
  			   
  			  	seg[si] = max(seg[2*si] , seg[2*si+1]);
  		  }
  		  static long query(int si , int ss , int se , int qs , int qe)
  		  {
  		  	if(ss > qe || se < qs) return Integer.MIN_VALUE;
  		   
  		  	if(ss >= qs && se <= qe) return seg[si];
  		   
  		  	int mid = (ss + se) / 2;
  		   
  		  	return max(query(2*si , ss , mid , qs , qe) , query(2*si+1 , mid+1 , se , qs , qe));
  		  }
  		  
  		 
  			
  		  
  		  
  
  
  
  static class Pair implements Comparable<Pair>
       {
      	 int x;
      	 int y;
      	 Pair(int x,int y){
      		 this.x=x;
      		 this.y=y;
      		 
      	 }
  		@Override
  		public int compareTo(Pair o) {
  			if(this.x>o.x)
  				return 1;
  			else if(this.x<o.x)
  				return -1;
  			else {
  				if(this.y>o.y)
  					return 1;
  				else if(this.y<o.y)
  					return -1;
  				else
  					return 0;
  			}
  		}
  		
  		/* FOR TREE MAP PAIR USE */
  		
  //		public int compareTo(Pair o) {
  // 			if (x > o.x) {
  // 				return 1;
  // 			}
  // 			if (x < o.x) {
  // 				return -1;
  // 			}
  // 			if (y > o.y) {
  // 				return 1;
  // 			}
  // 			if (y < o.y) {
  // 				return -1;
  // 			}
  // 			return 0;
  // 		}
  		public int hashCode() 
  		{ 
  			final int temp = 14; 
  			int ans = 1; 
  			ans =x*31+y*13; 
  			return ans; 
  		} 
    
  		// Equal objects must produce the same 
  		// hash code as long as they are equal 
  		@Override
  		public boolean equals(Object o) 
  		{ 
  			if (this == o) { 
  				return true; 
  			} 
  			if (o == null) { 
  				return false; 
  			} 
  			if (this.getClass() != o.getClass()) { 
  				return false; 
  			} 
  			Pair other = (Pair)o; 
  			if (this.x != other.x || this.y!=other.y) { 
  				return false; 
  			} 
  			return true; 
  		} 	
  		
       }
  //FRENWICK TREE
  static void update(int i, int x){
  	for(; i < bit.length; i += (i&-i))
  		bit[i] += x;
  }
  
  static int sum(int i){
  	int ans = 0;
  	for(; i > 0; i -= (i&-i))
  		ans += bit[i];
  	return ans;
  }
  //END
  static void add(int v) {
  	if(!map.containsKey(v)) {
  		map.put(v, 1);
  	}
  	else {
  		map.put(v, map.get(v)+1);
  	}
  }
  static void remove(int v) {
  	if(map.containsKey(v)) {
  		map.put(v, map.get(v)-1);
  		if(map.get(v)==0)
  			map.remove(v);
  	}
  }
  static int[] copy(int A[]) {
  	int B[]=new int[A.length];
  	for(int i=0;i<A.length;i++) {
  		B[i]=A[i];
  	}
  	return B;
  }
  static long[] copy(long A[]) {
  	long B[]=new long[A.length];
  	for(int i=0;i<A.length;i++) {
  		B[i]=A[i];
  	}
  	return B;
  }
  static int[] input(int n) {
  	int A[]=new int[n];
  	   for(int i=0;i<n;i++) {
  		   A[i]=sc.nextInt();
  	   }
  	   return A;
     }
  static long[] inputL(int n) {
  	long A[]=new long[n];
  	   for(int i=0;i<n;i++) {
  		   A[i]=sc.nextLong();
  	   }
  	   return A;
     }
  static String[] inputS(int n) {
  	String A[]=new String[n];
  	   for(int i=0;i<n;i++) {
  		   A[i]=sc.next();
  	   }
  	   return A;
     }
  static long sum(int A[]) {
  	long sum=0;
  	for(int i : A) {
  		sum+=i;
  	}
  	return sum;
  }
  static long sum(long A[]) {
  	long sum=0;
  	for(long i : A) {
  		sum+=i;
  	}
  	return sum;
  }
  static void reverse(long A[]) {
  	int n=A.length;
  	long B[]=new long[n];
  	for(int i=0;i<n;i++) {
  		B[i]=A[n-i-1];
  	}
  	for(int i=0;i<n;i++)
  		A[i]=B[i];
  	
  }
  static void reverse(int A[]) {
  	int n=A.length;
  	int B[]=new int[n];
  	for(int i=0;i<n;i++) {
  		B[i]=A[n-i-1];
  	}
  	for(int i=0;i<n;i++)
  		A[i]=B[i];
  	
  }
  static void input(int A[],int B[]) {
  	   for(int i=0;i<A.length;i++) {
  		   A[i]=sc.nextInt();
  		   B[i]=sc.nextInt();
  	   }
  }
  static int[][] input(int n,int m){
  	int A[][]=new int[n][m];
  	for(int i=0;i<n;i++) {
  		for(int j=0;j<m;j++) {
  			A[i][j]=i();
  		}
  	}
  	return A;
  }
  static char[][] charinput(int n,int m){
  	char A[][]=new char[n][m];
  	for(int i=0;i<n;i++) {
  		String s=s();
  		for(int j=0;j<m;j++) {
  			A[i][j]=s.charAt(j);
  		}
  	}
  	return A;
  }
  static int find(int A[],int a) {
  	  if(A[a]==a)
  		  return a;
  	  return A[a]=find(A, A[a]);
  }
  static int max(int A[]) {
  	int max=Integer.MIN_VALUE;
  	for(int i=0;i<A.length;i++) {
  		max=Math.max(max, A[i]);
  	}
  	return max;
  }
  static int min(int A[]) {
  	int min=Integer.MAX_VALUE;
  	for(int i=0;i<A.length;i++) {
  		min=Math.min(min, A[i]);
  	}
  	return min;
  }
  static long max(long A[]) {
  	long max=Long.MIN_VALUE;
  	for(int i=0;i<A.length;i++) {
  		max=Math.max(max, A[i]);
  	}
  	return max;
  }
  static long min(long A[]) {
  	long min=Long.MAX_VALUE;
  	for(int i=0;i<A.length;i++) {
  		min=Math.min(min, A[i]);
  	}
  	return min;
  }
  static long [] prefix(long A[]) {
  	long p[]=new long[A.length];
  	p[0]=A[0];
  	for(int i=1;i<A.length;i++)
  		p[i]=p[i-1]+A[i];
  	return p;
  }
  static long [] prefix(int A[]) {
  	long p[]=new long[A.length];
  	p[0]=A[0];
  	for(int i=1;i<A.length;i++)
  		p[i]=p[i-1]+A[i];
  	return p;
  }
  static long [] suffix(long A[]) {
  	long p[]=new long[A.length];
  	p[A.length-1]=A[A.length-1];
  	for(int i=A.length-2;i>=0;i--)
  		p[i]=p[i+1]+A[i];
  	return p;
  }
  static long [] suffix(int A[]) {
  	long p[]=new long[A.length];
  	p[A.length-1]=A[A.length-1];
  	for(int i=A.length-2;i>=0;i--)
  		p[i]=p[i+1]+A[i];
  	return p;
  }
  static void fill(int dp[]) {
  	Arrays.fill(dp, -1);
  }
  static void fill(int dp[][]) {
  	for(int i=0;i<dp.length;i++)
  	Arrays.fill(dp[i], -1);
  }
  static void fill(int dp[][][]) {
  	for(int i=0;i<dp.length;i++) {
  		for(int j=0;j<dp[0].length;j++) {
  			Arrays.fill(dp[i][j],-1);
  		}
  	}
  }
  static void fill(int dp[][][][]) {
  	for(int i=0;i<dp.length;i++) {
  		for(int j=0;j<dp[0].length;j++) {
  			for(int k=0;k<dp[0][0].length;k++) {
  			Arrays.fill(dp[i][j][k],-1);
  			}
  		}
  	}
  }
  static void fill(long dp[]) {
  	Arrays.fill(dp, -1);
  }
  static void fill(long dp[][]) {
  	for(int i=0;i<dp.length;i++)
  	Arrays.fill(dp[i], -1);
  }
  static void fill(long dp[][][]) {
  	for(int i=0;i<dp.length;i++) {
  		for(int j=0;j<dp[0].length;j++) {
  			Arrays.fill(dp[i][j],-1);
  		}
  	}
  }
  static void fill(long dp[][][][]) {
  	for(int i=0;i<dp.length;i++) {
  		for(int j=0;j<dp[0].length;j++) {
  			for(int k=0;k<dp[0][0].length;k++) {
  			Arrays.fill(dp[i][j][k],-1);
  			}
  		}
  	}
  }
  static int min(int a,int b) {
  	return Math.min(a, b);
  }
  static int min(int a,int b,int c) {
  	return Math.min(a, Math.min(b, c));
  }
  static int min(int a,int b,int c,int d) {
  	return Math.min(a, Math.min(b, Math.min(c, d)));
  }
  static int max(int a,int b) {
  	return Math.max(a, b);
  }
  static int max(int a,int b,int c) {
  	return Math.max(a, Math.max(b, c));
  }
  static int max(int a,int b,int c,int d) {
  	return Math.max(a, Math.max(b, Math.max(c, d)));
  }
  static long min(long a,long b) {
  	return Math.min(a, b);
  }
  static long min(long a,long b,long c) {
  	return Math.min(a, Math.min(b, c));
  }
  static long min(long a,long b,long c,long d) {
  	return Math.min(a, Math.min(b, Math.min(c, d)));
  }
  static long max(long a,long b) {
  	return Math.max(a, b);
  }
  static long max(long a,long b,long c) {
  	return Math.max(a, Math.max(b, c));
  }
  static long max(long a,long b,long c,long d) {
  	return Math.max(a, Math.max(b, Math.max(c, d)));
  }
  
  static long power(long x, long y, long p)
  {
  
  	if(y==0)
  		return 1;
  	if(x==0)
  		return 0;
      long res = 1;
      x = x % p;
  
      while (y > 0) {
  
          if (y % 2 == 1)
              res = (res * x) % p;
  
          y = y >> 1; 
          x = (x * x) % p;
      }
  
      return res;
  }
  static void print(int A[]) {
  	for(int i : A) {
  		System.out.print(i+" ");
  	}
  	System.out.println();
  }
  static void print(long A[]) {
  	for(long i : A) {
  		System.out.print(i+" ");
  	}
  	System.out.println();
  }
  static long mod(long x) {
  	  return ((x%mod + mod)%mod);
  }
  static String reverse(String s) {
  	StringBuffer p=new StringBuffer(s);
  	p.reverse();
  	return p.toString();
  }
  
       static int i() {
      	 return sc.nextInt();
       }
       static String s() {
      	 return sc.next();
       }
       static long l() {
      	 return sc.nextLong();
       }  
       static void sort(int[] A){
          int n = A.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i){
              int tmp = A[i];
              int randomPos = i + rnd.nextInt(n-i);
              A[i] = A[randomPos];
              A[randomPos] = tmp;
          }
          Arrays.sort(A);
       }
       static void sort(long[] A){
  	        int n = A.length;
  	        Random rnd = new Random();
  	        for(int i=0; i<n; ++i){
  	            long tmp = A[i];
  	            int randomPos = i + rnd.nextInt(n-i);
  	            A[i] = A[randomPos];
  	            A[randomPos] = tmp;
  	        }
  	        Arrays.sort(A);
  	     }
    static String sort(String s) {
   	 Character ch[]=new Character[s.length()];
   	 for(int i=0;i<s.length();i++) {
   		 ch[i]=s.charAt(i);
   	 }
   	 Arrays.sort(ch);
   	 StringBuffer st=new StringBuffer("");
   	 for(int i=0;i<s.length();i++) {
   		 st.append(ch[i]);
   	 }
   	 return st.toString();
    }
    static HashMap<Integer,Integer> hash(int A[]){
  	  HashMap<Integer,Integer> map=new HashMap<Integer, Integer>();
  	  for(int i : A) {
  		  if(map.containsKey(i)) {
  			  map.put(i, map.get(i)+1);
  		  }
  		  else {
  			  map.put(i, 1);
  		  }
  	  }
  	  return map;
    }
    static TreeMap<Integer,Integer> tree(int A[]){
  	  TreeMap<Integer,Integer> map=new TreeMap<Integer, Integer>();
  	  for(int i : A) {
  		  if(map.containsKey(i)) {
  			  map.put(i, map.get(i)+1);
  		  }
  		  else {
  			  map.put(i, 1);
  		  }
  	  }
  	  return map;
    }
       static boolean prime(int n) 
  	    { 
  	        if (n <= 1) 
  	            return false; 
  	        if (n <= 3) 
  	            return true; 
  	        if (n % 2 == 0 || n % 3 == 0) 
  	            return false; 
  	        double sq=Math.sqrt(n);
  	  
  	        for (int i = 5; i <= sq; i = i + 6) 
  	            if (n % i == 0 || n % (i + 2) == 0) 
  	                return false; 
  	        return true; 
  	    } 
       static boolean prime(long n) 
  	    { 
  	        if (n <= 1) 
  	            return false; 
  	        if (n <= 3) 
  	            return true; 
  	        if (n % 2 == 0 || n % 3 == 0) 
  	            return false; 
  	        double sq=Math.sqrt(n);
  	  
  	        for (int i = 5; i <= sq; i = i + 6) 
  	            if (n % i == 0 || n % (i + 2) == 0) 
  	                return false; 
  	        return true; 
  	    } 
       static int gcd(int a, int b) 
       { 
           if (a == 0) 
               return b; 
           return gcd(b % a, a); 
       } 
       static long gcd(long a, long b) 
       { 
           if (a == 0) 
               return b; 
           return gcd(b % a, a); 
       } 
       
          
      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; 
          } 
      } 
  } 
  