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: 			/*
  			TO LEARN
  			1-segment trees
  			2-euler tour
  		
  			*/
  			/*
  			TO SOLVE 
  			uva 1103
  			codeforces 722 kavi on pairing duty
  			*/
  			/*
  			bit manipulation shit
  			1-Computer Systems: A Programmer's Perspective
  			2-hacker's delight
  			3-(02-03-bits-ints)
  			4-machine-basics
  			5-Bits Manipulation tutorialspoint
  			*/
  			/*
  			TO WATCH
  			1-what is bitmasking by kartik arora youtube
  			*/
  			            import java.util.*;
  					    import java.math.*;
  					    import java.io.*; 
  					    import java.util.stream.Collectors;
  
  					       public class A{
  					     
  					  static InputStream inputStream = System.in;
  			            static FastScanner scan=new FastScanner();
  					     public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
  	static final long p=29;
  	static final long mod=(long)1e9+9;
  	static int n,m;
  	static String spotty[],plain[];
  	static boolean check(int l)
  	{
  		 Map<Long,Set<Pair>>hashes=new HashMap<Long,Set<Pair>>();
  					    HashSet<Long>hashes2=new HashSet<Long>();
  					    long pow_p[]=new long[m];
  					    pow_p[0]=1;
  					    for(int i=1;i<m;i++)
  					    	pow_p[i]=(pow_p[i-1]*p);
  					    for(int i=0;i<n;i++)
  					    {
  					    	String s=plain[i];
  					    	long h[]=new long[m+1];
  					    	for(int j=0;j<m;j++)
  					    	{
  					    		h[j+1]=(h[j]+(s.charAt(j)-'a'+1)*pow_p[j]);
  					    	}
  					    	
  					    		for(int j=0;j<=m-l;j++)
  					    		{
  					    			long cur_h=(h[j+l]-h[j]);
  					    			cur_h=(cur_h*pow_p[m-j-1]);
  					    			if(hashes.containsKey(cur_h))
  					    				hashes.get(cur_h).add(new Pair(j,j+l));
  					    			else 
  					    			{
  					    				hashes.put(cur_h,new HashSet());
  					    				hashes.get(cur_h).add(new Pair(j,j+l));
  					    			}
  					    			//map.getOrDefault(cur_h,new ArrayList()).add(new Pair(j,j+1));
  					    			//hashes.put(cur_h,);
  					    		//	out.println("FIR "+cur_h);
  					    		}				    	
  					    }
  
  					        for(int i=0;i<n;i++)
  					    {
  					    	String s=spotty[i];
  					    	long h[]=new long[m+1];
  					    	for(int j=0;j<m;j++)
  					    	{
  					    		h[j+1]=(h[j]+(s.charAt(j)-'a'+1)*pow_p[j]);
  					    	}
  					    	
  					    		for(int j=0;j<=m-l;j++)
  					    		{
  					    			long cur_h=(h[j+l]-h[j]);
  					    			cur_h=(cur_h*pow_p[m-j-1]);
  
  					    			if(hashes.containsKey(cur_h)){
  					    				if(!hashes.get(cur_h).contains(new Pair(j,j+l)))
  					    					return true;
  					    			}
  					    			else{
  					    				out.println(j+" "+i);
  					    			 return true;
  					    			}
  					    		
  					    		}
  					    	
  					    }	
  					    return false;
  	}
  
  				public static void main(String[] args)  throws Exception 
  			      {
  				
  						///scan=new FastScanner("cownomics.in");
  					//out = new PrintWriter("cownomics.out");
  					 
  					 /*
  					 currently doing 
  					 1-digit dp
  					 2-ds like fenwick and interval tree and sparse table 
  					 */
  					 /*
  					 READING 
  					 1-Everything About Dynamic Programming codeforces
  					 2-DYNAMIC PROGRAMMING: FROM NOVICE TO ADVANCED topcoder
  					 3-Introduction to DP with Bitmasking codefoces
  					 4-Bit Manipulation hackerearth
  					 5-read more about mobious and inculsion-exclusion 
  					 */
  		
  
  
  
  					    int tt=1;
  					tt=scan.nextInt();
  					int T=tt;
  					/*Map<Integer,Pair>map=new HashMap<Integer,Pair>();
  					for(int i=1;i<=333333334;i++)
  					{
  						map.put(i+2*i,new Pair(i,2*i));
  						map.put(i+(2*(i+1)),new Pair(i,i+1));
  						map.put(i+1+(2*i),new Pair(i+1,i));
  					}*/
  
  				 outer:while(tt-->0)
  					    {
  					    	 n=scan.nextInt();
  					    	 m=scan.nextInt();
  					    int k=scan.nextInt();
  					    if(n%2==0&&m%2==0&&k%2==0)
  					    {
  					    	out.println("YES");
  					    }	
  					    else if(n%2==0&&m%2==1&&k%2==0)
  					    {
  					    	//out.println("FUCK");
  					    	int max=n*(m-1)/2;
  					    	if(k>max)
  					    		out.println("NO");
  					    	else
  					    	out.println("YES");
  					    }
  					    else if(n%2==1&&m%2==0&&k%2==1){
  					    	int tmp=m/2;
  					   		if(k<tmp||k==0)
  					   			out.println("NO");
  					   		else{
  					   			k-=tmp;
  					   			if(k%2==0)
  					   		 out.println("YES");
  					   		else out.println("NO");
  					   		}
  					    }
  					   else if(n%2==1&&m%2==0&&k%2==0)
  					   {
  					   		int tmp=m/2;
  					   		if(k<tmp||k==0)
  					   			out.println("NO");
  					   		else{
  					   			k-=tmp;
  					   			if(k%2==0)
  					   		 out.println("YES");
  					   		else out.println("NO");
  					   		}
  					   }
  					    else out.println("NO");
  					    
  
  					   
  
  					   
  					    	
  					    	
  			}
  			   out.close();
  		}
  		  	 
  			 		  
  					   
  					
  					static class special{
  						boolean bool;
  						int n;
  						//int id;
  						special(boolean bool,int n)
  						{
  							this.bool=bool;
  							this.n=n;
  						}
  						@Override
  						    public int hashCode() {
  					                int hash = 7;
  		    hash = 31 * hash + (int) n;
  		   
  		    return hash;
  					            }
  					              @Override
  					            public boolean equals(Object o){
  					                if (o == this) return true;
  					                if (o.getClass() != getClass()) return false;
  					                special t = (special)o;
  					                return t.bool == bool && t.n == n;
  					            }
  					}
  
  					   
  					     static long binexp(long a,long n)
  					    {
  					        if(n==0)
  					            return 1;
  					        long res=binexp(a,n/2);
  					        if(n%2==1)
  					            return res*res*a;
  					        else 
  					            return res*res;
  					    }
  					     
  					    static long powMod(long base, long exp, long mod) {
  					           if (base == 0 || base == 1) return base;
  					           if (exp == 0) return 1;
  					           if (exp == 1) return (base % mod+mod)%mod;
  					           long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
  					           R *= R;
  					           R %= mod;
  					           if ((exp & 1) == 1) {
  					               return (base * R % mod+mod)%mod;
  					           }
  					           else return (R %mod+mod)%mod;
  					       }
  					    static double dis(double x1,double y1,double x2,double y2)
  					    {
  					        return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
  					    }
  					    static long mod(long x,long y)
  					        {
  					            if(x<0)
  					                x=x+(-x/y+1)*y;
  					            return x%y;
  					        }
  					     public static  long pow(long b, long e) {
  					                long r = 1;
  					                while (e > 0) {
  					                    if (e % 2 == 1) r = r * b ;
  					                    b = b * b;
  					                    e >>= 1;
  					                }
  					                return r;
  					            }
  					    private static void sort(long[] arr) {
  					            List<Long> list = new ArrayList<>();
  					            for (long object : arr) list.add(object);
  					            Collections.sort(list);
  					        //Collections.reverse(list);
  					            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
  					        }
  					    private static void sort2(long[] arr) {
  					            List<Long> list = new ArrayList<>();
  					            for (Long object : arr) list.add(object);
  					            Collections.sort(list);
  					        Collections.reverse(list);
  					            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
  					        }
  					     static class FastScanner
  			{
  			    private int BS = 1 << 16;
  			    private char NC = (char) 0;
  			    private byte[] buf = new byte[BS];
  			    private int bId = 0, size = 0;
  			    private char c = NC;
  			    private double cnt = 1;
  			    private BufferedInputStream in;
  			 
  			    public FastScanner() {
  			        in = new BufferedInputStream(System.in, BS);
  			    }
  			 
  			    public FastScanner(String s) {
  			        try {
  			            in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
  			        } catch (Exception e) {
  			            in = new BufferedInputStream(System.in, BS);
  			        }
  			    }
  			 
  			    private char getChar() {
  			        while (bId == size) {
  			            try {
  			                size = in.read(buf);
  			            } catch (Exception e) {
  			                return NC;
  			            }
  			            if (size == -1) return NC;
  			            bId = 0;
  			        }
  			        return (char) buf[bId++];
  			    }
  			 
  			    public int nextInt() {
  			        return (int) nextLong();
  			    }
  			 
  			    public int[] nextInts(int N) {
  			        int[] res = new int[N];
  			        for (int i = 0; i < N; i++) {
  			            res[i] = (int) nextLong();
  			        }
  			        return res;
  			    }
  			 
  			    public long[] nextLongs(int N) {
  			        long[] res = new long[N];
  			        for (int i = 0; i < N; i++) {
  			            res[i] = nextLong();
  			        }
  			        return res;
  			    }
  			 
  			    public long nextLong() {
  			        cnt = 1;
  			        boolean neg = false;
  			        if (c == NC) c = getChar();
  			        for (; (c < '0' || c > '9'); c = getChar()) {
  			            if (c == '-') neg = true;
  			        }
  			        long res = 0;
  			        for (; c >= '0' && c <= '9'; c = getChar()) {
  			            res = (res << 3) + (res << 1) + c - '0';
  			            cnt *= 10;
  			        }
  			        return neg ? -res : res;
  			    }
  			 
  			    public double nextDouble() {
  			        double cur = nextLong();
  			        return c != '.' ? cur : cur + nextLong() / cnt;
  			    }
  			 
  			    public double[] nextDoubles(int N) {
  			        double[] res = new double[N];
  			        for (int i = 0; i < N; i++) {
  			            res[i] = nextDouble();
  			        }
  			        return res;
  			    }
  			 
  			    public String next() {
  			        StringBuilder res = new StringBuilder();
  			        while (c <= 32) c = getChar();
  			        while (c > 32) {
  			            res.append(c);
  			            c = getChar();
  			        }
  			        return res.toString();
  			    }
  			 
  			    public String nextLine() {
  			        StringBuilder res = new StringBuilder();
  			        while (c <= 32) c = getChar();
  			        while (c != '\n') {
  			            res.append(c);
  			            c = getChar();
  			        }
  			        return res.toString();
  			    }
  			 
  			    public boolean hasNext() {
  			        if (c > 32) return true;
  			        while (true) {
  			            c = getChar();
  			            if (c == NC) return false;
  			            else if (c > 32) return true;
  			        }
  			    }
  			}
  
  					     static class Pair implements Comparable<Pair>{
  					            public long x, y,z;
  					            public Pair(long x1, long y1,long z1) {
  					                x=x1;
  					                y=y1;
  					                z=z1;
  					            }
  					             public Pair(long x1, long y1) {
  					                x=x1;
  					                y=y1;
  					    
  					            }
  					            
  					            @Override
  					            public int hashCode() {
  					                return (int)(x + 31 * y);
  					            }
  					            public String toString() {
  					                return x + " " + y+" "+z;
  					            }
  					            @Override
  					            public boolean equals(Object o){
  					                if (o == this) return true;
  					                if (o.getClass() != getClass()) return false;
  					                Pair t = (Pair)o;
  					                return t.x == x && t.y == y&&t.z==z;
  					            }
  					    public int compareTo(Pair o)
  					    {
  					    	if(x==o.x)
  					    		return -1;
  					    
  					    	return (int)(o.x-x);
  					     
  					        }
  					     
  					    }
  					    
  					    }
  
  					     
  