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 os,sys
  from io import BytesIO, IOBase
  
  from collections import deque, Counter,defaultdict as dft
  from heapq import heappop ,heappush
  from math import log,sqrt,factorial,cos,tan,sin,radians,log2,ceil,floor
  from bisect import bisect,bisect_left,bisect_right
  from decimal import *
  import sys,threading
  from itertools import permutations, combinations
  from copy import deepcopy
  input = sys.stdin.readline
  
  
  ii = lambda: int(input())
  si = lambda: input().rstrip()
  mp = lambda: map(int, input().split())
  ms=  lambda: map(str,input().strip().split(" "))
  ml = lambda: list(mp())
  mf = lambda: map(float, input().split())
  
  
  alphs = "abcdefghijklmnopqrstuvwxyz"
  
  
  # stuff you should look for
  	#  int overflow, array bounds
  	#  special cases (n=1?)
  	#  do smth instead of nothing and stay organized
  	#  WRITE STUFF DOWN
  	#  DON'T GET STUCK ON ONE APPROACH
  
  #
  
  def solve():
      
      n,m,k=mp()
      total=(n*m)//2
      rkne = (n*m)//2 - k
      if (n%2==0) and (m%2==0):
          if k%2==0:
              print("YES")
          else:
              print("NO")
      
      elif (n%2==0) and (m%2):
          if k%2==0 and (total-n//2>=k):
              print("YES")
          else:
              print("NO")
      else:
          
          k=(n*m)//2 - k
          n,m=m,n
          if k%2==0 and (total-n//2>=k):
              print("YES")
          else:
              print("NO")
          
      
      
      
  
   
  BUFSIZE = 8192
   
   
  class FastIO(IOBase):
      newlines = 0
   
      def __init__(self, file):
          self._fd = file.fileno()
          self.buffer = BytesIO()
          self.writable = "x" in file.mode or "r" not in file.mode
          self.write = self.buffer.write if self.writable else None
   
      def read(self):
          while True:
              b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
              if not b:
                  break
              ptr = self.buffer.tell()
              self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
          self.newlines = 0
          return self.buffer.read()
   
      def readline(self):
          while self.newlines == 0:
              b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
              self.newlines = b.count(b"\n") + (not b)
              ptr = self.buffer.tell()
              self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
          self.newlines -= 1
          return self.buffer.readline()
   
      def flush(self):
          if self.writable:
              os.write(self._fd, self.buffer.getvalue())
              self.buffer.truncate(0), self.buffer.seek(0)
   
   
  class IOWrapper(IOBase):
      def __init__(self, file):
          self.buffer = FastIO(file)
          self.flush = self.buffer.flush
          self.writable = self.buffer.writable
          self.write = lambda s: self.buffer.write(s.encode("ascii"))
          self.read = lambda: self.buffer.read().decode("ascii")
          self.readline = lambda: self.buffer.readline().decode("ascii")
   
   
  def print(*args, **kwargs):
      """Prints the values to a stream, or to sys.stdout by default."""
      sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
      at_start = True
      for x in args:
          if not at_start:
              file.write(sep)
          file.write(str(x))
          at_start = False
      file.write(kwargs.pop("end", "\n"))
      if kwargs.pop("flush", False):
          file.flush()
  
  if sys.version_info[0] < 3:
      sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
  else:
      sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
   
  input = lambda: sys.stdin.readline().rstrip("\r\n")
   
  # endregion
   
   
  if __name__ == "__main__":
      tc=1
      tc = ii()
      for i in range(tc):
      	solve()