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: 
  # Author : raj1307 - Raj Singh
  # Date   : 23.07.2021
  
  from __future__ import division, print_function
  
  import os,sys
  from io import BytesIO, IOBase
  
  if sys.version_info[0] < 3:
      from __builtin__ import xrange as range
      from future_builtins import ascii, filter, hex, map, oct, zip
  
  
  def ii():  return int(input())
  def si():  return input()
  def mi():  return map(int,input().strip().split(" "))
  def msi(): return map(str,input().strip().split(" "))
  def li():  return list(mi())
  
  def dmain():
      sys.setrecursionlimit(1000000)
      threading.stack_size(1024000)
      thread = threading.Thread(target=main)
      thread.start()
      
  #from collections import deque, Counter, OrderedDict,defaultdict
  #from heapq import nsmallest, nlargest, heapify,heappop ,heappush, heapreplace
  #from math import log,sqrt,factorial,cos,tan,sin,radians
  #from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right
  #from decimal import *
  #import threading
  #from itertools import permutations
  #Copy 2D list  m = [x[:] for x in mark] .. Avoid Using Deepcopy
  
  abc='abcdefghijklmnopqrstuvwxyz'
  abd={'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25}
  mod=1000000007
  #mod=998244353
  inf = float("inf")
  vow=['a','e','i','o','u']
  dx,dy=[-1,1,0,0,1,-1,1,-1],[0,0,1,-1,1,-1,-1,1]
  def getKey(item): return item[1] 
  def sort2(l):return sorted(l, key=getKey,reverse=True)
  def d2(n,m,num):return [[num for x in range(m)] for y in range(n)]
  def isPowerOfTwo (x): return (x and (not(x & (x - 1))) )
  def decimalToBinary(n): return bin(n).replace("0b","")
  def ntl(n):return [int(i) for i in str(n)]
  def ncr(n,r): return factorial(n)//(factorial(r)*factorial(max(n-r,1)))
  
  def ceil(x,y):
      if x%y==0:
          return x//y
      else:
          return x//y+1
  
  def powerMod(x,y,p):
      res = 1
      x %= p
      while y > 0:
          if y&1:
              res = (res*x)%p
          y = y>>1
          x = (x*x)%p
      return res
  
  def gcd(x, y):
      while y:
          x, y = y, x % y
      return x
      
  def isPrime(n) : # Check Prime Number or not 
      if (n <= 1) : return False
      if (n <= 3) : return True
      if (n % 2 == 0 or n % 3 == 0) : return False
      i = 5
      while(i * i <= n) : 
          if (n % i == 0 or n % (i + 2) == 0) : 
              return False
          i = i + 6
      return True
  
  
  
  def read():
      sys.stdin  = open('input.txt', 'r')  
      sys.stdout = open('output.txt', 'w') 
  
  
  
  
  
  def main():
  
  
  
      for _ in range(ii()):
  
          
          n,m,k=mi()
          t=(n*m)//2
          x=k
          y=t-k
          if n%2==0 and m%2==0:
  
  
              f=0
              for i in range(n+1):
                  if i%2==1: continue
  
                  p=k-i*(m//2)
                  if p<0:
                      break
  
                  b=n-i
  
                  if p==0:
                      f=1
                      break
  
                  if b==0:
                      break
  
                  r=p%b
                  d=ceil(p,b)
                  if d>m//2:
                      continue
                  if r%2==0:
                      f=1
                      break
  
  
          elif n%2==0:
  
              f=0
              for i in range(n+1):
                  if i%2==1: continue
  
                  p=k-i*(m//2)
                  if p<0:
                      break
  
                  b=n-i
  
                  if p==0:
                      f=1
                      break
  
                  if b==0:
                      break
  
                  r=p%b
                  d=ceil(p,b)
                  if d>m//2:
                      continue
                  if r%2==0:
                      f=1
                      break
  
          elif n%2==1:
  
              f=0
              for i in range(n+1):
                  if i%2==0: continue
  
                  p=k-i*(m//2)
                  if p<0:
                      break
  
                  b=n-i
  
                  if p==0:
                      f=1
                      break
  
                  if b==0:
                      break
  
                  r=p%b
                  d=ceil(p,b)
                  if d>m//2:
                      continue
                  if r%2==0:
                      f=1
                      break
  
  
  
  
          if f==0:
              print('NO')
          else:
              print('YES')
  
  
  
          
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
      
  
      
  
  
  
  
  
  
  
  
  
  
  # region fastio
  # template taken from https://github.com/cheran-senthil/PyRival/blob/master/templates/template.py
  
  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__":
      #read()
      main()
      #dmain()
  
  # Comment Read()
  