#include <bits/stdc++.h>
using namespace std;
string yno[2] = {"NO\n", "YES\n"};
void print(vector<int>& a) {
  for (int i : a) cout << i << ' ';
  cout << endl;
}
void print(pair<int, int> a) { cout << a.first << ' ' << a.second << endl; }
void print(int a[], int n) {
  for (int i = 1; i <= n; ++i) cout << a[i] << ' ';
  cout << endl;
}
void solve() {
  int n, m, k;
  cin >> n >> m >> k;
  bool ok = true;
  if (n & 1) {
    if (k < m / 2) ok = false;
    if (k >= m / 2 && ((k - m / 2) & 1)) ok = false;
  }
  if (m & 1) {
    if (k & 1) ok = false;
    if (k > (n * m - n) / 2) ok = false;
  }
  if ((n % 2 == 0) && (m % 2 == 0)) {
    if (k & 1) ok = false;
  }
  cout << yno[ok];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int t;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}
