#include <bits/stdc++.h>
const long long mod = 1e9 + 7;
using namespace std;
void test_case() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<vector<char>> table(n, vector<char>(m, '0'));
  int horizontal = 0;
  if (n % 2 == 1) horizontal = m / 2;
  int max_h = n * (m / 2);
  if (max_h < k)
    cout << "NO\n";
  else if (k >= horizontal && (k - horizontal) % 2 == 0) {
    cout << "YES\n";
  } else
    cout << "NO\n";
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int N;
  cin >> N;
  while (N--) {
    test_case();
  }
}
