#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
const int mod = 1e9 + 7;
void multisolve() {
  int n, m, k;
  cin >> n >> m >> k;
  if (n % 2 == 0) {
    if (m % 2 == 1)
      cout << ((n * (m - 1) >= k * 2 && k % 2 == 0) ? "YES" : "NO") << endl;
    else
      cout << ((n * m >= k * 2 && k % 2 == 0) ? "YES" : "NO") << endl;
  } else {
    cout << ((m / 2 <= k && (n - 1) * m >= (k - m / 2) * 2 &&
              (k - m / 2) % 2 == 0)
                 ? "YES"
                 : "NO")
         << endl;
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t = 1;
  cin >> t;
  while (t--) {
    multisolve();
  }
  return 0;
}
