#include <bits/stdc++.h>
using namespace std;
signed main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  long long _;
  for (cin >> _; _--;) {
    long long n, m, k;
    cin >> n >> m >> k;
    long long mn = (n % 2 == 1 ? m / 2 : 0);
    long long mx = n * m / 2 - (m % 2 == 1 ? n / 2 : 0);
    if (mn <= k and k <= mx and (k - mn) % 2 == 0)
      cout << "YES\n";
    else
      cout << "NO\n";
  }
}
